Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.3The Bridge Strategy (Scaling Ratios)

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use a ratio table to find equivalent ratios.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Ratio TablesSpanish: Tablas de razones Tables that organize pairs of equivalent ratios. 2:3, 4:6, and 6:9 belong in the same ratio table.
Ratio tableSpanish: Tabla de razones A table of equal ratios that shows a pattern. Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9
Equivalent ratioSpanish: Razón equivalente Two ratios that mean the same thing, like 1:2 and 2:4. 2:3 = 4:6 = 6:9
Scale factorSpanish: Factor de escala The number you multiply both parts of a ratio by to get an equal ratio. 2:3 × 2 → 4:6 (scale factor is 2)
PatternSpanish: Patrón A rule that numbers follow again and again. Each row adds 2 cups juice and 3 cups water
Additive patternSpanish: Patrón aditivo Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together. 2:3 → 4:6 → 6:9 (add 2 and 3 each time)

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A trail mix uses 6 cups of nuts for every 8 cups of raisins. How many cups of raisins go with 15 cups of nuts?

  1. 6 × a whole number never equals 15.
  2. Bridge down: 6 : 8 ÷ 2 = 3 : 4.
  3. Scale up: 3 : 4 × 5 = 15 : 20.

Answer: 20 cups of raisins

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I simplified : by dividing by .
  • The bridge ratio is : .
  • I multiplied the bridge by to reach .
  • It is called a bridge because .

Word bank bridgesimplifygreatest common factordividemultiplyboth termstargetreachmiddle stepsame numberscale

Watch out!A common mistake

A common mistake in Ratio Tables is scaling only ONE part of the ratio, or adding the scale factor to a part instead of multiplying by it

Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.3The Bridge Strategy (Scaling Ratios)

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can use a ratio table to find equivalent ratios.

  1. 1Complete each step, then write the final answer.
    Oats (cups)15Milk (cups)3?× ?× ?

    A recipe uses 1 cup of oats for every 3 cups of milk. How much milk goes with 5 cups of oats?

    Show your work

    Hint The scale factor is 5. Multiply the milk by 5.

    Final answer:
  2. 2Complete each step, then write the final answer.
    Red beads28White beads5?× ?× ?

    A bracelet has 2 red beads for every 5 white beads. How many white beads go with 8 red beads?

    Show your work

    Hint What number times 2 makes 8? Multiply the white beads by that number.

    Final answer:
  3. 3Complete each step, then write the final answer.
    Crackers2?Cheese slices16× ?× ?

    A snack uses 2 crackers for every 1 slice of cheese. How many crackers go with 6 slices of cheese?

    Show your work

    Hint The scale factor is 6. Multiply the crackers by 6.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.3The Bridge Strategy (Scaling Ratios)

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can use a ratio table to find equivalent ratios.

  1. 1Circle the letter of the best answer. Show how you know.
    Rice (cups)3?Water (cups)4?× ?× ?

    A ratio table starts with 3 cups of rice for every 4 cups of water. Raj adds 2 to each number and writes 5:6. Which row really belongs in the table?

    1. A9:12
    2. B5:6
    3. C6:7
    4. D4:5
    Show your work
  2. 2Complete each step, then write the final answer.
    Boxes417Pens12??÷ ?÷ ?× ?× ?

    A ratio table shows 12 pens for every 4 boxes. How many pens are in 7 boxes?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.
    Eggs3?Milk (cups)210× ?× ?

    A recipe uses 3 eggs for every 2 cups of milk. How many eggs go with 10 cups of milk?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.3The Bridge Strategy (Scaling Ratios)

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can use a ratio table to find equivalent ratios.

  1. 1Circle the letter of the best answer. Show how you know.

    A ratio table pairs 3 cups of flour with 2 cups of water. If the recipe is scaled to use 12 cups of flour, how much water is needed?

    1. A6 cups
    2. B8 cups
    3. C11 cups
    4. D24 cups
    Show your work
  2. 2Complete each step, then write the final answer.
    Rice (cups)10?15Beans (cups)4??÷ ?÷ ?× ?× ?

    A table shows 10 cups of rice for every 4 cups of beans. Kim says 15 cups of rice need 9 cups of beans, because 10 + 5 = 15 and 4 + 5 = 9. How many cups of beans are right?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.
    Red beads14?4Blue beads21??÷ ?÷ ?× ?× ?

    A ratio table shows 14 red beads for every 21 blue beads. How many blue beads go with 4 red beads?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help