Exploring Rates and Ratios in 7th Grade Math

This lesson covers seventh-grade concepts of ratios and rates, focusing on solving problems involving fractions and decimals. It explains unit rates using examples like inches per foot and demonstrates calculating rates with fractions through a runner's pace. The lesson also explores finding minutes per mile and highlights the reciprocal relationship between different rates. Finally, it compares strategies for solving ratio problems with and without fractions, emphasizing the similarity in approaches despite the complexity of the math involved.

What is the main goal of today's lesson?

• To learn about fractions

• To solve problems involving ratios of fractions and decimals

• To understand multiplication

• To study geometry

How many inches are there in one foot?

• 10 inches

• 11 inches

• 12 inches

• 13 inches

What operation is used to find unit rates with fractions?

• Subtraction

• Addition

• Division

• Multiplication

If a runner runs 3/4 of a mile in 11 1/2 minutes, how do you set up the division to find miles per minute?

• 11 1/2 multiplied by 3/4

• 3/4 multiplied by 11 1/2

• 3/4 divided by 11 1/2

• 11 1/2 divided by 3/4

What is the unit rate of miles per minute for the runner?

• 3/22

• 3/20

• 3/32

• 3/44

How do you find the number of minutes it takes to run one mile?

• Divide 3/4 by 11 1/2

• Multiply 3/4 by 11 1/2

• Divide 11 1/2 by 3/4

• Multiply 11 1/2 by 3/4

What is the runner's pace in minutes per mile?

• 3/4

• 11/2

• 22/3

• 44/6

What is surprising about the values of miles per minute and minutes per mile?

• They are equal

• They are reciprocals

• They are both fractions

• They are both whole numbers

How do the strategies for solving ratio problems with fractions compare to those without fractions?

• They are completely different

• They are identical

• They are somewhat similar

• They are very similar

What might take more time when solving ratio problems with fractions?

• Understanding the problem

• Setting up the problem

• The math involved

• Writing the answer