Lesson 1Introducing Ratios and Ratio Language

Learning Goal

Let’s describe two quantities at the same time.

Learning Targets

  • I can write or say a sentence that describes a ratio.

  • I know how to say words and numbers in the correct order to accurately describe the ratio.

Lesson Terms

  • ratio

Warm Up: What Kind and How Many?

Problem 1

Figures made up of squares. The figure is either red, green, yellow, or blue. There are differing amounts of squares and shapes.

Think of different ways you could sort these figures. What categories could you use? How many groups would you have?

Activity 1: The Teacher’s Collection

Problem 1

  1. Think of a way to sort your teacher’s collection into two or three categories. Count the items in each category, and record the information in the table.

    category name

    category amount

    Pause here so your teacher can review your work.

  2. Write at least two sentences that describe ratios in the collection. Remember, there are many ways to write a ratio:

    • The ratio of one category to another category is to .

    • The ratio of one category to another category is : .

    • There are of one category for every of another category.

Activity 2: The Student’s Collection

Problem 1

  1. Sort your collection into three categories. You can experiment with different ways of arranging these categories. Then, count the items in each category, and record the information in the table.

    category name

    category amount

  2. Write at least two sentences that describe ratios in the collection. Remember, there are many ways to write a ratio:

    • The ratio of one category to another category is to .

    • The ratio of one category to another category is : .

    • There are of one category for every of another category.

    Pause here so your teacher can review your sentences.

  3. Make a visual display of your items that clearly shows one of your statements. Be prepared to share your display with the class.

Are you ready for more?

Problem 1

  1. Use two colors to shade the rectangle so there are 2 square units of one color for every 1 square unit of the other color.

    A 4 by 6 grid of squares.

  2. The rectangle you just colored has an area of 24 square units.

    Draw a different shape that does not have an area of 24 square units, but that can also be shaded with two colors in a ratio. Shade your new shape using two colors.

    A 4 by 6 grid of squares.

Lesson Summary

A ratio is an association between two or more quantities. There are many ways to describe a situation in terms of ratios. For example, look at this collection:

A discrete diagram of squares and circles such that the top row contains 6 squares and the bottom row contains 3 circles.

Here are some correct ways to describe the collection:

  • The ratio of squares to circles is .

  • The ratio of circles to squares is 3 to 6.

Notice that the shapes can be arranged in equal groups, which allow us to describe the shapes using other numbers.

A discrete diagram of 6 squares and 3 circles organized into 3 equal groups of 2 squares and 1 circle each.

  • There are 2 squares for every 1 circle.

  • There is 1 circle for every 2 squares.