tag:blogger.com,1999:blog-62785404216866299192021-01-26T03:55:08.781-05:00The Math SpotElementary math materials including ideas, resources and lessons for K-5 teachers. The Math Spot promotes hands-on learning of elementary math concepts. The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comBlogger84125tag:blogger.com,1999:blog-6278540421686629919.post-60167908848967462052020-12-06T12:48:00.003-05:002020-12-06T12:48:31.466-05:00Independent Practice Strategy<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-2BQjK1uuga4/X8qJHv20I5I/AAAAAAAAfaE/4LtUbhwkq3oP16zMaN7QHxB67XtGAKIawCLcBGAsYHQ/s800/Independent%2BPractice%2BStrategy%2BBlog%2BHeader.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-2BQjK1uuga4/X8qJHv20I5I/AAAAAAAAfaE/4LtUbhwkq3oP16zMaN7QHxB67XtGAKIawCLcBGAsYHQ/s16000/Independent%2BPractice%2BStrategy%2BBlog%2BHeader.png" /></a></div><br /><div><br /></div>My third-grade teacher always told us <div><blockquote>Practice doesn't make perfect. Practice makes permanent!</blockquote><div><br /></div><div>When we were practicing our cursive lettering he wanted us to be sure not to get sloppy and practice incorrectly- the habits we formed during practice would be hard to break! </div><div><br /></div><div>The same is true of our students when it comes to their independent math practice! </div><div><br /></div><h4 style="text-align: left;">Try This!</h4><div><br /></div><div>This quick-to-implement strategy solves this problem when it comes to math centers and independent practice. </div><div><br /></div><div><ol style="text-align: left;"><li>Set aside small group math time FOR independent practice! If you have ever thought to yourself "They could do it at the small group table but then when they went back to their seat they fell apart!" then you have students who need to practice independently... with your support. <br /><br /></li><li>Position yourself so you are at the "hub" of the activity. For me, this meant staying at the small group table. Position your students in their own spaces nearby. For me, this meant that while I was at the small group table one student worked on the windowsill nearby, one student worked on a small rug next to the table, another student worked at my desk and another student stayed at the small group table. I had a VERY small intervention space but this is what worked for me. Any individual nearby workspaces will work. <br /><br /></li><li>Keep the activity materials at your table. For example, if your students need to roll a dice during the activity, keep the dice at your table. If they are selecting two playing cards to compare, keep the cards at your table. If there is a spinner involved... you get the picture! <br /><br /></li><li>Your students will come to you to roll dice, grab cards, spin the spinner, etc. and will move back to their space to do the actual math. </li></ol><h4 style="text-align: left;">Why Does It Work? </h4><div><br /></div><div>When you employ this strategy you will get to check-in, frequently, with your students as they are working. You can catch any misconceptions as soon as they happen so that your students aren't practicing incorrectly over and over. </div></div><div><br /></div><div>And, as a bonus, your students are getting up and moving after every single problem. They may be moving only a few feet but the movement gives your students' bodies the break that they need while practicing a task! </div><div><br /><hr /> <b>Pin For Later: </b><b><br /></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-PlwusraOTGg/X8qJNGHff0I/AAAAAAAAfaI/GiAnEhhfZE4GutuPh26mbkaCHI43FE7iQCLcBGAsYHQ/s1500/Independent%2BPractice%2BStrategy%2BPin.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="320" src="https://1.bp.blogspot.com/-PlwusraOTGg/X8qJNGHff0I/AAAAAAAAfaI/GiAnEhhfZE4GutuPh26mbkaCHI43FE7iQCLcBGAsYHQ/s320/Independent%2BPractice%2BStrategy%2BPin.png" /></a></div></div><b>Math Spot Newsletter: </b> <b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-12335706535425261012020-11-18T13:11:00.003-05:002020-11-18T13:12:59.132-05:00Why You Need to Plan Intervention Sequences<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-2vmalMYow1A/X7VA7yNyQJI/AAAAAAAAe08/3mFOCYVErPwUTFJcDAxBc49zS4cG7ZW0QCLcBGAsYHQ/s800/Planning%2Ban%2BIntervention%2BSequence.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-2vmalMYow1A/X7VA7yNyQJI/AAAAAAAAe08/3mFOCYVErPwUTFJcDAxBc49zS4cG7ZW0QCLcBGAsYHQ/s16000/Planning%2Ban%2BIntervention%2BSequence.png" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">It's a trap we have all fallen into. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">You teach your math lesson for the day and then pull aside the group that didn't quite get it yet. You work on the independent practice together. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Here's the problem. The next day? You're likely working with the same group of students. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">It's easy to fall into this trap - but there is a clear way out! </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Instead of planning individual lessons when it comes to math intervention you need to plan a sequence!</b></div><h4 style="clear: both; text-align: left;">Try This! </h4><div class="separator" style="clear: both; text-align: left;"><ol style="text-align: left;"><li>Take a look at your broad math topic- not just what you are working on in a given day. For example, "understanding teen numbers". </li><li>Brainstorm ways you can teach this topic with multiple hands-on materials. For example, building teen numbers on a double ten frame, building teen numbers using linking cubes, building teen numbers using cups of ten beans and some more beans, etc. </li><li>Brainstorm ways you can teach the topic with representational models. For example, representing teen numbers using a number bond, representing teen numbers using place value cards, representing teen numbers with a place value drawing. </li><li>Think about the end goal- how can your students demonstrate to you that they understand the topic? </li><li>Using your lists of models and representations, build a <i>sequence </i>of lessons that allows your students to start hands-on and move through representations before demonstrating that they understand the topic. </li></ol><br /><h4 style="text-align: left;">Why Does It Work? </h4><div>When you remediate each individual day (ex: how to build teen numbers on a ten frame) as a stand-alone topic, your students are left with a collection of individual skills that they may or may not have mastered with support. </div><div><br /></div><div>When you build your remediation plan as a <i>sequence </i>of lessons, your students will start at the foundation and build up their understanding as the lessons progress. </div><div><br /></div><div>You will <b>know</b> which of your students still needs hands-on materials. <i>And you will be prepared to give them these tools even during tier 1 instruction so that they can be successful! </i></div><div><i><br /></i></div><div>You will <b>know</b> which of your students are successful with a given representation. <i>And you will be able to build off of this success in your tier 1 instruction! </i></div><div><i><br /></i></div><div>You will <b>know</b> where your students are on the way to understanding the big idea you are working towards! </div></div><div><br /></div><hr /><b>Pin For Later: </b> <b><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-ODOZ7AuOMmo/X7Vjc6W72pI/AAAAAAAAe1M/y2AZ4hdfeM8qMZVqCN0gwedzvK1YhWYDwCLcBGAsYHQ/s1500/Why%2BMath%2BIntervention%2BSequence%2BPins%2B%25281%2529.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="320" src="https://1.bp.blogspot.com/-ODOZ7AuOMmo/X7Vjc6W72pI/AAAAAAAAe1M/y2AZ4hdfeM8qMZVqCN0gwedzvK1YhWYDwCLcBGAsYHQ/s320/Why%2BMath%2BIntervention%2BSequence%2BPins%2B%25281%2529.png" /></a></div></b><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-64329815657844743002020-10-25T16:37:00.006-04:002020-11-08T11:44:17.830-05:00Deficit vs. Asset Based Thinking In Math Class<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-rZjl_Mn0_l8/X6ggVveOBsI/AAAAAAAAeXg/0uMBZqFMS9wvRlDTzw10inGgQB5oUedTACLcBGAsYHQ/s800/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-rZjl_Mn0_l8/X6ggVveOBsI/AAAAAAAAeXg/0uMBZqFMS9wvRlDTzw10inGgQB5oUedTACLcBGAsYHQ/s16000/1.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div>A few years back I was talking with a colleague after a staff meeting. I mentioned that I had recently had a breakthrough with a student who had a multitude of "gaps" in their learning. </div><div><br /></div><div>This student was in an upper elementary grade level but had a very early primary understanding in all subject areas. It was initially very overwhelming! Instead of thinking about all of the things the student didn't know I instead started with what she <i>did </i>know and decided to use that strength and climb up from there. </div><div><br /></div><div>My colleague let me know that there was an academic term for this switch. Where I had initially become overwhelmed by need I was in a "<b>deficit</b>" mindset related to the student. When I stopped and instead focused on what she did know I had switched to "<b>asset-based thinking</b>". </div><div><br /></div><div>It's a simple swap with a BIG payoff! </div><div><br /></div><div>Let's look at how this mental shift can play out when deciding how to best support a student who isn't yet showing proficiency on the math strategy of making a ten to add. </div><div><br /></div><div>If I want a student to use this strategy they would solve a problem like 8+4 by thinking about how 8 + 2 makes a ten and then 2 more makes a total of 12. </div><div><br /></div><div>There are SO MANY skills that go into this strategy! </div><div><ul style="text-align: left;"><li>Knowing that addition means we are putting 8 and 4 together</li><li>Knowing that numbers can be decomposed</li><li>Knowing the partners of ten and that 8 + 2 makes a ten</li><li>Knowing that 4 can be decomoposed into 2 and 2 </li><li>Knowing that 8 + 2 + 2 will get the same result as 8 + 4</li><li>Being able to carry out each of these decompositions</li><li>Being able to successfully put numbers together</li></ul><div>In deficit thinking, we might approach this problem by saying </div><div><i>"I have a student who can't use the make a ten strategy. I used blocks, I used number bonds- they just don't get it!"</i></div><div><br /></div><div>When practicing asset-based thinking I am going to break this skill down and start with what my student DOES know... and move on from there! </div><div><br /></div><div>Continuing with the hypothetical, problem solving with an asset-based mindset may sound like this. </div><div><i>"I know my student is able to add two numbers together by counting-on. They also know all of their partners of ten. My student has a lot of the skills that are needed to use this strategy- let's keep building! The next step is being able to decompose single-digit numbers but they aren't fluent yet. No wonder blocks and number bonds didn't work- we are missing a foundational skill! I will work with this student on decomposing numbers to ten because that is the next skill they are ready for." </i> </div><div><br /></div><div>The next time you have a student who seems stuck, don't worry about all of the things they don't know. Break the skill down, notice what your student <b>is </b>able to do and work off of that strength to take the single next step! </div><div><b></b><br /><hr /></div><b>Pin For Later: <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-UdxDTzntowI/X5XiChEy2zI/AAAAAAAAdxk/8Fm-kRjiPDkm6n-lVwXra2Rksbgr32QdACLcBGAsYHQ/s1500/Copy%2Bof%2Bdeficit%2Bvs%2Basset%2Bpin.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="320" src="https://1.bp.blogspot.com/-UdxDTzntowI/X5XiChEy2zI/AAAAAAAAdxk/8Fm-kRjiPDkm6n-lVwXra2Rksbgr32QdACLcBGAsYHQ/s320/Copy%2Bof%2Bdeficit%2Bvs%2Basset%2Bpin.png" /></a></div></b><b><br /></b><b></b><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div><br /><span><a name='more'></a></span><span><!--more--></span><span><!--more--></span><span><!--more--></span>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-23981895050936250872020-09-28T13:16:00.002-04:002020-11-08T11:34:50.898-05:00Introducing Place Value to 1st and 2nd Graders<div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-CzMpmXsOPW8/X6geHuqpKuI/AAAAAAAAeWw/fzCUJwj-IssXdKAynx3NrPy5ZtfPQz9JACLcBGAsYHQ/s800/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-CzMpmXsOPW8/X6geHuqpKuI/AAAAAAAAeWw/fzCUJwj-IssXdKAynx3NrPy5ZtfPQz9JACLcBGAsYHQ/s16000/6.png" /></a></div><br /><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both;"><span style="text-align: left;">It's a common activity used to introduce place value. You give your students a pile of crackers, pretzel sticks and chocolate chips. You tell your students that the crackers are the hundreds, pretzel sticks are the tens and chocolate chips are the ones. You and your students take turns building numbers with a fun snack. </span></div><div><br style="text-align: left;" /></div></div><div><div>Highly engaging? </div><div>Yes. </div><div><br /></div><div>Highly effective? </div><div>Not for all of your students. </div><div><br /></div><div>If you are aiming to reach all of your students- even those who tend to struggle the most- you want to be sure that you are following a progression when introducing new concepts. </div><div><br /></div><div>Keep these two principles in mind. </div><div><br /></div><div>1) <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">Think CRA</a>. That means you are starting with hands-on materials, moving to representational models like place value drawings or a place value chart and then finally moving towards abstract models such as expanded form and unit form. </div><div><br /></div><div>2) <a href="https://www.k5mathspot.com/2014/08/i-love-base-ten-blocks.html" target="_blank">Remember that not all hands-on tools are created equally</a>! Start with groupable models like linking cubes where your students can physically put together groups of ten from ones or groups of 100 from tens. Next, move your students towards proportional, pre-grouped models such as base ten blocks. Last, tools such as place value disks that are pre-grouped and non-proportional can be used to support your students. </div><div><br /></div><div>Keeping both of these progressions in mind will ensure that you are reaching as many learners as possible as you introduce new (and important!) concepts to your students! <br /><hr /><b>Related Resources:</b></div><div><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-2-Digit-Place-Value-Lesson-Plans-Bundle-4884361" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-Tn_Zc6zFuKY/X3IZalLSgsI/AAAAAAAAc6s/Y32buJvsnh4AgorlmoxTXQTuAsPAVgo-QCLcBGAsYHQ/w200-h200/Unit%2B3.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Place-Value-Print-and-Digital-Unit-Numbers-to-1000-4935591" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-rxTiM7kdWGQ/X3IZauy3JRI/AAAAAAAAc6w/AKCudHPrWYkPLQ83jrZpQLcrOa7xnB57gCLcBGAsYHQ/w200-h200/Unit%2B4.jpg" width="200" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div></div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-40305817135798985752020-09-21T14:08:00.009-04:002020-11-08T11:41:48.664-05:005 Simple & Effective Games to Practice the Partners of Ten<p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: inherit; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-85-P9QHqr-M/X6geUnhuQHI/AAAAAAAAeW0/RWBDXj3KI1svDdz3vQ6Ekq7BFoXaFCWbwCLcBGAsYHQ/s800/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-85-P9QHqr-M/X6geUnhuQHI/AAAAAAAAeW0/RWBDXj3KI1svDdz3vQ6Ekq7BFoXaFCWbwCLcBGAsYHQ/s16000/2.png" /></a></div><br />Knowing the partners of ten opens up the world of fact fluency and flexibility for your students. The best part? There's no need to drill these facts! Your students can play engaging, hands-on, SIMPLE games to reinforce the partners of ten.</span></div><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: left;"><span style="font-family: inherit;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: left;"><span style="font-family: inherit;">The 5 games listed below will help your students to learn the partners of ten but will also help your students to boost their number sense. An absolute win-win combination! </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in; text-align: left;"><span style="font-family: inherit;"><br /></span></p><p style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;"><span style="font-family: inherit;"><i>Recording forms for each of the activities below have been included in the <br /></i></span><span style="font-family: inherit;"><i><a href="https://www.teacherspayteachers.com/Product/Partners-of-Ten-Intervention-Resources" target="_blank">Print & Digital Partners of 10 Math Intervention</a>.</i></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Jx6WU0u5kLE/X2jp1f5Md7I/AAAAAAAAcwY/cZB6Y8Kz5GADLbgobMIA4L0cOz4Tq6GPACLcBGAsYHQ/s1500/2.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="400" src="https://1.bp.blogspot.com/-Jx6WU0u5kLE/X2jp1f5Md7I/AAAAAAAAcwY/cZB6Y8Kz5GADLbgobMIA4L0cOz4Tq6GPACLcBGAsYHQ/w266-h400/2.png" width="266" /></a></div><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">This </span><span style="font-family: inherit;">solo activity allows your students to use a ten frame as a visual anchor for the partners of ten. The activity could not be more simple. Roll a dice, lay out that number of counters on the ten frame. How many spaces are filled? How many spaces are still empty on the ten frame? </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">Extend the activity by asking students to fill in a number bond to represent the combination of ten they have found and by writing an equation that matches their ten frame and number bond. </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-eKVpmcnZkgI/X2jqF_Aw0II/AAAAAAAAcwk/oBhKERFVr1I1s39YPT4iceaSiATLXhXdQCLcBGAsYHQ/s1500/1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="400" src="https://1.bp.blogspot.com/-eKVpmcnZkgI/X2jqF_Aw0II/AAAAAAAAcwk/oBhKERFVr1I1s39YPT4iceaSiATLXhXdQCLcBGAsYHQ/w266-h400/1.png" width="266" /></a></div><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">In this activity your students will need ten 2-sided counters and a cup. Their job? To shake and spill the counters noticing how many are red and how many are yellow. Ask your students to record the combination of ten on a number bond (represenative model) and as an equation (abstract model). </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></p><p></p> <p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;">Asking your students to use a number bond and equation to represent their findings helps your students to bridge the gap between this hands-on activity and fact fluency later down the line. </span></p><p></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Ekd1-ZKslcU/X2jqQUraOII/AAAAAAAAcwo/MLYfsIcPgqELEAFXovB6qvNWIJsaH4oDwCLcBGAsYHQ/s1500/3.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="400" src="https://1.bp.blogspot.com/-Ekd1-ZKslcU/X2jqQUraOII/AAAAAAAAcwo/MLYfsIcPgqELEAFXovB6qvNWIJsaH4oDwCLcBGAsYHQ/w266-h400/3.png" width="266" /></a></div><p></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;">As simple as it sounds, ask your students to spin a spinner and find the number that goes together with their number to make ten. <o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;"><br /></span></p> <p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;">In this activity your students don't have any hands-on tools at their disposal but you can still give them a method to find the partners of ten- their fingers! Show your students how they have 10 fingers and they can notice how many are up and down to find the partners of ten. </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-v2bvB0KhwZ0/X2jqabZsg5I/AAAAAAAAcww/Yqn09ogwlK0wG3Yhg_rTP_OfBcG_TfjqwCLcBGAsYHQ/s1500/4.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="400" src="https://1.bp.blogspot.com/-v2bvB0KhwZ0/X2jqabZsg5I/AAAAAAAAcww/Yqn09ogwlK0wG3Yhg_rTP_OfBcG_TfjqwCLcBGAsYHQ/w266-h400/4.png" width="266" /></a></div><p></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;">In this partner game your students need a cup and a set of ten objects. One partner will hide some of the objects beneath the cup. The next partner will have to use their knowledge of the partners of ten to determine how many items are hiding beneath the cup! </span></p><p class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 4;"><span style="font-family: inherit;"><br /></span></p> <p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">You can carry out this activity without the use of a hands-on tool or you can introduce a tool such as a rekenrek or beads on a string to make this activity more concrete for your students. </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-7JmWC2KBajU/X2jqlwcIObI/AAAAAAAAcw4/2MhN5f5VLoUdGro-r3k0kIY0W0QK3is-gCLcBGAsYHQ/s1500/5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="400" src="https://1.bp.blogspot.com/-7JmWC2KBajU/X2jqlwcIObI/AAAAAAAAcw4/2MhN5f5VLoUdGro-r3k0kIY0W0QK3is-gCLcBGAsYHQ/w266-h400/5.png" width="266" /></a></div><br /><span style="font-family: inherit;"><br /></span><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">This open-ended activity is a must-do in your classroom. The premise is that your students are looking at a pet shop and noticing that there are some dogs and some cats in the ten windows. </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></p><p></p> <p class="MsoNormal" style="line-height: normal; margin-bottom: 0in;"><span style="font-family: inherit;">How many windows <i>could </i>be filled with dogs? How many windows <i>could </i>be filled with cats? Your students will have to problem solve as they work through this open-ended task that requires them to generate partners of ten. </span></p><div><hr /><span style="font-family: inherit;"><b>Related Resources:</b><br /><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Partners-of-Ten-Intervention-Resources" target="_blank"><img border="0" data-original-height="768" data-original-width="768" height="320" src="https://1.bp.blogspot.com/-HJAthWijwDk/X2jpc-OhcpI/AAAAAAAAcwM/mnUXzoPlO0Av1sw_f9AKOs02ybiDaC8-QCLcBGAsYHQ/s320/Slide3.JPG" /></a></div><br /><hr /><span style="font-family: inherit;"><b>Pin For Later: </b><b><br /></b><b></b></span><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/-GnuQ0FJaGs8/X2jps7FqVOI/AAAAAAAAcwU/6do2ADnnAYgouIvHp67zxqXerZmNguBjACLcBGAsYHQ/Partners%2Bof%2BTen.png" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1500" data-original-width="1000" height="400" src="https://lh3.googleusercontent.com/-GnuQ0FJaGs8/X2jps7FqVOI/AAAAAAAAcwU/6do2ADnnAYgouIvHp67zxqXerZmNguBjACLcBGAsYHQ/w267-h400/Partners%2Bof%2BTen.png" width="267" /></a></div><br /><span style="font-family: inherit;"><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</span></div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-43575022166576343422020-08-30T10:00:00.001-04:002020-11-08T10:52:16.069-05:00The Simple & Effective Guide To Understanding Math Facts<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-CGYb3MkSCCI/X6gUJeXe2eI/AAAAAAAAeWQ/XdEnwT0KheUg6bCNCVdMFChL4jk4GXQywCLcBGAsYHQ/s800/Math%2BFacts%2B.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-CGYb3MkSCCI/X6gUJeXe2eI/AAAAAAAAeWQ/XdEnwT0KheUg6bCNCVdMFChL4jk4GXQywCLcBGAsYHQ/s16000/Math%2BFacts%2B.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>Addition & Subtraction Strategies.