Lesson 1: Practice Problems

Problem 1

A rectangle has a height to width ratio of $3 : 4.5$ . Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.

Problem 2

One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other? If so, find the scale factor. If not, briefly explain why.

Problem 3 From Unit 2 Lesson 5

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, $a$ , to the number of ant legs $l$ . Elena writes $a = 6 \cdot l$ and Andre writes $l = \frac{1}{6} \cdot a$ . Do you agree with either of the equations? Explain your reasoning.

Problem 4 From Unit 1 Lesson 4

On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor $\frac{2}{3}$ .

Quadrilateral ABCD is on a grid. Point a is 2 units right and 4 units down from the edge of the grid. Point B is 2 units right and 2 units up from point A. Point C is 6 units right from point A. Point D is 2 units right and 4 units down from point A.

Problem 5 From Unit 1 Lesson 5

Solve each equation mentally.

$\frac{5}{2} \cdot x = 1$
$x \cdot \frac{7}{3} = 1$
$1 \div \frac{11}{2} = x$

Problem 6 From Unit 1 Lesson 11

Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.

The height of the model train is 102 millimeters. What is the actual height of the train in meters? Explain your reasoning.
On the scale model, the distance between the wheels on the left and the wheels on the right is $1 \frac{1}{4}$ inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? Explain your reasoning.