Lesson 13: Practice Problems

Problem 1

Select all expressions that are equal to $3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$ .

$3 \cdot 5$
$3^{5}$
$3^{4} \cdot 3$
$5 \cdot 3$
$5^{3}$

Problem 2

Noah starts with 0 and then adds the number 5 four times. Diego starts with 1 and then multiplies by the number 5 four times. For each expression, decide whether it is equal to Noah’s result, Diego’s result, or neither.

$4 \cdot 5$
$4 + 5$
$4^{5}$
$5^{4}$

Problem 3

Decide whether each equation is true or false, and explain how you know.

$9 \cdot 9 \cdot 3 = 3^{5}$
$7 + 7 + 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3$
$\frac{1}{7} \cdot \frac{1}{7} \cdot \frac{1}{7} = \frac{3}{7}$
$4^{1} = 4 \cdot 1$
$6 + 6 + 6 = 6^{3}$

Problem 4

What is the area of a square with side lengths of $\frac{3}{5}$ units?
What is the side length of a square with area $\frac{1}{16}$ square units?
What is the volume of a cube with edge lengths of $\frac{2}{3}$ units?
What is the edge length of a cube with volume $\frac{27}{64}$ cubic units?

Problem 5 From Unit 6 Lesson 10

Select all the expressions that represent the area of the shaded rectangle.

A rectangle with a shaded blue part. The width is 10 and the white segment is c. The height is 3.

$3 (10 - c)$
$3 (c - 10)$
$10 (c - 3)$
$10 (3 - c)$
$30 - 3 c$
$30 - 10 c$

Problem 6 From Unit 5 Lesson 13

A ticket at a movie theater costs $8.50. One night, the theater had $29,886 in ticket sales.

Estimate about how many tickets the theater sold. Explain your reasoning.
How many tickets did the theater sell? Explain your reasoning.

Problem 7 From Unit 4 Lesson 12

A fence is being built around a rectangular garden that is $8 \frac{1}{2}$ feet by $6 \frac{1}{3}$ feet. Fencing comes in panels. Each panel is $\frac{2}{3}$ of a foot wide. How many panels are needed? Explain or show your reasoning.