<div><br /></div><div>Fact Fluency.</div><div><br /></div><div>Fact Memorization.</div><div><br /></div><div>Three different sides of the same coin. Thinking about teaching math facts as being learned at <b>each </b>of these three levels will change your perspective on instruction altogether! </div><h4 style="text-align: left;">Addition & Subtraction Strategies</h4><div>Counting on fingers, using manipulatives, using a number line, counting on, counting up, counting backward, etc. </div><div><br /></div><div>Each of these are <b>strategies </b>you can teach your students so that they can accurately add and subtract numbers. When we are teaching strategies we are helping our students understand the operations of addition and subtraction, we are helping them to become more efficient when solving and we are giving them an opportunity to manipulate and practice with addition and subtraction. </div><div><br /></div><div>At the end of the day, while strategies help to build understanding and may work towards fluency, strategies can end up looking a lot like procedures. While they are an important first step, you will need to move beyond strategies to build fluency. </div><div><br /></div><div><i>Consider this example: I want to ultimately build towards fluency and memorization of +2 facts. At the strategy level, I may choose to review the counting on strategy with my students to connect the ideas that counting and addition are related. I mix together +1 and +2 facts and ask my students to use the counting on strategy to find the sums. </i></div><div><br /></div><h4 style="text-align: left;">Fact Fluency </h4><div>Fact fluency is the idea that your students can quickly and accurately solve an addition or subtraction problem. They may be using a strategy that they learned above or they may be flexibly thinking about numbers in a way that will help them to arrive at their answer. </div><div><br /></div><div>If you are thinking that the line between strategies and fluency is fuzzy, it absolutely can be. The biggest difference is that at the fluency level we are focusing on building efficiency. </div><div><br /></div><div>At the fact fluency level, I am often looking to fold in number sense relationships to help my students move toward a more natural and fluent understanding of the facts they are working on. </div><div><br /></div><div><i>Continuing the previous example, my students now know that counting and addition are related and can use the counting on strategy to find 1 or 2 more. I know that spatial reasoning is a number sense relationship I can use to move my students towards fluency in this case. I lay out a human-sized number line and ask my students to play a game where they spin a spinner to add 1 or 2 to a given number moving their counter along a number line. They are still building on the counting on strategy but by seeing the numbers on a number line my students are building their mental number line so that they are more efficient in "knowing" one or two more rather than having to employ the full counting-on strategy. </i></div><div><i><br /></i></div><h4 style="text-align: left;">Fact Memorization</h4><div>The good news is that you don't need to teach fact memorization at all. Memorization is simply the idea that your students have accessed these facts so many times that they don't need to use a strategy or flexible thinking at all- they already know the answer. </div><div><br /></div><div>You don't need to teach memorization, repetition and time will move facts over to long term memory! </div><div><br /></div><div>If you would like to help facilitate the process, allow your students the opportunity to access and recall these facts often as this will help the facts to move to long-term memory more quickly. </div><div><br /></div><div><i>Following our example one final time, I may ask my students to play a simple board game. They flip a card, answer the math fact, and get to roll a dice to advance along the game board when they are correct. In the case of this example, I may only include cards with math facts involving adding one or two. In this way, my students will get an abundance of practice with these facts and their fluent thinking. As they play and have repeated exposure to this game, your students will stop using overt strategies and drawing on their flexible thinking- they will just KNOW the answers from memory and begin to answer much more quickly! </i></div><div><br /></div><div><div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-SJu6gSLXtqQ/X0ux3pNkfzI/AAAAAAAAcJE/jbfQ5N8MzNYRGDOxRr0sZvBFg5Y7NyuRQCLcBGAsYHQ/s960/Bundle%2BCover.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="960" height="210" src="https://1.bp.blogspot.com/-SJu6gSLXtqQ/X0ux3pNkfzI/AAAAAAAAcJE/jbfQ5N8MzNYRGDOxRr0sZvBFg5Y7NyuRQCLcBGAsYHQ/w210-h210/Bundle%2BCover.jpg" width="210" /></a></div><br /><hr /><b>Pin For Later: </b><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-BtL41niKcA8/X0uzu1IqZoI/AAAAAAAAcJU/uGK1wc2k4pcgE-Cgm0O7ux-J4_nGIggVwCLcBGAsYHQ/s1500/9_7_20%2BPin%2BFact%2BFluency.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="410" src="https://1.bp.blogspot.com/-BtL41niKcA8/X0uzu1IqZoI/AAAAAAAAcJU/uGK1wc2k4pcgE-Cgm0O7ux-J4_nGIggVwCLcBGAsYHQ/w274-h410/9_7_20%2BPin%2BFact%2BFluency.png" width="274" /></a></div></div><div><br /></div><div><hr /><b>Math Spot Newsletter: </b> <b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-42235234284442707592020-08-30T09:20:00.001-04:002020-11-08T11:36:31.188-05:00Skip the Deficit Mindset in Your Math Class<div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-wcya9izj8Jw/X6geg3ZILCI/AAAAAAAAeW8/hJhJ2_u8DrQMV4neXK7Hb9RYp8UjNu2ogCLcBGAsYHQ/s800/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-wcya9izj8Jw/X6geg3ZILCI/AAAAAAAAeW8/hJhJ2_u8DrQMV4neXK7Hb9RYp8UjNu2ogCLcBGAsYHQ/s16000/3.png" /></a></div><br />Remi comes into your math classroom as a 2nd grader. She is presented with the problem 3 + 5 and immediately freezes. She holds up 3 fingers... and pauses, putting them back down. She holds up 5 fingers and pauses again. </span></div><div>She's stuck. </div><div><br /></div><div><b>You have 2 options at this point. </b></div><div><b><br /></b></div><div style="text-align: center;"><i>You can classify Remi as a 2nd grader who doesn't know how to do addition and has no strategies for how to add. </i></div><div><br /></div><div>Or</div><div><br /></div><div style="text-align: center;"><i>You can classify Remi as a 2nd grader who knows what 3 fingers look like, knows how to show 5 on her fingers and who needs to understand what a + sign means and does. </i></div><div><br /></div><div><h4 style="text-align: left;">Deficit Mindset Vs. Asset-Based Thinking </h4><div>This simple shift in thinking demonstrates the difference between the <b>deficit mindset (</b>where the focus is on the pieces a student doesn't yet know) and <b>asset-based thinking (</b>where the focus is on what a student does know and builds and works from there). </div><div><br /></div><div>This school year, focus on asset-based thinking with your students- it will get you far! Asset-based thinking helps you take inventory of what a student does know which <u>will lead you more naturally to your next steps with a child. </u></div><div><br /></div><h4 style="text-align: left;">Deficit Vs. Asset-Based Examples </h4><div>In the scenario where we start with a deficit mindset, our student Remi can't add and has no strategies. This might cause us to jump straight into strategies such as counting on or using a number line or even focusing on +1 facts. We know she can't add so we start plugging in addition strategies. Are we sure the strategy we have chosen is right for Remi? No, not necessarily, but we're teaching addition strategies so it <i>feels </i>productive. </div><div><br /></div><div>In the example where we started with asset-based thinking, we noticed that Remi has some good subitizing skills when it comes to using her fingers. We know addition is nothing more than putting parts together so we are going to build off of the skills Remi already has to teach her how to put parts together using her fingers. In our long-term plan, we may move to counters and other concrete manipulatives before moving to level two strategies such as counting on! </div><div><br /></div><hr /><b>Pin For Later: </b><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-M9dxywRwXJg/X0unadkBbpI/AAAAAAAAcIo/ECeHHjgmsK029HxsedOK6TvnAiAnyHtbgCLcBGAsYHQ/s1500/8_31_20%2BBlog%2BPin%2BAsset%2BBased%2BThinking.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="640" src="https://1.bp.blogspot.com/-M9dxywRwXJg/X0unadkBbpI/AAAAAAAAcIo/ECeHHjgmsK029HxsedOK6TvnAiAnyHtbgCLcBGAsYHQ/s640/8_31_20%2BBlog%2BPin%2BAsset%2BBased%2BThinking.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><hr style="text-align: left;" /><b style="text-align: left;">Math Spot Newsletter: </b><span style="text-align: left;"> </span><b style="text-align: left;"><br /></b><span style="text-align: left;">Click </span><a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" style="text-align: left;" target="_blank">HERE </a><span style="text-align: left;">to receive notes, tips, freebies & special discounts from The Math Spot</span></div><br />The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-124187918808940032020-08-22T08:47:00.007-04:002020-11-08T12:33:25.320-05:00FREE Printable Math Manipulatives<div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nLXdOZfhatM/X6gr09iPpeI/AAAAAAAAeXs/_QkxImfz5rs0dJ-4FndZGxJ6m3uwFqG1wCLcBGAsYHQ/s800/New%2BBlog%2BHeaders%2B%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-nLXdOZfhatM/X6gr09iPpeI/AAAAAAAAeXs/_QkxImfz5rs0dJ-4FndZGxJ6m3uwFqG1wCLcBGAsYHQ/s16000/New%2BBlog%2BHeaders%2B%25281%2529.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>Students learn math best when they can touch, feel, experiment and manipulate the concepts they are learning. Math manipulatives absolutely help facilitate this process. These FREE printable manipulatives are perfect for first or second-grade students. </span></div><div><h3 style="text-align: left;">Why Use Printable Math Manipulatives? </h3><div><div>Using a research-based CRA progression your students will move from concrete tools to drawings and representational models and will ultimately be proficient with abstract equations and ideas. Without manipulatives in the hands of our students we are missing the first and arguably most critical step!</div></div><div><br /></div><h3 style="text-align: left;">How to Prepare Free Printable Math Manipulatives</h3><div>The possibilities are endless but focus on a strategy that will give you the longest use to you and your students through the least personal work for yourself! </div><div><br /></div><div><ul style="text-align: left;"><li>Print on computer paper and laminate.</li><li>Print directly onto cardstock.</li><li>Print pre-colored manipulatives onto white paper.</li><li>Print black and white options onto a variety of brightly colored</li><li>papers.</li><li>Make a full toolkit for each student.... or only prepare the manipulatives you need one unit at a time.</li><li>Print, cut, and put into baggies for your students.</li><li>Print, donâ€™t cut, and send home in gallon-sized baggies for your families to prepare.</li><li>Make preparing and exploring manipulatives a whole lesson!</li></ul></div><div>Some of these materials are tedious to prepare. Consider laminating so that they last longer in the hands of your students!</div><div><br /></div><h2 style="text-align: center;"><a href="https://mailchi.mp/52a3ad570056/free-printable-math-manipulatives" target="_blank">Click HERE to Grab Your Free Printable Now! </a></h2><hr /><b>Pin For Later: </b><b><br /></b><b></b><a href="https://1.bp.blogspot.com/-Mi6sSf1moVc/X0EOhfGzQcI/AAAAAAAAcAM/rYL40vVC6gc4lbOK_AV6IBhpeL3ihoJ8ACLcBGAsYHQ/s1500/8_24_20%2BPinterest%2BPrintable%2BManipulatives.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1500" data-original-width="1000" height="328" src="https://1.bp.blogspot.com/-Mi6sSf1moVc/X0EOhfGzQcI/AAAAAAAAcAM/rYL40vVC6gc4lbOK_AV6IBhpeL3ihoJ8ACLcBGAsYHQ/w219-h328/8_24_20%2BPinterest%2BPrintable%2BManipulatives.png" width="219" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-57279123181100476732020-08-15T09:32:00.001-04:002020-11-08T11:37:14.693-05:00Getting Started with Tier 3 Math Intervention <div><b><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NeiobRdQDAY/X6gesACy_PI/AAAAAAAAeXE/8CrXmQIl3Vs1mndeImCXgedo_Wne3As2gCLcBGAsYHQ/s800/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" src="https://1.bp.blogspot.com/-NeiobRdQDAY/X6gesACy_PI/AAAAAAAAeXE/8CrXmQIl3Vs1mndeImCXgedo_Wne3As2gCLcBGAsYHQ/s16000/5.png" /></a></div><br /><span style="color: #fd0390;"><br /></span></b></div><b><span style="color: #fd0390;">My first year teaching math intervention I was in over my head by the second week of school. </span></b>Funny thing is, by the second week of school I really hadn't done anything other than assessing students and starting to form groups. <div><br /></div><div>I was given the advice to look at the (overwhelming) amount of data I had on these students and to choose intervention groups for tier 3 pull-out services. </div><div><br /></div><div>Ask how that went...</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">I felt confident in the groupings I had determined but the grade-level teams I was working with weren't so sure! They had students sitting in their classroom with a variety of needs and they were so confused about how "Billy" didn't get picked up for math. </span></div><div><br /></div><div>So I spent the next week in off-the-records individual meetings with teachers trying to explain that while Billy did have a number of needs that there were 16 other students who had needs that were much greater than Billy and that I would be happy to help with Billy's tier 2 needs. </div><div><br /></div><div>Ask how that went...</div><div><br /></div><div>YUCK. I hadn't even serviced my first group and already there was a teacher vs. interventionist dynamic that I absolutely hated. I was absolutely NEVER going into another round of groupings using this method. In the future, I promised myself and my teachers that we would always determine tier 3 groupings together.</div><div><br /></div><div><b><span style="color: #fd0390;">After that first grouping, I formed a new strategy for student groupings and was so pleased that it yielded: </span></b></div><div><ul style="text-align: left;"><li>Stronger teacher/interventionist relationships</li><li>More fluid and successful intervention groups</li><li>Methods for keeping students "on the radar" so teachers didn't feel alone</li><li>Outside of the box thinking about math intervention groupings. </li></ul><div>Let's dive in. </div></div><h3 style="text-align: left;">5 Steps for Creating Tier 3 Math Intervention Groups</h3><div><u><b>1) Determine your caseload capabilities</b></u></div><div>For me, I had an hour per day devoted to each grade level. I could see up to 4 students in a group for 30-minute groups. This meant that each day I could see a maximum of 8 students daily. </div><div><br /></div><div>Going to school Monday-Friday gave us a nice 5 day outline that we could work from but our school ran on a 6-day schedule. This is where the outside the box thinking comes in! Rather than having a caseload of 8 kids at a grade level for 5 days a week and 30 minutes a day, what if I saw groups for 4x30 and then saw a separate caseload of 8 more students who had the next highest needs for 2x30 to target specific skills and number sense? </div><div><br /></div><div>I DID NOT make this decision on my own! I presented each team with the option of 5x30 for the 8 most struggling learners or 4x30 and 2x30 for a wider variety of learners and let them choose. </div><div><br /></div><div><b><u>2) Have Your Data Ready</u></b></div><div>Before beginning grade level meetings I made a spreadsheet of every piece of math data I had on our students. </div><div><br /></div><div>Yes. I used Excel. </div><div><br /></div><div>No. Not everyone loves Excel. </div><div><br /></div><div>Yes. I recommend you get comfortable with at least the very basics. It will make your life 100x easier and your groupings 100x more effective. </div><div><br /></div><div>This will absolutely vary from school to school but, for me, this included AIMS Web data, end of year math grades from the previous year, state test scores, any beginning of the year screeners we had conducted and any end of year assessments from the previous year. </div><div><br /></div><div>I broke the data into "green" on level scores, "yellow" approaching level scores and "red" below grade level scores and color-coded the spreadsheet. </div><div><br /></div><div>This helped to be sure that we were looking at the grade level as a whole and that everyone was (literally) on the same page about the needs of the grade level- not just their students. Billy's teacher could now see that even though Billy had the highest needs in their class that he was nowhere near the highest needs in the grade level! </div><div><br /></div><div><b><u>3) Start Sorting</u></b></div><div>At this point, we choose priorities and started sorting students. In first grade, for example, maybe we started by looking at the students' computational assessments. Assuming that teachers chose the 4x30 and 2x30 schedule, we have 16 spots for students. We see that 24 of the students scored below grade level on the computational assessment. Looking at the end of year data we see that 5 of these students were on grade level at the end of last year and 3 more were approaching grade level. We look farther into the data from those students and see that the rest of their data doesn't paint the picture of a tier 3 student and so we take them off the list for consideration. </div><div><br /></div><div>No, it won't be this clean and easy but you get the idea. Choose a starting point and then consider the bigger picture to widdle down your list. </div><div><b><br /></b></div><div><b>It is important that you preview the data and do a bit of pre-sorting yourself before the meeting just to be sure that this meeting doesn't last too long! Be flexible and ready to listen to the teachers and change your initial findings but also come prepared so you aren't all starting from scratch! </b></div><div><b><br /></b></div><div><b><u>4) Have a Plan to Monitor Students</u></b></div><div>One of the biggest game-changers for both me and the teachers I was working with was in having a plan to monitor and discuss their tier 2 students. There will absolutely still be students, like Billy, who you and the teams will want to keep "on the radar" have a plan for making sure these students don't fall through the cracks! This might include: </div><div><ul style="text-align: left;"><li>A weekly meeting to consult on progress</li><li>A progress monitoring probe that you use with tier 3 students that will also be used with select tier 2 students</li><li>A plan to collect and review classroom data on these students on a regular basis</li></ul><div><u style="font-weight: bold;">5) Stay In Contact!! </u></div></div><div>It can be so easy to form your groups, start teaching and then turn the intervention room into Vegas. What happens in Vegas stays in Vegas.</div><div><br /></div><div>Here's the problem. In 10 weeks you may want to revisit your intervention groupings. Maybe you are feeling very confident that the work that Lydia is doing and you are ready to release her from intervention and pick-up Billy (he's falling further and further behind in class!) </div><div><br /></div><div>Billy's teacher is thrilled to get Billy the support he needs but Lydia's teacher is dumbfounded because in the classroom she is absolutely NOT keeping up. <i>What do you mean she is being released from intervention!? </i></div><div><b><i><br /></i></b></div><div>This whole problem could have been avoided by close weekly contact with Lydia's teacher throughout the semester. Whether it be a face to face meeting or a weekly email, be sure that your teachers know exactly what you are working on and exactly how their students are doing. This way, when you say a student is performing really well on "x" skill and the teacher is surprised by that, you can dive into work in both settings and find the discrepancy and the reason carryover isn't happening right off the bat. Not 10 weeks later. </div><div><br /></div><div>I can tell you with confidence that after that very first grouping my very first year I started this system and absolutely never looked back. I had stronger relationships with my teams, stronger groupings, met the needs of more students and worked as a team to be sure that no student fell through the cracks. </div><div><hr /><b>Pin For Later: </b><b><br /></b><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-HlSZLb_DnJg/Xzfi2-yefoI/AAAAAAAAb5g/MZ-Di5MHge0Aum8VLKTICk1l5Qyg-pyxgCLcBGAsYHQ/s1500/Copy%2Bof%2B5%2BDay%2BFocus%2BBlog%2BHeader.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="410" src="https://1.bp.blogspot.com/-HlSZLb_DnJg/Xzfi2-yefoI/AAAAAAAAb5g/MZ-Di5MHge0Aum8VLKTICk1l5Qyg-pyxgCLcBGAsYHQ/w274-h410/Copy%2Bof%2B5%2BDay%2BFocus%2BBlog%2BHeader.png" width="274" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><hr style="text-align: left;" /><b style="text-align: left;">Math Spot Newsletter: </b><span style="text-align: left;"> </span><b style="text-align: left;"><br /></b><span style="text-align: left;">Click </span><a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" style="text-align: left;" target="_blank">HERE </a><span style="text-align: left;">to receive notes, tips, freebies & special discounts from The Math Spot</span></div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-80421071945776593782020-06-27T13:47:00.003-04:002020-06-28T09:54:34.960-04:00All About 5 Day Focus Math Intervention CurriculumAs a new math interventionist, I was given no real direction other than <i>Here's a few grade levels of kids. Find the tier 3 kids, put them in groups and improve their math. Thanks! </i><br /><i><br /></i>Been there? Sound familiar?<br /><br /><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank"><img border="0" src="https://3.bp.blogspot.com/-C9VS8voG9Ns/XveDgyIaWZI/AAAAAAAAaaU/-Wy4kdAZ8jAB0Tsei3oLTmOMc2i94sI_ACK4BGAYYCw/s1600/5%2BDay%2BFocus%2BBlog%2BHeader.png" /></a><br /><br />In looking for resources, I found highly restrictive intervention curriculums that wanted me to follow a day by day, jam-packed schedule. <i>Today you will work on decomposing the number 6. Tomorrow, your students will decompose the number 7! </i><br /><i><br /></i>But what if my students weren't ready to move on? The curriculum was so packed in that there was no room to catch-up if my students didn't master a concept in a day. What could I skip? What was essential? There was no way to know.<br /><br />At the other end of the spectrum were these vague math practices. <i>Work on their number sense! Do number talks! Students need to discover their understanding of math! </i><br /><i><br /></i>Ok, great... but what will they know and be able to do at the end of this week that they didn't know last week? How will I know if we are closing the gap between where they are and their grade level expectations?<br /><br />I was not finding a solution that would work for my students and their goals long term. I spent time poring over math textbooks studying best practices and in landing on Van De Walle's book "Teaching Student-Centered Mathematics" everything became very clear.