1.3 Adding and Subtracting Within 20

Unit Goals

  • Students add and subtract within 20. Students apply the properties of operations and the relationship between addition and subtraction.

Section A Goals

  • Build toward fluency with adding and subtracting within 10.

Section B Goals

  • Add and subtract one-digit numbers from teen numbers without composing or decomposing a ten.
  • Find the value that makes an addition or subtraction equation true, involving 10.
  • Understand 10 ones as a ten and the numbers 11 to 19 as a ten and some ones.

Section C Goals

  • Add within 20, including three addends.

Section D Goals

  • Subtract within 20.
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Section A: Develop Fluency with Addition and Subtraction within 10

Problem 1

Pre-unit

Practicing Standards:  K.CC.B.5

For each picture, write a number for how many you see.

  1.  
    Dots. 2 groups of 9 dots.
  2.  
    Ten frame, full. Below, 7 counters.
  3.  
    Squares arranged in a circle.

Solution

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Problem 2

Pre-unit

Practicing Standards:  K.NBT.A.1

Match each picture with an expression.

A:
Ten frame, full. Below, 4 counters.

B:
Ten frame, full. Below, 8 counters.

C:
Five frame, full. Below, 4 counters.

D:
Ten frame, full. Below, 6 counters.
1:  \(10 + 8\)

2:

 \(5 + 4\)

3:

 \(10 + 4\)

4:

 \(10 + 6\)

Solution

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Problem 3

Pre-unit

Practicing Standards:  K.OA.A.2

There were 5 monkeys swinging in the tree.
Then 2 more monkeys came to join them.
How many monkeys are in the tree now?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 4

Find the value of each sum.

  1. \(7 + 1\)
  2. \(4 + 2\)
  3. \(5 + 5\)

Solution

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Problem 5

Find the value of each sum.

  1. \(6+2\)
  2. \(1+8\)
  3. \(2+7\)
  4. \(9+1\)

Solution

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Problem 6

Select 3 true equations.

A: 7 + 2 = 5 + 4
B: 1 + 6 = 3 + 2
C: 4 + 4 = 2 + 6
D: 5 + 3 = 5 + 4
E: 3 + 7 = 5 + 5

Solution

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Problem 7

  1. Write an equation that matches this 10-frame.

    Ten frame, full. 9 red counters. 1 yellow counter.
  2. Write 2 equations that show other ways to make 10.

Solution

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Problem 8

Find the value of each expression.
Show your thinking using drawings, numbers, or words.

  1. \(4 + 3\)
  2. \(7 - 3\)
  3. \(8 - 2\)

Solution

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Problem 9

There are some counters in the cup.
Lin puts in 5 more counters.
Now there are 9 counters in the cup.
How many counters were in the cup before Lin added more?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 10

Exploration

Here are some numbers:

1

2

4

5

7

  1. Can you make 10 using 2 of the numbers? Show your thinking using drawings, numbers, or words.
  2. Can you make 10 using 3 of the numbers? Show your thinking using drawings, numbers, or words.

Solution

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Problem 11

Exploration

Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.

  1. \(7 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}} + 5\)
  2. \(3 + \boxed{\phantom{\frac{aaai}{aaai}}} = 5 + 5\)
  3. \(\boxed{\phantom{\frac{aaai}{aaai}}} + 1 = 3 + 5\)

Solution

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Section B: Add and Subtract using Ten as a Unit

Problem 1

  1. How many cubes are there?
    How do you see them? 
    Connecting cubes. 1 tower of 10 cubes. 7 single cubes.

  2. Show 14 with connecting cubes.

Solution

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Problem 2

Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.

  1. \(10 + 3 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(10  + \boxed{\phantom{\frac{aaai}{aaai}}} = 13\)

Solution

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Problem 3

  1. Find the number that makes each equation true.

    \(18 -  \boxed{\phantom{\frac{aaai}{aaai}}} = 10\)

    \(10 +  \boxed{\phantom{\frac{aaai}{aaai}}} = 18\)

  2. How are the 2 equations the same?
    How are they different?

Solution

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Problem 4

Find the number that makes each equation true.

  1. \(15 + 1 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(12 +6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  3. \( \boxed{\phantom{\frac{aaai}{aaai}}} = 10 + 7\)
  4. \(\boxed{\phantom{\frac{aaai}{aaai}}} = 13 + 5 \)

Solution

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Problem 5

Find the number that makes each equation true.

