*"5 and above, give it a shove. 4 and below, let it go"*

*"5 or more, raise the score, 4 or less, let it rest"*

*... No, really, let it rest already.*I propose that we

*. While they might seem like a great trick to get students to round small numbers there will, inevitably, be students who misunderstand, don't remember the poem quite right, and, worst of all, DON'T ACTUALLY UNDERSTAND ROUNDING!!*

**let these poems go**Does the following conversation sound familiar?

Teacher: What is 42 rounded to the nearest ten?

Student: 30

Teacher: Tell me more about your thinking

Student: Well, my teacher last year said "5 or above, give it a shove, 4 or below, let it go" So that means you have to go down.

....

....

So you see the problem...

Teaching the skill of rounding is an excellent opportunity to help students to develop number sense, to earn command over their internal number line, and to understand scale and magnitude of numbers.

The following is a protocol I have developed and have used with my students who are struggling with the skill of rounding. I would caution you that, if you would like to use this strategy, you start at the beginning and

*don't skip a single step*. This year I have used this protocol with both 4th and 5th grade students and, although the first few steps seem easy, they aren't necessarily and you will learn A LOT about your students!

__Step #1: Numbers 0 - 10__On tiles, write the numbers from zero to ten. You will also need a "game board" with 11 spaces.

Start by giving your students the tiles for 0 and 10 guiding them to put these numbers in the first and last spaces.

As students work their way though this activity, you will give them 1 tile at a time modeling the thinking about where a tile may be placed but encouraging students NOT to count the spaces.

The purpose of the spaces is to help students to see the even spacing between numbers. Have you ever seen a student working with an unhashed number line pointing and counting the line in a way which does NOT reflect understanding of scale? This step helps students to gain an understanding of this spacing.

I have done the next step in a number of different ways. Sometimes I give students the 5 to see where they may place the number. Sometimes, I flat out tell the students the 5 will be in the middle and allow them to see and use that pattern moving forward. Sometimes, I give them tiles that work from the outside in and then we discuss the number that falls in the middle later. You can use whichever method works for you. Each has their merits at various times.

Last, I give students the other tiles one at a time saying things like "If you know where the 5 goes, you can figure out where the 4 goes". This gets students thinking about the relationship between numbers on a number line rather than counting the spaces.

__Step #2: Numbers 0-10 On A Number Line__**This step is almost identical to the first step. You are using the same tiles, 0-10, you are going about the process in a similar order, the only change is that students are placing the tiles on a number line rather than on the game board.**

When I go through this step, we usually "play" 2-3 times. The first time though, I don't usually say too much. I can tell you that it is likely that students will put the tiles much too far apart, close together, and in the wrong places on the number line.

As I see students make changes to their arrangement as they get more and more tiles, I ask questions so that they can verbalize their thinking. For example, a student who left room between the 4 & 5 will eventually have to push them together to make room for the other numbers. When they do this, or make other changes, I ask questions like:

"What made you push those numbers closer together?"

"Why don't you need any space between those numbers?"

"What made you put space between those numbers?"

"How did you know how much space to leave?"

As I mentioned above, we usually repeat this sequence a few times. You will find your students become more accurate as you go!

__Intermediate teachers, please, please, pretty please, do not skip these first two steps. Although you are working with numbers to 10 this will give you a lot of information about your student's abilities with number lines and scale.__

__Step #3: Numbers 0-100 Counting by 10__**At this point you will need to move back to the original "game board" configuration along with tiles for the numbers 0-100 counting by 10.**

You will follow the same steps you followed in step one, however, this time, students are skip counting by 10s from 0 to 100.

I generally find that students do quite well on this activity after noticing the patterns from 1-10.

You will notice that I have used different colored tiles for numbers to 10 and numbers to 100. This is purely a materials management preference. I usually do this activity in a small group of 2-3 students at a time. I place all of the tiles for each student in a cup. It is then very easy to get out the tiles I need without having to go through and make sure that I have the right set.

After students have laid the tiles out on a game board, as before, move to the number line. You may have to "play the number line game" a few times through but you will find that students are much more accurate when grounded in the numbers 0-10 activity.

__Step #4: Looking for Hidden Numbers__When students have laid out all of the tiles from 0-100, have students go looking for "hidden numbers".

I will tell students "Between which two tens would you find the number...." we start out slowly at first but as students realize that it is between the 10 in the number you say and the next ten up, they will move more quickly. I give them a LOT of examples, probably upwards of 15-20 examples coming quite rapid fire towards the end of the exercise.

It was at this point in the activity that the student in the scenario at the top of my post let me know what he had learned about when he should "round up" and "round down". With his firm understanding based on the first few parts of the activity, he quickly realized his error and was able to move forward- abandoning his rhyme about rounding.

__Step 5: Zooming in__**At this point, the activity still doesn't**

*really*feel like you are teaching rounding. That's ok, it's all about to come together and pay off in a big way!

Teacher: Between which two tens would you find 34

Student: Between 30 and 40

Teacher: Here are tiles for the numbers 30-40. I will give them to you one at a time as I did before and I want you to do your best to put each number in the correct space the FIRST time, without sliding your tiles around. Think about what you know, the distance between numbers, and you will be fine!

Student: {Easily places tiles for #s 30-40}

Teacher: Which number is directly in the middle of 30 and 40?

Student: 35

Teacher: Good, let's push the 35 up a bit so we can see that mid point. Now, the number 34. Which ten is it closer to?

Student: 30!

Your student will get even that first question right a vast majority of the time. I have seen it again and again and again. They understand the number line, they understand the scale of numbers, they understand the mid point and all of a sudden there is no need for a riddle, poem or rhyme to help them to round. THEY UNDERSTAND.

