Lesson 11Representing Ratios with Tables

Learning Goal

Let’s use tables to represent equivalent ratios.

Learning Targets

  • If I am looking at a table of values, I know where the rows are and where the columns are.

  • When I see a table representing a set of equivalent ratios, I can come up with numbers to make a new row.

  • When I see a table representing a set of equivalent ratios, I can explain what the numbers mean.

Lesson Terms

  • table

Warm Up: How Is It Growing?

Look for a pattern in the figures.

A growing pattern of tiles arranged in rows. The first figure: row 1, 3 green tiles; row 2, 4 blue tiles. The second figure: row 1, 3 green tiles; row 2, 3 green tiles; row 3, 4 blue tiles; row 4, 4 blue tiles. The third figure: row 1, 3 green tiles; row 2, 3 green tiles; row 3, 3 green tiles; row 4, 4 blue tiles; row 5, 4 blue tiles; row 6, 4 blue tiles.

Problem 1

How many total tiles will be in:

  1. the 4th figure?

  2. the 5th figure?

  3. the 10th figure?

Problem 2

How do you see it growing?

Activity 1: A Huge Amount of Sparkling Orange Juice

Problem 1

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

  1. Use the double number line to show how many liters of each ingredient to use for different-sized batches of sparkling orange juice.

    open applet in presentation mode

  2. If someone mixes 36 liters of orange juice and 45 liters of soda water, how many batches would they make?

  3. If someone uses 400 liters of orange juice, how much soda water would they need?

  4. If someone uses 455 liters of soda water, how much orange juice would they need?

  5. Explain the trouble with using a double number line diagram to answer the last two questions.

Print Version

Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.

  1. Use the double number line to show how many liters of each ingredient to use for different-sized batches of sparkling orange juice.

    A double number line with 11 evenly spaced tick marks. The top number line is labeled "orange juice, in liters" and the bottom number line is labeled "soda water, in liters."

  2. If someone mixes 36 liters of orange juice and 45 liters of soda water, how many batches would they make?

  3. If someone uses 400 liters of orange juice, how much soda water would they need?

  4. If someone uses 455 liters of soda water, how much orange juice would they need?

  5. Explain the trouble with using a double number line diagram to answer the last two questions.

Activity 2: Batches of Trail Mix

Problem 1

A recipe for trail mix says: “Mix 7 ounces of almonds with 5 ounces of raisins.” Here is a table that has been started to show how many ounces of almonds and raisins would be in different-sized batches of this trail mix.

  1. Complete the table so that ratios represented by each row are equivalent.

    almonds (oz)

    raisins (oz)

  2. What methods did you use to fill in the table?

  3. How do you know that each row shows a ratio that is equivalent to ? Explain your reasoning.

Are you ready for more?

Problem 1

You have created a best-selling recipe for chocolate chip cookies. The ratio of sugar to flour is .

Create a table in which each entry represents amounts of sugar and flour that might be used at the same time in your recipe.

  • One entry should have amounts where you have fewer than 25 cups of flour.

  • One entry should have amounts where you have between 20–30 cups of sugar.

  • One entry can have any amounts using more than 500 units of flour.

Lesson Summary

A table is a way to organize information. Each horizontal set of entries is called a row, and each vertical set of entries is called a column. (The table shown has 2 columns and 5 rows.) A table can be used to represent a collection of equivalent ratios.

Here is a double number line diagram and a table that both represent the situation: “The price is $2 for every 3 mangos.”

A double number line with 6 evenly spaced tick marks: For "price in dollars" the numbers 0, 2, 4, 6, 8, and 10 are indicated. For "number of mangos" the numbers 0, 3, 6, 9, 12, and 15 are indicated.
A 2-column table with 5 rows of data. First column is labeled "price in dollars" and the second column is labeled "number of mangos." The data is as follows: Row 1: 2, 3 Row 2: 4, 6 Row 3: 6, 9 Row 4: 8, 12 Row 5: 10, 15