Lesson 1: Practice Problems

Problem 1

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

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

Problem 2

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

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

Problem 3

Match each equation to one of the two tape diagrams.

Tape diagram A has 3 segments each labeled x and the diagram is labeled 9. Tape diagram B has 2 uneven segments labeled x and 3 and the diagram is labeled 9.

$x + 3 = 9$
$3 \cdot x = 9$
$9 = 3 \cdot x$
$3 + x = 9$
$x = 9 - 3$
$x = 9 \div 3$
$x + x + x = 9$

Problem 4

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

$x + 9 = 16$
$4 \cdot x = 28$

Problem 5 From Unit 5 Lesson 13

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.

Problem 6 From Unit 3 Lesson 14

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.

Problem 7 From Unit 3 Lesson 11

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.

A double number line with 2 tick marks at either end of the line. The top number line is labeled “calcium in milligrams” and the tick marks are labeled 0 and 1200. The bottom number line is not labeled and the tick marks are labeled 0 and 100 percent.