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.
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Section A: Make and Break Apart Numbers to 9

Problem 1

  1.  
    1 connecting cube tower. Blue, 3. 

    How can you break apart 3 connecting cubes into 2 parts?

    Show your thinking using drawings, numbers, words, or objects.

  2.  
    1 connecting cube tower. Blue, 5. 

    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.

Pattern block design.

  1. How many pattern blocks did Jada use? _____________

  2. 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.

1 connecting cube tower. Blue, 5. Yellow, 2.

  1. Write an expression for Mai’s connecting cubes.

  2. 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.

Pattern block design.

He wrote the expression \(6 + 2\) to describe his design.

What pattern blocks did Han use?

Solution

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Problem 5

Exploration

  1. Show all the ways to snap a tower of 4 cubes into 2 parts.
  2. Show all the ways to snap a tower of 5 cubes into 2 parts.
  3. Show all the ways to snap a tower of 6 cubes into 2 parts.
  4. 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

  1. 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.

  2. 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?

  1.  
    Ten frame. 8 counters.

    _______________

  2.  
    Ten frame. 6 counters.

    _______________

  3.  
    Ten frame. Full.

    _______________

Solution

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Problem 2

Draw a line from the fingers to the ten-frame that shows the same number.

A:
Fingers showing 6.

 

B:
Fingers showing 8.

 

C:
Fingers showing 9.
1:

Ten frame, 8 counters.
2:

Ten frame, 9 counters.
3:

Ten frame, 6 counters.

Solution

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Problem 3

Circle the equation that matches the 10-frame.

Ten frame. Full with 7 red counters, 3 yellow counters.

A:

\(7 = 5 + 2\)

B:

\(10 = 7 + 3\)

C:

\(10 = 8 + 2\)

Solution

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Problem 4

Draw a line from each 10-frame to the equation it matches.

A:
Ten frame. Full with 5 red counters, 5 yellow counters.

B:
Ten frame. Full with 7 red counters, 3 yellow counters.

C:
Ten frame. Full with 8 red counters, 2 yellow counters.

D:
Ten frame. Full with red counters.

1:

\(10 = 8 + 2\)

2:

\(10 = 10 + 0\)

3:

\(10 = 5 + 5\)

4:

\(10 = 7 + 3\)

Solution

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Problem 5

Write a number to show how many counters are needed to fill the 10-frame.

  1.  
    Ten frame, 5 counters.

    _______________

  2.  
    Ten frame, 9 counters.

    _______________

  3.  
    Ten frame, 2 counters.

    _______________

Solution

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Problem 6

For each number, write the number you need to add to make 10.

Use a 10-frame and two-color counters if it helps you.

  1.  

    6

    _______________

  2.  

    8

    _______________

  3.  

    1

    _______________

  4.  

    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.

2 connecting cube towers. Blue, 5. Yellow, 3.

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.

Connecting cube tower, 3 cubes.

How many cubes could be in Diego’s other two towers?

Solution

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