__Step #6: Next Steps__**In terms of next steps, you want to get your students away from the tiles and able to round on paper or even in their head.**

I have developed a number of rounding games for my students that start to get to this piece. They are, basically, a way for students to practice rounding to the nearest 10 on a number line. Over and over and over.

In this game, students pick out a pirate ship, determine the two closest tens (at first, I leave out the 10-100 number line to help, later they won't need it) and then count on by one from the first ten to see where the ship lands. Students record their findings on a sheet I have slipped into a paper protector.

In a 30 minute lesson with 2 students, this is as far as I was able to get. They were able to complete about 5-6 examples before their time was up. The very cool part was that, just before they walked out the door, I showed them a few pirate ships and asked if they could solve the problem in their head and, with minimal subvocalizing... "

*54 is between 50 and 60, but it's closer to...*they were able to do it!

**50**!" ...This same protocol (with additional tiles) can be created for numbers rounded to the nearest 100 as well!

Another next step is to move away from ANY manipulatives or game boards and to have students draw their own number line to round. The picture to the left is the work of the student who, just one day before, told me that 42 was between 30 and 40.

*It's amazing what can happen when students learn rounding through understanding rather than rhymes!*

If you would like the materials needed to teach this lesson, I have bundled the lesson instructions, materials and game (an apple theme rather than the ship theme) into a Rounding Without Rhymes pack on TPT. Click on the picture below to check it out!

I am in 100% agreement with you and think that teaching our students "tricks" is never a good idea! They absolutely have to understand the math in order to be able to apply concepts in new situations. Thanks for linking up this month!

ReplyDeleteI am so in L.O.V.E. with this post!! I just emailed it to my 5th and 6th grade teachers as well as to the elementary math specialist to send to her teachers! YES! YES ALL OF THIS YES!!!

ReplyDeleteJamie aka MissMathDork

What a compliment to pass the post on. Thank you!

DeleteTHANK YOU! As a high school teacher, I SO appreciate when teachers of the younger ones actually take the time to explain the mathematical thinking. It makes my job easier.

ReplyDeleteThere is an ebook called "Nix the Tricks" that you might find interesting. It is about common "tricks" that math teachers use and how it can distort student's understanding of concepts. If you google it, it is a free download. It's organized very well so you can just skip to the parts that interest you :)

I will definitely look into that book. Thank you so much for the recommendation!

DeleteThank you so much for this recommendation, I devoured reading that book!

DeleteLove the lesson and the idea behind it! I hate tricks and rhymes and think all kids can develop good conceptual understanding. Looks like you are doing a fantastic job in your new role as a math interventionist!

ReplyDeleteTara

The Math Maniac

Thank you for the sweet compliment! I am LOVING my new position!

DeleteThank you! I stumbled onto your post and needed this strategy so badly. My LS students still struggle with rounding here at the end of 5th grade. They say the little rhyme, but then forget which number to "shove." Is it the one I underlined? The one I drew an arrow to? And we round to the wrong place value because we don't get the concept. I <3 conceptual teaching, and I needed this one! Off to spend a lot of money in your TPT store!

ReplyDeleteThank you for sharing this blog post and resource. I always have the hardest time teaching rounding and this break it down into such a practical, hands-on approach. My kids are going to loovvvve this!

ReplyDeleteLaura Santos

Core Inspiration by Laura Santos

Great blog post! I love this because it is hands on and helps students visualize the concept of rounding.

ReplyDeleteGreg

Mr Elementary Math

I love this idea. Would you use this to introduce rounding? I have a class of 21 and am wondering if it would be too ambitious of me to try and do this with all of them at once to introduce rounding. What is your opinion?

ReplyDeleteI, personally, have only used this strategy with small groups of students, however, I have taught the strategy to teachers in my building who have successfully used it with a full class of students. My suggestion would be to start on the SMART board or to make the tiles out of full sized 8 1/2 by 11 sheets of paper with magnets on the white board. As you ask the students where a number would fall, have them "point" from their seats so that all students are thinking about number placement. The big idea here is for students to round by accessing their own mental number line and by moving the tiles and predicting their placement you are helping your students to build that mental number line. You may have a few students who need small group attention and individual manipulatives to solidify the concept but I would most certainly use this strategy to teach rounding to a full class.

DeleteJust did this with my class today! It was great! I had a parent volunteer cut out the tiles for each kid. I used your page of "gameboards" to make multiple copies of each number tiles set then copied them on different colored paper. I did it on the visualizer as my students followed along (no smartboard in this classroom).

DeleteI'm going to try it with rounding 3-digit numbers to the nearest ten soon! Thanks for the fabulous idea!

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ReplyDeleteI see that this lesson is limited to rounding in the tens place. Have you seen students extend their understanding to round to other place values, such as billions place or hundredths/tenths place? How can you help your students extend this lesson to work for other place values?

ReplyDeleteThis approach saved my sanity! I'm a first-year teacher and have been searching EVERYWHERE for conceptually grounded rounding activities and approaches with very little success. I started using this approach with my RTI group this week and so far it's going great! These third graders have a pre-K/K sense of numbers and sequence, so rounding has been a real struggle for them. Thank you!

ReplyDeleteThis was one of the best math lessons I have ever taught. My students are 4th and 5th graders with special needs, and I was AMAZED by how well they did with this. We had to spend a few days on the first few parts, which told me a lot about my learners. I cannot thank you enough for sharing this! By the time we got to the last part, rounding was a breeze!

ReplyDelete