Lesson Topic: From Ratio Tables to Equations Using the Value of a Ratio Lesson Objective: I can… Restate a ratio in terms of its value. Use the value of the ratio to problem-solve.

Review What 2 things do we need in an algebraic expression? What does a variable represent? ___________ How can we get from R=3N to show us what N equals?

Exercise 1 Julia mixes 1 gallon of red paint with 3 gallons of yellow paint. Based on this ratio, which of the following statements are true? Explain why. 3 4 of a 4−gallon mix would be yellow paint. Every 1 gallon of yellow paint requires 1 3 gallon of red paint. Every 1 gallon of red paint requires 3 gallons of yellow paint. There is 1 gallon of red paint in a 4-gallon mix of total paint. There are 2 gallons of yellow paint in an 8-gallon mix of total paint.

Exercise 2 Complete a table for the 1 red to 3 yellow ratio, including a “relationship” column. How is the amount of yellow paint related to the amount of red paint? What’s the value of my ratio? How could we figure out how many gallons of yellow paint to use if we have 100 for red?

Exercise 2 Continued If we were given R gallons of red paint, how many gallons of yellow paint would I need? Write an equation to model this relationship. Create an equation that tells us how much red paint to use if we are given the amount of yellow paint? How is the value of the ratio related to the equation?

Exercise 3 I need 1 gallon of blue paint to 4 gallons of red paint. Make a ratio table including blue, red, the relationship (to help you out), and total What’s the value of my ratio? What variables could we use to write equations from this ratio?

Exercise 3 Continued… Write an equation that will let me calculate the amount of red paint I will need for any given amount of blue paint. Write an equation that will let me calculate the amount of blue paint I will need for any given amount of red paint. Where do we see the value of our ratio in each of the equations?

Exercise 3 Continued… If I have 24 gallons of red paint, how much blue paint will I need? If I have 24 gallons of blue paint, how much red paint will I need? What’s the value of the ratio of total paint to blue? Write an equation to model this relationship. How is the value of the ratio related to the equation?

Exercise 4 The ratio of the number of men to the number of women is 6:1. Use a ratio table to create at least 2 equations that model the relationship of the ratio. If there are 200 women, use one of your equations to calculate the number of men.

Exercise 5 Malia sees 18 cars and 6 trucks during the first 5 minutes of her road trip. Complete a ratio table. What is the value of the ratio of the number of cars to the number of trucks? What equation would model the relationship between cars and trucks? Malia saw 1,254 trucks. How many cars did she see?

Lesson Summary… The value of a ratio can be determined using a ratio table. This value can be used to write an equation that also represents the ratio. Example: The multiplication table can be a valuable resource to use in seeing ratios. Different rows can be used to find equivalent ratios. 1 4 2 8 3 12 16

Rate Your Learning… 1 – I do not understand this lesson. 2 – I can do this lesson with help. 3 – I understand this lesson 4 – I could teach this lesson. How will you expand your knowledge?