Lesson 3: Determine Equivalent Ratios Using Tables6.AT.3a

I can…

I can use a ratio table to find equivalent ratios.

Key words

• Ratio Tables — Tables that organize pairs of equivalent ratios.
• Ratio table — A table of equal ratios that shows a pattern.
• Equivalent ratio — Two ratios that mean the same thing, like 1:2 and 2:4.
• Scale factor — The number you multiply both parts of a ratio by to get an equal ratio.
• Pattern — A rule that numbers follow again and again.
• Additive pattern — Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together.
• Equivalent ratios — Ratios that use different numbers but compare the same way.
• Simplify — Divide both terms of a ratio by the same number.
• Greatest common factor — The largest number that divides both terms evenly.

Steps

1. The pancake recipe is 2 cups of mix for every 3 cups of milk, so the ratio is 2:3.
2. To make 2 batches, my scale factor is 2.
3. I multiply both numbers by 2: 2 x 2 = 4 cups of mix, and 3 x 2 = 6 cups of milk.
4. Now my row is 4:6, which is the same ratio as 2:3.
5. I do NOT add 2 to each number; I multiply both by the same factor.

Try it

To make light blue paint, Maya mixes 3 cups of blue paint with every 7 cups of white paint. How many cups of blue paint does she need for 21 cups of white paint?

Check your answer

9

Scale factor: 21 ÷ 7 = 3. Multiply the blue paint by 3: 3 × 3 = 9 cups of blue paint.

Sentence starter

I know ___ because ___.

Goal: I can explain my table using the words ratio table, equivalent ratio, scale factor, and pattern.