Comparing Numbers with Ratios

Comparing Numbers with Ratios

Introduction to Ratios

Opening

Introduction to Ratios

Look at the picture of stars and triangles and read the following information.

  • One way that you can compare the number of stars and the number of triangles is to say that there are 7 more stars than there are triangles. This comparison looks at the difference between two quantities; it uses the operation of subtraction.
  • Another way that you can compare the number of stars and the number of triangles is to say that for every 3 triangles there are 10 stars. You can say that the ratio of triangles to stars is 3 to 10 or 3:10. This comparison uses the operation of division.
  • The value of the ratio of triangles to stars is 310, or 0.3.

Ratio of Egginess

Opening

Ratio of Egginess

A ratio is a comparison of two numbers by division.

The value of a ratio is the quotient that results from dividing the two numbers. For example, the value of the ratio 35:7 is 5, which you find by computing 35 ÷ 7 = 5.

In the previous lesson, you looked at how to fix the egginess in a mixture. Watch the Egginess
Part 2 video.

  • What is the ratio in the egginess problem?

VIDEO: Egginess Part 2

Math Mission

Opening

Explain how ratios are used to compare quantities.

Ms. Lee’s Class

Work Time

Ms. Lee's Class

There are 15 boys and 17 girls in Ms. Lee's math class.

  • What is the difference between the number of girls and the number of boys in the class?
  • What is the ratio of boys to girls?
  • What is the ratio of girls to boys?

Ask yourself:

  • When you need to find the difference between two numbers, what operation do you use?
  • For the ratio of boys to girls, what should the first number be, ”the number of girls or the number of boys?
  • For the ratio of girls to boys, what should the first number be, the number of girls or the number of boys

A Tennis Game

Work Time

A Tennis Game

The ratio of the number of females watching a tennis game to the number of males watching the tennis game is 3 to 2. You can write that as 32, or 3:2.

  • Can you tell from this ratio how many females are watching the tennis game? Explain.
  • Can you tell from this ratio how many people are watching the tennis game? Explain.
  • Can you tell from this ratio whether more males or more females are watching the game? Explain.
  • Can you tell from this ratio the difference between the number of males and the number of females watching the game? Explain.
  • Could you use this ratio to write the ratio of the number of males watching the tennis game to the number of females watching the tennis game? Explain.

Ask yourself:

  • Sketch a diagram showing several possible numbers of females and males watching the game. Can you tell which numbers are correct based on the ratio?
  • In looking at a ratio, how can you tell which number represents the larger amount?
  • What would you need to know to find the difference between the number of males and females watching the game?
  • In determining whether the ratio can be rewritten to represent males to females, think about the definition of a ratio.

Prepare a Presentation

Work Time

Prepare a Presentation

Explain what types of conclusions you can and cannot make based on the tennis game ratio.

In your own words, explain what a ratio is.

Challenge Problem

As two quantities get closer to each other, the value of the ratio of the quantities approaches 1.

  • Is the above statement always true, sometimes true, or never true? Explain.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates' explanations of the conclusions that can and cannot be made based on the tennis game ratio, and their explanations of what a ratio is.

As your classmates present, ask questions such as:

  • What possible numbers of females and males watching the tennis game did you find?
  • How did you determine these numbers?
  • How did you decide what types of conclusions you can and cannot make based on the tennis game ratio?
  • Is there anything you can add to your explanation to make it more specific or precise?

What I Know about Ratios

Formative Assessment

Summary of the Math: What I Know about Ratios

Write a summary of what you learned about ratios.

Check your summary.

  • Do you explain what a ratio is?
  • Do you discuss what types of conclusions can and cannot be made based on a ratio?
  • Do you explain how using ratios to compare two numbers is different from using subtraction to compare two numbers?

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.

Something I wonder about ratios is …