Use Ratio Language in Context

Students practice reading and writing ratio statements from real-world situations and descriptions. They describe relationships using phrases such as 'for every,' 'for each,' and 'per,' and connect these phrases to the corresponding ratio notation.

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Grade 6 · Ratios and Rates · question 1 of 3

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20 rungs. A star at the top.

On a library shelf, 4 out of every 5 books are mysteries. The shelf holds 15 books. How many of the books are mysteries?

How it is taught

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A ratio compares two quantities in order.

For every some of one, there are some of the other.

The total is all the equal parts added together.

Read it: Equal ratios in a table

3 adults for every 8 children. The table keeps that ratio in every column: 6 to 16, 9 to 24, 12 to 32. Each column is 3 : 8 times a number.

Put the ratio in the first column: 3 adults over 8 children.
Find the factor: 12 adults is 3 adults × 4.
Multiply the other row by the same factor: 8 × 4 = 32 children.

Every column is the first column times a number, so each one keeps the ratio 3 : 8.

Multiplying both terms by 4 makes 4 groups of 3 adults and 8 children: 12 adults, 32 children.

Dividing both terms by the same number works the other way: 12 : 32 = 3 : 8.

Equal ratios multiply or divide both terms by the same number; they never add the same number.

Adding 9 to both terms and writing 3 : 8 = 12 : 17.

12 is 3 × 4, so the other term is 8 × 4 = 32: 3 : 8 = 12 : 32.

13 : 18 = 39 : ___ — 54. 39 is 13 × 3, so the other term is 18 × 3 = 54.

Lemonade recipe: 2 cups lemon juice for every 5 cups water

Sam is mixing lemonade. Let's describe his recipe using ratio language.

For every 2 cups of lemon juice he pours...

...he adds 5 cups of water.

We say it like this: for every 2 cups of lemon, there are 5 cups of water.

We can write that ratio with a colon — two to five.

Or in words: the ratio of lemon to water is 2 to 5.

Grade 6 · Describing a real-world ratio three different ways

We can also write it like a fraction — two over five — meaning 2 lemon parts for every 5 water parts.

And 'per' means the same idea: 5 cups of water per 2 cups of lemon.

Order matters! Lemon to water is 2 to 5, not 5 to 2. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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