Unit 5 Family Materials

Composing and Decomposing Numbers to 10

Composing and Decomposing Numbers to 10

In this unit, students compose and decompose numbers to 10 in different ways. We call this “making” and “breaking apart” numbers.

Section A: Compose and Decompose Numbers to 9

In this section, students compose and decompose numbers to 9. At first, students only work with numbers up to 5 to build fluency with addition and subtraction within 5 as they compose and decompose numbers in different ways. 

Students understand that there are different ways to compose and decompose a given number. They work with physical objects, such as counters and connecting cubes, that they can use to compose and decompose numbers.


6 is 3 and 3

6 is 4 and 2

6 is 5 and 1

Section B: More Types of Story Problems

In this section, students represent and solve story problems. Students compose and decompose numbers as they solve story problems where both addends are unknown. For example,

Jada made 6 paletas with her brother.
They made two flavors, lime and coconut.
How many of the paletas were lime?
Then how many of the paletas were coconut?

These problems may be more challenging to make sense of because there is no action in the story and they have more than one solution. By the end of the section, students find multiple solutions to problems. Students use math tools and drawings to represent and solve story problems. It is important that students can explain how their representation shows the story. Some students may be interested in finding all the solutions to a problem and they should be encouraged to do so, though this is not an expectation for kindergarten.

Section C: Make and Break Apart 10

The number 10 is foundational to the place value work students will do in later grades. In this section, students are introduced to a 10-frame by putting together two 5-frames which allows them to build on previous understandings of the numbers 6–9 in relation to 5. 

Ten frame. 9 counters.

Students use the 10-frame, as well as their fingers, to make and break apart 10 in different ways. These tools are helpful because the blank squares in the 10-frame and the fingers that are down allow students to see or count how many more are needed to make 10. Students use these tools to figure out the number to add to any number from 1 to 9 to make 10. 

Try it at home!

Near the end of the unit, ask your student to draw a picture that goes with this story:

At the market, you get 10 apples from a bin.
Some of the apples are green and some of the apples are red.
How many of the apples are green?
Then, how many of the apples are red?

Questions that may be helpful as they work:

  • Explain your picture to me.
  • How many green apples and how many red apples did you draw?
  • Does this story match the expression \(10 = 1 + 9\), \(10 = 2 + 8\), \(10 = 3 + 7\), \(10 = 4 + 6\) or \(10 =  5 + 5\)? How do you know?
  • Is there another way you can make 10 apples?