Relate Ratio Tables to Graphs

Relate Ratio Tables to Graphs

Ratio Tables and Graphs

Opening

Ratio Tables and Graphs

Ms. Lopez sells muffins at her bakery. She sells them in packages.

She uses a ratio table to determine the number of packages she will need for different numbers of muffins. The table she uses shows equivalent ratios of number of packages to number of muffins.

She can also use a graph to show this information.

Complete the ratio table with your class.

Using the graph on the handout, graph paper, or a graphing tool, plot all the points in the ratio table on a graph.

Examine the graph. How is the information in the ratio table represented in the graph?

HANDOUT: Ratio Tables and Graphs

Math Mission

Opening

Explore the relationship between ratio tables and graphs and use them to solve problems.

Biscuits

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Biscuits

Ms. Lopez also sells biscuits in packages.

She uses this ratio table to determine the number of packages she will need for different numbers of biscuits.

  • Complete the ratio table.
  • Make a graph that shows the information in the ratio table.
  • Use the ratio table to find the number of biscuits that will fill 39 packages.

Ask yourself:

  • The second column of the ratio table (with a 1 in the top cell) tells you the number of biscuits in 1 package.
  • Each pair of numbers in the columns of the ratio table represents an ordered pair that defines the coordinates of a point on the graph.
  • How could you add to or subtract from numbers in the table to find the number of biscuits in 39 packages?

Granola

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Granola

Ms. Lopez makes granola in her bakery. Her friend, Mr. Lee, has a bakery on the other side of town, and he makes granola, too.

Both Ms. Lopez and Mr. Lee use ratio tables to show equivalent ratios of almonds to oats in their granola.

  • Use the ratio tables to determine whose granola has a higher ratio of almonds to oats. Explain your answer.
  • Using a piece of graph paper or a graphing tool, make a graph of the information from each granola ratio table using the same coordinate grid.
  • Use the two graphs to justify your answer as to whose granola has the higher ratio of almonds to oats.

Hint:

  • To compare the amounts of oats and almonds in the two types of granola, find a row from each table that has either the same number for oats or the same number for almonds.
  • The steepness of each graph—called the slope —gives you a visual way to compare the ratios of almonds to oats for the two types of granola.

Prepare a Presentation

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Prepare a Presentation

Be prepared to show:

How you completed the ratio table of packages to biscuits

How you used the information in the table to make a graph

How you found the number of biscuits in 39 packages

Also be prepared to demonstrate and explain:

How you used the granola ratio tables to determine whose granola has a higher ratio of almonds to oats

How you graphed the information from the two tables

How the graphs provide support for your answer as to whose granola has the higher ratio of almonds to oats

Challenge Problem

Anna graphed the ratios of cups of almonds to cups of oats, using the x-axis to represent cups of oats and the y-axis to represent cups of almonds. She says that if you make this type of graph for any two types of granola mixtures, the graph of the granola that has the higher ratio of almonds to oats will always be steeper.

Is she right? Explain and give examples.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates' work with ratio tables and graphs.

As your classmates present, ask questions such as:

  • Can you say more about how the ratio table relates to the corresponding graph? For example, can you show how an increase in the number of packages would be reflected in the table and on the graph?
  • How could you use the graph you made from the ratio table of biscuits to packages to find the number of biscuits in 39 packages? Compare this to how you would use the ratio table.
  • How do the graphs of the two granola mixtures tell you which mixture has the higher ratio of almonds to oats?

Representing Ratios

Formative Assessment

Summary of the Math: Representing Ratios

Read and Discuss

  • Suppose the ratio of cups of milk to cups of flour in a recipe is 3:2.
    • You can show this ratio with a ratio table, a double number line, or a graph.
    • For each pair of values in a ratio table, you can place a corresponding lined-up pair of numbers on a double number line and make a graph by plotting a corresponding point (using an ordered pair) on a coordinate grid.

Can you:

  • Explain what a ratio table is?
  • Describe how to make a graph that shows the information from a ratio table?
  • Describe how to make a graph that shows the information from a double number line?

Reflect On Your Work

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Reflection

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

One thing that still confuses me about ratios is …