Lesson 1Introducing Ratios and Ratio Language

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.

1.1 What Kind and How Many?

  1. If you sorted this set by color, how many groups would you have?
  2. If you sorted this set by area, how many groups would you have?
  3. Think of a third way you could sort these figures. What categories would you use? How many groups would you have?

1.2 The Teacher’s Collection

  1. Think of a way to sort your teacher’s collection into two or three categories. Record your categories in the top row of the table and the amounts in the second row.
    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.

1.3 The Student’s Collection

  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?

  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.
  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 2:1 ratio. Shade your new shape using two colors.

A 4 by 6 grid of squares.

Lesson 1 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 6:3 .
  • 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.

Glossary Terms

ratio

A ratio is an association between two or more quantities.

For example, the ratio 3:2 could describe a recipe that uses 3 cups of flour for every 2 eggs, or a boat that moves 3 meters every 2 seconds. One way to represent the ratio 3:2 is with a diagram that has 3 blue squares for every 2 green squares.

Lesson 1 Practice Problems

  1. In a fruit basket there are 9 bananas, 4 apples, and 3 plums. 

    1. The ratio of bananas to apples is ________  ________.
    2. The ratio of plums to apples is ________ to ________.
    3. For every ________ apples, there are ________ plums.
    4. For every 3 bananas there is one ________.
  2. Complete the sentences to describe this picture.

    4 cats and 3 dogs.
    1. The ratio of dogs to cats is _______.
    2. For every _____ dogs, there are _____ cats.
  3. Write two different sentences that use ratios to describe the number of eyes and legs in this picture.

    "A hippopotamus with 2 eyes and 4 legs and a giant turtle with 2 eyes and 4 legs."
  4. Choose an appropriate unit of measurement for each quantity.

    1. area of a rectangle
    2. volume of a prism
    3. side of a square
    4. area of a square
    5. volume of a cube
    • cm
    • cm3
    • cm2
  5. Find the volume and surface area of each prism. 

    1. Prism A: 3 cm by 3 cm by 3 cm
    A cube whose length, width, and height are each 3 centimeters.
    1. Prism B: 5 cm by 5 cm by 1 cm
    1. Compare the volumes of the prisms and then their surface areas. Does the prism with the greater volume also have the greater surface area?

  6. Which figure is a triangular prism? Select all that apply.