K.5 Composing and Decomposing Numbers to 10
Unit Goals
 Students compose and decompose numbers within 10.
Section A Goals
 Compose and decompose numbers up to 9 in more than 1 way.
 Write expressions to represent decompositions.
Section B Goals
 Solve Put Together, Total Unknown, Put Together/Take Apart, Both Addends Unknown, Add To, Result Unknown, and Take From, Result Unknown story problems.
Section C Goals
 For any number from 1 to 9, find the number that makes 10 when added to the given number.
Section A: Make and Break Apart Numbers to 9
Problem 1

How can you break apart 3 connecting cubes into 2 parts?
Show your thinking using drawings, numbers, words, or objects.

How can you break apart 5 connecting cubes into 2 parts?
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 2
Jada made this pattern block design.

How many pattern blocks did Jada use? _____________

Write an expression to show Jada's pattern blocks.
Solution
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Problem 3
Mai wanted to break apart 7 into 2 parts.
She made this tower to show her 2 parts.

Write an expression for Mai’s connecting cubes.

Show 1 more way to break apart 7 cubes into 2 parts.
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 4
Exploration
Han made this pattern block design using two different kinds of pattern blocks.
He wrote the expression \(6 + 2\) to describe his design.
What pattern blocks did Han use?
Solution
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Problem 5
Exploration
 Show all the ways to snap a tower of 4 cubes into 2 parts.
 Show all the ways to snap a tower of 5 cubes into 2 parts.
 Show all the ways to snap a tower of 6 cubes into 2 parts.
 What patterns do you notice?
Solution
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Section B: More Types of Story Problems
Problem 1
There are 6 red crayons and 3 blue crayons on the desk.
How many crayons are on the desk?
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 2
There are 9 crayons on the desk.
Some of the crayons are red and the rest are blue.
Use drawings, numbers, words, or objects to show what the crayons could look like.
Solution
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Problem 3
There are 8 students eating lunch at the table.
Some of them are drinking milk.
The rest are drinking water.
How many of the students were drinking milk?
Then how many of the students were drinking water?
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 4
There are 9 animals swimming in the water.
Some of them are dolphins and the rest are seals.
How many of the animals are dolphins?
Then how many of the animals are seals?
Show your thinking using drawings, numbers, words, or objects.
Find more than 1 solution to the story problem.
Solution
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Problem 5

There are 3 kids playing hopscotch.
There are 4 kids playing tag.
How many kids are there playing altogether?
Show your thinking using drawings, numbers, words, or objects.

There are 8 kids on the playground.
Some of the kids are playing hopscotch.
Some of the kids are playing tag.
How many of the kids are playing hopscotch?
Then how many of the kids are playing tag?
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 6
Exploration
Students need a connecting cube and number mat 1–5.
There are 8 ducklings hiding in the grass.
Some of the ducklings are brown and the rest of the ducklings are yellow.
Roll the cube onto the mat to find how many brown ducklings there are.
Then write the number of yellow ducklings.
brown  yellow 
Did you find all of the possible numbers of brown and yellow ducklings?
Solution
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Problem 7
Exploration
There are 7 turtles.
Some of the turtles are swimming in the pond.
The rest of the turtles are lying in the sun.
How many turtles are swimming in the pond?
Then how many are lying in the sun?
Andre says that the solution:
6 turtles swimming and 1 turtle lying in the sun
is the same as the solution:
1 turtle swimming and 6 turtles lying in the sun.
Do you agree with Andre?
Solution
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Section C: Make and Break Apart 10
Problem 1
How many counters are there?

_______________

_______________

_______________
Solution
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Problem 2
Draw a line from the fingers to the tenframe that shows the same number.
Solution
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Problem 3
Circle the equation that matches the 10frame.
\(7 = 5 + 2\)
\(10 = 7 + 3\)
\(10 = 8 + 2\)
Solution
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Problem 4
Draw a line from each 10frame to the equation it matches.
Solution
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Problem 5
Write a number to show how many counters are needed to fill the 10frame.

_______________

_______________

_______________
Solution
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Problem 6
For each number, write the number you need to add to make 10.
Use a 10frame and twocolor counters if it helps you.

6
_______________

8
_______________

1
_______________

7
_______________
Solution
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Problem 7
Mai has a tower of 10 connecting cubes.
She snaps the tower into 2 parts and puts one part behind her back.
She shows her partner 3 cubes.
How many cubes is Mai hiding?
_______________
Show your thinking using drawings, numbers, words, or objects.
Solution
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Problem 8
Exploration
Clare is playing What’s Behind My Back? She has a tower of 10 cubes.
She accidentally snaps the tower into 3 pieces.
She shows these two towers.
How many cubes does Clare have behind her back?
_______________
Solution
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Problem 9
Exploration
Diego is playing What’s Behind My Back? He has a tower of 10 cubes.
He accidentally snaps the tower into 3 pieces.
He shows this tower.
How many cubes could be in Diego’s other two towers?
Solution
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