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/First-Grade-Math-Intervention-Lesson-Bundle-3372096" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="400" src="https://1.bp.blogspot.com/-tUqpMK9ii4U/XveECqtGh8I/AAAAAAAAaac/B8DdLP0Oasc7_ZzhsdCUS58Atrhk2LBGwCLcBGAsYHQ/w300-h400/Slide1.JPG" width="300" /></a></div><br /><h3 style="text-align: center;"><b>Why Did I Write the 5 Day Focus Math Intervention Curriculum? </b></h3><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-dssK52yipjs/XveEQpfUBCI/AAAAAAAAaag/k6kZ-F9rEcQWLH1igU3IxVt-OUpEY9YZgCLcBGAsYHQ/s320/Slide6.JPG" width="240" /></a>I never set out to write a curriculum. I set out to write a unit for myself about finding 10 more and 10 less than a given 2-digit number.<br /><br />I knew that I wanted a unit that had a <b><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">thoughtful targeted teaching sequence </a></b>that used the principles of the CRA progression to drive my students from where they were to where they needed to go.<br /><br />I knew I wanted a unit that had a<b> finite start and finish. </b>I didn't want to spin my wheels "exploring 10 more and 10 less" for some undetermined amount of time. I needed time to teach the concept well, to be responsive to my students and I needed my students to master the concept at the independent level.<br /><br /><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-ODNOlAChn4E/XveEXs1mesI/AAAAAAAAaao/W1k4K9woeDUjzWUY45IHmVrdpBofqvu_wCLcBGAsYHQ/s320/Slide8.JPG" width="240" /></a>I knew I wanted a unit that had <b>assessment built-in</b>. I already knew what I needed my students to know and be able to do at the end of the unit so I needed to build the assessment as well as my progress monitoring before I began instruction so I could always have our end goals in mind.<br /><br />And last, but most important of all, I knew I wanted my students to be <b>independent </b>at the end of the unit. I couldn't have a scenario where they were solid in the intervention space... but not carrying the skills over to their classroom. So I knew independent practice needed to be a BIG portion of our work.<br /><br />After writing and using that unit with my students, I was so thrilled with the results. Every one of my tier 3 students was incredibly successful in this skill. I had my yearly observation during this unit and my administrator (a former math interventionist herself) was astounded with the confidence, skills, and math language being demonstrated by my tier 3 students.<br /><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank"><br /></a><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">I had to write more units.</a><br /><br /><h3 style="text-align: center;">What Is Included In the <a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">5 Day Focus Math Intervention Curriculum </a></h3>Each grade level includes 14 units.<br /><br />Each unit includes:<br /><ul style="text-align: left;"><li>A pre and post-assessment</li><li>5 detailed lessons that will walk you and your students through the CRA progression (concrete, representational, abstract) on the targeted unit skill. </li><li>Daily independent practice activities </li><li>Daily exit tickets on days 1-4 so you can monitor your students' progress on their way to a new skill. </li></ul><ul style="text-align: left;"></ul><div style="text-align: left;">The lessons and activities encourage opportunities for students to <b>problems solve</b>, <b>talk </b>and explain their thinking, use <b>math language</b>, use <b>math tools</b>, <b>connect </b>to prior learning and ultimately develop <b>confidence</b> in their new skills. <b> </b><br /><b><br /><div style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">In short, these units are incredibly simple to use and incredibly effective. </a></b><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" style="clear: left; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="500" src="https://1.bp.blogspot.com/-5MuCBUmuyjM/XveEqvly9TI/AAAAAAAAaaw/dIqy-kkydQISFtJccGVxjwPr_AJL1-fIACLcBGAsYHQ/w375-h500/Slide10.JPG" width="375" /></a></div></b><br /></div><h3 style="text-align: center;">How Is This Different Than A Big Box Math Intervention Curriculum? </h3>14 units x 5 lessons each = 70 days of math instruction.... that doesn't add up to a full year, so what gives?<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="400" src="https://1.bp.blogspot.com/-_6SmKGdpZxI/XveE2k6wSqI/AAAAAAAAaa0/vdEYtRxvXuUzOn7JWWdZF5RmiMZHUuaHQCLcBGAsYHQ/w300-h400/Slide10.JPG" width="300" /></a></div>The purpose of this curriculum is to give you everything you need to teach 14 of the most core skills that your intervention students need to master in order to be successful in the next grade level.<br /><br /><div style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">Unlike the big box curriculums, you can feel confident that your students will actually master each of these 14 core skills through thoughtful, targeted, responsive instruction. </a></b></div><br />In order to be responsive to your students and their needs and in order to give your students time to practice and become <b>independent </b>time has been built in so that you can spread the 5 days of instruction out over the course of two weeks.<br /><br />You will use your pre-assessment data along with your daily exit tickets to determine when your group is ready to move on and when you need to pause.<br /><br />Your data will tell you who is ready to drop hands-on materials or math drawings and who still needs that scaffold.<br /><br />The independent practice activities have been designed to be used again and again so that the students who need repeated practice have the time. space, and materials to get the practice they need.<br /><br /> At all times, you will know where your instruction is going and <i>why </i>you are moving in that direction. You will know your students and their math understanding better than you ever have before and you will have the tools and data to move them along with confidence.<div><div style="text-align: center;"><img border="0" data-original-height="960" data-original-width="720" height="500" src="https://1.bp.blogspot.com/-Dai-12n9FZ8/XveE9YLnA4I/AAAAAAAAaa8/WqMxReI4n-0mPrnPV84CG3VdWoBQi486QCLcBGAsYHQ/w375-h500/Slide7.JPG" width="375" /></div><br /><h3 style="text-align: center;">Anything Else I Need To Know? </h3><div>A quick story. In the early days of my career as a math interventionist, I was down in the office getting my mail. I was making small talk with a teacher who was new to my school but who was a veteran in the district. He had previously been a math interventionist but had decided to move back into the classroom. </div><div><br /></div><div>He asked me how I was liking the new position so far and I probably gave some vague response about how it was different but I was loving it. </div><div><br /></div><div>And then he shared with me the reason he decided to go back into the classroom. </div><div><br /></div><div>He said that he wasn't fulfilled as a math interventionist because he felt he was stuck in the mud. Every year students would be identified for tier 3 and he would work with them. Throughout the year they would work hard, learn and make progress. The next year time would come to make math intervention groups and those same students would bubble up to the surface. They were still at the "bottom" of their grade level. What was the point? What had he done for the previous year if those students were right back at square one in their new grade? </div><div><br /></div><div>And that's when I made a decision. Right then and there. I would <b>know </b>I was successful as a math interventionist if my kids never came back. If I was making groupings the next fall and didn't get to see my kids again, I would know I was successful. If I looked at the table of the math interventionist meeting with the older students and I didn't know any of them, I would know I was successful. I would not allow myself or my students to get stuck in the mud. </div><div><br /></div><div>By following my <a href="https://www.teacherspayteachers.com/Store/The-Math-Spot/Category/Math-Intervention-258099" target="_blank">5 Day Focus</a> system, by targeting the most critical skills, by encouraging math talk, by assessing and using that data to give my students <i>exactly </i>the time they needed, by making sure that my students were independent and confident in each of these math skills, I can say that I met that goal. </div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"></div>I would look over to my colleague's math groups daily and the vast majority of her kids were students that <i>I didn't know. </i>The kids weren't running over at the end of their groups for hugs... they didn't know me! An overwhelming majority of my kids were back in their classrooms doing grade-level work because we had succeeded. </div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://4.bp.blogspot.com/-33f0y2OrQmk/XveGASiJKtI/AAAAAAAAabY/BHK2_aSJwLEKT8J0qyyAjj7Z46wvXJkkACK4BGAYYCw/s1600/Top%2B10%2BAugust%2BPins.png" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-33f0y2OrQmk/XveGASiJKtI/AAAAAAAAabY/BHK2_aSJwLEKT8J0qyyAjj7Z46wvXJkkACK4BGAYYCw/s320/Top%2B10%2BAugust%2BPins.png" width="213" /></a><a href="http://1.bp.blogspot.com/-pn9mprTjvHY/XveGBnp9Q_I/AAAAAAAAabg/GTPer899vy0hafKfAvYY6Kg3iMYlotzzACK4BGAYYCw/s1600/Top%2B10%2BAugust%2BPins%2B%25281%2529.png"><img border="0" height="320" src="https://1.bp.blogspot.com/-pn9mprTjvHY/XveGBnp9Q_I/AAAAAAAAabg/GTPer899vy0hafKfAvYY6Kg3iMYlotzzACK4BGAYYCw/s320/Top%2B10%2BAugust%2BPins%2B%25281%2529.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot<br /><br /><br /></div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-7900333598959541972020-05-01T14:17:00.001-04:002021-01-25T11:41:51.549-05:00Teaching 10 More and 10 Less with Strategies that Work! <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-wtkKSZbV5Fc/XqwSZrDZ3vI/AAAAAAAAZJA/TzW_vDPVM6oaCZu7cTGPkvSpgJzVybH7ACLcBGAsYHQ/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-wtkKSZbV5Fc/XqwSZrDZ3vI/AAAAAAAAZJA/TzW_vDPVM6oaCZu7cTGPkvSpgJzVybH7ACLcBGAsYHQ/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader.png" /></a></div><br />Hands down, this is one of my absolute favorite math skills to teach. You take something that seems like such an abstract mix between place value and operations and without fail teach 6 and 7 year old how to be successful in manipulating these numbers.<br /><br />It's almost like magic.<br /><br />As with most (all?) other math strategies, I find a CRA approach is the most effective way to support students towards proficiency.<br /><br />Yes, ultimately this will be a mental math skill... but that doesn't mean that's where we need to start!<br /><br /><a href="http://4.bp.blogspot.com/-5aJ_Wu-3cm4/Xqxjg1bSnXI/AAAAAAAAZKw/vZt_9BlJcy8pLfUwe-pYKMyWgesbo-ODACK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25281%2529.png"><img border="0" src="https://4.bp.blogspot.com/-5aJ_Wu-3cm4/Xqxjg1bSnXI/AAAAAAAAZKw/vZt_9BlJcy8pLfUwe-pYKMyWgesbo-ODACK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25281%2529.png" /></a><br /><br /><b><u>Concrete</u></b><br />I prefer to begin teaching this skill with a focus on adding ten with base ten blocks or linking cubes and then move to subtracting ten using money. I'm not as fussy about groupable models vs. pre-grouped models when teaching this skill because we aren't asking our students to compose or decompose a ten.<br /><br />If your students struggle to subtract using money, you can always use base ten blocks or linking cubes for that skill as well, but be aware! You are looking to get all of the way to the abstract/mental math stage on this skill in first grade so using a non-proportional manipulative such as $1 and $10 bills.<br /><br /><b><i>The Ten Dollar Store </i></b><br />A really fun activity I like to do with my students is called the "Ten Dollar Store". I put out a number of items and everything in the store costs $10. Students then get a "wallet" and have to represent that amount of money using $10 and $1 bills. They choose one of the items from the store and model what it looks like to subtract $10 and then write a related equation. The students get very into it and have a lot of fun but they also practice building 2-digit numbers and subtracting ten over and over. It's a win-win!<br /><br /><a href="http://2.bp.blogspot.com/-QCUIt7fgsAk/Xqxk49J445I/AAAAAAAAZK8/r7ekkkmNhBEkEqyyJ4Yem7zHt_lorIqrgCK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25282%2529.png"><img border="0" src="https://2.bp.blogspot.com/-QCUIt7fgsAk/Xqxk49J445I/AAAAAAAAZK8/r7ekkkmNhBEkEqyyJ4Yem7zHt_lorIqrgCK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25282%2529.png" /></a><br /><br /><b><u>Representational</u></b><br />Moving away from hands-on materials, using a place value drawing to show how to add or take away a ten is a step in the direction of less scaffolding to perform this skill. When you first introduce the place value drawing, do so directly alongside a tool like linking cubes or base ten blocks that visually looks a lot like a place value drawing.<br /><br />At this point (if not sooner!) I also like to be sure to mix in adding and subtracting 1. It may seem like a skill that your students have already mastered but mixing in addition, subtraction, tens and ones will ensure that your students are attending to place value when they are this skill rather than just "changing the tens place".<br /><br /><a href="http://1.bp.blogspot.com/-Dn_aDisTx-g/XqxloGgm9jI/AAAAAAAAZLI/OrBjb4loPvgDq_WS2BlwKTHjVSPTps1AACK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25283%2529.png"><img border="0" src="https://1.bp.blogspot.com/-Dn_aDisTx-g/XqxloGgm9jI/AAAAAAAAZLI/OrBjb4loPvgDq_WS2BlwKTHjVSPTps1AACK4BGAYYCw/s1600/10%2BMore%2B10%2BLess%2BBlog%2BHeader%2B%25283%2529.png" /></a><br /><br /><b><u>Abstract </u></b><br />Alongside each of the concrete and representational activities above, asking your students to talk about what they are doing with place value language and asking your students to write related equations will ensure that they are ahead of the game when it comes to being ready to demonstrate this skill at the abstract level. With no hands-on math tools of drawings at all!<br /><br />In fact, you can even take it a step further! When your student shows you their "wallet" with $57 and tells you they are going to buy a microphone for $10 ask them "How much money do you <i>think </i>you will have left if you take $10 away?" Asking your students to make these predictions and then carry-out their work to confirm their thinking will allow them to get a head start on being able to demonstrate this skill at the abstract level!<br /><br /><b><i>The Guessing Game</i></b><br />Another fun game you can play to reinforce this skill is the guessing game. One partner is the "picker" and chooses a starting number, whether they want to add or subtract, and whether they are going to change by a 1 or a ten. Both players record the "picker's" choices on their recording form. Next, with a divider between the students, the picker builds the scenario using a math manipulative while the guessed writes a related equation and solves mentally. When both partners are ready, the divider is lifted and both players check their work. Students trade who is the "picker" and the "guesser" and play continues!<br /><br />So, as with any other math skill:<br /><br /><ul><li>Think C-R-A. Know your end goal of abstract thinking but start in the concrete to build a strong foundation. </li><li>Link Along the Way. When you are using hands-on materials, ask for related equations and predictions to activate abstract thinking! When you are drawing place value drawings, link back to the hands-on materials your students have already had success with! </li></ul><div>Comment below if you use any or all of these strategies! If you are looking for a more comprehensive unit, the unit linked below is ideal for small group math and walks through a 5-lesson progression that will bring your students from concrete to abstract! </div><br /><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/10-More-10-Less-Print-and-Digital-Math-Intervention-Unit-for-Distance-Learning-2558891?st=7e3a0bd014129e960b7da08dd660c7cd" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="960" height="320" src="https://1.bp.blogspot.com/-Jz1RdivN5oY/XqwSld7VAJI/AAAAAAAAZJE/drZxIWkB-hs8zJ4ncqoi6WcNtyb2-lElwCLcBGAsYHQ/s320/Cover%2BUpdate%2B5.jpg" width="320" /></a></div><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://1.bp.blogspot.com/-aQ7XNwEJJO4/Xqxh6b45gQI/AAAAAAAAZKk/FPJMxEC1aQMXFHgJPATWymi4zYBalLAPQCK4BGAYYCw/s1600/10%2BMore%2Band%2BLess%2BTeaching%2BStrategies%2BPin.png"><img border="0" height="320" src="https://1.bp.blogspot.com/-aQ7XNwEJJO4/Xqxh6b45gQI/AAAAAAAAZKk/FPJMxEC1aQMXFHgJPATWymi4zYBalLAPQCK4BGAYYCw/s320/10%2BMore%2Band%2BLess%2BTeaching%2BStrategies%2BPin.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-38117039445061830572020-04-18T10:50:00.000-04:002020-04-18T10:50:04.597-04:00How to Introduce Place Value in 1st Grade <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-k1PlpGiNY6A/XmfHOzgVq9I/AAAAAAAAXc0/0wG-k_HkfbQ5dyypb-cUN8XRLKSzzsQ0gCLcBGAsYHQ/s1600/1st%2BGrade%2BPlace%2BValue%2BBlog%2BHeader.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-k1PlpGiNY6A/XmfHOzgVq9I/AAAAAAAAXc0/0wG-k_HkfbQ5dyypb-cUN8XRLKSzzsQ0gCLcBGAsYHQ/s1600/1st%2BGrade%2BPlace%2BValue%2BBlog%2BHeader.png" /></a></div><br />1st-grade students get the first real taste of place value. In kindergarten, your students may have learned to rotely count to 100 and they may have had experiences with teen numbers as ten ones and some more ones, but here in 1st grade you are introducing the idea that the <i>place </i>a digit is in in a number is important.<br /><br /><h4>Place Value Activity #1</h4><div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-dHihPZGK_Ds/XmfO4rP6hRI/AAAAAAAAXec/NQXm-thiL9oGyvXN4Xigd5zZ2__VHorjgCLcBGAsYHQ/s1600/Slide10.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-dHihPZGK_Ds/XmfO4rP6hRI/AAAAAAAAXec/NQXm-thiL9oGyvXN4Xigd5zZ2__VHorjgCLcBGAsYHQ/s320/Slide10.JPG" width="240" /></a></div>Give your students a hundred chart and ask them to write the numbers from 1-100. When your students have completed the activity, ask them to highlight the decade numbers.<br /><br />This activity lends so much more meaning to the counting by 10s count sequence because your students will see that the decade numbers keep track of the number of tens.<br /><br />To extend the activity, ask your students to cut their hundred chart in strips to create "ten strips".<br /><br />Your students can reuse the activity by putting their strips back together to once again create a hundred chart.<br /><br /><br /><br /></div><div><br /><h4>Place Value Activity #2</h4><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NGY6l4VH8ZA/XmfQco7_GsI/AAAAAAAAXeo/NQn1zaTlrzoz9ruQqaptqKQy_oGRrRvxwCLcBGAsYHQ/s1600/Slide11.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-NGY6l4VH8ZA/XmfQco7_GsI/AAAAAAAAXeo/NQn1zaTlrzoz9ruQqaptqKQy_oGRrRvxwCLcBGAsYHQ/s320/Slide11.JPG" width="240" /></a></div><div>Have a variety of cards each delineating a number of tens or ones. <a href="https://www.teacherspayteachers.com/Product/2-Digit-Number-Place-Value-Unit-4535655" target="_blank">The peanut butter and jelly cards pictured here are a part of this unit</a>. </div><div><br /></div><div>Your students will grab a tens card and a ones card and will build the number of tens and ones using linking cubes. </div><div><br /></div><div>**Linking cubes are a fantastic <b>concrete tool </b>for introducing place value because your students can physically see that a ten is made from ten ones. </div><div><br /></div><div>Ask your students to record the number of tens and ones on a place value chart and then to count by tens and ones to find the resulting number. </div><div><br /></div><div><br /></div><div><br /></div><h4>Place Value Activity #3</h4><div><a href="https://1.bp.blogspot.com/-esa3DXJWpDU/XmfQ5b2JdjI/AAAAAAAAXew/vKUwSqMftBo5pnJq_3JLQoHM5aEj4kniQCLcBGAsYHQ/s1600/Slide9.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-esa3DXJWpDU/XmfQ5b2JdjI/AAAAAAAAXew/vKUwSqMftBo5pnJq_3JLQoHM5aEj4kniQCLcBGAsYHQ/s320/Slide9.JPG" width="240" /></a>Another <b>concrete groupable model, </b>stirring straws can be physically bundled together in groups of ten making them an excellent tool for 1st-grade students who are learning about place value for the first time! </div><div><br /></div><div>In this activity, provide your students with a 2-digit number and ask them to create that number using bundles of ten straws and individual straws. </div><div><br /></div><div>Ask your students to record both a <b>place value drawing </b>and the number of tens and ones in their number on a place value chart. </div><div><br /></div><div>By asking your students to use place value drawings and place value charts, you are planting the seeds they will need to move from <b>concrete, hands-on tools to representational models. </b></div><div><br /></div><h4>Place Value Activity #4</h4><div><a href="https://1.bp.blogspot.com/-7fD5CFisFZQ/XmfRsS8IB6I/AAAAAAAAXe4/DXDiKakrKaMXpvpGddAhuFcybtvPZlKLwCLcBGAsYHQ/s1600/Slide8.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-7fD5CFisFZQ/XmfRsS8IB6I/AAAAAAAAXe4/DXDiKakrKaMXpvpGddAhuFcybtvPZlKLwCLcBGAsYHQ/s320/Slide8.JPG" width="240" /></a>Once your students are <i>consistently </i>comfortable with concrete manipulatives, it's time to start peeling them away. </div><div><br /></div><div>In this simple activity, students use number cards only from a deck and choose two cards. They then arrange those cards on a <b>place value chart</b>. Students will then draw a <b>place value drawing</b> and will determine the number that matches the number of tens and ones in the place value chart. </div><div><br /><br /><br /><br /><br /><br /><br /><h4>My Gift To You</h4></div><div><a href="https://drive.google.com/file/d/1Kpp-XnDre_tVZL2Sot7p-Xo8UZ5UEWWc/view?usp=sharing" target="_blank">Print this cheat sheet & keep it handy</a> while you are planning your place value lessons! </div><div><a href="https://drive.google.com/file/d/1Kpp-XnDre_tVZL2Sot7p-Xo8UZ5UEWWc/view?usp=sharing" target="_blank"><img border="0" height="320" src="https://3.bp.blogspot.com/-ZYSQE6G0XKE/XpsTUZT4hlI/AAAAAAAAY3I/HZ8C2yoFkdMK_edWbrFpBYpxpU6rHTF8gCK4BGAYYCw/s320/1st%2BGrade%2BDifferentiation%2BCheat%2BSheets%2B.jpg" width="247" /></a></div><div class="separator" style="clear: both; text-align: center;"></div></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-xippmI0-xaQ/XmfKrxn_H-I/AAAAAAAAXdw/jH4MF9ajAvwp7jM5F_rJb3YlQkYV37Y3wCLcBGAsYHQ/s1600/Cover%2BUpdate%2B5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="960" height="320" src="https://1.bp.blogspot.com/-xippmI0-xaQ/XmfKrxn_H-I/AAAAAAAAXdw/jH4MF9ajAvwp7jM5F_rJb3YlQkYV37Y3wCLcBGAsYHQ/s320/Cover%2BUpdate%2B5.jpg" width="320" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-DvkM_WYJKd8/XmfKUFKUenI/AAAAAAAAXdY/b0khNyPI3vE2dVj7lBzzGLNOKNlmytx0ACLcBGAsYHQ/s1600/1st%2BGrade%2BPlace%2BValue%2BBlog%2BPin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="320" src="https://1.bp.blogspot.com/-DvkM_WYJKd8/XmfKUFKUenI/AAAAAAAAXdY/b0khNyPI3vE2dVj7lBzzGLNOKNlmytx0ACLcBGAsYHQ/s320/1st%2BGrade%2BPlace%2BValue%2BBlog%2BPin.png" width="213" /></a></div><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-79748028260331080662020-03-19T13:58:00.001-04:002020-03-21T11:04:10.704-04:00The 5 Tools You Need to Build a Math Toolkit<i style="background-color: white; color: #101010; letter-spacing: 0.3px;"><span style="font-family: inherit; font-size: x-small;"><span style="color: #333333; line-height: 33px;">A portion of the links and recommendations below are affiliate links. This means that at </span><span style="box-sizing: border-box; color: #333333; line-height: 33px;">no additional cost to you</span><span style="color: #333333; line-height: 33px;">, I will earn a commission if you choose to make a purchase. I have personally used each of these math tools and would not recommend them if I did not appreciate the effectiveness of each tool. </span></span></i><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-SVQ8fmZjN0c/XnOp1xPvriI/AAAAAAAAXzM/YJZb1SWFOkojLQ_BuIb79Rkyax2IC7zpQCLcBGAsYHQ/s1600/Math%2BToolkit%2B1st%2Band%2B2ndGrade%2BBlog%2BHeader.