Writing Ratios

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Objective

SWBAT understand ratios and what they represent.

Big Idea

What are the different ways we can write ratios?

Introduction to Ratios

15 minutes

I will lead the class through a series of exercises that will be used to explain what ratios are.  For each exercise, I will ask the class "What are the two things being compared?"

1 - I will select 4 boys and 3 girls to stand at the front of the class.

2- I will give each group 7 red blocks and 2 green blocks.

3 - I will ask students who have a dog to stand on one side of the room and students who have a cat to stand on the other side of the room.

 

I will explain to the class:

Each situation we saw represented a ratio.  How would you define a ratio?

After hearing from students, I will give them a formal definition of ratio.

Ratio - a comparison of two numbers by division

Lesson

15 minutes

This lesson will focus on the various ways that ratios can be written and interpreted.  I will lead students through a couple of examples using a Think-Pair-Share strategy.  With this strategy students will take a few minutes to individually think about the questions, discuss it with a partner (or group), and then we will discuss it as a class.

Example 1 (Writing Ratios - Example 1)

The coed basketball league has five times as many boys on it as girls.  What is the ratio of boys to girls?  How can the ratio be written?

As we discuss the example as class, most students will have reached the comparison of five to one.  I will introduce the different ways of writing this ratio.

  • We can write ratios using a colon symbol.         5 : 1
  • We can write ratios using the word "to"             5 to 1
  • We can write ratios using fractional notation.     5/1
  • We can write a ratio using words "For every…"            For every 5 boys, there is 1 girl.

I will also show students how this ratio can be represented visually through a ratio table and tape diagram.  These will be used more in later lessons.

 

Example 2

What is the ratio of boys to girls in the class?  Choose 3 different ways of representing this ratio.

Students will be given 5 minutes to work on the question independently. Then I will randomly call students to the board to show how they wrote the ratio.

Group Work

10 minutes

To assess students' understanding of writing ratios, they will be given the following group work.  

 

Group Work

Describe a situation that represents each ratio below.  Think about real life examples!  

Example:   1 : 2    Possible ratio relationship. For every 1 grade in the school, there are 2 classes. 

1)1 : 12

2)2 : 48

3)5 : 2

4)8: 1

 After 10 minutes, I will ask students to share their answers.

Possible Answers

1)  For every 1 carton there are 12 eggs.

2)  For every 2 days there are 48 hours.

3)  For ever 5 weekdays there are 2 days in the weekend.

4)  For every 8 periods there is 1 day.

Lesson Summary

5 minutes

For the lesson summary, I want students to begin thinking about equivalent ratios.  I will pose questions to the class to lead them into a discussion.

Can ratios be scaled up or down?  Can you give an example using one of the ratios from today's lesson?

Students should discuss that since ratios are fractions, they can be scaled up or down to find equivalent ratios.  (Look for MP3)