Lesson 3Defining Equivalent Ratios

Learning Goal

Let’s investigate equivalent ratios some more.

Learning Targets

  • If I have a ratio, I can create a new ratio that is equivalent to it.

  • If I have two ratios, I can decide whether they are equivalent to each other.

Lesson Terms

  • equivalent ratios

Warm Up: Dots and Half Dots

Problem 1

Dot Pattern 1:

(Tactile is recommended for this image) An image of dots arranged in groups. There are 6 groups of 9 dots arranged in a 3 by 3 square pattern.

Dot Pattern 2:

(A tactile is recommended for this image.) An image of half-dots arranged in columns and rows. There are 6 columns of 7 half-dots.

Activity 1: Tuna Casserole

Here is a recipe for tuna casserole.

Ingredients

  • 3 cups cooked elbow-shaped pasta

  • 6 ounce can tuna, drained

  • 10 ounce can cream of chicken soup

  • 1 cup shredded cheddar cheese

  • cups French fried onions

A picture of a cooked tuna casserole.

Instructions

Combine the pasta, tuna, soup, and half of the cheese. Transfer into a 9-inch-by-18-inch baking dish. Put the remaining cheese on top. Bake 30 minutes at 350 degrees. During the last 5 minutes, add the French fried onions. Let sit for 10 minutes before serving.

Problem 1

What is the ratio of the ounces of soup to the cups of shredded cheese to the cups of pasta in one batch of casserole?

Problem 2

How much of each of these 3 ingredients would be needed to make:

  1. twice the amount of casserole?

  2. half the amount of casserole?

  3. five times the amount of casserole?

  4. one-fifth the amount of casserole?

Problem 3

What is the ratio of cups of pasta to ounces of tuna in one batch of casserole?

Problem 4

How many batches of casserole would you make if you used the following amounts of ingredients?

  1. 9 cups of pasta and 18 ounces of tuna?

  2. 36 ounces of tuna and 18 cups of pasta?

  3. 1 cup of pasta and 2 ounces of tuna?

Are you ready for more?

Problem 1

The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold:

  1. Twice the amount of casserole

  2. Half the amount of casserole

  3. Five times the amount of casserole

  4. One-fifth the amount of casserole

Activity 2: What Are Equivalent Ratios?

Problem 1

The ratios and are equivalent ratios.

  1. Is the ratio equivalent to these? Explain your reasoning.

  2. Is the ratio equivalent to these? Explain your reasoning.

  3. Give two more examples of ratios that are equivalent to .

  4. How do you know when ratios are equivalent and when they are not equivalent?

  5. Write a definition of equivalent ratios.

    Pause here so your teacher can review your work and assign you a ratio to use for your visual display.

  6. Create a visual display that includes:

    • the title “Equivalent Ratios”

    • your best definition of equivalent ratios

    • the ratio your teacher assigned to you

    • at least two examples of ratios that are equivalent to your assigned ratio

    • an explanation of how you know these examples are equivalent

    • at least one example of a ratio that is not equivalent to your assigned ratio

    • an explanation of how you know this example is not equivalent

    Be prepared to share your display with the class.

Lesson Summary

All ratios that are equivalent to can be made by multiplying both and by the same number.

For example, the ratio is equivalent to because both 9 and 6 are multiplied by the same number: 2.

A diagram for a ratio. At the top, the expression 9:6 is indicated. Directly below it, the expression 18:12 is indicated. Two arrows are drawn, one starting at 9 and pointing to 18 and the other starting at 6 and pointing to 12. On the left of the first arrow, multiplied by 2 is labeled and to the right of the second arrow, multiplied by 2 is labeled.

is also equivalent to , because both 9 and 6 are multiplied by the same number: .

A diagram like the last except the sides are show multiplied by one-third and the bottom ratio is 3:2

Is equivalent to ?

No, because 18 is , but 15 is not .

A diagram like the last but the bottom ratio is 18:15 with the left side being multiplied by 2, but the word "Nope" written on the right