  1. \(18 - 3 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(17 - \boxed{\phantom{\frac{aaai}{aaai}}} = 10\)
  3. \(13 + \boxed{\phantom{\frac{aaai}{aaai}}} = 17\)
  4. \(15 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  5. \(16 - 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)

Solution

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Problem 6

There are 12 kids playing soccer.
Then 4 more come to play with them.
How many kids are playing soccer now?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

Solution

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Problem 7

Exploration

Jada has 17 cards on her desk. 
She gives Han 4 cards. 
Now Han and Jada have the same number of cards.
How many cards were on Han's desk to start?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 8

Exploration

Jada has 14 cards on her desk. 
Han has 15 cards on his desk.
Jada gives Han 3 cards.

  1. How many cards does Jada have on her desk now?
    Show your thinking using drawings, numbers, or words.
  2. How many cards does Han have on his desk now?
    Show your thinking using drawings, numbers, or words.

Solution

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Problem 9

Exploration

number name
16 sixteen
17 seventeen
18 eighteen
19 nineteen

What do you notice about the numbers and names in the table?

Solution

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Section C: Add within 20

Problem 1

There are 5 bananas, 6 oranges, and 4 apples in a bowl.
How many pieces of fruit are in the bowl?
Show your thinking using objects, drawings, numbers, or words.

Equation: ____________________________________________

Solution

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Problem 2

Select 3 expressions that are equal to \(10 + 8\).

A: 5 + 5 + 8
B: 9 + 7 + 3
C: 1 + 9 + 9
D: 3 + 8 + 7
E: 8 + 4 + 6

Solution

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Problem 3

Find the value of each sum.
Show your thinking using drawings, numbers, or words.

  1. \(9 + 6\)

  2. \(4 + 9\)

  3. \(7 + 5\)

  4. \(8 + 4\)

Solution

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Problem 4

Select 3 expressions that have the same value as 10 + 3.

A:

9 + 4

B:

2 + 12

C:

5 + 8

D:

7 + 6

E:

5 + 9

Solution

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Problem 5

Find the value of each sum.
Show your thinking using drawings, numbers, or words.

  1. \(3 + 9\)
  2. \(6 + 5\)
  3. \(8 + 7\)

Solution

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Problem 6

Jada has 6 connecting cubes.
Han has 8 connecting cubes.
Lin has 5 connecting cubes.
How many cubes do Jada, Han, and Lin have all together?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 7

Exploration

  1. Tyler started counting up from 3.
    Mai started counting back from 15.
    Which number do Tyler and Mai say at the same time?
    Show your thinking using drawings, numbers, or words.
  2. Clare started counting up from 1.
    Andre started counting back from 20.
    Do Andre and Clare say the same number at the same time?
    Show your thinking using drawings, numbers, or words.

Solution

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Problem 8

Exploration

  1. Write an addition story problem using 3 numbers from the list:
    • 3
    • 5
    • 7
    • 4
    • 9
    • 6

  2. Solve your story problem.

  3. Write an equation that matches the story problem.

    Equation: ________________________________

Exchange your story with a classmate and solve each other's problem.

Solution

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Section D: Subtract within 20

Problem 1

Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.

  1. \(12 - 3 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(19 - 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)

Solution

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Problem 2

Find the value of each difference.
Show your thinking using drawings, numbers, or words.

  1. \(16 - 10\)
  2. \(16 - 9\)

Solution

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Problem 3

Find the value of each difference.
Use the 10-frames if they help.

  1. \(13 - 9\)

    Double ten frame. 9 counters.

  2. \(14 - 6\)

    Double ten frame. 10 counters not crossed out. 4 counters crossed out.

Solution

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Problem 4

Find the number that makes each equation true.

  1. \(15 - 11 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  2. \(14 - 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)

Solution

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Problem 5

There are some children skating on the pond.
Then 8 more children come to join them.
Now there are 14 children skating on the pond.
How many children were skating on the pond before more joined?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 6

Exploration

Mai was playing Number Card Subtraction. 
She started with a teen number. 
Then she drew a card and subtracted. 
Mai's answer was the same as the number she subtracted. 
What could Mai's teen number and card have been?

Solution

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Problem 7

Exploration

Find the value of the expression in as many ways as you can.

\(16 - 9\)

What is your favorite way?

Solution

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