Neft Teacher · Learn It

Unit 3 · Standard 6.AT.3a

Determine Equivalent Ratios Using Tables

Lesson 3-3 · Learn It — how the math works

Why we're learning this

Brian will use the recipe shown to make clay. He needs to make multiple batches of clay. How can Brian determine how much baking soda and cornstarch he needs for multiple batches of clay to get the same consistency?

✱ Math Workbench

Learn It

How do ratio tables work?

A ratio table lists equal ratios in rows. To make a new row, you multiply BOTH numbers by the same amount, called the scale factor.

Picture itSee what the math looks like before you read about it

Brian will use the recipe shown to make clay, and he needs to make several batches. Every batch has to come out with the same consistency.
Where you see this in real lifeBrian will use the recipe shown to make clay, and he needs to make several batches. Every batch has to come out with the same consistency.

Watch me solve itI do — read one step at a time

The problem looks like this
A bar model comparing 2 parts of mix with 3 parts of milk, a ratio of 2 to 3.mix milk ratio = 2 : 3 For every 2 mix there are 3 milk.
  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 is 2.
  3. I multiply both numbers by 2: 2 x 2 = 4 cups of mix, and 3 x 2 = 6 cups of milk.2 x 2 = 4
  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.

Watch out — mistakes students make here

  • Check the scale factor: 5 × ? = 20, then apply it to the oil.
  • Recompute the scale factor from vinegar and apply it to 2.
  • 10 doesn't come from scaling the butter. Find the factor with 12 ÷ 3, then apply it to the 2.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. A drink uses 1 cup of juice for every 4 cups of water, so the ratio is 1:4.
  2. To double it, what do we use?
    Check this step
    We use 2.
  3. Multiply both by 2: 1 x 2 = 2 cups of juice and 4 x 2 = 8 cups of water, giving 2:8.1 x 2 = 2

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Multiply both numbers by the same for each row.

Solve: In a , the ratio of sugar to butter is 3:2. If you use 12 cups of sugar, how many cups of butter do you need?

My answer

Stuck? Open one hint at a time.

Hint 1

The sugar grew from 3 cups to 12 cups. The butter has to keep up with the same jump.

Hint 2

Divide the new sugar by the recipe's sugar to find the scale factor, then multiply the butter (2 cups) by it.

Hint 3

Divide 12 ÷ 3 to get the scale factor — then multiply 2 cups of butter by that number.

Check my answer
✅ Answer: 8
Scale factor: 12 ÷ 3 = 4. Multiply butter by 4: 2 × 4 = 8 cups of butter.

Turn & TalkSay it out loud with a partner

The clay recipe uses 2 cups of baking soda for every 1 cup of cornstarch. If Brian doubles the batch, what happens to each ingredient — and what stays the same?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsRatio TablesRatio tableEquivalent ratioScale factorPattern