Lesson 1 & 2 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.

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.

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

1 to 12

12:1

2 to 5

5 to 2

10:2

2:10

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.

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.

"to"

"for each"

"for every"

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).