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-SVQ8fmZjN0c/XnOp1xPvriI/AAAAAAAAXzM/YJZb1SWFOkojLQ_BuIb79Rkyax2IC7zpQCLcBGAsYHQ/s1600/Math%2BToolkit%2B1st%2Band%2B2ndGrade%2BBlog%2BHeader.png" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><i style="background-color: white; color: #101010; letter-spacing: 0.3px;"><span style="font-family: inherit; font-size: x-small;"><span style="color: #333333; line-height: 33px;"><br /></span></span></i>When you walk into a classroom, you see shelves filled with books, supplies and math manipulatives. At home? You don't have the resources or (or space!) to build such an extensive academic library. There are a few simple math tools you can stock up on that will make math homework a breeze.<br /><h4 style="text-align: center;">What Is A Math Toolkit? </h4><div>If you have ever sat at the table helping your child with their homework on a night when it <i>just isn't clicking </i>a math toolkit will be your saving grace. In math education research points to teaching students first with concrete, hands-on materials next moving to representational models like drawings and finally moving to abstract ideas like equations. </div><div><br /></div><div>Chances are you have been working in the representational or abstract when your child got stuck and the piece that could get you over the hump is a set of hands-on tools!<br /><br /></div><h4 style="text-align: center;"><u>1st Grade Math Toolkit</u></h4><div>In first grade, students are <i>most</i> focused on strategies for addition and subtraction to 20 and place value to 100. Are there other topics first graders learn and study? Absolutely; but these are the two areas where your child will spend the majority of their time.<br /><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/ETA-hand2mind-Linking-Educational-Counting/dp/B01D9KHJ5Q/ref=as_li_ss_il?keywords=linking+cubes&qid=1584473549&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyM1BOVUNISUNVV0U5JmVuY3J5cHRlZElkPUEwMDc1MDE5S1pKR1pWQ1BaSUlaJmVuY3J5cHRlZEFkSWQ9QTA0ODEzNzkxRkUwNUpFQ1BUUDJKJndpZGdldE5hbWU9c3BfYXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==&linkCode=li3&tag=the0c319-20&linkId=7b72c83be53977746c1b52d1c90c1102&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01D9KHJ5Q&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Linking Cubes</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01D9KHJ5Q" style="border: none !important; margin: 0px !important;" width="1" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><u style="font-weight: bold;">Linking Cubes</u></span><span style="text-align: left;">- A pack of 100 linking cubes will suffice for most of the work done in first grade. These cubes can be used for basic </span><a href="https://www.k5mathspot.com/2019/07/help-what-you-need-to-know-if-your.html" style="text-align: left;" target="_blank">addition</a><span style="text-align: left;"> and </span><a href="https://www.k5mathspot.com/2019/07/a-quick-and-clever-way-to-teach.html" style="text-align: left;" target="_blank">subtraction</a><span style="text-align: left;">, to build </span><a href="https://www.k5mathspot.com/2019/01/5-strategies-for-teaching-addition-and.html" style="text-align: left;" target="_blank">fact families</a><span style="text-align: left;">, and to build </span><a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" style="text-align: left;" target="_blank">early place value concepts</a><span style="text-align: left;">. Linking cubes can be used as individual pieces or stacked together which make them a valuable and flexible tool. </span></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/ETA-hand2mind-Two-Color-Counters-Practice/dp/B01N7RNXRC/ref=as_li_ss_il?keywords=red+and+yellow+chips&qid=1584473638&sr=8-2&linkCode=li3&tag=the0c319-20&linkId=f311685655762c7368791b1d8e5ca1a2&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01N7RNXRC&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Counting Chips</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01N7RNXRC" style="border: none !important; margin: 0px !important;" width="1" /></div><div><br /></div><div style="text-align: center;"><b style="text-align: center;"><u>Red & Yellow Chips</u></b><span style="text-align: center;">- These are small plastic or foam disks that are red on one side and yellow on the other. They can be used to model addition or subtraction, to practice </span><a href="https://www.k5mathspot.com/2019/06/how-to-prevent-teen-number-reversals.html" style="text-align: center;" target="_blank">teen numbers </a><span style="text-align: center;">and for practice decomposing numbers such as the </span><a href="https://www.k5mathspot.com/2015/07/sing-it-out.html" style="text-align: center;" target="_blank">partners of ten</a><span style="text-align: center;">. </span><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li2&o=1&a=B01N7RNXRC" style="border: none; margin: 0px;" width="1" /></div><div style="text-align: center;"><div class="separator" style="clear: both;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Counters-Recognition-Assorted/dp/B0006PKZ7W/ref=as_li_ss_il?keywords=counting+bears&qid=1584474099&sr=8-6&linkCode=li3&tag=the0c319-20&linkId=f8ddc0e1b7b0181baf8a71c66f012ba7&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B0006PKZ7W&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Counting Bears</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B0006PKZ7W" style="border: none !important; margin: 0px !important;" width="1" /><br /><u><b>Counters -</b></u><b> </b>Counters can come in any shape or form. They are simply individual little pieces that can be used to count and represent numbers. Mini Erasers, counting bears and craft stones are all examples of counters. Use something that your child is interested in! </div><u style="font-weight: bold;"></u><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/1000-Bulk-Plastic-Stirrers-Straws/dp/B084GD4W8G/ref=as_li_ss_il?keywords=stir+straws&qid=1584474208&sr=8-3-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExR1FaOU5ZRTZNVjBCJmVuY3J5cHRlZElkPUEwOTQ3MDM3M01ZOU9POUlZSzJRNyZlbmNyeXB0ZWRBZElkPUEwNjE3MjkwMVJZUkJQTEJLWTZPMCZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=&linkCode=li3&tag=the0c319-20&linkId=256f05411b5d8a9dffb438d11d58c6fa&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B084GD4W8G&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Stir Straws</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B084GD4W8G" style="border: none !important; margin: 0px !important;" width="1" /></div><div style="text-align: center;"><b><u>Straws-</u></b> This is primarily a <a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" target="_blank">place value tool </a>but straws can also be used individually as counters. Straws, like linking cubes, are another tool that can be physically put together by a child to show that ten ones make a ten. Your child will use small rubber bands to make bundles of ten straws to represent tens and single straws to represent ones. </div><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Plastic-Pattern-Blocks/dp/B00004WKPP/ref=as_li_ss_il?dchild=1&keywords=pattern+blocks&qid=1584637356&sr=8-3-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEzRVlLTEZHN1AzWktBJmVuY3J5cHRlZElkPUEwMDA1MjIzNVFFVDZNSTFSMVpMJmVuY3J5cHRlZEFkSWQ9QTAxODQ1MzIzTTVJOEZaMTRHODBMJndpZGdldE5hbWU9c3BfYXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==&linkCode=li3&tag=the0c319-20&linkId=5b3a687e3fc9234d6d488355936e9754&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B00004WKPP&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Pattern Blocks</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B00004WKPP" style="border: none !important; margin: 0px !important;" width="1" /></div><div style="text-align: center;"><b><u>Pattern Blocks- </u></b>Your child will do geometry work in 1st grade and the tool that will serve them from first grade on through <i>fifth grade </i>is a set of pattern blocks. These blocks can be used for activities as simple as naming shapes to activities where shapes are used to compose a new shape. In 3rd grade on, pattern blocks are an excellent hands-on tool for representing <a href="https://www.k5mathspot.com/2015/02/fly-on-math-teachers-wall-fractions.html" target="_blank">fractions</a>.<br /><br /></div><ol></ol></div><div><h4 style="text-align: center;"><u>2nd Grade Math Toolkit</u></h4><div>In second grade, students are <i>most</i> focused place value including <i>flexible </i>strategies for addition and subtraction to 100, they are using <i>place value based </i>strategies for addition and subtraction to 1,000.<br /><br />The <a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" target="_blank">most important thing to know about math tools for place value</a> is that there are 3 main types. Groupable tools are tools that your child can physically put together like linking cubes or bundles of straws. Pre-grouped proportional models are already constructed, such as base ten blocks. They are a bit less cumbersome than groupable models once your child is ready for them. Last, pre-grouped non-proportional models such as place value discs or coins are each worth a different value but the value and the size aren't proportionate. Again, this tool is MUCH less cumbersome to work with and, in the case of money, they lend a real life context.<br /><br />Each of these tools will be useful to your child throughout the school year.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/ETA-hand2mind-Linking-Educational-Counting/dp/B01D9KHJ5Q/ref=as_li_ss_il?keywords=linking+cubes&qid=1584473549&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyM1BOVUNISUNVV0U5JmVuY3J5cHRlZElkPUEwMDc1MDE5S1pKR1pWQ1BaSUlaJmVuY3J5cHRlZEFkSWQ9QTA0ODEzNzkxRkUwNUpFQ1BUUDJKJndpZGdldE5hbWU9c3BfYXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==&linkCode=li3&tag=the0c319-20&linkId=7b72c83be53977746c1b52d1c90c1102&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01D9KHJ5Q&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Linking Cubes</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01D9KHJ5Q" style="border: none !important; margin: 0px !important;" width="1" /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><u style="font-weight: bold;">Linking Cubes (Groupable Model) </u></span><span style="text-align: left;">- A pack of 100 linking cubes will suffice for most of the work done in first grade. These cubes can be used for basic </span><a href="https://www.k5mathspot.com/2019/07/help-what-you-need-to-know-if-your.html" style="text-align: left;" target="_blank">addition</a><span style="text-align: left;"> and </span><a href="https://www.k5mathspot.com/2019/07/a-quick-and-clever-way-to-teach.html" style="text-align: left;" target="_blank">subtraction</a><span style="text-align: left;">, to build </span><a href="https://www.k5mathspot.com/2019/01/5-strategies-for-teaching-addition-and.html" style="text-align: left;" target="_blank">fact families</a><span style="text-align: left;">, and to build </span><a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" style="text-align: left;" target="_blank">early place value concepts</a><span style="text-align: left;">. Linking cubes can be used as individual pieces or stacked together which make them a valuable and flexible tool. </span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><br /></span></div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/1000-Bulk-Plastic-Stirrers-Straws/dp/B084GD4W8G/ref=as_li_ss_il?keywords=stir+straws&qid=1584474208&sr=8-3-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExR1FaOU5ZRTZNVjBCJmVuY3J5cHRlZElkPUEwOTQ3MDM3M01ZOU9POUlZSzJRNyZlbmNyeXB0ZWRBZElkPUEwNjE3MjkwMVJZUkJQTEJLWTZPMCZ3aWRnZXROYW1lPXNwX2F0ZiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=&linkCode=li3&tag=the0c319-20&linkId=256f05411b5d8a9dffb438d11d58c6fa&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B084GD4W8G&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Stir Straws</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B084GD4W8G" style="border: none !important; margin: 0px !important;" width="1" /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"></span></div><div style="text-align: center;"><b><u>Straws (Groupable Model)-</u></b> This is primarily a <a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" target="_blank">place value tool </a>but straws can also be used individually as counters. Straws, like linking cubes, are another tool that can be physically put together by a child to show that ten ones make a ten. Your child will use small rubber bands to make bundles of ten straws to represent tens and single straws to represent ones.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://www.amazon.com/Didax-Educational-Resources-Plastic-Starter/dp/B01G7037J2/ref=as_li_ss_il?dchild=1&keywords=base+ten+blocks&qid=1584640461&sr=8-10&linkCode=li3&tag=the0c319-20&linkId=64d58c0bc05a882d6330d0a71a9a9af9&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01G7037J2&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Base Ten Blocks</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01G7037J2" style="border: none !important; margin: 0px !important;" width="1" /><br /><b><u>Base Ten Blocks (Pre-Grouped Proportional Model)-</u></b> Base ten blocks are one of the most <a href="https://www.k5mathspot.com/2014/08/i-love-base-ten-blocks.html" target="_blank">versitile tools you can put in your toolkit</a>. You can use base ten blocks to model 2 and 3 digit numbers, they are an aid in number comparison, and you can use them to model addition and subtraction of 2 and 3 digit numbers. When your child is in 4th and 5th grade you can even use this tool to model multi-digit multiplication and division!<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://www.amazon.com/EAI-Education-QuietShape-Thousandths-Millions/dp/B074CNBQTJ/ref=as_li_ss_il?dchild=1&keywords=place+value+disks&qid=1584640504&sr=8-8&linkCode=li3&tag=the0c319-20&linkId=efb4412aad996a8b1077445f2bebee0f&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B074CNBQTJ&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Place Value Discs</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B074CNBQTJ" style="border: none !important; margin: 0px !important;" width="1" /><br /><b><u>Place Value Discs (Pre-Grouped Non-Proportional Model)-</u></b> This little tool is much more compact than base ten blocks for modeling place value concepts as you move into larger numbers. Most sets also include numbers into the ten and hundred thousands down through decimal numbers. This tool will give you a lot of bang for your buck for years to come.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://www.amazon.com/Learning-Journey-Kids-Bank-Money/dp/B001Y66JU4/ref=as_li_ss_il?dchild=1&keywords=play+money&qid=1584640546&sr=8-10&linkCode=li3&tag=the0c319-20&linkId=394cae6695163fb201cc0744e30c9c52&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B001Y66JU4&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Play Money</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B001Y66JU4" style="border: none !important; margin: 0px !important;" width="1" /><br /><b><u>Play Money (Pre-Grouped Proportional Model)-</u></b> When will I use place value in my real life? All of the time. But, for our children, money is an immediate connection. Use pennies to represent ones, dimes to represent tens and dollars to represent hundreds when your child is in 2nd grade. This tool will continue to serve you well.<a href="https://www.k5mathspot.com/2019/08/teaching-modeling-decimal-numbers.html" target="_blank"> In 5th grade you can use the same exact tool to model decimal numbers! </a><br /><br /><h4 style="text-align: center;"><u>3rd Grade Math Toolkit</u></h4><div style="text-align: start;">In third grade, your students are spending the majority of their school year on the topics of basic multiplication and division as well as understanding fractions at a basic level. The tools I recommend will support your students in their work towards those goals.<br /><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Fun-Express-Mini-Insect-Erasers/dp/B00JVWD3H0/ref=as_li_ss_il?dchild=1&keywords=mini+erasers&qid=1584802015&sr=8-8&linkCode=li3&tag=the0c319-20&linkId=11a2d9b08668d8f8f7749ddfb526314e&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B00JVWD3H0&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Click to Shop Counters</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B00JVWD3H0" style="border: none !important; margin: 0px !important;" width="1" /></div><b style="text-align: center;"><u>Counters-</u></b><span style="text-align: center;"> When you are teaching basic multiplication and division, your students will need experiences with putting equal groups together and breaking into equal groups. You can do this with many items you already have in your home. Beans, crayons, and even shoes would work for this purpose. Another fun tool to use is mini erasers. Because you can find so many shapes and themes you can use them in a variety of math stories and contexts. </span><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/hand2mind-Plastic-Square-Assorted-Counting/dp/B01J6FPZU4/ref=as_li_ss_il?dchild=1&keywords=SQUARE+TILES&qid=1584802235&sr=8-1&linkCode=li3&tag=the0c319-20&linkId=dd0d116ba2f5be0a2174174a76b86988&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01J6FPZU4&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Click to Shop Tiles</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01J6FPZU4" style="border: none !important; margin: 0px !important;" width="1" /></div><b style="text-align: center;"><u>Square Tiles-</u></b><span style="text-align: center;"> Your 3rd grader isn't only understanding multiplication in terms of equal groups, arrays are a HUGE part of multiplication and division understanding. Arrays also lead into an understanding of area as well. Having square tiles on hand allows your child to create and manipulate arrays. </span><br /><span style="text-align: center;"><br /></span><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Plastic-Pattern-Blocks/dp/B00004WKPP/ref=as_li_ss_il?dchild=1&keywords=pattern+blocks&qid=1584802273&sr=8-2-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUE4MTAxTkxPME0ySEMmZW5jcnlwdGVkSWQ9QTA5OTk0ODRBMFRIVklMMzhHVUUmZW5jcnlwdGVkQWRJZD1BMDE4NDUzMjNNNUk4RloxNEc4MEwmd2lkZ2V0TmFtZT1zcF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl&linkCode=li3&tag=the0c319-20&linkId=1fb9870b42fbeb75a977e8c6bd834dfb&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B00004WKPP&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Click to Shop Pattern Blocks</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B00004WKPP" style="border: none !important; margin: 0px !important;" width="1" /></div><span style="text-align: center;"><u style="font-weight: bold;">Pattern Blocks- </u>In building an understanding of fractions, pattern blocks are an excellent introductory tool. Students can layer the pattern blocks on top of one another to explore fraction comparison and fraction equivalence. Generally, the hexagon is regarded at "one whole" and students use the other blocks to discover the half, third and sixth. This tool can also be used to meet geometry skills such as composing and decomposing 2-dimensional shapes. </span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/ETA-hand2mind-Assorted-Wooden-Alternative-Cuisenaire/dp/B016DU8UR0/ref=as_li_ss_il?dchild=1&keywords=cuisenaire+rods&qid=1584802315&sr=8-6&linkCode=li3&tag=the0c319-20&linkId=46229c4e9fe28bf97663e02edf5ab799&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B016DU8UR0&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Click to Shop Cuisenaire Rods</td></tr></tbody></table><span style="text-align: center;"><u style="font-weight: bold;"><br />Cuisenaire Rods-</u> This is an <i>incredibly versatile </i>fraction tool that will support your child in 3rd, 4th and 5th grade. This tool is used to explore fraction equivalence and fraction comparisons. There are no fractions written on the rods so they can be used flexibly and for a variety of applications. </span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Magnetic-Rainbow-Fraction/dp/B000QDTYMQ/ref=as_li_ss_il?dchild=1&keywords=fraction+bars&qid=1584802355&sr=8-20&linkCode=li3&tag=the0c319-20&linkId=990bd364149bcface5790895d60ab68c&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B000QDTYMQ&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Click to Shop Fraction Bars</td></tr></tbody></table><span style="text-align: center;"></span><span style="text-align: center;"><br /><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B000QDTYMQ" style="border: none !important; margin: 0px !important;" width="1" /></span><br /><div style="text-align: left;"><u style="font-weight: bold;">Fraction Bars- </u>A tool that is a bit more supportive than Cuisenaire rods would be fraction bars. These bars are pre-labeled and are broken into unit fractions. Your child can represent a variety of fractions by putting the bars together, can use the bars to add fractions with like denominators and can use the bars for fraction comparison and fraction equivalence. If another tool is not in your budget, you can print a set of fraction bars for free online, however, you will get a lot of use out of this tool so investing in a plastic set will serve you well!<br /><br /><br /><h4 style="text-align: center;"><u>4th Grade Math Toolkit</u></h4><div style="text-align: start;">In fourth grade, your child is spending the majority of the year on three main goals. First, extending their place value understanding to 1,000,000 and dipping their toe into the idea of decimals. Second, developing an understanding of multi-digit multiplication and division. Finally, your students will further their understanding of fractions.