1.5 Adding Within 100

Unit Goals

  • Students use place value understanding and properties of operations to add within 100.

Section A Goals

  • Add within 100 without composing a ten.
  • Use equations to represent addition methods.

Section B Goals

  • Add a one-digit and a two-digit number within 100 with composing a ten.
  • Use equations to represent addition methods.

Section C Goals

  • Add 2 two-digit numbers within 100, with composing a ten.
  • Use equations to represent addition methods.
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Section A: Add Without Making a Ten

Problem 1

Pre-unit

Practicing Standards:  1.NBT.A.1, 1.NBT.B.2

How many do you see?

a.Ten frames. 2 full. Below, ten frame, 7 counters.
b.Ten frames. 4 full. Below, ten frame, 5 counters.
c.Ten frames. 3 full. Below, ten frame, 9 counters.

Solution

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Problem 2

Pre-unit

Practicing Standards:  1.OA.A.1

There are 9 ducks in the pond.
There are 7 ducks on the grass.
How many ducks are on the pond and in the grass?
Show your thinking using drawings, numbers, or words.

Solution

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Problem 3

Pre-unit

Practicing Standards:  1.OA.D.8

Find the number that makes each equation true.

  1. \(10 + \boxed{\phantom{\frac{aaai}{aaai}}} = 18\)
  2. \(17 - \boxed{\phantom{\frac{aaai}{aaai}}} = 7\)
  3. \(9 + 8 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
  4. \(19 = \boxed{\phantom{\frac{aaai}{aaai}}} +14\)

Solution

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Problem 4

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

  1. \(65 + 3\)
  2. \(65 + 30\)

Solution

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Problem 5

Find the value of \(31 + 24\).
Show your thinking using drawings, numbers, or words.

Solution

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Problem 6

  1. Find the value of \(26 + 53\)
    Show your thinking using drawings, numbers, words, or equations.
  2. Can you find the value in a different way?

Solution

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Problem 7

Exploration

  1. Find different ways you can use 2 two-digit numbers to make 86.

    Use the drawing or connecting cubes, if they are helpful.

    Base 10 diagram. 8 towers of 10 cubes. 6 single cubes.
  2. Can you make 86 by adding a two-digit number to itself?

Solution

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Problem 8

Exploration

Together Mai and Han have 75 counters. 
How many counters could Mai have?
Then how many counters would Han have?
Find at least 5 different solutions. 

Solution

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Section B: Make a Ten: Add One- and Two-digit Numbers

Problem 1

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

  1. \(47 + 3\)

  2. \(47 + 8\)

Solution

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Problem 2

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

  1. \(78 + 6 \)

  2. \(6 + 78 \)

Solution

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Problem 3

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

  1. \(63 + 5\)
  2. \(63 + 8 \)

  3. How are the problems the same?

    How are they different?

Solution

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Problem 4

Exploration

Choose five numbers from below to make a sum with a value greater than 50 but less than 99.

3

5

6

7

8

10

20

30

40

Use equations or drawing to show your thinking.

Solution

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Problem 5

Exploration

Here is how Lin found the value of \(58 + 9\).

“I know \(8 + 9 = 17\). Then I add 5 tens and get 67.”

  1. Why does Lin's method work? Show your thinking using drawings, numbers, or words.
  2. Use Lin's method to find the value of \(83 + 8\).

Solution

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Problem 6

Exploration

Noah’s brother spilled water on his math work.
Help Noah figure out what the missing number is.

  1. The missing number makes the value of the sum greater than 50, with a 0 in the ones place.

    Expression. 41 plus water mark.

    What could the missing number be?

  2. The missing number is a two-digit number that makes the value 75.

    Expression. 58 plus water mark.

    What could the missing number be?

  3. The missing number is a two-digit number that makes a value that is more than 80 but less than 90.

    Expression. 65 plus water mark.

    What could the missing number be?

Solution

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Problem 7

Exploration

Priya is playing the game Target Numbers.
Priya starts at 25 and picks these six cards:

1

2

3

5

6

8

She chooses whether to add that many tens or ones for each card.
What is the highest score she can get without going over 95?
Use equations to show your thinking.

Solution

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Section C: Make a Ten: Add Within 100

Problem 1

Find the value of \(35 + 48\).
Show your thinking using drawings, numbers, or words.

Solution

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Problem 2

  1. Find the value of \(16 + 55\).

    Show your thinking using drawings, numbers, or words.
  2. Can you find the value in a different way?

Solution

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Problem 3

Use your favorite method to find the value of \(34 + 59\).

Why do you like the method you chose?

Solution

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Problem 4

Choose a two-digit number to add to 46 so that you make a new 10.
Add the numbers.
Write equations to show your thinking.

Solution

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Problem 5

Exploration

Elena has a way to find the value of \(28 + 47\) without making a 10. Here is her work.

\(30 - 2 = 28\)
\(50 - 3 = 47\)
\(80 - 5 = 75\)

  1. Explain why Elena's work is correct. Use connecting cubes if it is helpful.
  2. Use Elena's method to find the value of \(39 + 55\).

Solution

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Problem 6

Exploration

Diego and his friends are working on the same addition problem.

Diego’s method

\(40 + 20 = 60\)
\(60 + 15 = 75\)

Lin’s method

\(48 + 2 + 5= 55\)
\(55 + 20 = 75\)

Priya’s method

\(40 + 27 = 67\)
\(67 + 3 + 5 = 75\)

  1. What is the addition problem Diego and his friends are working on?

  2. Which method is your favorite?

    Solve \(56 + 28\) using your favorite method.

Solution

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Problem 7

Exploration

Clare wrote some expressions.
Each expression makes a ten.
She spilled water on her work.
Find the digit that could be under each water mark.

  1.  
    Expression. 2 in the tens place. Water mark in the ones place. Plus. 3. 

  2.  
    Expression. 48 plus water mark.

  3.  
    Expression. 6 in the tens place. Water mark in the ones place. Plus. 9.  

  4.  
    Expression. 75 plus water mark.

  5.  
    Expression. Water mark in the tens place, 4 in the ones place. Plus. 6.

Solution

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