# 2.2 Adding and Subtracting within 100

## Unit Goals

• Students add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. They then use what they know to solve story problems.

### Section A Goals

• Add and subtract within 100 using strategies based on place value and the relationship between addition and subtraction. Problems in this section are limited to the problems like 65 – 23, where decomposing a ten is not required.

### Section B Goals

• Subtract within 100 using strategies based on place value, including decomposing a ten, and the properties of operations.

### Section C Goals

• Represent and solve one- and two-step problems involving addition and subtraction within 100, including different problem types with unknowns in all positions.

### Problem 1

#### Pre-unit

Practicing Standards:  1.OA.A.1

There are 17 squirrels in a pine tree. There are 12 squirrels in an oak tree.

1. How many fewer squirrels are in the oak tree than in the pine tree? Show your thinking.

2. Write an equation for this situation.

### Problem 2

#### Pre-unit

Practicing Standards:  1.OA.D.8

Fill in the blank to make each equation true.

1. $$7 + 9 = \underline{\hspace{0.9cm}}$$
2. $$15 - 8 = \underline{\hspace{0.9cm}}$$
3. $$6 + \underline{\hspace{0.9cm}} = 11$$
4. $$\underline{\hspace{0.9cm}} - 4 = 13$$

### Problem 3

#### Pre-unit

Practicing Standards:  1.OA.A.1

There are some frogs in the pond. Then 5 more frogs jump into the pond. Now there are 11 frogs in the pond. How many frogs were in the pond? Show your thinking.

### Problem 4

Here are some connecting cubes.

1. How many connecting cubes are there altogether? Show your thinking.
2. How many more cubes are there in train 1 than in train 2? Show your thinking.

### Problem 5

Find the number that makes each equation true in a way that makes sense to you. Show your thinking.

1. $$26 + 51 = \underline{\hspace{0.9cm}}$$

2. $$35 + \underline{\hspace{0.9cm}} = 67$$

### Problem 6

There are 34 children in Mai’s classroom. There are 21 children in Noah’s classroom. How many more children are in Mai’s classroom than in Noah’s classroom? Show your thinking using drawings, numbers, or words and write an equation.

### Problem 7

#### Exploration

Jada added 3 different numbers between 1 and 9 and got 20.

1. What could Jada’s numbers be? Give three different examples.
2. If Jada used 6, what are the other two numbers? Explain your reasoning.

### Problem 8

#### Exploration

1. Make a list of 10 pairs of numbers that add together to make 100.
2. What patterns do you notice in your pairs of numbers?

### Problem 9

#### Exploration

Tyler likes representing addition using base-ten blocks. Here is how Tyler represented a sum.

1. How can Tyler’s base-ten blocks help to find the solution to the equation $$25 + \underline{\hspace{1.5 cm}} = 43$$?
2. What other addition equations could Tyler’s cubes show?
3. What could he do to make his meaning clearer?

### Problem 1

Find the value of each difference. Show your thinking.

1. $$60 - 5$$
2. $$76 - 9$$

### Problem 2

Here is Mai’s work with a subtraction expression.
1. What subtraction expression does Mai’s diagram show?
2. What is the value of the expression?
3. Use Mai’s method to find the value of $$51 - 9$$.

### Problem 3

Find the value of $$55 - 39$$. Show your thinking. Use blocks if it helps.

### Problem 4

Here is how Clare found the value of $$46 - 29$$.

$$\begin{array}{l} 46 - 20 = 26 \\ 26 - 6 = 20\\ 20- 3 = 17\\ 46-28 = 17 \end{array}$$

Here is how Han found the value of $$46 - 29$$.

How are Han’s and Clare’s calculations the same?

How are they different?

### Problem 5

Find the value of each expression. Show your thinking.

1. $$35 + 57$$
2. $$81 - 43$$

### Problem 6

#### Exploration

Here is Han’s method for finding the value of $$73 - 58$$.

$$58 + 2 = 60$$
$$60 + 10 = 70$$
$$70 + 3 = 73$$
$$2 + 10 + 3 = 15$$

1. Show each step of Han’s work with base-ten blocks.

2. Explain or show why Han’s method works.

### Problem 7

#### Exploration

Here is Jada’s method for finding the value of $$73 - 58$$.

$$73 - 60 = 13$$

$$13 + 2 = 15$$

1. Explain why Jada’s method works.
2. Use Jada’s method to find the value of $$85 - 49$$.

### Problem 1

There are some comic books on the shelf.
Mai puts 18 more comic books on the shelf.
Now there are 47 comic books on the shelf.
How many comic books were on the shelf?

1. Draw a diagram representing the situation.
2. How many comic books are on the shelf now? Explain or show your thinking.

### Problem 2

There are 83 people on the stairs. 47 of them are going up and some of them are coming down.

1. Explain why the tape diagram shows the story.

2. How many people are coming down the stairs? Explain or show your reasoning.

### Problem 3

Lin read 25 pages of a book. Clare was reading the same book. Lin read 19 fewer pages of the book than Clare.

1. Draw a diagram representing the situation.
2. Write an equation using a question mark for the unknown value.
3. How many pages did Clare read? Explain or show your reasoning.

### Problem 4

1. At a lake, there are 42 people swimming. Then 25 more people go to swim in the lake. How many people are swimming in the lake? Explain or show your reasoning.
2. Now there are 18 fewer people swimming in the lake than there are playing on the beach. How many people are playing on the beach? Explain or show your reasoning.

### Problem 5

#### Exploration

Here is a tape diagram.

1. Write a story problem that could be represented by the tape diagram.
2. Label the tape diagram to match your story.

### Problem 6

#### Exploration

1. Write a story problem that this tape diagram could represent.

2. Fill in the tape diagram with the information from your story.