<br /><br style="text-align: center;" /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://www.amazon.com/Didax-Educational-Resources-Plastic-Starter/dp/B01G7037J2/ref=as_li_ss_il?dchild=1&keywords=base+ten+blocks&qid=1584640461&sr=8-10&linkCode=li3&tag=the0c319-20&linkId=64d58c0bc05a882d6330d0a71a9a9af9&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B01G7037J2&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Base Ten Blocks</td></tr></tbody></table><div style="text-align: center;"><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B01G7037J2" style="border: none !important; margin: 0px !important;" width="1" /></div><div style="text-align: center;"><b><u>Base Ten Blocks (Pre-Grouped Proportional Model)-</u></b> Base ten blocks are one of the most <a href="https://www.k5mathspot.com/2014/08/i-love-base-ten-blocks.html" target="_blank">versitile tools you can put in your toolkit</a>. This was a tool used back in 2nd grade and it makes a reappearance in 4th. While this place value tool represented ones, tens and hundreds in 2nd grade, you can now rename flats as "one" and use the sticks as "one tenth" and cubes as "one hundredth" to practice decimal work. On a completely different topic, base ten blocks can be used to model multi-digit multiplication and division through the area model! </div><div style="text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="https://www.amazon.com/EAI-Education-QuietShape-Thousandths-Millions/dp/B074CNBQTJ/ref=as_li_ss_il?dchild=1&keywords=place+value+disks&qid=1584640504&sr=8-8&linkCode=li3&tag=the0c319-20&linkId=efb4412aad996a8b1077445f2bebee0f&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B074CNBQTJ&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Place Value Discs</td></tr></tbody></table><div style="text-align: center;"><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B074CNBQTJ" style="border: none !important; margin: 0px !important;" width="1" /></div><div style="text-align: center;"><b><u>Place Value Discs (Pre-Grouped Non-Proportional Model)-</u></b> Place value disks are going to be your go-to tool for all things place value and decimals in 4th grade. Pair them with a place value chart (you can find one online or recreate your own on scrap paper or a white board) and this tool will support place value AND operations for numbers from the decimals to the millions!<br /><br /><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Plastic-Pattern-Blocks/dp/B00004WKPP/ref=as_li_ss_il?dchild=1&keywords=pattern+blocks&qid=1584802273&sr=8-2-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUE4MTAxTkxPME0ySEMmZW5jcnlwdGVkSWQ9QTA5OTk0ODRBMFRIVklMMzhHVUUmZW5jcnlwdGVkQWRJZD1BMDE4NDUzMjNNNUk4RloxNEc4MEwmd2lkZ2V0TmFtZT1zcF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl&linkCode=li3&tag=the0c319-20&linkId=1fb9870b42fbeb75a977e8c6bd834dfb&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B00004WKPP&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Pattern Blocks</td></tr></tbody></table><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B00004WKPP" style="border: none !important; margin: 0px !important;" width="1" /></div><span style="text-align: center;"><u style="font-weight: bold;">Pattern Blocks- </u>In building an understanding of fractions, pattern blocks are an excellent introductory tool. Students can layer the pattern blocks on top of one another to explore fraction comparison and fraction equivalence. Generally, the hexagon is regarded at "one whole" and students use the other blocks to discover the half, third and sixth. This tool can also be used to meet geometry skills such as composing and decomposing 2-dimensional shapes. </span><br /><span style="text-align: center;"><br /></span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/ETA-hand2mind-Assorted-Wooden-Alternative-Cuisenaire/dp/B016DU8UR0/ref=as_li_ss_il?dchild=1&keywords=cuisenaire+rods&qid=1584802315&sr=8-6&linkCode=li3&tag=the0c319-20&linkId=46229c4e9fe28bf97663e02edf5ab799&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B016DU8UR0&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Cuisenaire Rods</td></tr></tbody></table><span style="text-align: center;"><u style="font-weight: bold;"><br />Cuisenaire Rods-</u> This is an <i>incredibly versatile </i>fraction tool that will support your child in 3rd, 4th and 5th grade. This tool is used to explore fraction equivalence and fraction comparisons. There are no fractions written on the rods so they can be used flexibly and for a variety of applications. </span><br /><span style="text-align: center;"><br /></span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.amazon.com/Learning-Resources-Magnetic-Rainbow-Fraction/dp/B000QDTYMQ/ref=as_li_ss_il?dchild=1&keywords=fraction+bars&qid=1584802355&sr=8-20&linkCode=li3&tag=the0c319-20&linkId=990bd364149bcface5790895d60ab68c&language=en_US" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=B000QDTYMQ&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a></td></tr><tr><td class="tr-caption" style="font-size: 12.8px;">Click to Shop Fraction Bars</td></tr></tbody></table><span style="text-align: center;"></span><span style="text-align: center;"><br /><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=B000QDTYMQ" style="border: none !important; margin: 0px !important;" width="1" /></span><br /><div style="text-align: left;"><u style="font-weight: bold;">Fraction Bars- </u>A tool that is a bit more supportive than Cuisenaire rods would be fraction bars. These bars are pre-labeled and are broken into unit fractions. Your child can represent a variety of fractions by putting the bars together, can use the bars to add fractions with like denominators and can use the bars for fraction comparison and fraction equivalence. If another tool is not in your budget, you can print a set of fraction bars for free online, however, you will get a lot of use out of this tool so investing in a plastic set will serve you well!</div></div></div></div></div></div></div><hr /><b>Pin For Later: </b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NmDAODpKhZE/XnOs8N_QELI/AAAAAAAAXzk/TTPKAndDfNI_RiQ2k1B3tZxHalABZjTlwCLcBGAsYHQ/s1600/At%2BHome%2BToolkit%2BPin.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1500" data-original-width="1000" height="320" src="https://1.bp.blogspot.com/-NmDAODpKhZE/XnOs8N_QELI/AAAAAAAAXzk/TTPKAndDfNI_RiQ2k1B3tZxHalABZjTlwCLcBGAsYHQ/s320/At%2BHome%2BToolkit%2BPin.png" width="213" /></a></div><b><br /></b><b></b><br /><hr /><b>Math Spot Newsletter: </b> <b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-50210016087713347992020-03-15T21:15:00.004-04:002020-03-20T14:58:49.397-04:00FREE Math Activities To Use At Home.... Without Any Screentime! <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-UauJRwhttvA/XnUSUVIQkfI/AAAAAAAAX2U/56QI9Q2eNuIfFuKvO9pHj-aDJe6-N9UjgCLcBGAsYHQ/s1600/Math%2BAt%2BHome%2BBlog%2BHeader.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-UauJRwhttvA/XnUSUVIQkfI/AAAAAAAAX2U/56QI9Q2eNuIfFuKvO9pHj-aDJe6-N9UjgCLcBGAsYHQ/s1600/Math%2BAt%2BHome%2BBlog%2BHeader.png" /></a></div><br />If you are looking for quick, fun, meaningful math activities to use at home for your 1st or 2nd grader, I've got you covered.<br /><br />And no, not a single one of the activities requires any screen time at all!<br /><br />And no, it won't cost a cent. Absolutely and completely free.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://mailchi.mp/73bb124fac53/1stgradeathomemath" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-E3hnJtn_WsU/Xm7QrzE9EKI/AAAAAAAAXlc/pioWDZuLoTAqydEfmMo42QgrtQBET0WxwCLcBGAsYHQ/s200/Cover.jpg" width="200" /></a> <a href="https://mailchi.mp/cb62ea752172/2ndgradeathomemath" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-sbDWtzciNH8/Xm7QqMn50jI/AAAAAAAAXlY/YvctRbX6kKAjzw1Q2AUIndLVdFBGBh2ywCLcBGAsYHQ/s200/Cover%2BUpdate%2B6.jpg" width="200" /></a></div><br />So here's the basic At Home Math gist:<br /><br /><ul><li>Each day you will pick an activity strip. </li><li>Do the activity on the strip with the aid of my "helpful tips" they'll let you know why the activity is so useful to your child and their learning! </li><li>After you have completed the activity, turn the activity strip into a loop and add it to the activity chain. Every day as your child practices, sharpens their skills, and grows- the activity chain will grow as well! </li></ul><div>Activities range from making a picture graph of a load of laundry to making an "addition machine" with paper towel rolls. The activities are set to match specific first grade and second-grade math skills so they will be geared towards the work your child will benefit from most! </div><div><br /></div><div>And one last thing. </div><div><br /></div><div style="text-align: center;"><b>I will be on Instagram Monday - Friday for the next 4 weeks (starting 3/16/2020) sharing these activities for 1st and 2nd graders each day so we can walk through the activities together! Join me @themathspot! </b></div><div style="text-align: center;"><br /></div><br /><div style="text-align: center;"><div style="text-align: start;"><br /></div><div class="separator" style="clear: both;"><a href="https://mailchi.mp/73bb124fac53/1stgradeathomemath" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-E3hnJtn_WsU/Xm7QrzE9EKI/AAAAAAAAXlc/pioWDZuLoTAqydEfmMo42QgrtQBET0WxwCLcBGAsYHQ/s200/Cover.jpg" width="200" /></a> <a href="https://mailchi.mp/cb62ea752172/2ndgradeathomemath" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-sbDWtzciNH8/Xm7QqMn50jI/AAAAAAAAXlY/YvctRbX6kKAjzw1Q2AUIndLVdFBGBh2ywCLcBGAsYHQ/s200/Cover%2BUpdate%2B6.jpg" width="200" /></a></div><div style="text-align: start;"><br /></div></div><b></b> <hr /><b>Pin For Later: </b><br /><a href="http://1.bp.blogspot.com/-DEN1J_mUG5U/Xm7TLiY-lJI/AAAAAAAAXl4/Q0fRxoB7caUXSDYyJeQzHeiuquDELiX1QCK4BGAYYCw/s1600/Math%2BAt%2BHome%2BPin.png" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-DEN1J_mUG5U/Xm7TLiY-lJI/AAAAAAAAXl4/Q0fRxoB7caUXSDYyJeQzHeiuquDELiX1QCK4BGAYYCw/s320/Math%2BAt%2BHome%2BPin.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-89262154001033751392019-12-27T14:40:00.000-05:002019-12-27T14:40:43.274-05:00How to Teach Numberless Word Problems for 3rd Grade StudentsIf you have landed on this page, you are likely curious about how numberless word problems might be helpful for your 3rd grade students. I'm sure you have "number pluckers" in your classroom who routinely read a word problem, pluck the numbers out and add them together... or multiply them together if that is what you have been working on most recently.<br /><br />Numberless word problems are the solution to combating number pluckers.<br /><br /><h3>What are Numberless Word Problems? </h3><div>Simply put, numberless word problems are story contexts that don't (yet) have numbers associated with them. This allows your students to focus on the context and action of a story problem and to make sense of what is happening in the problem. </div><div><br /></div><h3>Why Use Numberless Word Problems? </h3><div>When the numbers are taken out of a word problem and your students are forced to focus on context and action, they move from "doing something to numbers" to thinking about which operation or operations could represent that action. </div><div><br /></div><div>In an oversimplified example, "Some dogs are playing at the dog park. Some of the dogs leave and go home. How many dogs are left to play at the dog park?" given this context, your students can't possibly jump to number plucking, instead, they would notice that in the story the major action is that some of the dogs went home. A conversation with your students will help them to connect the action of dogs leaving with the operation of subtraction. Once numbers are introduced back into the problem, your students can use the operation matching the action of the problem to solve. </div><div><br /></div><h3>How Do You Use Numberless Word Problems? </h3><div>While there is no specific right or wrong way to use a numberless word problem, there are techniques that allow for more discussion and therefore deeper understanding of a word problem. I favor a <a href="https://bstockus.wordpress.com/numberless-word-problems/" target="_blank">technique described by Brian Bushart</a> that unravels a problem step-by-step process that moves from a numberless scenario to a numbered word problem. </div><div><br /></div><div>In this approach, you begin with a story context void of numbers AND void of a question. </div><div> <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-KW_DeO7XcYM/XgZZSzQ0wEI/AAAAAAAAWRI/Co98qwMCblsGQqHd4C-3KFkKKhzKiTOYgCLcBGAsYHQ/s1600/Slide6.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="225" src="https://1.bp.blogspot.com/-KW_DeO7XcYM/XgZZSzQ0wEI/AAAAAAAAWRI/Co98qwMCblsGQqHd4C-3KFkKKhzKiTOYgCLcBGAsYHQ/s400/Slide6.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">You ask your students what they notice about the question, what (if anything) is happening in the question and you ask your students questions about the math that could occur surrounding this scenario. For example: </div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>What is happening in this problem? </li><li>What could we be wondering about the mittens? </li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Vp2xDbJOJSs/XgZZwcDKNnI/AAAAAAAAWRQ/FpYCS_GMwzg6rHUJqO_Xu5HamaZRJstDQCLcBGAsYHQ/s1600/Slide7.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="225" src="https://1.bp.blogspot.com/-Vp2xDbJOJSs/XgZZwcDKNnI/AAAAAAAAWRQ/FpYCS_GMwzg6rHUJqO_Xu5HamaZRJstDQCLcBGAsYHQ/s400/Slide7.JPG" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div>Next, you introduce back a small bit of information </div><div><ul><li>What do we know about the mittens now? </li><li>What does it mean if we have pairs of mittens? </li><li>Could we have 11 mittens in the box? Why or why not? </li><li>Name some other numbers of mittens that could or could not be in the box. </li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-H4U55BQly7g/XgZaCyKqAdI/AAAAAAAAWRY/WNnqW1gEQXY6Ah_zakEHT6dEgCvUu6u0ACLcBGAsYHQ/s1600/Slide8.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="225" src="https://1.bp.blogspot.com/-H4U55BQly7g/XgZaCyKqAdI/AAAAAAAAWRY/WNnqW1gEQXY6Ah_zakEHT6dEgCvUu6u0ACLcBGAsYHQ/s400/Slide8.JPG" width="400" /></a></div><div><br /></div></div><div>Add in another piece of information. It could be the rest of the numeric information as in the case above or it could even be the question- your students may wonder what information they still need to answer that question. </div><div><ul><li>What new information did we get about our story? </li><li>What question might we be wondering about the mittens in the box? </li></ul><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-899dQEittKE/XgZaw7gN-HI/AAAAAAAAWRk/PFuv6efVPZ4yVf85pqgC9zJdM2tcCrAOQCLcBGAsYHQ/s1600/Slide9.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="225" src="https://1.bp.blogspot.com/-899dQEittKE/XgZaw7gN-HI/AAAAAAAAWRk/PFuv6efVPZ4yVf85pqgC9zJdM2tcCrAOQCLcBGAsYHQ/s400/Slide9.JPG" width="400" /></a></div><div><br /></div></div><div>Finally, you will reveal the last piece of information in the story context and your students will have the opportunity to solve. </div><div><ul><li>What operation did you use to solve the problem? </li><li>How did (operation) match what was happening in the story? </li><li>Does your answer make sense? </li><li>How do you know?</li></ul><h3 style="text-align: center;">What Do I Need To Use Numberless Word Problems With 3rd Graders? </h3></div><div>Specifically, when working with 3rd graders, you are highlighting the problem types for multiplication and division. Don't get caught up in always using equal groups with a missing product type problems! Vary your word problems so that you are sometimes looking for a missing product, and sometimes looking for a missing group or group size. Be sure to incorporate area and measurement questions as well as comparison type problems. </div><div><br /></div><div>And, if that isn't enough, be sure to slip in addition and subtraction questions as well. The Common Core Standards include a <a href="http://www.corestandards.org/Math/Content/mathematics-glossary/Table-2/" target="_blank">helpful table to keep you varying your problem types</a> as you work with your students. </div><div><br /></div><h3 style="text-align: center;">Numberless Word Problems for 3rd Graders</h3><div><a href="https://www.teacherspayteachers.com/Product/Numberless-Word-Problems-3rd-Grade-Multiplication-and-Division-5121450?ref=feed%2Fsellers_updates_product&utm_source=k5mathspot.com&utm_campaign=3rd%20Grade%20Numberless%20Blog%20Post" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-fwHF2NppQBc/XgZcx7n-jNI/AAAAAAAAWRw/1MAGY_1ZRyg_xBAV54Hu9R6WuGdvefQ4wCLcBGAsYHQ/s200/Slide11.JPG" width="200" /></a>If you are feeling like you understand the process for using numberless word problems but that you would prefer to have a bank of ready-made projectable problems you can find themed problems for the entire school year <a href="https://www.teacherspayteachers.com/Product/Numberless-Word-Problems-3rd-Grade-Multiplication-and-Division-5121450?ref=feed%2Fsellers_updates_product&utm_source=k5mathspot.com&utm_campaign=3rd%20Grade%20Numberless%20Blog%20Post" target="_blank">at this link</a>. </div></div><br /><br /><br /><br /><br /><br /><br /><br /> <b></b><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://3.bp.blogspot.com/-bhuBuNaFbag/XgZdxzyDxgI/AAAAAAAAWR8/0CNizY8UgsQkiX9yBAPOAoGMQJaYAI2QgCK4BGAYYCw/s1600/How%2BTo%2BTeach%2BNumberless%2BWP.png" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-bhuBuNaFbag/XgZdxzyDxgI/AAAAAAAAWR8/0CNizY8UgsQkiX9yBAPOAoGMQJaYAI2QgCK4BGAYYCw/s320/How%2BTo%2BTeach%2BNumberless%2BWP.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-66399728685087376512019-11-10T10:06:00.004-05:002020-08-15T10:25:29.601-04:00CREATING MATH GROUPS & GOALS IN 4 EASY STEPSNothing feels better than working with a small group of students who are just <i>getting it. </i>During whole group instruction, there are always some students who seem to be drowning and getting them into the <b>right math groups </b>with the <b>right math goals </b>can be the absolute make or break difference in their success.<div><br /><a href="http://2.bp.blogspot.com/-JxNu0A9QpSQ/XcgWbmhVwlI/AAAAAAAAU5s/rP84WZ8Iie4EqL01IuQDoUcD-EKDgGuTwCK4BGAYYCw/s1600/Groups%2B%2526%2BGoals.png"><img border="0" src="https://2.bp.blogspot.com/-JxNu0A9QpSQ/XcgWbmhVwlI/AAAAAAAAU5s/rP84WZ8Iie4EqL01IuQDoUcD-EKDgGuTwCK4BGAYYCw/s1600/Groups%2B%2526%2BGoals.png" /></a><br /><p style="text-align: center;"><span style="color: #fd0390;">To be entirely clear- these steps will help you to form groups for tier 2 or tier 3 math intervention. This is NOT how I would suggest forming groups for a tier 1 guided math approach! Following these steps will ensure that you are forming targeted, skill-based intervention groups. </span></p><h3>Step 1: Determine What Should ALREADY be Mastered</h3><div>Tier 2 and tier 3 math instruction are about being responsive to students around instruction that has already been delivered. This is content that your students should have <i>previously </i>learned. </div><div><ul><li>Think about the last unit that you taught and list out the standards or goals that you would expect your students would have mastered coming out of that unit. </li><li>As an alternative approach, look at the <i>upcoming </i>unit. What foundational skills or standards do your students need to be successful in that unit? List out the skills and standards you know your students must have to be successful. </li></ul><div><h3>Step 2: Look At Your Data</h3><div>No! Please don't stop reading! I know that the "d" word can make you run for cover but there is absolutely no way that you will set effective groups and set effective goals without taking a look at where your students are now. </div><div><ul><li>Look at your assessment or student work from that past unit- what questions can you look at to determine whether or not your students have met the skills and standards you identified in step 1? </li><li>Don't have enough information to make effective groups? Create a short but meaningful assessment or performance tasks so that you have the information you need. </li><li>Short on time? If you are looking at a performance task- don't assess all of your students! Only assess the students who you are questioning. </li><li>For each standard or skill list the names of the students who have NOT yet met that standard. </li></ul></div></div><h3>Step 3: Make Your Math Groups </h3></div><div>Looking at the list of names for each standard, you have some decisions to make. </div><div><ul><li>For skills and standards with a long list of names, intervention groups may not be the answer. Should you consider a whole group reteach? Make that a priority! </li><li>For lists that are shorter, can you create one or more small groups to address this skill? </li><li>Do you have students that show up on every single list? Consider grouping those students together and determining which skill or standard you will start with. You will need to meet with this group more frequently because you have more work to do! </li></ul><div><h3>Step 4: Get Out Your Calendar </h3></div></div><div>Or better yet, click and download the <a href="https://mailchi.mp/893f479d0778/mathspotgroupsandgoals" target="_blank">free guide</a> (including a calendar) below! This plan is entirely useless if you don't have a plan for <i>how </i>you will show up and follow-through for your group. </div><div><a href="https://mailchi.mp/893f479d0778/mathspotgroupsandgoals" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-aZqhQ3RHUy0/Xcgl7PojYjI/AAAAAAAAU6M/BtzLetqzx5QLhbc3b2jEQ6QYWSZaTQitwCLcBGAsYHQ/s320/Setting%2BGroups%2Band%2BGoals%2BCover.jpg" width="240" /></a><ul><li>Find a time that you can commit to meeting with these groups. Maybe you only have time for one 15 minute group each day- that's fine! Not ideal... but fine none the less. Put that 15 minutes on your calendar IN PEN. </li><li>Looking at the month, block off the days where you have an assembly, sub, party, etc. that will be getting in the way of your groups. </li><li>Look at the remaining days and write in the group or groups that will meet each day. Keep in mind that groups with more goals will need to meet more frequently. Groups with fewer goals will need to meet less frequently. </li></ul><div><a href="https://mailchi.mp/893f479d0778/mathspotgroupsandgoals" target="_blank">Download this free planning guide </a>to put these strategies into practice. The sooner you fill out the guide, the sooner you will have a solid plan for your small groups and the sooner you will be experiencing their joy as they are successfully meeting math goals in your classroom! </div></div><b></b><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://2.bp.blogspot.com/-9Bo3N5fWEQc/Xcgh1_doPPI/AAAAAAAAU54/R7QyA25RW-IawlBiHaMvhqNAuEJrKnEPACK4BGAYYCw/s1600/Small%2BGroup%2BMath%2BGroups%2Band%2BGoals.png"><img border="0" height="320" src="https://2.bp.blogspot.com/-9Bo3N5fWEQc/Xcgh1_doPPI/AAAAAAAAU54/R7QyA25RW-IawlBiHaMvhqNAuEJrKnEPACK4BGAYYCw/s320/Small%2BGroup%2BMath%2BGroups%2Band%2BGoals.png" width="213" /> </a><a href="http://1.bp.blogspot.com/-18ts3D-q8Dw/XcgmxXfph3I/AAAAAAAAU6Y/RAlfPqRnRgESdbaolLkNZwP55-pnMUBBgCK4BGAYYCw/s1600/Copy%2Bof%2BSmall%2BGroup%2BMath%2BGroups%2Band%2BGoals.png"><img border="0" height="320" src="https://1.bp.blogspot.com/-18ts3D-q8Dw/XcgmxXfph3I/AAAAAAAAU6Y/RAlfPqRnRgESdbaolLkNZwP55-pnMUBBgCK4BGAYYCw/s320/Copy%2Bof%2BSmall%2BGroup%2BMath%2BGroups%2Band%2BGoals.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-71055417179192670852019-11-02T11:49:00.000-04:002019-11-02T11:49:15.658-04:00How Benchmarks of 5 and 10 Build Remarkable Number SenseIf you have been with me for any length of time you know that I am all about <i>simple</i> and <i>effective</i> math instruction. Finding opportunities to build number sense by illuminating the benchmarks of 5 and 10 fits the bill on both counts.