# Unit 2 Family Materials

Introducing Proportional Relationships

### Introducing Proportional Relationships

Here are the video lesson summaries for Grade 7, Unit 2: Introducing Proportional Relationships. Each video highlights key concepts and vocabulary that students learn across one or more lessons in the unit. The content of these video lesson summaries is based on the written Lesson Summaries found at the end of lessons in the curriculum. The goal of these videos is to support students in reviewing and checking their understanding of important concepts and vocabulary. Here are some possible ways families can use these videos:

• Keep informed on concepts and vocabulary students are learning about in class.
• Watch with their student and pause at key points to predict what comes next or think up other examples of vocabulary terms (the bolded words).
• Consider following the Connecting to Other Units links to review the math concepts that led up to this unit or to preview where the concepts in this unit lead to in future units.

Grade 7, Unit 2: Introducing Proportional Relationships

Vimeo

Video 1: Representing Proportional Relationships with Tables (Lessons 2–3)

Video 2: Representing Proportional Relationships with Equations (Lessons 4–6)

Video 3: Comparing Proportional and Nonproportional Relationships (Lessons 7–8)

Video 4: Representing Proportional Relationships with Graphs (Lessons 10–13)

Video 1

Video 2

Video 3

Video 4

Connecting to Other Units

• Coming soon

### Representing Proportional Relationships with Tables

This week your student will learn about proportional relationships. This builds on the work they did with equivalent ratios in grade 6. For example, a recipe says “for every 5 cups of grape juice, mix in 2 cups of peach juice.” We can make different-sized batches of this recipe that will taste the same.

The amounts of grape juice and peach juice in each of these batches form equivalent ratios.

The relationship between the quantities of grape juice and peach juice is a proportional relationship. In a table of a proportional relationship, there is always some number that you can multiply by the number in the first column to get the number in the second column for any row. This number is called the constant of proportionality.

In the fruit juice example, the constant of proportionality is 0.4. There are 0.4 cups of peach juice per cup of grape juice.

Using the recipe “for every 5 cups of grape juice, mix in 2 cups of peach juice”

1. How much peach juice would you mix with 20 cups of grape juice?
2. How much grape juice would you mix with 20 cups of peach juice?

Solution:

1. 8 cups of peach juice. Sample reasoning: We can multiply any amount of grape juice by 0.4 to find the corresponding amount of peach juice, $$20 \boldcdot (0.4) = 8$$.
2. 50 cups of grape juice. Sample reasoning: We can divide any amount of peach juice by 0.4 to find the corresponding amount of grape juice, $$20 \div 0.4 = 50$$.