# Decomposing Numbers in Kindergarten

There are many important math skills for children to learn in kindergarten, but a key foundational skill they need to learn is number decomposition. Teaching decomposing numbers in kindergarten can sometimes be overlooked. But, it should be embedded into whole group and small group activities all year long.

## What is Number Decomposition and Why is it Important?

Number decomposition is the ability to break apart numbers. For example, I know that 5 can be broken into 3 and 2. This skill is incredibly important for addition and subtraction. If students know how to break apart numbers, then they will be able to think flexibly with numbers. For example, a child that knows that 5 can be broken up into 3 and 2 will be able to quickly solve 7+5 by adding 7+3 (taken from the 5) to make 10 and then add in the remaining 2 to get 12. This key foundational skill will be built on every year in math.

## How to Teach Decomposing Numbers in Kindergarten

There are four steps for teaching number decomposition. These four steps stretch from the concrete to the abstract.

## Teaching Early Math Learners Decomposing Numbers in Kindergarten

When teaching new concepts with children, it is important to start with concrete materials and visuals. Students need to touch and move and see the math. I always start teaching number decomposition in kindergarten with giving my students opportunities to see different groups of numbers in a bigger group of numbers. I do this with subitizing and you can read more about subitizing here. When I show an image with different amounts, for example 5 dots, I ask how my students knew there were 5 dots. Some might say I counted all the dots. Some students might say I saw 3 dots and then 2 dots and I knew that made 5.

Additionally, sorting objects is another great way to see different numbers inside other larger numbers. If I have my students counting 10 animals, then I might have them sort by color or by animal type. When they are done, we talk about how the five fish and three dogs and two birds make up the 10 animals total. It’s a great first step to see how numbers can be broken apart.

A great game to practice this skill is with either two-sided chips or a coin. Students take a certain amount of chips or coins (at this stage I would stick to 3-5). Then, they toss the coins onto the table and see how they land. They write down how many heads and how many tails. They can see that their 5 coins can be broken up into 4 heads and 1 tail or 2 heads and 3 tails, etc.

## Decomposing Numbers in Kindergarten – Step 2

The next step in teaching number decomposition in kindergarten is to start taking away some of the visuals or objects. Students still need the concrete objects or visuals so that after hiding some, they can count the hidden amount to figure out how many were hiding or missing. They may not automatically know at this point that 5 can be broken up into 3 and 2 so when you are only showing them 2, they might need to count out the 3 hiding objects. I love using Splat by Steve Borney. Splat visually shows the total amounts and the hiding of some of the total. It’s also a great math lesson warm-up. I love that after the students guess the hidden amount they can then reveal the answer and see if they were right. ​​

Another game that is really fun for children is Cover Up. Take a small amount of objects (no more than 5 for most students in kindergarten). Show the student the total amount of objects. Then cover up some of the objects. You can use a plastic container, cup, paper, or just hide some behind your back. After the child guesses how many are hidden, let them check to see if they are right. When they are done, talk about the different parts and the total. For example, there were 2 bears showing and 3 bears hiding that makes 5 bears total.

## Number Decomposition in Kindergarten – Step 3

The next level of teaching decomposing numbers in kindergarten is to start adding in numerals and equations. Connecting the abstract to the concrete objects in front of them. Playing all the same games we had been playing above, I start adding in equation sheets or whiteboards for my students to write down the equations of what they are seeing. When we are subitizing as a class, I ask my students to start explaining how they see the different amounts by giving an equation. If they say they saw 5 dots on the left and then 2 dots on the right and that’s how they knew there were 7 dots, I would add, or encourage them to add, 5+2 = 7.

Number bonds are a great way to visualize breaking apart the numbers. I like having them available when my students are working on these activities. The total number goes at the top (or bottom, it doesn’t really matter). Then the two parts split off from that total.

## Number Decomposition – Step 4

The last step when teaching decomposing numbers in kindergarten, and in older grades, is to take away all the visuals and concrete objects. You can use number bonds and have students fill in the missing numbers (either the total or one or both parts).

Want to hear more? I talk all about number decomposition and kindergarten math with Mona on the Honest Math Chat!

## Conclusion

When teaching decomposing numbers in kindergarten, it is important to start with visuals and concrete objects and then progress toward the abstract. Start with concrete objects and then move towards taking away some, but not all the visuals. Then start adding in abstract with the concrete by using numerals and equations. Number decomposition is a critical math skill for students to learn and so should be taught throughout kindergarten and beyond.

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