<br /><br /><a href="http://1.bp.blogspot.com/--nUOSRzGk3Y/Xb2YSORFQtI/AAAAAAAAUsA/o3VUNs4rjl0qHrQ3td7hyWRo1wdimFC-QCK4BGAYYCw/s1600/Benchmarks%2Bof%2B5%2Band%2B10%2Bblog%2Bheader.png" imageanchor="1"><img border="0" src="https://1.bp.blogspot.com/--nUOSRzGk3Y/Xb2YSORFQtI/AAAAAAAAUsA/o3VUNs4rjl0qHrQ3td7hyWRo1wdimFC-QCK4BGAYYCw/s1600/Benchmarks%2Bof%2B5%2Band%2B10%2Bblog%2Bheader.png" /></a><br /><h4 style="text-align: center;"><i><b>Students with <a href="https://www.k5mathspot.com/2019/10/4-things-you-need-to-know-to-develop.html" target="_blank">number sense</a> understand how numbers relate to 5 and 10. </b></i></h4>A <i><b>kindergartner</b></i> with number sense sees 7 on a ten frame and notices that it is 2 more than 5 and 3 less than 10.<br /><br />A <b><i>first-grader</i> </b>with number sense knows that 9 is only 1 away from 10 and uses that to solve problems like 9 + 4.<br /><br />A <i><b>second-grader</b> </i>with number sense knows that 80 is 20 away from 100 because 8 tens + 2 tens = 10 tens.<br /><br />Fast forward...<br /><br />A <b><i>fifth-grader</i></b> with number sense knows that 0.7 + 0.4 is the same as 0.7 + 0.3 + 0.1<br /><br /><h4 style="text-align: center;">Tools for Benchmarks of 5 and 10</h4>Benchmarks of 5 and 10 are one of the four <a href="https://www.k5mathspot.com/2019/10/4-things-you-need-to-know-to-develop.html" target="_blank">number relationships</a> and that means that incorporating opportunities for your students to see, use and relate their learning to these relationships is an incredibly effective way to build number sense.<br /><br />You can <i>simply </i>incorporate benchmarks of 5 and 10 into your instruction by selecting tools that lend themselves to this relationship.<br /><br /><ul><li>A 5 frame of a 10 frame makes this relationship visual for your students. And, yes, because you are using a visual tool you are ALSO boosting <a href="https://www.k5mathspot.com/2019/10/what-is-subitizing-and-why-will-it-help.html" target="_blank">spatial relationships</a> and getting more bang for your number sense buck :) </li><li>Using a rekenrek allows your students to see the 5s and 10s embedded in numbers. </li><li>Even some dot pictures or dice patterns will highlight the relationship of numbers to 5 and 10! </li></ul><h4 style="text-align: center;">Number Sense Games for Benchmarks of 5 and 10</h4><div><ul><li><b>Which Is Closer? </b>Give your students a number. They simply have to determine whether it is closer to 5 or 10. You say "7" and your students respond, "5"! Ask a student to report out "how they know" looking for an answer that states 7 is only 2 away from 5 but is 3 away from 10.</li><ul><li><i>Differentiate</i></li><ul><li>Give your students a number path to refer to as they answer the questions if they need visual support when you begin the activity. </li><li>Adjust the numbers in the game depending on your grade level. In 1st grade ask students, for example, whether a number is closer to 20, 25 or 30. In 4th grade ask if a number is closer to 1,000, 1,500 or 2,000. In 5th grade ask if a number is closer to 0, 0.5 or 1.0.</li></ul><li><i>Spice it Up! </i></li><ul><li>Turn this activity into an active game by putting the benchmark numbers on index cards on the whiteboard. Break your students up into lines and for each example, have the first person in each line run-up to the board to touch the closest benchmark number. Either keep score and create a competition between the teams or ask both players to return to the line of the winning player for a less competitive, longer playing game. </li></ul></ul></ul><div><br /></div><ul><li><b>Name My Number- </b>Show your students an image of either a ten frame or a rekenrek and ask your students to name the number as quickly as possible. </li><ul><li><i>Differentiate</i></li><ul><a href="https://1.bp.blogspot.com/-H1SSrm6EuMI/Xb2iyU9TshI/AAAAAAAAUsw/J47YVK06-jkqVPgn8LQYvW4e_NMwyD5OwCLcBGAsYHQ/s1600/Slide10.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-H1SSrm6EuMI/Xb2iyU9TshI/AAAAAAAAUsw/J47YVK06-jkqVPgn8LQYvW4e_NMwyD5OwCLcBGAsYHQ/s320/Slide10.JPG" width="240" /></a><li>In kindergarten, this may be the full extent of the activity! Using a regular or irregular pattern on a five or ten frame will allow your students to see the numbers they are naming relative to five and ten. </li><li>In second grade, consider filling the ten frame with place value disks. For example, fill the frame with 6 disks each labeled "10" and ask your students what number you have made. How quickly are they able to identify 90? Ask your students how they <i>knew </i>it was 90 so quickly. Did they see 5 tens and 4 tens? Did they see that they were only one ten shy of 100? </li><li>In fourth grade, play using place value disks but also ask your students to consider how place values related. EX: If you know seven "one-thousands" is 7,000 <i>what do you think we would have if I filled the same number of spaces with "ten-thousands"?</i></li></ul></ul></ul><i><br /></i><ul><ul><ul></ul></ul></ul><a href="https://mailchi.mp/f81b284e9b52/mathspotbenchmarsof5and10" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-vQC5MH56uqw/Xb2iNIXfe2I/AAAAAAAAUso/0JtleGnpPmoc9RsiVnvTbvnsX1_W9G2IACLcBGAsYHQ/s320/Benchmarks%2Bof%2B5%2Band%2B10%2BCover.jpg" width="240" /></a>Think about your current instruction- is there a way to illuminate the relationship of numbers to 5 and 10? Can you make this relationship visible and tangible for your students? It's a simple and effective shift you can make to get more bang for your number sense buck during your math instruction!<br /><br />Click the <a href="https://mailchi.mp/f81b284e9b52/mathspotbenchmarsof5and10" target="_blank">image to the right</a> to grab a free set of number sense cards so you can try "Name My Number" with your students. I have included differentiated cards for numbers to 10, 100, 1,000, 10,000 and tenths!<br /><br /><br /><br /><br /><br /><br /><br /></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Partners-of-Ten-1st-Grade-Math-Unit-1934695?aref=c2vov443" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-mBAuxQmPa-w/Xb2hJzEP4hI/AAAAAAAAUsg/dEW-Tvvj-achToiEjt01UKNIKB-JuQnwwCLcBGAsYHQ/s200/Cover%2BUpdate%2B4.jpg" width="200" /></a></div><b><span id="goog_1097381426"></span><span id="goog_1097381427"></span><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://4.bp.blogspot.com/-pFFCBG8pUcg/Xb2ZqEwsKcI/AAAAAAAAUsU/Mg7NvVRg79s5-BY6DDoNUXu-IZrLfrvKQCK4BGAYYCw/s1600/Benchmarks%2Bof%2B5%2Band%2B10%2Bblog%2Bpin.png" imageanchor="1"><img border="0" height="320" src="https://4.bp.blogspot.com/-pFFCBG8pUcg/Xb2ZqEwsKcI/AAAAAAAAUsU/Mg7NvVRg79s5-BY6DDoNUXu-IZrLfrvKQCK4BGAYYCw/s320/Benchmarks%2Bof%2B5%2Band%2B10%2Bblog%2Bpin.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-35376077974138711532019-10-27T12:18:00.001-04:002019-10-28T13:16:15.084-04:00How to use Simple Number Sense Activities to Boost Part Whole Thinking<i style="background-color: white; color: #101010; font-family: Lora, sans-serif; font-size: 15px; letter-spacing: 0.3px;"><span style="color: #333333; font-family: "sorts mill goudy" , sans-serif; line-height: 33px;"><span style="font-size: xx-small;">THIS POST CONTAINS AFFILIATE LINKS. THIS MEANS, THAT AT NO ADDITIONAL COST TO YOU, I WILL EARN A COMMISSION IF YOU CHOOSE TO MAKE A PURCHASE. I HAVE PERSONALLY USED THESE RESOURCES AND WOULD NOT RECOMMEND THEM IF I DID NOT APPRECIATE THE QUALITY OF THE RESOURCE PRIOR TO RECOMMENDATION. </span></span></i><br /><i style="background-color: white; color: #101010; font-family: Lora, sans-serif; font-size: 15px; letter-spacing: 0.3px;"><span style="color: #333333; font-family: "sorts mill goudy" , sans-serif; line-height: 33px;"><span style="font-size: xx-small;"><br /></span></span></i>That moment when one of your first graders tells you, <i>in October</i>, that 24 + 34 is 58 "because 20 and 30 is 50 and 4 and 4 is 8 so it must be 58!" You haven't done any number sense activities around 2-digit addition but you KNOW that student "has number sense". They must <i>just have a mind for math</i>.<br /><br />One of the most recognizable tenents of <a href="https://www.k5mathspot.com/2019/10/4-things-you-need-to-know-to-develop.html" target="_blank">number sense</a> is flexible thinking. The good news is that, like anything else, this is not a "you have it or you don't" proposition for your students. You can BUILD this flexible part-whole thinking in your students. <b>And if you read to the end of this post, I have a set of free number sense activities to help you do just that! </b><br /><b><br /></b><br /><a href="http://3.bp.blogspot.com/-w7cxeqCLKAw/XbW5li7hCbI/AAAAAAAAUlk/sRdZHrjfzZQ_TA1LwoNd4pSvltjOlwpOwCK4BGAYYCw/s1600/Part%2BWhole%2BNumber%2BSense%2BBlog%2BHeader.png" imageanchor="1"><img alt="This blog post features number sense activities for building part whole thinking in elementary math students. " border="0" src="https://3.bp.blogspot.com/-w7cxeqCLKAw/XbW5li7hCbI/AAAAAAAAUlk/sRdZHrjfzZQ_TA1LwoNd4pSvltjOlwpOwCK4BGAYYCw/s1600/Part%2BWhole%2BNumber%2BSense%2BBlog%2BHeader.png" title="Number Sense Activities for Part Part Whole Thinking Header" /></a><br /><br /><h4 style="text-align: center;">Part-Whole Thinking in Kindergarten</h4>In kindergarten, we see this type of thinking built when we ask students to decompose numbers to 10. Students are playing simple shake and spill games to practice number combinations for numbers up to ten.... and with <i>extra </i>attention to partners of 10!<br /><br />Later in the kindergarten year, your students decompose teen numbers into a ten and "some" ones. These activities build both number sense AND a foundation for place value understanding!<br /><br /><h4 style="text-align: center;">Part-Whole Thinking in 1st Grade</h4>In first grade, your students are applying their understanding of part-whole thinking to solve addition and subtraction facts. For example, students who are using the "<a href="https://www.k5mathspot.com/2016/01/double-ten-frames.html" target="_blank">make a ten</a>" strategy to add numbers together will be <i>decomposing an addend</i> to make <i>partners of ten</i> and <i>composing a ten and some ones to create a teen number</i>.<br /><br />Yes. ALL of those kindergarten part-whole activities are synthesized together and applied to first grade standards.<br /><br />Do you have a first-grade student who is struggling with these number sense activities? Go back and check their fluency with number decomposition for all numbers to 10 and allow your students to play simple activities like Shake & Spill or Break a Rod to become fluent in decompositions to ten.<br /><br />While your students are applying the decompositions they learned in kindergarten, you are also studying place value to prepare your students for second grade. 1st Grade students are composing and decomposing so that they understand 2-digit numbers as tens and ones.<br /><h4 style="text-align: center;">Part-Whole Thinking in 2nd Grade</h4>Are you starting to see a pattern? In first grade your students worked to understand 2-digit numbers by composing and decomposing tens and ones. In second grade, your students are now <i>applying </i>this understanding so that they can flexibly <a href="https://www.k5mathspot.com/2014/10/fly-on-math-teachers-wall-teaching.html" target="_blank">add and subtract numbers to 100</a> using strategies based on place value.<br /><br />Have students who are struggling? By 2nd grade, your students have had more opportunity for gaps. At this point, you will need to go back and check your students' decompositions for numbers to 10 along with your students understanding of 2-digit numbers as tens and ones.<br /><br />Those SAME number sense activities you used for 1st graders can apply here as well! Allow your students to play shake and spill but, this time, write "10" on each of the chips your students are spilling out so that they can practice composing and decomposing decade numbers.<br /><h4 style="text-align: center;">Part-Whole Thinking in Third Grade</h4>Part-Whole thinking becomes more complex in third grade as you add on additional topics of study. In third grade, your students are becoming flexible "part-whole-thinkers" relative to factors of numbers to 100 as well as unit fractions.<br /><br />The main aim in 3rd grade is much like the goals of kindergarten- become fluent in terms of composing and decomposing equal groups and become fluent in terms of composing and decomposing fractions with unit fractions.<br /><br />Your students will ALSO start to apply their understanding of decompositions of equal groups in order to use the distributive property to multiply.<br /><h4 style="text-align: center;">Part-Whole Thinking in 4th Grade</h4>In third grade, you laid a foundation for multiplication and work with fractions. In fourth grade, you will apply these understandings further.<br /><br />In terms of multiplication, your students are applying their place value understanding (from back in 1st and 2nd grade!) to multiply larger numbers using strategies such as the area model.<br /><br />Your students are also applying understanding of unit fractions to perform fraction operations such as addition and subtraction.<br /><h4 style="text-align: center;">Part-Whole Thinking in 5th Grade</h4>In 5th grade, your students are expected to compose and decompose whole numbers, fractions, and <a href="https://www.k5mathspot.com/2019/08/teaching-modeling-decimal-numbers.html" target="_blank">decimals</a> in order to flexibly apply all 4 operations.<br /><br />If you have students who are struggling to think flexibly in 5th grade you have a lot of ground to cover in order to "drill back" to find where the breakdown occurred. The most simple way to accomplish this task is to begin your number sense activities with WHOLE NUMBERS.<br /><br /><ul><li>Determine whether or not your students are fluent with decompositions of numbers to 10</li><li>Move to learn if your students are fluent decomposing 2, 3, 4, 5 or 6 digit numbers into unit form. </li><li>Ask your students to perform SIMPLE whole number calculations mentally such as "42 + 23" in order to determine whether or not your students are comfortable breaking a number apart to solve. <i>Yes. You may have 5th-grade students who fall out at this point. Go back and solidify their understanding at THIS LEVEL. Trying to move ahead will do your students no service if you skip this foundation. </i></li><li>Continue layering on one skill at a time using increasingly complex numbers until your students are working at the 5th-grade level. </li></ul><div><a href="https://www.amazon.com/Teaching-Student-Centered-Mathematics-Developmentally-Appropriate/dp/0134556437/ref=as_li_ss_il?ie=UTF8&linkCode=li2&tag=the0c319-20&linkId=991e38fc4e33a357f4dfcc4639838aaa&language=en_US" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0134556437&Format=_SL160_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a>If you are interested in learning more about part-whole thinking in Kindergarten through 5th grade, I highly recommend the text "Teaching Student-Centered Mathematics". This text goes far above and beyond part-whole thinking but is a wealth of knowledge around building number sense and understanding operations for elementary students. <img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li2&o=1&a=0134556437" style="border: none !important; margin: 0px !important;" width="1" /><i>This is an affiliate link meaning, at no additional cost to you, if you do make a purchase I will receive a small amount of compensation. I own and truly value this book and would NOT make a recommendation that I didn't think was worth your while! </i></div><h4 style="text-align: center;">Number Sense Activities for Part-Whole Thinking </h4><div><b>Shake and Spill-</b> Draw or print a simple graphic on paper. Give your students a cup with a given number of counters (ex: 10). Your students will spill the counters onto the paper and write the parts and total in a variety of representations (ex: on a number bond and in an equation). </div><div><br /></div><div><b>Break the Stick- </b>Give your students a stick of linking cubes of a given number. Ask your students to find as many ways as they can to break the stick and record each decomposition in a variety of ways (ex: Break a stick of 5 and record the number of 5ths on a tape diagram and as an addition equation). </div><br /><b>Word Problems- </b>State a simple open-ended word problem for your students that asks your student to break a whole into parts. (Ex: I have 24 flowers in my garden laid out in rows of 3. Some rows are made of tulips and some rows are made of daisies. Draw a picture that shows 3 different ways my garden might look and find the total number of daisies and tulips in my garden in each drawing).<br /><br />Grab a set of Shake & Spill activities (Differentiated for use in kindergarten through 5th grade!) for free at the link <a href="https://mailchi.mp/e91f1dc17749/mathspotpartwhole" target="_blank">HERE</a>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://mailchi.mp/e91f1dc17749/mathspotpartwhole" target="_blank"><img alt="Click this cover to sign up to receive a set of free number sense activities for building part whole thinking. " border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-01_XwHvotqM/XbXCdugtJPI/AAAAAAAAUmg/q9avQzYpS58QXKGttY062pfWWFzSilP3wCLcBGAsYHQ/s320/Part-Whole%2BCover.jpg" title="FREE Number Sense Activities Cover" width="240" /></a></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Partners-of-Ten-Intervention-Resources" target="_blank"><img alt="This related unit for teaching partners of ten can be found on Teachers Pay Teachers. " border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-Le-11Kwk6kk/XbW55HysiuI/AAAAAAAAUl0/sNIYpxlS5IoM4dRyG2cErSCnXTxSonrUwCLcBGAsYHQ/s200/Cover%2BUpdate%2B4.jpg" title="Partners of 10 Unit" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2-Digit-Number-Place-Value-Unit-4535655" target="_blank"><img alt="This related unit for teaching two digit place value can be found on Teachers Pay Teachers." border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-GVNEM4T6dr4/XbW580QMCDI/AAAAAAAAUl4/Mep_TaCngG8afNnccJdeA_2vSsCVIQZOQCLcBGAsYHQ/s200/Cover%2BUpdate%2B5.jpg" title="2-Digit Place Value Unit" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Place-Value-Unit-Math-Intervention-4935591" target="_blank"><img alt="This related unit for teaching place value of 3 digit numbers can be found on Teachers Pay Teachers." border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-3rYeqKtQimE/XbW6CsSx90I/AAAAAAAAUl8/tI68aAUZ3JcnMLrQmwOPALZ7rMeNKbTaQCLcBGAsYHQ/s200/Cover%2BUpdate%2B6.jpg" title="3 Digit Place Value Unit" width="200" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://4.bp.blogspot.com/-dHGDuOdrhYU/XbW51JhAoKI/AAAAAAAAUls/n9s3E5N4RMIqQRm5rvCECao2oRwbe1D_QCK4BGAYYCw/s1600/Copy%2Bof%2BCopy%2Bof%2BNumber%2BSense%2BBlog%2BPin.png" imageanchor="1"><img alt="Click this pin to save this post on number sense activities for building part whole thinking onto Pinterest. " border="0" height="320" src="https://4.bp.blogspot.com/-dHGDuOdrhYU/XbW51JhAoKI/AAAAAAAAUls/n9s3E5N4RMIqQRm5rvCECao2oRwbe1D_QCK4BGAYYCw/s320/Copy%2Bof%2BCopy%2Bof%2BNumber%2BSense%2BBlog%2BPin.png" title="Blog Post Pin for Building Number Sense Part Part Whole Thinking" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-31546226570039416072019-10-19T09:46:00.002-04:002019-11-01T13:44:15.705-04:00Unbelievably Simple Number Sense Activities To Build One More One Less ThinkingLast week, we talked about how <a href="https://www.k5mathspot.com/2019/10/4-things-you-need-to-know-to-develop.html" target="_blank">number sense</a> activities don't need to be a completely separate entity from your standards-based math instruction while specifically <a href="https://www.k5mathspot.com/2019/10/what-is-subitizing-and-why-will-it-help.html" target="_blank">discussing spatial relationships</a>. This week we will look at how the idea of <b>one more and one less</b> (an important concept that students with number sense use flexibly!) can be built into your instruction across a variety of grades and subjects.<br /><a href="http://2.bp.blogspot.com/-7P9xltxmc-Y/XasTswyNfTI/AAAAAAAAUVQ/daauLeboT5MZCz1n_KthrHWnmR078wckQCK4BGAYYCw/s1600/One%2BMore%2BOne%2BLess%2BBlog%2BHeader%2B.png" imageanchor="1"><img border="0" src="https://2.bp.blogspot.com/-7P9xltxmc-Y/XasTswyNfTI/AAAAAAAAUVQ/daauLeboT5MZCz1n_KthrHWnmR078wckQCK4BGAYYCw/s1600/One%2BMore%2BOne%2BLess%2BBlog%2BHeader%2B.png" /></a><br /><h4 style="text-align: center;"><b>One More and One Less Across Elementary Math</b></h4>In kindergarten, your students are becoming acclimated with the idea that when we are counting forward we are referring to increasingly larger amounts and when we count backward we are referring to amounts getting smaller and smaller.<br /><br />As grade levels increase, your students are STILL developing their fluency with one more and one less.... but they are talking about UNITS rather than individual ones.<br /><br /><div style="text-align: center;"><b>Kindergarten- One More/One Less</b></div><div style="text-align: center;"><b>1st Grade- A "Ten" More or a "Ten" Less</b></div><div style="text-align: center;"><b>2nd Grade- A "Hundred" More or a "Hundred" Less</b></div><div style="text-align: center;"><b>3rd Grade - A "Unit Fraction" More or a "Unit Fraction" Less</b></div><div style="text-align: center;"><b>4th Grade- A "Thousand, Ten Thousand, Hundred Thousand" or "Million" More or less</b></div><div style="text-align: center;"><b>5th Grade- A "Tenth, Hundredth or Thousandth" More or Less </b></div><br />We don't need to take time away from your grade level goals to build number sense. These number concepts are BUILT-IN to your standards!<br /><br />Using a <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">concrete, representational, abstract approach</a>, you can move your students to the abstract level and help them to build fluency around these concepts.<br /><br /><h4 style="text-align: center;">Spinner Number Sense Activity</h4>A simple spinner game can help your students (at all levels!) to develop fluency with this skill.<br /><br />Your student will need a game board (<a href="https://mailchi.mp/74e21f384101/mathspotonemoreoneless" target="_blank">included in the free resource below</a>), a spinner labeled "one more" and "one less" and a cube or counter. Ask your students to start at the center of the game board. They will then move their counter and state aloud how they moved. For example, in the kindergarten version of the game, students would state "5, one more is 6" or "5, one less is 4". Your students will continue spinning, moving and speaking aloud until they reach either the upper or lower limit of the board.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-YtodybdaY38/XasSdtBMXdI/AAAAAAAAUVA/WgpZA-_CIWofD7npyL5_cq1uvVVDDOsLQCLcBGAsYHQ/s1600/onemoreless.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="616" data-original-width="692" height="284" src="https://1.bp.blogspot.com/-YtodybdaY38/XasSdtBMXdI/AAAAAAAAUVA/WgpZA-_CIWofD7npyL5_cq1uvVVDDOsLQCLcBGAsYHQ/s320/onemoreless.png" width="320" /></a></div><br /><br />This game can be played by students at a variety of grade levels using differentiated game boards and spinners (grab for free below).<br /><br />You may consider playing in a small group allowing each student, in turn, to spin the spinner, move the counter and then asking the whole group to state the sentence frame aloud together.