Lesson 2

Introducing Proportional Relationships with Tables

Let’s solve problems involving proportional relationships using tables.

Problem 1

When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes. Use the information in the table to complete the statements. Some terms are used more than once.

Table with 2 columns and 4 rows of data. 
  1. The table shows a proportional relationship between ______________ and ______________.
  2. The scale factor shown is ______________.
  3. The constant of proportionality for this relationship is______________.
  4. The units for the constant of proportionality are ______________ per ______________.

Bank of Terms: tablespoons of chocolate syrup, 4, cups of milk, cup of milk, \(\frac32\)

Problem 2

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

  1. How many cups of red paint should be added to 1 cup of white paint?
    cups of white paint cups of red paint
    7 3
  2. What is the constant of proportionality?

Problem 3

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.

  1. What is the actual area of the park? Show how you know.

  2. The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure? Show your reasoning.

(From Unit 1, Lesson 12.)

Problem 4

Noah drew a scaled copy of Polygon P and labeled it Polygon Q.

Polygon Q on a grid. 

If the area of Polygon P is 5 square units, what scale factor did Noah apply to Polygon P to create Polygon Q? Explain or show how you know.

(From Unit 1, Lesson 6.)

Problem 5

Select all the ratios that are equivalent to each other.