Two pages of visual notes for students to keep: the key words with pictures, the two ways to solve any proportion, four solved problems in the style of the Proportional Plates game, and where proportions show up in real life. To make a PDF, click Print and choose "Save as PDF."

Visual Notes: Ratios and Proportions

Grades 6–7 · CCSS 7.RP.A.2 · Pairs with the Proportional Plates game

Name

Key vocabulary

Ratio

A comparison of two amounts: 2 : 4, 2 to 4, or 2/4.

Equivalent ratios

flour	2	6
pancakes	4	12

Ratios that make the same comparison: 2 : 4 = 6 : 12.

Rate

A ratio of two different units: $6 for 3 drinks.

Unit rate

The amount for 1: $6 ÷ 3 = $2 per drink.

Proportional relationship

Two amounts that always change by the same factor. Its graph is a straight line through 0.

Scale factor

4 × 3 → 12 pancakes

What every amount is multiplied by: 12 ÷ 4 = 3.

Constant of proportionality

y = kx

The unit rate k: $2 per drink means cost = 2 × drinks.

Two ways to solve a proportion (4 pancakes use 2 cups of flour. How much for 12?)

Method 1: Scale factor

pancakes	4	× 3 →	12
flour	2	× 3 →	6

12 ÷ 4 = 3, so multiply the flour by 3 too: 6 cups.

Method 2: Unit rate

pancakes	4	1	12
flour	2	½	6

Flour for 1 pancake: 2 ÷ 4 = ½ cup. Then ½ × 12 = 6 cups.

Solved Step by Step: In the Kitchen and at the Market

Visual Notes: Ratios and Proportions, page 2

1. Scale up a recipe

3 cups of flour make 12 cookies. How much flour for 36 cookies?

Scale factor: 36 ÷ 12 = 3
Multiply: 3 × 3 cups = 9 cups

✓ Check: 9 : 36 simplifies to 3 : 12

2. A fraction scale factor

4 lemons make 6 cups. How many lemons for 9 cups?

Scale factor: 9 ÷ 6 = 1½
Multiply: 4 × 1½ = 6 lemons

✓ Unit rate check: ⅔ lemon per cup × 9 = 6

3. The better deal

16 oz of cereal for $4.00, or 24 oz for $5.40?

Unit price A: $4.00 ÷ 16 = $0.25 per oz
Unit price B: $5.40 ÷ 24 = $0.225 per oz
B costs less per ounce: 24 oz is the better deal.

✓ Compare unit prices, not total prices

4. Is it proportional?

servings x	2	4	6
cups y	3	6	9

Divide each y by x: 3/2, 6/4, 9/6 all = 1.5
Same every time, so yes: y = 1.5x

✓ The graph is a straight line through (0, 0)

Watch out

Never add the difference. 4 pancakes use 2 cups; 12 pancakes is 8 more, but you need 6 cups, not 10.
Keep units lined up: pancakes over pancakes, flour over flour.
For “better deal” problems, find the price of one unit for each choice.

Where you see it in real life

Cooking: double the recipe, double every ingredient.

Drinks: the same mix tastes the same in any size pitcher.

Shopping: unit prices find the best deal.

Travel: miles per hour and cost per mile are rates.