<br /><br /><h4 style="text-align: center;"><b>Partner Game Number Sense Activity </b></h4><div>This activity (<a href="https://www.teacherspayteachers.com/Product/10-More-10-Less-1-More-1-Less-Activities-2558891" target="_blank">full 1st grade unit found here</a>) allows your students to manipulate units to practice 1 and 10 more and less to gain fluency in this skill. Playing with a partner, player one selects a number and indicates whether they will be adding or subtracting units from that number. Player 2 uses mental math to determine the resulting number while player 1 models the addition or subtraction using a hands-on material such as counters, base ten blocks or place value disks. Players alternate being the number chooser/builder and being the player to use mental math.<br /><br /><a href="https://mailchi.mp/74e21f384101/mathspotonemoreoneless" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-g7pg0wQVeaQ/XasR2SEy8_I/AAAAAAAAUU4/wPg26B6bfUww61AB-B3rolgkRPYQR8jlQCLcBGAsYHQ/s320/One%2BMore%2Band%2BOne%2BLess%2BCover.jpg" width="240" /></a>Through repetitions of this activity, your students will become more fluent with the skill of adding or subtracting a single unit.<br /><br />Each of these activities boosts number sense around your own grade-level standards but imagine the quick connections your students will be able to make when you ask them to generalize this idea in future grade levels. Because the activity focuses on fluency with one more and one less unit your students will have a stronger number sense around similar concepts even as numbers get larger!<br /><br /><div style="background-color: white; color: #101010; font-size: 15px; letter-spacing: 0.3px; margin: 0px; padding: 0px;"><span style="font-family: inherit;"><a href="https://mailchi.mp/74e21f384101/mathspotonemoreoneless" target="_blank">I would love to share these two activities with you so that you can give them a try and get your own juices flowing in terms of how you can incorporate activities that build the one more and one less relationship into the instruction you are already delivering! Click the graphic to the right and grab your (free) copy of these activities now! </a></span></div></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Adding-and-Subtracting-Ten-Mentally-2558891" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-W7-xCqcnIss/XasGWtJs_2I/AAAAAAAAUUE/m-lLSMeWcRk19iQ8j4wmOSNkpV8EKULnQCLcBGAsYHQ/s200/Cover%2BUpdate%2B5.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/First-Grade-Place-Value-Game-2546241" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-J9CkwWd0I1s/XasGbGud11I/AAAAAAAAUUI/S8sW9CThJm0CwnMLtKYH2-dCx8kw-vUBQCLcBGAsYHQ/s200/Cover%2BUpdate%2BSquare%2B.jpg" width="200" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/5th-Grade-Place-Value-Decimal-Game-3997461" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-azj3sweHBhA/XasGdL6krHI/AAAAAAAAUUM/GqN9GSYVlIMrRTaxS6ubyZ1c3Nzc2to1wCLcBGAsYHQ/s200/Cover%2BUpdate%2B%255BAutosaved%255D.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Place-Value-Game-to-1000-3994935" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-wXSrrNxXlgY/XasGgJ98OII/AAAAAAAAUUQ/SPFCpgO2BoAZyckIqg0KiTM4klaKpEkxgCLcBGAsYHQ/s200/Cover%2BUpdate.jpg" width="200" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://1.bp.blogspot.com/-THvzBUkq8OI/XasTwUby93I/AAAAAAAAUVY/ShQs5SYeWn8WiXDhBZP5dD4TTTKPUyGcQCK4BGAYYCw/s1600/One%2BMore%2BOne%2BLess%2BBlog%2BPin%2B%2B.png" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-THvzBUkq8OI/XasTwUby93I/AAAAAAAAUVY/ShQs5SYeWn8WiXDhBZP5dD4TTTKPUyGcQCK4BGAYYCw/s320/One%2BMore%2BOne%2BLess%2BBlog%2BPin%2B%2B.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-30447611718963735152019-10-13T12:23:00.000-04:002019-10-13T12:44:54.150-04:00What are Spatial Relationships and How Does It Help Build Number Sense? Last week we talked about <a href="https://www.k5mathspot.com/2019/10/4-things-you-need-to-know-to-develop.html" target="_blank">4 number relationships</a> that build number sense in your students. In other words, students with number sense are strong in these number relationships!<br /><br />Building number relationships is one of those <b>simple & effective </b>strategies you can layer on top of the instruction you are already delivering in order to get BIG bang for your buck when it comes to your time with your students.<br /><br />Because here is the thing. You are welcome to stop teaching [<i>insert topic here</i>] and do "number sense work". But why?<br /><br /><a href="http://4.bp.blogspot.com/-AwcrRGAuow0/XaNOc4sLGuI/AAAAAAAAUG4/zcFvEezs-3ovEwEe1Du44VqXpnBMVYlnQCK4BGAYYCw/s1600/Spatial%2BRelationships%2BHeader.png" imageanchor="1"><img border="0" src="https://4.bp.blogspot.com/-AwcrRGAuow0/XaNOc4sLGuI/AAAAAAAAUG4/zcFvEezs-3ovEwEe1Du44VqXpnBMVYlnQCK4BGAYYCw/s1600/Spatial%2BRelationships%2BHeader.png" /></a><br /><br />I don't have the time OR organizational capacity to juggle adding in new activities or units of study that are completely disconnected from the goals I am looking to meet with my students.<br /><br />And once we open Pandora's box of "number sense work" are we going to want to stop working towards our goals to do "story problem work" and "fact fluency work" too?<br /><br />We can and should meld this work together! Let's take a look at <b>spatial relationships</b> and how you can build this number relationship through the instruction you already delivering.<br /><br /><h4 style="text-align: center;">Subitizing to Support Fact Fluency (1st Grade Example)</h4><div><a href="https://1.bp.blogspot.com/-1pI-oYVPckU/XaNOm-TZx1I/AAAAAAAAUHE/SnsBP7A5X4IkPSawASFgZdnlQMrq5lkJgCLcBGAsYHQ/s1600/Slide3.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-1pI-oYVPckU/XaNOm-TZx1I/AAAAAAAAUHE/SnsBP7A5X4IkPSawASFgZdnlQMrq5lkJgCLcBGAsYHQ/s320/Slide3.JPG" width="240" /></a>In first grade, you spend a TON of time on developing your students' understanding of addition and subtraction and beginning to work towards fact fluency. Imagine you are working on facts for 5 (5 + 1, 5 + 2, etc.). In math centers, you introduce a game where students start with a ten frame filled with 5 counters across the top row. Your students spin a spinner and add 1, 2, 3, 4 or 5 to the ten frame. Your students record their work in a number bond and write an equation to match.<br /><br /></div><div><br /></div><div>Your students will have the support of a ten frame so that they are able to quickly "see" the answer to their equation. This activity supports spatial relationships and allows your students to subitize numbers to 10 in a ten frame. Through this activity, you are BOOSTING your students' spatial relationships, you are still working towards your goals around understanding addition, you are improving fact fluency and, as an added bonus, you are boosting your students' awareness of benchmarks of 5 and 10 as well. </div><div><br /></div><div>It's a beautiful thing. Isn't it? </div><div><br /></div><div>Let's take a look at another example. </div><div><br /></div><h4 style="text-align: center;">Spatial Relationships in Fractions (3rd Grade Example) </h4><div><a href="https://1.bp.blogspot.com/-U1FLwhxkeHs/XaNOu9XeErI/AAAAAAAAUHM/JGUCQEmjO_QD7tACRO_zGb_FBwur1PZLwCLcBGAsYHQ/s1600/Slide4.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-U1FLwhxkeHs/XaNOu9XeErI/AAAAAAAAUHM/JGUCQEmjO_QD7tACRO_zGb_FBwur1PZLwCLcBGAsYHQ/s320/Slide4.JPG" width="240" /></a>In third grade, your students are learning about unit fractions and are composing and decomposing unit fractions and are beginning to compare fractions as well. A roadblock we can anticipate in terms of fraction comparison is that the numbers aren't intuitive to students relative to the learning they have done in kindergarten through 2nd grade.<br /><br /></div><div><br /></div><div>For the first time and "8" indicates a SMALLER piece than a "3" when these numbers are in the denominator of a fraction. Building spatial relationships is the answer here. </div><div><br /></div><div>Consider an activity where students are using fraction strips to build and compare fractions. Your students choose a task card with two different fractions and are asked to build using unit fractions in order to compare. The hands-on material will help your students to develop spatial relationships around fraction numbers. On a recording form, your students color fractions to further steep in the visual representations. </div><div><br /></div><div>All of a sudden the "roadblock" has been overcome as your students are developing a new schema around fractions and the "confusion" of 8 and 3 having new meaning isn't so confusing anymore.</div><div><br /></div><div>Ok. One more. </div><div><br /></div><h4 style="text-align: center;">Rounding Decimal Numbers on a Number Line (5th Grade Example) </h4><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-hWcVAwWhSBI/XaNO458tj6I/AAAAAAAAUHU/daI6mhcr33IY1xN3OBDIQPtvAiBxmFv4ACLcBGAsYHQ/s1600/Number%2BFlags.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="605" data-original-width="1600" height="121" src="https://1.bp.blogspot.com/-hWcVAwWhSBI/XaNO458tj6I/AAAAAAAAUHU/daI6mhcr33IY1xN3OBDIQPtvAiBxmFv4ACLcBGAsYHQ/s320/Number%2BFlags.png" width="320" /></a></div><br />I've written quite a bit about <a href="https://www.k5mathspot.com/2018/09/how-to-teach-rounding-to-struggling.html" target="_blank">rounding</a> in the past. I am passionate about the idea that most students do not have a <i>rounding issue </i>but rather have a <i>number sense issue. </i>Students who struggle to round have difficulty identifying benchmark numbers and have further difficulty recognizing which of those benchmark numbers is closer to the number they are rounding. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Build spatial relationships around decimal numbers by building a life-sized number line! Hang a string across two cabinets or along the whiteboard. Prepare number flags with numbers spanning between two decimal numbers (ex: 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 1.0). Hand these number flags to your students out of order and ask your students, one at a time, to use a clothespin to hang the flag on the number line in the place where they think that number would go.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><a href="https://mailchi.mp/9cdd0fa23f36/mathspotspatialrelationships" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-zt4wSezugSY/XaNLQNmExvI/AAAAAAAAUGs/V_2gOu6H2nE5Rj7AZUkxKN0L_YCLjEsrACEwYBhgL/s320/Spatial%2BRelationships%2BCover.jpg" width="240" /></a>In early attempts at this activity, you will find that your students will need to move and slide numbers as they go. In later attempts, you will find that your students' <b>spatial relationships </b>have developed and your students have better sense of which numbers are closer or farther apart on a number line. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Your students' internal number lines are strengthened when they work with number lines that they can see and touch in real life because your students strengthen their spatial relationships through interaction. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">I would love to share each of these three activities with you so that you can give them a try and get your own juices flowing in terms of how you can incorporate activities that build spatial relationships into the instruction you are already delivering!<a href="https://mailchi.mp/9cdd0fa23f36/mathspotspatialrelationships" target="_blank"> Click the graphic to the right and grab your (free) copy of these activities now! </a></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Addition-and-Subtraction-Games-4523918" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-DAi3b-WvdfQ/XaHL7_D7W0I/AAAAAAAAUFA/_bX9LsWlceoq6EtyqtzJr-JSQF7PRX22ACLcBGAsYHQ/s200/Bundle%2BCover.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/Comparing-Fractions-Math-Intervention-and-RtI-3090278" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-rveMwTjC87w/XaHMAIWWewI/AAAAAAAAUFE/mypSJQ8XZTc1e5USbGwW6kjRC-4dVvLuwCLcBGAsYHQ/s200/Cover%2BUpdate.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/Rounding-Decimal-Numbers-4053362" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-bPvIBBZKtEc/XaHMDqCWOfI/AAAAAAAAUFI/q9B6Sud4GN4DyK-q16UZmcbBnfnVFP5XACLcBGAsYHQ/s200/Cover%2BUpdate%2B2.jpg" width="200" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://2.bp.blogspot.com/-HpxVIgySwhY/XaNOgEV0ftI/AAAAAAAAUHA/021p0QY7ciUi0x2799NjNSG_yIUNjGPvQCK4BGAYYCw/s1600/Spatial%2BRelationships%2BPin.png" imageanchor="1"><img border="0" height="320" src="https://2.bp.blogspot.com/-HpxVIgySwhY/XaNOgEV0ftI/AAAAAAAAUHA/021p0QY7ciUi0x2799NjNSG_yIUNjGPvQCK4BGAYYCw/s320/Spatial%2BRelationships%2BPin.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-2559444825065113552019-10-01T14:31:00.001-04:002019-10-04T15:29:18.706-04:004 Things You Need to Know to Develop Number Sense<i style="background-color: white; color: #101010; font-family: Lora, sans-serif; letter-spacing: 0.3px;"><span style="color: #333333; font-family: "sorts mill goudy" , sans-serif; line-height: 33px;"><span style="font-size: x-small;">THIS POST CONTAINS AFFILIATE LINKS. THIS MEANS, THAT AT NO ADDITIONAL COST TO YOU, I WILL EARN A COMMISSION IF YOU CHOOSE TO MAKE A PURCHASE. I HAVE PERSONALLY USED THESE RESOURCES AND WOULD NOT RECOMMEND THEM IF I DID NOT APPRECIATE THE QUALITY OF THE RESOURCE PRIOR TO RECOMMENDATION. </span></span></i><br /><i style="background-color: white; color: #101010; font-family: Lora, sans-serif; letter-spacing: 0.3px;"><span style="color: #333333; font-family: "sorts mill goudy" , sans-serif; line-height: 33px;"><br /></span></i>You intuitively know which of your students <i>has number sense</i> and, even more evident, you know which students <i>do not </i>have number sense. But how can you develop your students' number sense?<br /><br /><a href="http://3.bp.blogspot.com/-CPusttMBiH8/XZObaMX1kGI/AAAAAAAAT1I/mxh2CimROEscnXgoWxZhb1BhzkqEzjosQCK4BGAYYCw/s1600/Number%2BSense%2BBlog%2BHeader.png" imageanchor="1"><img border="0" src="https://3.bp.blogspot.com/-CPusttMBiH8/XZObaMX1kGI/AAAAAAAAT1I/mxh2CimROEscnXgoWxZhb1BhzkqEzjosQCK4BGAYYCw/s1600/Number%2BSense%2BBlog%2BHeader.png" /></a><br /><br />I used to be incredibly frustrated when it came to talking about developing number sense. I knew that some students had it, some students didn't and that there were dozens of textbooks full of activities that promised to build number sense in my students. And yet, I still didn't have a good picture of what number sense WAS and WHY these activities were supposed to be building number sense in my students.<br /><br />I knew that number talks weren't number sense... but they were supposed to help.<br />I knew that board games weren't number sense... but somehow they helped to develop strength.<br />And I surely knew you couldn't "teach" number sense.... but then what was I supposed to do?!?<br /><br />Enter in John Van de Walle's text "Teaching Student-Centered Mathematics". If you have not picked up this text,<b> I can not recommend it highly enough</b>. I started with the pre-k -2 edition of the book and quickly picked up the 3-5 text as well. That's saying a lot because these books are not necessarily inexpensive- but they are well worth every single penny.<br /><br /><a href="https://www.amazon.com/Teaching-Student-Centered-Mathematics-Developmentally-Appropriate/dp/0134556437/ref=as_li_ss_il?crid=3IRSAZNYO9H0G&keywords=teaching+student+centered+mathematics+prek-2&qid=1569692113&sprefix=teaching+student+center,aps,169&sr=8-1&linkCode=li3&tag=the0c319-20&linkId=a376cfba53996f333bcd9a7437a01309&language=en_US" target="_blank"><img border="0" src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0134556437&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=the0c319-20&language=en_US" /></a><img alt="" border="0" height="1" src="https://ir-na.amazon-adsystem.com/e/ir?t=the0c319-20&language=en_US&l=li3&o=1&a=0134556437" style="border: none !important; margin: 0px !important;" width="1" /><br /><br />Van de Walle breaks number sense down into 4 main relationships and makes very clear what it means for a student to "have number sense".<br /><br /><h4 style="text-align: center;">What Does It Mean to Have Number Sense?</h4><div>Having number sense means having <b>flexibility with numbers</b> relative to: </div><div><ul><li>Knowing one more/one less and two more/two less</li><li>Spatial relationships</li><li>Part/Part Whole Thinking </li><li>Benchmarks of 5 and 10</li></ul><div>The brilliant thing about understanding that students who have flexibility using and understanding these four relationships have number sense is that you can quickly and easily build these relationships into the teaching you are already doing.<br /><br /></div></div><div></div><div><b>Let me say that again. </b></div><div><br /></div><div>Building number sense does NOT need to be a separate part of your day, routines, teaching and instruction. You can develop number sense in your students through the instruction you are already preparing to deliver. </div><div><br /></div><div><h4 style="text-align: center;">Number Sense Examples </h4></div><div style="text-align: center;"><b><u>Building Number Sense with Teen Numbers </u></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Jr4SgRWbvVg/XZDC4O-2oMI/AAAAAAAATw4/1JRSG5mTNVY1vVowRuR_r-NeFx_d5pASwCLcBGAsYHQ/s1600/numsense2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="516" data-original-width="460" height="320" src="https://1.bp.blogspot.com/-Jr4SgRWbvVg/XZDC4O-2oMI/AAAAAAAATw4/1JRSG5mTNVY1vVowRuR_r-NeFx_d5pASwCLcBGAsYHQ/s320/numsense2.png" width="285" /></a></div><div>In this example, students are composing and decomposing teen numbers. This activity will help your students to <b>develop number sense around teen numbers </b>as it involves 3 of the 4 number relationships that students with strong number sense are able to rely on. </div><div><br /></div><div><b>Spatial Relationships- </b>When the number 13 is laid out on a double ten frame, your students will become quick and effective at <a href="https://www.k5mathspot.com/2016/08/subitizing-not-just-for-kindergarteners.html" target="_blank">subitizing</a> teen numbers by thinking about the relationship between the ten and ones. This conceptual subitizing reinforces number relationships. </div><div><br /></div><div><b>Part/Part/Whole- </b>Using a number bond to write about the ten and ones embedded in the number 13 supports your students in being able to flexibly be able to compose and decompose this number. </div><div><br /></div><div><b>Benchmarks of 5 and 10- </b>By building the number 13 on a double ten frame, students can readily see a thirteen as a ten and 3 more. The embedded ten is readily apparent in this model. </div><div><br /></div><div style="text-align: center;"><b><u>Building Number Sense with Decimal Numbers </u></b></div><div style="text-align: center;"><b><u><br /></u></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/5th-Grade-Place-Value-Decimal-Game-3997461" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="441" data-original-width="480" height="294" src="https://1.bp.blogspot.com/-XhEQRayh94w/XZDC4IqGVII/AAAAAAAATxE/JXn7eUR6UpoXUvvJWICvXaNLZ7OIlwaLQCEwYBhgL/s320/numsense3.png" width="320" /></a></div><div style="text-align: left;">In this example, students are playing a game called "<a href="https://www.teacherspayteachers.com/Product/5th-Grade-Place-Value-Decimal-Game-3997461" target="_blank">1 or Bus</a>t" in which cards dictate whether students should add or subtract a tenth or a hundred. This game supports number sense around decimal numbers as it hits on all 4 number sense relationships. </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Spatial Relationships </b>- The growing (or shrinking!) decimal number is displayed on a place value template. Students will practice quickly recognizing the value of their number given these visual cues. </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>1 More/1 Less 2 More/2 Less- </b>It is the nature of this game to practice one more and one less. The activity boosts number sense because students are asked to think about the number that would be produced if they have "one more tenth" or "one more hundredth" they will develop flexibility in place value thinking by practicing this relationship. </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Part/Part/Whole - </b>In naming the current value of their number, students will compose tenths and hundredths. This part/whole thinking reinforces that a number such as 0.63 is the same as 0.60 and 0.03. This type of understanding leads to flexibility in our students as they deal with decimal operations in the future. </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Benchmarks of 5 and 10- </b>In this activity, students are able to compose ten hundredths to create a new tenth. Students will also recognize that 9 hundredths, for example, is only one hundredth less than 1 tenth. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">The next time you see an activity that promises to "build number sense" stop and consider how the activity might support one or more of the four number relationships that are true markers of number sense. Or, better yet, in your instruction, look for opportunities to highlight these relationships for your students. </div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/5th-Grade-Place-Value-Decimal-Game-3997461" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-0TNLN8BlvHU/XZDG0ngUuzI/AAAAAAAATxM/fwD927na618hIhldwx-m_vQL8wcWxiz2gCLcBGAsYHQ/s200/Cover%2BUpdate%2B%255BAutosaved%255D.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/First-Grade-Place-Value-Game-2546241?aref=dg71h772" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-daXXQ4TM4ck/XZDG2b22Y2I/AAAAAAAATxQ/IndY_X6JdCUOsFrPxWjUdOEE8PVWNgK7QCLcBGAsYHQ/s200/Cover%2BUpdate%2BSquare%2B.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Place-Value-Game-3994935?aref=dg71h772" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-HbF348mWqZE/XZDG6VnYRkI/AAAAAAAATxU/I1yPddFl59cTVMqbifyvCvZxBQ6cjAZ7wCLcBGAsYHQ/s200/Cover%2BUpdate.jpg" width="200" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><a href="http://2.bp.blogspot.com/-aZl0DGQjLpE/XZObV4cFgsI/AAAAAAAAT1A/JeynLoDZVlUuF7Q2YUqQZ78UBE5fdynGgCK4BGAYYCw/s1600/Teach%2BNumber%2BSense%2BBlog%2BPin%2B2.png" imageanchor="1"><img border="0" height="320" src="https://2.bp.blogspot.com/-aZl0DGQjLpE/XZObV4cFgsI/AAAAAAAAT1A/JeynLoDZVlUuF7Q2YUqQZ78UBE5fdynGgCK4BGAYYCw/s320/Teach%2BNumber%2BSense%2BBlog%2BPin%2B2.png" width="213" /></a><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-50459687717410441112019-09-23T14:10:00.000-04:002019-09-23T14:10:29.904-04:00How to Overcome the Top 5 CRA Math Model ObstaclesThere's math theory and then there is real life in the classroom. You may LOVE the idea of the <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">CRA math model</a> but you may wonder how you can incorporate this type of model with a classroom full of students with varying needs.<br /><br />Let's dive into some common roadblocks to the <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">CRA math model</a> so that you can simply incorporate this practice into your teaching.<br /><a href="http://2.bp.blogspot.com/-3smxWp4ZFCY/XYkAVQhdkzI/AAAAAAAATpU/T1T_aEKhBuIXPHUOtRgmIqc2W_Hbq40QgCK4BGAYYCw/s1600/CRA%2BHurdles%2BBlog%2BHeader.png" imageanchor="1"><img border="0" src="https://2.bp.blogspot.com/-3smxWp4ZFCY/XYkAVQhdkzI/AAAAAAAATpU/T1T_aEKhBuIXPHUOtRgmIqc2W_Hbq40QgCK4BGAYYCw/s1600/CRA%2BHurdles%2BBlog%2BHeader.png" /></a><br /><h4>How to Choose Math Manipulatives</h4><div>Right off the bat, you may be turned off by the use of so many hands-on materials in the CRA method. The materials management alone can be enough to make you second guess whether or not you want to go ahead with an activity. </div><div><br /></div><div>As much as I would love to see all students with hands-on materials whenever needed and as frequently as possible- that's not a realistic expectation in all classroom settings. You know your students best.