Lesson 1 & 2 Ratios

Lesson 1 & 2 Ratios (6.RP.A.1, 6.RP.A.3a)

Ms. Dewey

Eureka Math

Lesson 1 Ratios

• A ratio is always a pair of numbers, such as 2: 3.

• It is never a pair of quantities such as 2 cm: 3 sec.

•  Statements about quantities in word problems that define ratios are ratio relationship descriptions.

Student Outcomes

• Students understand that a ratio is an ordered pair of numbers which are not both zero. Students understand that a ratio is often used instead of describing the first number as a multiple of the second. 

• Students use the precise language and notation of ratios (e.g., 3: 2, 3 to 2). Students understand that the order of the pair of numbers in a ratio matters and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio.

Multiple Choice

A ratio is always a pair of quantities.

• True

• False

Multiple Choice

A ratio relationship defines quantities in a word problem.

• True

• False

Multiple Choice

A ratio is always a pair of numbers.

• True

• False

Multiple Select

The ratio for 3 cups to 4 cups is.

• 3:2

• 3:4

• 4:3

• 3 to 4

Multiple Select

The ratio for 5 miles in 4 hours is.

• 5:3

• 5:4

• 4:5

• 5 to 4

Tape Diagram

• A diagram that uses rectangles to represent the parts of a ratio.

• Visual representations that represent the sections of a ratio by using rectangles.

• It is a graphic tool used commonly in solving ratio-based mathematical word problems.

Tape Diagram Example

Cameron has 5 shirts and 1 baseball cap. The multiplicative comparison is Cameron has 5 times as many shirts as he has baseball caps. This can be represented with a tape diagram:

Create a tape diagram representing the ratio of 3 boys to 2 girls on the team.

Ratio Table

• A structured list of equivalent (equal value) ratios that helps us understand the relationship between the ratios and the numbers.

• Shows pairs of corresponding values, with an equivalent ratio between each pair.

Ratio Table Example

The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of boys to the number of girls on the team is 𝟒:𝟏. We read this as four to one.

Using a Ratio Table, what are some other ratios that show four times as many boys as girls of 4 to 1?

Multiple Choice

A ratio is always a pair of numbers.

• True

• False

Multiple Choice

A diagram that uses rectangles to represent the parts of a ratio is a

• Ratio Table

• Tape Graph

• Tape Diagram

• Table Diagram

Multiple Choice

A diagram that shows pairs of corresponding values, with an equivalent ratio between each pair.

• Ratio Table

• Tape Graph

• Tape Diagram

• Table Diagram

Multiple Choice

Is it ok to use either the colon symbol or the word to between the two numbers of the ratio.

• Yes, period

• No, never

Multiple Choice

Do the ratio itself does not have units or descriptive words attached.

• Yes, period

• No, never

Stand If...

• You traveled out of state this summer. 

• You did not travel out of state this summer.

• You have at least one sibling. 

• You are an only child.

• Your favorite class is math.

• Your favorite class is not math.

• Your favorite teacher is Ms. Dewey

Describe a ratio relationship that represents each ratio

• 1 to 12

• 12:1

• 2 to 5

• 5 to 2

• 10:2

• 2:10

Lesson Summary

• A ratio is an ordered pair of numbers, which are not both zero.

• A ratio is denoted 𝑨:𝑩 to indicate the order of the numbers—the number 𝑨 is first and the number 𝑩 is second.

• The order of the numbers is important to the meaning of the ratio. Switching the numbers changes the relationship.

• The description of the ratio relationship tells us the correct order for the numbers in the ratio.

• Ratios can be modeled using a tape diagram or a ratio table.

• A tape diagram uses rectangles to represent the parts of a ratio.

• A ratio table shows pairs of corresponding values, with an equivalent ratio between each pair.

Lesson 2: Ratios

Student Outcomes

• Students reinforce their understanding that a ratio is an ordered pair of nonnegative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (e.g., 3: 2, 3 to 2). Students demonstrate their understanding that the order of the pair of numbers in a ratio matters.

• Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio.

Exercise 1

Come up with two examples of ratio relationships that are interesting to you.

Example 1: My brother watches twice as much television as I do. The ratio of number of hours he watches in a day to the number of hours I watch in a day is usually 2:1.

Example 2: For every 𝟐 chores my mom gives my brother, she gives 𝟑 to me. The ratio is 𝟐:3.

Verbal Cues for Describing Ratio Relationships

• "to"

• "for each"

• "for every"

Exploratory Challenge

A T-shirt manufacturing company surveyed teenage girls on their favorite T-shirt color to guide the company’s decisions about how many of each color T-shirt they should design and manufacture. The results of the survey are shown here. 

Open Ended

Give a ratio relationship for 4:3

Open Ended

Give a ratio relationship 3 to 4

Open Ended

Give a ratio relationship 19:7

Open Ended

Give a ratio relationship 7 to 26

Lesson Summary

• Ratios can be written in two ways: 𝐴 to 𝐵 or 𝐴:B

• We describe ratio relationships with words, such as to, for each, for every

• The ratio 𝐴:𝐵 is not the same as the ratio 𝐵:𝐴 (unless 𝐴 is equal to 𝐵).