# 2.4 Addition and Subtraction on the Number Line

## Unit Goals

• Students learn about the structure of a number line and use it to represent numbers within 100. They also relate addition and subtraction to length and represent the operations on the number line.

### Section A Goals

• Represent whole numbers within 100 as lengths from 0 on a number line.
• Understand the structure of the number line.

### Section B Goals

• Represent sums and differences on a number line.

### Problem 1

#### Pre-unit

Practicing Standards:  1.OA.D.8

Write the number that makes each statement true.

1. $$9 + 7 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$15 - \boxed{\phantom{\frac{aaai}{aaai}}} = 8$$
3. $$\boxed{\phantom{\frac{aaai}{aaai}}} - 11 = 8$$

### Problem 2

#### Pre-unit

Practicing Standards:  1.NBT.B.3

Put a < or > in each box to make each statement true.

1. $$91\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}19$$
2. $$84\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}87$$
3. $$52\phantom{a} \boxed{\phantom{\frac{aaai}{aaai}}} \phantom{a}36$$

### Problem 3

#### Pre-unit

Practicing Standards:  2.NBT.B.5

1. Write an equation that matches the tape diagram.

2. Find the unknown value.

### Problem 4

#### Pre-unit

Practicing Standards:  2.OA.A.1

There are 37 frogs in the pond. There are 16 more goldfish than frogs in the pond.

1. Complete the diagram to match the story problem.

2. How many goldfish are there in the pond? Explain or show your reasoning.

### Problem 5

1. Label each tick mark with the number it represents.

2. Locate 7 on the number line. Mark it with a point.

### Problem 6

Here is Mai's number line. How should she revise her number line?

### Problem 7

1. Count by 10 starting at 50 and ending at 100. Label each of the numbers in your count on the number line.

2. Locate and label 78 on the number line.

### Problem 8

Locate and label each pair of numbers on the number line. Then use $$<$$ or $$>$$ to compare the numbers.

1. 23 and 27

2. 34 and 43

### Problem 9

What number could this be? Explain your reasoning.

### Problem 10

#### Exploration

1. Locate and label where you think 35 could be on the number line. Explain or show your reasoning.

2. Elena and Han located where they think 83 is.

Why do you think they put their points at different locations on the number line?

Where do you think 83 is on the number line?

### Problem 11

#### Exploration

1. Here is a picture of a thermometer.

How is the thermometer the same as a number line? How is it different?

2. Here is a picture of a rain gauge.

How is the rain gauge the same as a number line? How is it different?

### Problem 1

Which equation does the number line represent? Explain your reasoning.

1. $$7 + 6 = 13$$
2. $$13 - 6 = 7$$

### Problem 2

Here is a number line.

1. Write an equation that the number line represents.

2. Explain how your equation matches the number line.

### Problem 3

1. Explain or show how each number line represents the value of $$47 - 41$$.

2. Which method do you prefer to calculate $$47 - 41$$?

### Problem 4

Find the value of $$32 + 26$$. Represent your thinking on the number line.

### Problem 5

Find the value of $$65 - 58$$ in two different ways. Show your thinking on the number lines.

1. Method 1:

2. Method 2:

### Problem 6

I started at a number on the number line and jumped back 37. I landed at 26. Where did I start?

1. Write an equation with a ? for the unknown.

2. Find the number that makes the equation true.

3. Represent your thinking on the number line.

### Problem 7

There are 18 students in the classroom. Then 13 more students join them.

1. Label the tape diagram to match the story.

2. Label the number line to match the story.

3. How are the tape diagram and number lines the same? How are they different?

4. How many students are in the classroom now?

### Problem 8

#### Exploration

1. Using addition or subtraction, how many equations can you make with these three numbers: 20, 13, 7?

2. Draw number lines to match each of the equations you wrote.

3. How are the number lines the same? How are they different?