Using Ratio Tables to Solve Problems

Using Ratio Tables to Solve Problems

Introduction to Ratio Tables

Opening

Introduction to Ratio Tables

Discuss:

  • This ratio table shows the relationship between the number of students and the number of computers in a class that has 35 students and 28 computers.
    • Column A shows the ratio of students to computers, which is 35:28.
    • Column B shows that there are 1.25 students for every 1 computer.
    • Column C shows that the simplest whole-number ratio is 5:4.
    • Columns D through G show other ways to express the ratio of students to computers using whole numbers.

More About Ratio Tables

Opening

More About Ratio Tables

If you multiply both quantities in a ratio by the same number, the resulting ratio will be equivalent to the original ratio. The calculations that follow illustrate how you can use this method to generate the ratio in column G by starting with the ratios in columns B or C.

1.25:1=1.251=1.253641364=455364=455:364

 


5:4=54=591491=455364=455:364

 

Notice that the numbers in the ratio table are not arranged in order of size. The values in ratio tables in general do not have to follow any particular order.

  • If the ratio of students to computers stays the same, how many computers would be needed if the class size grew to 40 students?

 

Math Mission

Opening

Use ratio tables to solve ratio problems.

Fruit Punch

Work Time

Fruit Punch

Carlos makes his own fruit punch using grape juice and club soda to serve at his parties. He makes different amounts of punch depending on the size of the party. He has found that using the ratio 2:3 for cups of club soda to cups of grape juice makes the tastiest fruit punch.

  • Complete the ratio table.
  • Use the table to determine how many cups of grape juice Carlos will need if he uses 80 cups of club soda. HANDOUT: Fruit Punch

How can you use the ratio 2 : 3 and the information in the ratio table to find an equivalent ratio that will enable you to determine the amount of punch needed for 80 cups of club soda?

Maple Syrup

Work Time

Maple Syrup

A maple tree farmer can get 30 gallons of maple syrup from 65 maple trees.

Make a ratio table to help you solve this problem. The table should show the ratio of the number of trees to the number of gallons of maple syrup for various numbers of trees.

  • How many maple trees would the farmer need to get 144 gallons of maple syrup?
  • How many gallons of maple syrup can he get from other numbers of maple trees?

Ask yourself:

  • What ratio should you start with when making your ratio table?
  • How can you get from 30 gallons of maple syrup to 144 gallons of maple syrup?

 

HANDOUT: Maple Syrup

Prepare a Presentation

Work Time

Prepare a Presentation

Present your ratio table.

  • Explain the strategy you used for constructing a ratio table that helps you solve the problem of determing how many trees would be needed to make 144 gallons of maple syrup.
  • Explain how you put other pairs of numbers representing equivalent ratios into the table.

Challenge Problem

Would using a ratio table help you solve problems about calculating the costs of items in a store if the store offered special deals for buying large quantities of an item? Explain.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates' strategies for using ratio tables to solve ratio problems.

As your classmates present, ask questions such as:

  • What were some of the challenges you encountered in making your ratio table?
  • What does your ratio table show?

What I Learned about Ratio Tables

Formative Assessment

Summary of the Math: What I Learned about Ratio Tables

Write a summary about making and using ratio tables.

Check your summary.

  • Do you explain what a ratio table is?
  • Do you explain how to make a ratio table?
  • Do you describe how you can use a ratio table to solve ratio problems?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful.

I think a ratio table is similar to a double number line because …

I think a ratio table is different from a double number line because …