Understand Proportional Relationships

Ratio

A ratio demonstrates a mathematical relationship between two quantities, and can be represented as a fraction, two numbers joined by a colon, or two numbers joined by the word “to.”

Multiple Choice

A Ratio is:

• A formula based on numbers.

• A comparison of two quantities.

• Values in an equation.

• Numbers found in groups.

Multiple Choice

If a baseball team won 70 games and lost 40 games, which one of the following ratios is representative of the number of games won to the number of games lost?

• 7:2

• 4:7

• 7:9

• 7:4

Equivalent Ratios

Two or more ratios with the same value

Multiple Choice

Equivalent means....

• very important

• one

• equal to

• to solve

Multiple Choice

Is this an example of an equivalent ratio?

• True

• False

Multiple Select

Find two equivalent ratios for 3 : 4 using multiplication

• 6 : 8

• 6 : 12

• 9 : 12

Multiple Select

Find two equivalent ratios for 12 : 18 using division

• 6 : 6

• 6 : 9

• 4 : 6

Multiple Choice

4. Reduce or Simplify $$\frac{6}{9}$$  

• 2/3

• 3/3

• 9/6

• 1/9

Multiple Choice

Express the following ratio in simplest form:

16:40

• 4:10

• 8:20

• 2:5

• 5:2

Multiple Choice

The recipe for a homemade glass cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. Elyse used 3 tablespoons of vinegar and 12 tablespoons of water to make the cleaner. ​

Did Elyse maintain the proportional relationship presented in the recipe? Explain.

• Yes

• No

Open Ended

The recipe for a homemade glass cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. Elyse used 3 tablespoons of vinegar and 12 tablespoons of water to make the cleaner. ​

Explain why you believe Elyse maintained the proportional relationship.

Multiple Choice

The recipe for a homemade glass cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. ​

Marcus mixed 1.5 cups of vinegar and 6 cups of water to make his cleaner.

Did Marcus maintain the proportional relationship presented in the recipe? Explain. ​

• Yes

• No

Open Ended

The recipe for a homemade glass cleaner indicates to use a ratio of 1 part vinegar to 4 parts water. ​

Marcus mixed 1.5 cups of vinegar and 6 cups of water to make his cleaner.

Explain why you believe Marcus maintained the proportional relationship.

Multiple Choice

One type of yarn costs $4 for 100 yards. Another type of yarn costs $5 for 150 yards. Is the relationship between the number of yards and the cost the same between the two types of yarn? Explain.  ​

• Yes

• No

Fill in the Blanks

Apply: Christine is building a deck in her backyard. In order to place the posts, she will make concrete using a mixture. The dry part of the mix requires 1 part cement to 2 parts sand to 3 parts gravel. The relationship between cement, sand, and gravel is proportional. If she has 25 pounds of cement and will use it all, how many pounds will the mix of cement, sand, and gravel weigh before she adds water to make the concrete?

Fill in the Blanks

Apply: A basic slime recipe calls for 1 part borax, 24 parts white glue, and 48 parts water. The relationship between borax, white glue, and water is proportional.

If Catalina has 3 tablespoons of borax and will use it all, how many cups of white glue will she need? (Hint: 1 cup = 16 tablespoons) ​

Open Ended

Have you ever wondered when you might use the concepts you learn in math class? What are some everyday scenarios in which you might use what you learned today?

Multiple Choice

Exit Ticket

Suppose one person used 2 parts blue paint to 3 parts yellow paint. Another person used 4 parts blue paint to 6 parts yellow paint. Do the ratios of blue paint to yellow paint form a proportional relationship? Explain. ​

• Yes

• No

Open Ended

Exit Ticket

Suppose one person used 2 parts blue paint to 3 parts yellow paint. Another person used 4 parts blue paint to 6 parts yellow paint.

Explain why the two rations of blue paint to yellow paint are proportional. ​

Multiple Choice

A specific shade of orange paint calls for 2 parts yellow and 3 parts red. Catie uses 3 cups of yellow paint and 4 cups of red paint to make orange paint.

Does this represent a proportional relationship?

• Yes

• No

Multiple Select

One blend of garden soil is 1 part minerals, 1 part peat moss, and 2 parts compost. Select all of the mixtures below that are in a proportional relationship with this blend.

• 5 ft³ minerals,

  5 ft³ peat moss,

  10 ft³ compost

• 10 ft³ minerals,

  15 ft³ peat moss,

  15 ft³ compost

• 12 ft³ minerals,

  12 ft³ peat moss,

  24 ft³ compost

• 20 ft³ minerals,

  20 ft³ peat moss,

  40 ft³ compost

• 50 ft³ minerals,

  50 ft³ peat moss,

  50 ft³ compost

Multiple Choice

A salad dressing calls for 3 parts oil and 1 part vinegar. Manuela uses 2 tablespoons of vinegar and 6 tablespoons of oil to make her salad dressing.

Does this represent a proportional relationship?

• Yes

• No

Fill in the Blanks

The pizza dough recipe shown makes one batch of dough. Charlie wants to make a half batch.

She has 1 cup of flour. How much more flour does she need?

Enter your answer as a number only.

Multiple Choice

A saltwater solution for an aquarium calls for 35 parts salt to 1000 parts water. Tareq used 7 tablespoons of salt and 200 tablespoons of water.

Does this represent a proportional relationship?

• Yes

• No

Multiple Choice

A conveyor belt moves at a constant rate of 12 feet in 3 seconds. A second conveyor belt moves 16 feet in 4 seconds.

Does this represent a proportional relationship?

• Yes

• No

Multiple Choice

A tectonic plate in Earth’s crust moves at a constant rate of 4 centimeters per year. In a different part of the world, another tectonic plate moves at a constant rate of 30 centimeters in ten years.

Does this represent a proportional relationship?

• Yes

• No

Multiple Choice

A strand of hair grows at a constant rate of  inch per month. A different strand of hair grows at a constant rate of 4 inches per year.

Does this represent a proportional relationship?

• Yes

• No

Open Ended

How can you use a unit rate to determine if a relationship is proportional?