Understanding Proportions and Variables

In this video tutorial, the teacher introduces Go Math Module 7, Lesson 2, focusing on applying ratios and rates with variables. The lesson begins with an introduction to key vocabulary: proportion and variables. Two example problems are solved using proportions: one involving profit calculation and the other involving distance calculation. The teacher demonstrates how to set up and solve these problems using cross multiplication. The lesson concludes with practice problems for students to solve on their own.

What is a proportion?

• An equation that states two ratios or rates are equivalent.

• A symbol representing an unknown number.

• A method to solve equations.

• A type of variable.

What is a variable in the context of algebra?

• A fixed number.

• A mathematical operation.

• A type of equation.

• A symbol or letter representing an unknown number.

In the first example, what is the ratio of Sheldon's profit to Leonard's profit?

• 2 to 5

• 2 to 7

• 3 to 5

• 5 to 2

How do you solve for a variable using cross multiplication?

• Subtract the smaller number from the larger one.

• Multiply the numbers diagonally and set them equal.

• Add the numbers on both sides.

• Divide the numbers directly.

What is the final profit Sheldon makes in the first example?

• $8

• $5

• $10

• $7

In the second example, what is the distance Ally runs in 40 minutes?

• 3 miles

• 2 miles

• 5 miles

• 4 miles

How far can Ally run in 60 minutes at the same rate?

• 5 miles

• 4.5 miles

• 4 miles

• 3 miles

What is the first step in setting up a proportion for a word problem?

• Identify the total amount.

• Write the ratios in fraction form.

• Solve for the variable.

• Cross multiply immediately.

What is the purpose of dividing by the number next to the variable?

• To eliminate the variable.

• To check the solution.

• To find the total sum.

• To isolate the variable.

Which method is used to solve the practice problems at the end?

• Division

• Addition

• Subtraction

• Cross multiplication