Lesson 3: Practice Problems

Problem 1

Select all the equations that represent the hanger.

Balanced hanger with 3 circles on the left labeled x and 6 squares on the right unlabeled.

$x + x + x = 1 + 1 + 1 + 1 + 1 + 1$
$x \cdot x \cdot x = 6$
$3 x = 6$
$x + 3 = 6$
$x \cdot x \cdot x = 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1$

Problem 2

Write an equation to represent each hanger.

Problem 3

Balanced hanger with 2 circles on left, x, on right a square, 14.62

Write an equation to represent the hanger.
Explain how to reason with the hanger to find the value of $x$ .
Explain how to reason with the equation to find the value of $x$ .

Problem 4

Andre says that $x$ is 7 because he can move the two 1s with the $x$ to the other side.

A balanced hanger. On left is circle, x and two squares, 1 each. On right are 5 squares, 1 each.

Do you agree with Andre? Explain your reasoning.

Problem 5 From Unit 6 Lesson 1

Match each equation to one of the diagrams.

$12 - m = 4$
$12 = 4 m$
$m - 4 = 12$
$\frac{m}{4} = 12$

Problem 6 From Unit 4 Lesson 13

The area of a rectangle is 14 square units. It has side lengths $x$ and $y$ . Given the following values for $x$ , find $y$ .

$x = 2 \frac{1}{3}$
$x = 4 \frac{1}{5}$
$x = \frac{7}{6}$

Problem 7 From Unit 3 Lesson 11

Lin needs to save up $20 for a new game. How much money does she have if she has saved the following percentages of her goal? Explain your reasoning.

25%
75%
125%