Lesson 10: Practice Problems

Problem 1

There is a closed carton of eggs in Mai’s refrigerator. The carton contains $e$ eggs and it can hold 12 eggs.

What does the inequality $e < 12$ mean in this context?
What does the inequality $e > 0$ mean in this context?
What are some possible values of $e$ that will make both $e < 12$ and $e > 0$ true?

Problem 2

Here is a diagram of an unbalanced hanger.

A hanger diagram with a red circle on the left hanging lower than the blue square on the right.

Write an inequality to represent the relationship of the weights. Use $s$ to represent the weight of the square in grams and $c$ to represent the weight of the circle in grams.
One red circle weighs 12 grams. Write an inequality to represent the weight of one blue square.
Could 0 be a value of $s$ ? Explain your reasoning.

Problem 3 From Unit 7 Lesson 8

Jada is taller than Diego. Diego is 54 inches tall (4 feet, 6 inches). Write an inequality that compares Jada’s height in inches, $j$ , to Diego’s height.
Jada is shorter than Elena. Elena is 5 feet tall. Write an inequality that compares Jada’s height in inches, $j$ , to Elena’s height.

Problem 4

Tyler has more than $10. Elena has more money than Tyler. Mai has more money than Elena. Let $t$ be the amount of money that Tyler has, let $e$ be the amount of money that Elena has, and let $m$ be the amount of money that Mai has. Select all statements that are true:

$t < m$
$m > 10$
$e > 10$
$t > 10$
$e > m$
$t < e$

Problem 5 From Unit 7 Lesson 3

Which is greater, $\frac{- 9}{20}$ or -0.5? Explain how you know. If you get stuck, consider plotting the numbers on a number line.

Problem 6 From Unit 6 Lesson 13

Select all the expressions that are equivalent to ${(\frac{1}{2})}^{3}$ .

$\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$
$\frac{1}{2^{3}}$
${(\frac{1}{3})}^{2}$
$\frac{1}{6}$
$\frac{1}{8}$