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*That moment when one of your first graders tells you,*

*in October*, 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

*just have a mind for math*.

One of the most recognizable tenents of number sense 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.

**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!**

#### Part-Whole Thinking in Kindergarten

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*extra*attention to partners of 10!

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!

#### Part-Whole Thinking in 1st Grade

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 "make a ten" strategy to add numbers together will be*decomposing an addend*to make

*partners of ten*and

*composing a ten and some ones to create a teen number*.

Yes. ALL of those kindergarten part-whole activities are synthesized together and applied to first grade standards.

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.

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.

#### Part-Whole Thinking in 2nd Grade

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*applying*this understanding so that they can flexibly add and subtract numbers to 100 using strategies based on place value.

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.

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.

#### Part-Whole Thinking in Third Grade

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.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.

Your students will ALSO start to apply their understanding of decompositions of equal groups in order to use the distributive property to multiply.

#### Part-Whole Thinking in 4th Grade

In third grade, you laid a foundation for multiplication and work with fractions. In fourth grade, you will apply these understandings further.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.

Your students are also applying understanding of unit fractions to perform fraction operations such as addition and subtraction.

#### Part-Whole Thinking in 5th Grade

In 5th grade, your students are expected to compose and decompose whole numbers, fractions, and decimals in order to flexibly apply all 4 operations.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.

- Determine whether or not your students are fluent with decompositions of numbers to 10
- Move to learn if your students are fluent decomposing 2, 3, 4, 5 or 6 digit numbers into unit form.
- 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.
*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.* - Continue layering on one skill at a time using increasingly complex numbers until your students are working at the 5th-grade level.

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.

*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!*#### Number Sense Activities for Part-Whole Thinking

**Shake and Spill-**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).

**Break the Stick-**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).

**Word Problems-**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).

Grab a set of Shake & Spill activities (Differentiated for use in kindergarten through 5th grade!) for free at the link HERE.

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