Double Number Line for Modeling

Double Number Line for Modeling

Model With Mathematics

Opening

Model With Mathematics

  • Watch the first video, which introduces the problem in Protein Shake Mistake.
    • Can you explain what the problem is asking?
  • Then watch the second video, in which students use ratios to model the mathematics in the problem.
    • How did Carlos, Denzel, and Jan model the protein shake problem?
    • How did they adjust the model to determine the amount they needed?

VIDEO: Protein Shake Mistake

VIDEO: Model with Mathematics

Math Mission

Opening

Represent equivalent ratios on a double number line.

Stars to Triangles

Work Time

Stars to Triangles

Refer to the diagram and answer the following questions.

  • What is the ratio of the number of stars to the number of triangles?
  • What is the ratio of the number of triangles to the number of stars?

Ask yourself:

  • What does the first number in a ratio represent?
  • What does the second number in a ratio represent?

Sketch It!

Work Time

Sketch It!

Use the ratio of stars to triangles that you found in Task 3.

  • Sketch a set of objects that has the same ratio but not the same number of objects.
  • Show that the ratio that you made in your picture is equivalent to the ratio in task 3. Draw a double number line to show this; or, use the Double Number Line Tool.
  • On your double number line, find three pairs of numbers that represent the same ratio of stars to triangles.

Ask yourself:

  • In your diagram, what should the ratio of stars to triangles be equivalent to?
  • What pairs of numbers do you need to line up on your double number line?

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you made a set of stars and triangles that has the same ratio of stars to triangles as the ratio in the given diagram.

Show how you made a double number line that represents equivalent ratios of stars to triangles.

Suppose you find the difference between the number of stars and triangles in the original set. Explain why making a set of stars and triangles with the same difference will not result in sets with equivalent ratios.

Challenge Problem

Find the difference between each pair of aligned numbers on your double number line.

  • What do you observe about the differences?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates' strategies for making sets of stars and triangles and for representing equivalent ratios on a double number line.

As your classmates present, ask questions such as:

  • What is the ratio in your diagram?
  • Why is this ratio equivalent to the ratio in the given diagram?
  • How do you know that the ratios on your double number line are equivalent?
  • Can you give an example of sets of stars and triangles that have the same difference but not equivalent ratios?

Find Equivalent Ratios

Work Time

Find Equivalent Ratios

  • The ratio 15:20 is equivalent to the ratio 3:4. Explain why and make a double number line to support your explanation.
  • Express each of these ratios as a fraction in simplest form:
    1. 14:35
    2. 15:18
    3. 26:39
  • Show the ratio 2:3 and three other equivalent ratios on a double number line.
  • The ratio 2:5 can be expressed as the decimal 0.4. Explain why.

Ask yourself:

  • When you make a double number line, what pairs of numbers do you need to line up?
  • What operation do you use to express a ratio as a decimal?

Overview of Equivalent Ratios

Formative Assessment

Summary of the Math: Overview of Equivalent Ratios

Read and Discuss

  • A ratio is often represented as a pair of numbers, either in colon notation (280:210 or 4:3) or as a fraction (280210=43).
  • You can determine whether two ratios are equivalent in the following way:
    The ratios 2:3 and 4:6 are equivalent if 23=46.
  • You can represent equivalent ratios using a double number line. A double number line shows the relationship between two quantities by lining up the quantities at the same tick marks. Each of these pairs of numbers represents a ratio, and all of the ratios on a given double number line are equivalent; that is, the ratios all have the same value.

Can you:

  • Find equivalent ratios?
  • Represent equivalent ratios on a double number line?

Reflect On Your Work

Work Time

Reflection

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

The double number line helps me understand equivalent ratios because ...