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Lesson 7: Creating Double Number Line Diagrams

Learning Target: I can create a double number line diagram and correctly place and label tick marks to represent equivalent ratios.

Unit 2: Introducing Ratios

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There are 3 milliliters of yellow water for every 1 milliliter of blue water.
There are 3 milliliters of yellow water per milliliter of blue water.

Activity 7.2: Just a Little Green

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In Activity 7.2, we explored how to to use double number lines to find how many milliliters of yellow water per 1 milliliter of blue water. As we know that there are 15 ml of yellow water for every 5 ml of blue water, we can use division 15 ÷ 5 to show that for every 1 ml of blue water there are 3 ml of yellow water.

Teacher Action: Complete the two double number lines by putting in the tick marks in the correct places. Then label them with the correct number starting with 1 ml blue water corresponding to 3 ml of yellow water. Then 2 ml of blue water to 6 ml of yellow water.

Let’s describe the ratio we see in this situation.

*Click to reveal sentence.

There are 3 milliliters of yellow water for every 1 milliliter of blue water.

*Click to reveal sentence.

The word per means “for every.” This is the same as saying there are 3 milliliters of yellow water per milliliter of blue water.

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The word per means “for each.”

For example, if the price is $5 per ticket, that means you will pay $5 for each ticket.

4 tickets would cost $20, because 4 • 5 = 20.

Vocabulary: Per

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Guidelines for drawing a double number line diagram:

The two parallel lines should have labels.
The tick marks and numbers should be spaced equally.
Numbers that line up vertically make equivalent ratios.

Creating Double Number Line Diagrams

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The ratio of the number of eggs to cups of milk in a recipe is 4 : 1.

Creating Double Number Line Diagrams

This recipe uses 4 eggs per cup of milk.

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Let’s put those guidelines to action. The ratio of the number of eggs to cups of milk in a recipe is 4 : 1. We can create a double number line using this information.

Teacher Action: Label the top line eggs and the bottom line cups of milk. Add tick marks on each line that you label 0 and 0 and 4 and 1.

Let’s add some additional tick marks to see how we could make more batches of this same recipe.

Embedded Question (Multiple Choice): How many eggs and cups of milk would we need to double the recipe?

Teacher Action: Add more tick marks to each line and label 8 and 2.

We could double the recipe with 8 eggs and 2 cups of milk. We multiplied each number by 2.

To triple the original recipe, we could multiple each number in the original recipe by 3.

Teacher Action: Add more tick marks to each line and label 12 and 3.

Embedded Question (Multiple Choice): How many eggs would we need to create a recipe that tastes the same if we use 4 cups of milk?

*Click to reveal sentence.

We can also say that this recipe uses “4 eggs per cup of milk” because the word per means “for each.”

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This slide deck was created by Modern Classrooms Project in 2024. It was adapted from the IM K–8 Math™ curriculum authored by Illustrative Mathematics^®.

Curriculum excerpts are used under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, copyright 2017-2019 Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0), including its disclaimer of warranties. OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0), including its disclaimer of warranties.