# Lesson 1

Tape Diagrams and Equations

### Problem 1

Here is an equation: $$x + 4 = 17$$

1. Draw a tape diagram to represent the equation.
2. Which part of the diagram shows the quantity $$x$$? What about 4? What about 17?
3. How does the diagram show that $$x+4$$ has the same value as 17?

### Solution

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### Problem 2

Diego is trying to find the value of $$x$$ in $$5 \boldcdot x = 35$$. He draws this diagram but is not certain how to proceed.

1. Complete the tape diagram so it represents the equation $$5 \boldcdot x = 35$$.
2. Find the value of $$x$$.

### Solution

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### Problem 3

Match each equation to one of the two tape diagrams.

1. $$x + 3 = 9$$
2. $$3 \boldcdot x = 9$$
3. $$9=3 \boldcdot x$$
4. $$3+x=9$$
5. $$x = 9 - 3$$
6. $$x = 9 \div 3$$
7. $$x + x+ x = 9$$

### Solution

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### Problem 4

For each equation, draw a tape diagram and find the unknown value.

1. $$x+9=16$$

2. $$4 \boldcdot x = 28$$

### Solution

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### Problem 5

A shopper paid $2.52 for 4.5 pounds of potatoes,$7.75 for 2.5 pounds of broccoli, and \$2.45 for 2.5 pounds of pears. What is the unit price of each item she bought? Show your reasoning.

### Solution

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(From Unit 5, Lesson 13.)

### Problem 6

A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? Show your reasoning.

### Solution

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(From Unit 3, Lesson 14.)

### Problem 7

The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of milk has 25% of the recommended daily allowance of calcium. How many milligrams of calcium are in a cup of milk? If you get stuck, consider using the double number line.

### Solution

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(From Unit 3, Lesson 11.)