Neft Teacher · Learn It

Unit 3 · Standard 6.AT.1

Understand Ratios

Lesson 3-1 · Learn It — how the math works

Why we're learning this

Welcome to Chef Academy! Head Chef Reyes is teaching new students how to read recipes like a pro. Her sparkling cranberry-apple fruit drink calls for 3 cups of apple juice for every 2 cups of sparkling water. Before the students can mix the drink, they need to understand how these ingredient amounts compare to each other.

✱ Math Workbench

Learn It

What is a ratio?

A ratio compares two amounts. It tells how much of one thing there is for another thing.

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

The recipe card shows the ingredients needed to make one batch of sparkling cranberry-apple fruit drink.
Where you see this in real lifeThe recipe card shows the ingredients needed to make one batch of sparkling cranberry-apple fruit drink.

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

The problem looks like this
A bar model comparing 3 parts of apple juice with 2 parts of sparkling water, a ratio of 3 to 2.apple juice sparkling water ratio = 3 : 2 For every 3 apple juice there are 2 sparkling water.
  1. Chef Reyes uses 3 cups of apple juice for every 2 cups of sparkling water.
  2. I am comparing two amounts: apple juice and sparkling water.
  3. I write apple juice to sparkling water, in that order, as 3 to 2, or 3:2.
  4. I can also draw the . On a I give apple juice 3 equal parts and sparkling water 2 equal parts, so one batch is 5 parts in all.
  5. Those same 5 parts show a second : apple juice to the whole fruit drink is 3 to 5.
  6. On a I line the two amounts up: 5 cups of fruit drink pairs with 3 cups of apple juice, and 10 cups of fruit drink pairs with 6 cups of apple juice.

Watch out — mistakes students make here

  • The order matters — what is named first should be first in the ratio.
  • Re-check: does this show a part being compared to the whole group?
  • 5 is the total number of cups, not the amount of cream. This compares the whole recipe to one part instead of milk to cream.

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

Same steps, new numbers.

  1. A bowl has 4 apples and 1 orange. What two amounts are we comparing?
  2. We write apples to oranges in order: 4 to 1, or 4:1.
  3. Now draw it: 4 equal parts for apples beside 1 part for oranges, 5 parts of fruit in all.
  4. So apples to total fruit is 4 to 5.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: a real compares two amounts, and the order matters.

Solve: A fruit salad has 5 pieces of melon, 3 pieces of pineapple, and 2 grapes. What is the of pineapple to melon?

My answer

Stuck? Open one hint at a time.

Hint 1

Three fruits are listed, but the question only compares pineapple and melon — the grapes are extra info.

Hint 2

Pick out just the two amounts you need, then write them in the order the question names: pineapple first.

Hint 3

Circle the pineapple count (3) and the melon count (5). Write them in the order 'pineapple to melon.'

Check my answer
✅ Answer: 3:5
The ratio of pineapple to melon compares pineapple (3) to melon (5), so the ratio is 3:5.

Turn & TalkSay it out loud with a partner

Chef Reyes's drink recipe uses 3 cups of apple juice for every 2 cups of sparkling water. How would you describe how these two ingredient amounts compare?

Try starting with:

  • The recipe compares ___ to ___.La receta compara ___ con ___.
  • For every ___ cups of apple juice there are ___ cups of sparkling water.Por cada ___ tazas de jugo de manzana hay ___ tazas de agua con gas.
Use these wordsRatioComparisonPart-to-part