Understanding Proportional Relationships and Rates

This lesson covers the concept of proportional relationships, explaining how two rates or ratios can be equivalent. It uses a bar diagram to illustrate how to calculate unit rates and discusses the concept of constant rates with real-world applications. The lesson also examines non-proportional rates using a bean plant growth example and demonstrates how to check for proportionality using cross multiplication. The lesson concludes with a summary and a preview of the next topic.

What is a proportion?

• A method to calculate speed.

• A comparison of two different units.

• A statement that two rates or ratios are equivalent.

• A way to measure time.

What does a proportional relationship imply?

• The quantities are always decreasing.

• The quantities are always increasing.

• The quantities are unrelated.

• The ratio of one quantity to another is constant.

In the bar diagram, how far does Tala walk in one second?

• 75.6 inches

• 50.4 inches

• 100.8 inches

• 25.2 inches

How can you calculate the distance Tala walks in three seconds?

• Multiply the distance of one second by three.

• Add the distance of one second three times.

• Divide the total distance by three.

• Subtract the distance of one second from the total.

What is the unit rate of Tala's walking speed?

• 25.2 inches per second

• 75.6 inches per second

• 100.8 inches per second

• 50.4 inches per second

How far will Tala walk in one minute at her constant rate?

• 1008 inches

• 1260 inches

• 756 inches

• 1512 inches

What is a constant rate?

• A rate that decreases over time.

• A rate that fluctuates randomly.

• A rate that does not change over time.

• A rate that increases over time.

Why can't Tala maintain her constant rate indefinitely?

• She needs to rest and hydrate.

• She will run out of space.

• She will get bored.

• She will forget the path.

What is the unit rate of the bean plant's growth?

• 1.5 cm per day

• 1.0 cm per day

• 0.5 cm per day

• 2.0 cm per day

Why is the bean plant's growth not proportional?

• The plant stops growing after a while.

• The rate of growth changes over time.

• The plant grows at a constant rate.

• The plant grows in a straight line.