Representing Ratios with Diagrams

Warmup

Activity #1

Create Ratios.

Use the applet below to create ratios using squares and circles.

• The activity starts with 10 circles and 2 squares. This is alo displayed in two columns A and B on the left.
• Slowly move the slider to the right to create two rows. Notice how many circles and squares are now displayed both in pictures and in numbers.
• Continue adding the rows in step-wise manner; 3, 4, 5, …….and noting the ratio of circles to squares. ​

Activity #2

Interpret Diagrams.

In this activity, you are going to match ratios to diagrams that represent them. Read the descriptions carefully and match them with their corresponding diagram.

The applet below describes different recipes for spaghetti sauce. In the diagrams:

• a circle represents a cup of tomato sauce
• a square represents a tablespoon of oil
• a triangle represents a teaspoon of oregano

• Drag the sentences or use the tools to match the sentence to the diagram.

• Answer the questions below.

(4.) Select one of the other diagrams and invent another sentence that could describe the ratio shown in the diagram.

Activity #3

Create a Ratio Diagram.

In the exercise below, you are going to create a ratio diagram that comprises 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds. 

• Create a diagram to represent the quantities of each ingredient in this recipe.

• Answer the questions below.

(1.) Use your diagram to complete each sentence.

The ratio of __________________ to __________________ to __________________ is ________ : ________ : ________.

(2.) To make a snack mix, combine 2 cups of raisins with 4 cups of pretzels and 6 cups of almonds. Use your diagram to complete each sentence.

(a.) There are ________ cups of pretzels for every cup of raisins.

(b.) There are ________ cups of almonds for every cup of raisins.

(c.) A square is 3 inches by 3 inches. What is its area?

(d.) A square has a side length of 5 feet. What is its area?

(d.) The area of a square is 36 square centimeters. What is the length of each side of the square?

Challenge #1

Elena mixed 2 cups of white paint with 6 tablespoons of blue paint. Here is a diagram that represents this situation.

Challenge #2

Here is a diagram that describes the cups of green and white paint in a mixture.

Challenge #3

If 30 kids in the class like grape juice, how many kids like pineaple juice?