This blog post is about teaching primary learners how to decompose numbers in more than 1 way using hands-on activities.

# What is decomposing?

Decomposing is an important mathematical concept because it helps students develop an understanding of how addition and subtraction works. Students can put together (compose) or take apart (decompose) objects to represent addition and subtraction.

# Teaching students to decompose

To teach students how to decompose, you should provide them with a variety of opportunities with concrete objects. Here’s how I usually teach it.

Objects – Drawings – Writing Addition and Subtraction Expressions and Equations

Objects I use: I use 2 colored counters, linking cubes or unfix cubes and a ten frame. You can use almost any objects to teach students how to decompose!

# Always Teach Vocabulary First!

For students to be success in ALL grades in math, students need to be able to use academic language. Academic language allows students to express their understanding of how they solved a mathematical problem as well as share their thinking with others.

To teach addition and subtraction academic language, I have students sort these visual vocabulary cards with me. Students can figure out what is “put together” and “take apart” by looking at the pictures. We also briefly discuss what these terms look like by practice putting cubes together (composing) and taking them apart (decomposing).

Also, before introducing addition and subtraction symbols, make sure that you provide your students with **numerous** experiences with joining and taking apart objects and explaining how they decomposed a number with their partner and to you.

### Model how to Decompose and Give students sentence frames

Remember to model how to decompose numbers and how to use academic language to explain your thinking.

Teach students to say, “**1 and 4 is the same as 4” or “1 and 4 is the same amount as 5” or “1 and 4 objects is the same amount as 5 objects.”**

Remember it is just as important for students to be able to *explain what they are doing* as it is for them to get the correct answer!

Here are 2 activities that you can play with your students that teaches them how to decompose numbers.

# Activity #1 Shake and Spill the Counters Game

What you need: You need 2 colored counters, crayons and these recording sheets.

Students pick a number. Then, they put that many counters in a cup. They gently shake the cup and the counters will spill on the table. They count how many red and how many yellow. Next, the use their crayons to show how many red and how many yellow.

For students that are working on writing expressions, they write the sentence.

For students that are working on writing equations, they can write an equation.

There are additional recording sheets for students to write an equation with the equal sign first.

Some students are not ready to write equations on their own yet and that’s okay! For the students that are not ready yet, I have them write a number sentence using “and” and “is” and for the students that are ready to write an equation I let them. Let them explain how they decompose a number orally too.

For students that are still need support with keeping track of how many they have counted, allow students to use a ten frame to help them.

# Activity #2 – Build it and Break it!

What you need: You need counting cubes, crayons and these recording sheets.

Students pick a number. Then, they grab that many cubes and build a tower by snapping them together. Next, they break the cubes. They count how many cubes in their left hand and how many cubes in their right hand. Last, they draw a picture recording how they broke the cubes into 2 parts. They put the cubes back together and break the cubes a different way. Last, they record the equation.

That’s it! I love Build It and Break It and Shake and Spill! These are fun games that you can put in your math centers for hands-on decomposing learning!

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If you need more ideas, activities and free printables on how to engage students with decomposing, check out my Pinterest Board.

If you like build it and break it, you may also like Interactive Math Games! Read about my computer learning games by clicking the image.

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