</div><div><br /></div><div>There are options that can make manipulative use less cumbersome. </div><div><ul><li>Model with hands-on materials whole group and then allow students to practice in a small group setting. </li><li>Keep "math manipulative" kits in each students' desks with materials periodically changed out to avoid material distribution during each and every lesson. </li><li>Use hands-on materials with a partner to decrease the number of materials needed. </li><li>Set up a "manipulative center" where students can access manipulatives as needed for independent work time. </li></ul><div>As far as determining <i>which</i> manipulatives to use, this blog post outlines the different types of concrete manipulatives that may be most useful to your students. Believe it or not, there is a progression to manipulatives - not all are created equally! <a href="https://www.k5mathspot.com/2019/08/what-i-have-learned-about-place-value.html" target="_blank">This post will help you to determine the best tools for each of your students. </a></div></div><h4>How to Differentiate Math Instruction</h4><div>Small. Group. Instruction. </div><div><br /></div><div>I am NOT advocating for leveled small groups on a daily basis, however, there will be times when you are working on a specific skill in your classroom and you will have students who need guided practice at different levels. Take subtraction with ungrouping as an example. </div><div><ul><li>Some students may need linking cubes that they can quite literally take apart. </li><li>Some students may have progressed to base ten blocks who are able to "make a trade". </li><li>Some students may feel comfortable with base ten blocks- they are working on making accurate place value drawings that match their work. </li><li>Some students may be quite proficient with place value drawings and they are attaching their drawings to the standard algorithm. </li></ul><div>Small groups will allow you to meet each of these groups of students exactly where they are. </div></div><div><br /></div><div>Another option is to pose a question or situation to the group and <i>strategically assign students to a given model. </i>You may ask a group of students to solve the problem using counters and a math drawing, another group to solve using a math drawing and an equation and a final group to solve the problem using an equation and base ten blocks. </div><h4>How to Decrease Dependence on Teacher</h4><div>The CRA model requires that a teacher is in-tune with their students. A teacher knows where a student is performing and works in a skilled way to help the student to make connections and progress. </div><div><br /></div><div>While this model requires skilled teacher work upfront, the purpose of the model is to move your students toward a more abstract understanding where they will not need the teacher to intervene! </div><div><br /></div><div>Trust the process. More targeted intervention on the part of the teacher upfront in order to support students in using the most appropriate model will ultimately lead to <i>less </i>teacher dependence down the line! </div><h4>How to Incorporate Problem Solving</h4><div>Another misconception about CRA is that it doesn't involve problem-solving. Although it would be possible to use CRA to teach a procedure, that is not the goal! </div><div><br /></div><div>Problem-solving and story problems are a prime opportunity for this strategy. Consider the following problem: <i>I have $0.48 cents in my pocket made up entirely of dimes and pennies. How many dimes and pennies might I have? </i><br /><br />This problem can be solved while honoring the CRA math model. Ask your students to model the story using base ten blocks and to record the different combinations of dimes and pennies both in place value drawings and words. </div><h4>How to Assess</h4><div>"If I give my students linking cubes to use during instruction, do I need to give them linking cubes during the assessment?" </div><div><br /></div><div>No. </div><div><br /></div><div>Or yes. </div><div><br /></div><div>It depends! </div><div><br /></div><div>Take a look at your standards, talk to your grade level about expectations and allow those factors to drive your decision making around assessments. There are Common Core standards that state "Use objects, pictures and/or numbers to..." in those cases, it would be very appropriate to allow your students to use a hands-on material during an assessment. </div><div><br /></div><div>Other standards might require that your students are able to demonstrate an understanding using "strategies based on place value" with no wording around using objects. In that case, it may be your goal to use hands-on materials in order to support your students towards higher-level understandings. In that case, you want your students to be prepared to demonstrate proficiency without any hands-on materials. </div><div><br /></div><div>The CRA Math Model is just that- a model for instruction- not a life sentence to a specific prescribed set of teaching steps. If you are noticing where your students are performing, thinking about the models that will be most supportive and helping your students to move to more abstract thinking you are 100% on the right track! </div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/1st-Grade-Math-Intervention-RtI-Bundle-3372096" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-fM50DYBab0g/XYkAdftLROI/AAAAAAAATpY/u6q2TGjuQFIZ6UnTbTfKXNC5UZHJ17g6wCLcBGAsYHQ/s200/Bundle%2BCover.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Math-Intervention-Lesson-Bundle-4804518" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-j4yT7mAPrMg/XYkAgXUwOyI/AAAAAAAATpc/xwIXTaRa17kqEgV3Vj-xv4EmdYJTMtgpQCLcBGAsYHQ/s200/Cover%2BUpdate%2B6%2BThrough%2BUnit%2B3.jpg" width="200" /></a></div><b></b> <hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-wkrR_13uhE0/XYkBXoTSbTI/AAAAAAAATpw/FzYi7X0L4xsS67emWkclKZFCFWrcSw9jACK4BGAYYCw/s1600/CRA%2BObstacles%2BBlog%2BPin%2B.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-wkrR_13uhE0/XYkBXoTSbTI/AAAAAAAATpw/FzYi7X0L4xsS67emWkclKZFCFWrcSw9jACK4BGAYYCw/s320/CRA%2BObstacles%2BBlog%2BPin%2B.png" width="213" /></a></div><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-48693628620941984752019-09-15T11:07:00.000-04:002019-09-17T14:00:36.685-04:00How To Effectively Use the CRA Progression You used hands-on materials all last week in math. Your students were rockstars. This week you were <i>sure </i>your students were ready to take the blocks away and move to a drawing instead.<br /><br />And your students fell flat.<br /><br />You were <i>sure </i>they were ready and you are left questioning what went wrong.<br /><br /><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-W8YULHwzkm0/XX5SqB7kgNI/AAAAAAAATY0/o9xiCnod7noRRmvoPsvsX8vRMxqqGIwQQCLcBGAsYHQ/s1600/CRA%2BProgression%2BBlog.png" /></div><br /><br />The <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">CRA </a>progression is much like any other scaffold in the classroom. It's a great tool but you need to plan strategically if you want to take that tool away.<br /><br />If your end goal is that your students reach the abstract level with a given skill, you need to build in clear opportunities for your students to make connections between concrete, representational and abstract so that when you take the scaffolds away your students are still successful.<br /><br />The good {great} news is that there are multiple easy ways to build these connections that don't require additional planning or materials on your part.<br /><br /><h3><b>2 Activities to Build Connections in your Math Lessons Using the CRA Approach</b></h3><b>1. The absolute easiest way to promote connections is to ask your students to complete activities that require them to use more than one model alongside each other.</b><br /><b><br /></b><ul><li><span style="font-weight: normal;">Ask your students to use base ten blocks to add 24 + 10. After they use their blocks to solve the problem, ask them to create a place value drawing and number bond that matches their blocks. <i>(Connects concrete and two representational models) </i></span></li></ul><ul><li><span style="font-weight: normal;">Ask your students to use pattern blocks to show the different ways you can create a whole with a variety of shapes. For each solution your students find, ask them to write an equation that adds the unit fractions together to make a whole. <i>(Connects concrete with abstract) </i></span></li></ul><ul><li><span style="font-weight: normal;">Allow your students to shake out 10 2-sided disks and to place them on a ten frame by color. Ask your students to write a number bond and equation that match the ten frame to show the partner of 10 they discovered. <i>(Connects concrete, representational and abstract)</i></span></li></ul><i><br /></i><ul></ul><b>2. Asking linking questions requires NO preparation and NO additional materials. Ask questions that require your students to notice how their different models all show the same information in different ways. The questions below match the associated examples above.</b><br /><b><br /></b><ul><li>I see you built 24 with your blocks over here. Where can you see the 24 in your place value drawing? --Where do you see the total in your place value drawing? Does that match the total in your blocks? --What are the parts you built in your blocks? Do you have the same parts in your place value drawing? Can you circle the two parts in your drawing? </li></ul><ul><li>Which tile took the most pieces to create a whole? What did your equation look like when you made a whole out of 6ths? -- I see you wrote 1/3 + 1/3 + 1/3 = 1. Show me the pattern blocks that match that equation. How did you know they were thirds? -- If you had blocks that were 1/8 size, what do you think your equation might look like? </li></ul><ul><li>I see a 4 part and a 6 part in your number bond. Where is the 4 part in your disks? Where is the 6 part in your disks? -- Your equation says it equals 10. Where are the 10 disks? </li></ul><br /><div><div>Failing to explicitly build connections will ensure that your students will fall flat when you try to progress towards more abstract models. Employ these simple strategies to allow your students to build powerful connections that serve them well as scaffolds are taken away! </div></div><hr /><b>Related Resources:</b><br />5 Day Focus Intervention Units were created on the premise of building from concrete to abstract by using activities that link multiple representations together so that your students can build their skills (and their confidence!) in a simple, systematic and effective manner.<br /><div><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/1st-Grade-Math-Intervention-RtI-Bundle-3372096" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-IcXR4_9Ojpg/XX5RWEZygOI/AAAAAAAATYg/cs-rNOmbkXAh2lIGjeWTWxkEXcQYxfBNACLcBGAsYHQ/s200/Bundle%2BCover.jpg" width="200" /></a><a href="https://www.teacherspayteachers.com/Product/2nd-Grade-Math-Intervention-Lesson-Bundle-4804518" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="200" src="https://1.bp.blogspot.com/-CcoX_eCVAEQ/XX5RMKCOHSI/AAAAAAAATYU/-T3BSmB5Q1stz8b0GGGxAUP_oXYTeeDsgCLcBGAsYHQ/s200/Growing%2BBundle%2BCover%2B1.jpg" width="200" /></a></div><br /><br /><div><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-DNZoB1J8_4E/XX5ThELvIfI/AAAAAAAATY8/5VpU9t_3W1YiGdZEoWh-KIY2nb3mUJMdQCLcBGAsYHQ/s1600/CRA%2BProgression%2BBlog%2BPin%2B.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1102" data-original-width="735" height="320" src="https://1.bp.blogspot.com/-DNZoB1J8_4E/XX5ThELvIfI/AAAAAAAATY8/5VpU9t_3W1YiGdZEoWh-KIY2nb3mUJMdQCLcBGAsYHQ/s320/CRA%2BProgression%2BBlog%2BPin%2B.png" width="213" /></a></div><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math Spot</div></div>The Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-12692145154930592342019-09-14T10:04:00.001-04:002019-09-15T11:10:58.205-04:00How to Makeover Your Math Lessons with CRATeaching math from a scripted program is less than inspiring. And that is putting it kindly.<br /><br />You likely didn't sign up to be made to feel like a robot.<br />You didn't sign up to teach lessons you don't believe in.<br />And you <b>certainly </b>didn't sign up to choose between keeping up with pacing or leaving your students in your dust.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-fiTAyOHwR2Q/XXzxxCjoSNI/AAAAAAAATTY/S-5dhYWiFDQf-nv13zKPbDw95Iga0uggwCLcBGAsYHQ/s1600/Math%2BLesson%2BMakeover%2BBlog.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-fiTAyOHwR2Q/XXzxxCjoSNI/AAAAAAAATTY/S-5dhYWiFDQf-nv13zKPbDw95Iga0uggwCLcBGAsYHQ/s1600/Math%2BLesson%2BMakeover%2BBlog.png" /></a></div><br />Giving lessons (yes. even lessons from a scripted curriculum) a <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">CRA</a> makeover can help you to feel more confident in the content you are teaching and will help you to reach all of your learners where they are while supporting them to where you would like them to be.<br /><br />Below are the steps you can follow to quickly and easily makeover your lesson. Follow through until the end of the post- I have a free CRA model template for you to use!<br /><h4 style="text-align: center;">Concrete, Representational, Abstract Math Lesson Makeover</h4><div><b>Step 1: Take Inventory</b> </div><div>Check through the lesson and jot down the concrete models, representational models and abstract models that are already being used. </div><div><ul><li>Concrete- Hands-on materials</li><li>Representational- Sometimes called pictorial includes drawings, pictures, and diagrams such as a number bond or place value chart. </li><li>Abstract- Numbers and equations on their own. </li></ul></div><div><br /></div><div><b>Step 2: Connect The Dots </b></div><div>Look for linking questions or activities that ask your students to use more than one model at a time. </div><div><ul><li>Are your students building with base ten blocks and then recording their work on a number bond? </li><li>Are your students reading a word problem, drawing a picture and then recording an equation? </li></ul></div><div><br /></div><div><b>Step 3: Fill in the Gaps</b></div><div>If you found only abstract models in the lesson, are there representational or concrete models you can add to the lesson so that all learners can access the content? These models can be incorporated in a variety of ways. </div><div><ul><li>A whole group model with hands-on materials. </li><li>Providing some students with hands-on materials to use as they work independently. </li><li>Adding in a directions for your students to use a model such as a place value chart alongside the algorithm. </li></ul></div><div><b>Step 4: Link It Together</b></div><div>You have already taken stock of opportunities to link models together but if you had a chance to add in additional models, or if the lesson was using concrete, representational or abstract models in isolation this is your chance to link them together. Linking can be done through direct questioning and/or by asking your students to use multiple models side by side. </div><div><ul><li>I see the number 47 in your equation. Where did you represent 47 in your place value drawing? </li><li>The story problem talked about 13 pigs. Where are the 13 pigs in your equation? </li><li>As you add 23 + 58 using place value disks can you draw a picture on a place value chart to show your work? </li></ul><div>Giving your students the chance to work with a concept at the concrete, representational and abstract level helps them to build explicit connections in their mind and become fluent with concepts more easily. </div></div><div><br /></div><div>As you get used to giving your lessons a CRA makeover it will become <i>second nature to you</i>. This will not be a time consuming or tedious process! Grab the freebie below and believe in your math lessons again! </div><hr /><b>FREE CRA Lesson Makeover:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://mailchi.mp/c4b429421d6c/mathspotcramakeover" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-qf-jeX9mWrE/XXzxAjdXjnI/AAAAAAAATTQ/csPdrnsjqyQG_887RucF0SmCbqG5MGO2wCLcBGAsYHQ/s320/CRA%2BLesson%2BMakeover%2BCover.jpg" width="240" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="1102" data-original-width="735" height="320" src="https://1.bp.blogspot.com/-kZ9nmMm-e9I/XXzzS3N2kmI/AAAAAAAATT0/K6_ejGrX4H01peQkZrCK3dThjLOloXU1wCLcBGAsYHQ/s320/CRA%2BLesson%2BMakeover%2BPins%2B%25282%2529.png" width="213" /><a href="https://1.bp.blogspot.com/-_ddaq8Ua1iU/XXzzBPRHRHI/AAAAAAAATTo/EmUliOXpuJEOrNRNjmgztpJFR0piXrDggCLcBGAsYHQ/s1600/CRA%2BLesson%2BMakeover%2BPins.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1102" data-original-width="735" height="320" src="https://1.bp.blogspot.com/-_ddaq8Ua1iU/XXzzBPRHRHI/AAAAAAAATTo/EmUliOXpuJEOrNRNjmgztpJFR0piXrDggCLcBGAsYHQ/s320/CRA%2BLesson%2BMakeover%2BPins.png" width="213" /></a></div><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.comtag:blogger.com,1999:blog-6278540421686629919.post-67316922074613755902019-08-28T20:45:00.001-04:002019-09-15T11:09:33.209-04:00Which is the BEST Hands-On Tool for Teaching Decimals?<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-znO7oeAin3A/XWcgA_Bo2ZI/AAAAAAAASwQ/7uz_KwBbltwlFO0k0ZtBhD2oSm-IkEppgCLcBGAs/s1600/Decimal%2BPV%2BTools.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" src="https://1.bp.blogspot.com/-znO7oeAin3A/XWcgA_Bo2ZI/AAAAAAAASwQ/7uz_KwBbltwlFO0k0ZtBhD2oSm-IkEppgCLcBGAs/s1600/Decimal%2BPV%2BTools.png" /></a></div>5th-grade teachers are set with a difficult task. Your students previously spent the majority of their time working with whole numbers in the base ten system. Now, you are supporting your students to build numbers that may be very difficult to model and conceptualize.<br /><br />Thinking <a href="https://www.k5mathspot.com/2015/12/when-they-still-dont-get-it.html" target="_blank">CRA</a> is helpful but what tools do you have at your disposal to model a number like 4.315?<br /><br /><h4 style="text-align: center;">Not All Manipulatives Are Created Equally! </h4><div>When thinking about place value manipulatives you have 3 main options: </div><div><ol><li>Groupable, Proportional Models</li><li>Pre-Grouped, Proportional Models</li><li>Pre-Grouped, Non-Proportional Models </li></ol><div>As you move down this list of materials, the manipulatives <i>themselves </i>are more abstract to work with. </div><div><br /></div><div>To model the number 1.5 with a groupable, proportional model, I may consider linking cubes. Tell your students that each cube represents one-tenth and ask them if they could use them to build the number 1.5. </div></div><div><br /></div><div>To model that same number with a pre-grouped, proportional model, you may consider using base ten blocks. Again, you would designate the whole to your student (perhaps a flat is considered a whole in this case) and you would ask your students to create the number. </div><div><br /></div><div>Lastly, when using a pre-grouped, non-proportional model such as place value disks, you will see that your students will be able to create a number such as 1.5 incredibly easily. You are losing a bit of conceptual work (<i>If a whole looks like this... what does a tenth look like?) </i>but you are affording yourself the opportunity to build much more complex numbers that you couldn't readily build using base ten blocks or linking cubes. </div><div><br /></div><h4 style="text-align: center;">Ask Linking Questions </h4><div>When moving through this variety of hands-on materials, the most powerful thing you can do for your students is to ask them to use multiple materials alongside each other and ask LINKING QUESTIONS.</div><div><br /></div><div>Linking questions sound like: </div><div><ul><li>Show me the part in your [manipulative #1] model that matches the "0.5" your [manipulative #2] model? </li><li>What does your whole look like in [manipulative #1]? How is it different than the whole in [manipulative #2]? </li><li>How would it look different if you built 3.4 with these different materials? </li><li>Which manipulative do you think would be easier to use to build a number such as... </li></ul><h4 style="text-align: center;"><span style="font-weight: normal;">FREE Printable</span></h4><div><div class="separator" style="clear: both; text-align: left;"><a href="https://drive.google.com/file/d/1FLihP9F9sLuOuM63SRdQTvXVMWBjtlIv/view" target="_blank"><img border="0" data-original-height="960" data-original-width="720" height="320" src="https://1.bp.blogspot.com/-eC73ZuHL1LU/XWcgh2aAZCI/AAAAAAAASwc/1hjTfDvFnJg-NeiI0ZUh-yLRKU-59kqNACLcBGAs/s320/Manipulatives%2BPrintable.jpg" width="240" /></a></div><span style="background-color: white; color: #101010; font-family: "lora" , sans-serif; font-size: 15px; letter-spacing: 0.3px;">I have created a </span><i style="background-color: white; color: #101010; font-family: Lora, sans-serif; font-size: 15px; letter-spacing: 0.3px;"><a href="https://drive.google.com/file/d/1FLihP9F9sLuOuM63SRdQTvXVMWBjtlIv/view?usp=sharing" style="color: #dea08c; max-width: calc(800px); outline: none; text-decoration-line: none; transition: all 0.2s ease 0s;" target="_blank">free printable</a> </i><span style="background-color: white; color: #101010; font-family: "lora" , sans-serif; font-size: 15px; letter-spacing: 0.3px;">for you. Keep this handy on your desk or taped inside of your math manual. Keeping in mind the different types of place value manipulatives will allow you to </span><b style="background-color: white; color: #101010; font-family: Lora, sans-serif; font-size: 15px; letter-spacing: 0.3px;">quickly and easily </b><span style="background-color: white; color: #101010; font-family: "lora" , sans-serif; font-size: 15px; letter-spacing: 0.3px;">differentiate for the variety of learners you have in your classroom.</span></div></div><hr /><b>Related Resources:</b><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/5th-Grade-Place-Value-Math-Centers-1334394?aref=gzprjlpr" target="_blank"><img border="0" data-original-height="960" data-original-width="960" height="320" src="https://1.bp.blogspot.com/-Ot3ADwWH_Gw/XWcdoAs9z4I/AAAAAAAASv8/TKvOf2pmA0k3UHkbGy_2mMRq9xn6t_EjgCLcBGAs/s320/Cover%2BUpdate.jpg" width="320" /></a></div><b><br /></b><b></b><br /><hr /><b>Pin For Later: </b><b><br /></b><b></b><br /><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="1102" data-original-width="735" height="320" src="https://1.bp.blogspot.com/-ZHpz3GC607s/XWcfzvka-OI/AAAAAAAASwM/voMxYKWbTHQrv5JvORdNxFYgx5nvM4fggCLcBGAs/s320/2.png" width="213" /><a href="https://1.bp.blogspot.com/-7z65qpgvEkU/XWcfzkfJeEI/AAAAAAAASwI/yAaIGhGOpTc5oKB4l7zTZuc5pLAA4juRwCLcBGAs/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1102" data-original-width="735" height="320" src="https://1.bp.blogspot.com/-7z65qpgvEkU/XWcfzkfJeEI/AAAAAAAASwI/yAaIGhGOpTc5oKB4l7zTZuc5pLAA4juRwCLcBGAs/s320/1.png" width="213" /></a></div><br /><hr /><b>Math Spot Newsletter: </b><b><br /></b>Click <a href="https://mailchi.mp/81c140b4f4d4/mathspotnewsletter" target="_blank">HERE </a>to receive notes, tips, freebies & special discounts from The Math SpotThe Math Spothttp://www.blogger.com/profile/09845707996634790905noreply@blogger.com