Lesson 3.3The Bridge Strategy (Scaling Ratios)
Start hereWords, worked example, and sentence starters
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.
| Word | What it means | Example |
|---|---|---|
| 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 exampleusing the bridge when you cannot multiply directly
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A glaze uses 8 spoons honey to 20 spoons water. How much water for 12 spoons of honey?
- Notice the problem: 8 × a whole number never equals 12.
- — simplify DOWN to the bridge. 8 : 20 ÷ 4 → 2 : 5
- — multiply the bridge UP to the target. 2 × 6 = 12
- Use the same factor on the other term. 5 × 6 = 30
Answer: 12 spoons of honey need 30 spoons of water.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A stain uses 14 drops brown to 21 drops black. How much black for 8 drops brown?
- Can you multiply 14 by a whole number to reach 8?
- Simplify DOWN to the bridge. 14 : 21 ÷ → :
- Multiply the bridge UP. × = 8
- Use the same factor. × = drops black
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 outA 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 — for example, turning 2:3 into 6:3 (multiplying only the first number by 3 and forgetting the second) or into 4:5 (adding the scale factor 2 to the second number instead of multiplying, since 3+2=5 but 3×2=6). Before you submit, multiply BOTH numbers by the same scale factor and check that your new ratio simplifies back to the original.
Lesson 3.3The Bridge Strategy (Scaling Ratios)
Apply Day · Version ASupported practice
Learning target I can use a ratio table to find equivalent ratios.
-
1Complete each step, then write the final answer.
A recipe uses 1 cup of oats for every 3 cups of milk. How much milk goes with 5 cups of oats?
Show your workHint The scale factor is 5. Multiply the milk by 5.
Final answer: -
2Complete each step, then write the final answer.
A bracelet has 2 red beads for every 5 white beads. How many white beads go with 8 red beads?
Show your workHint What number times 2 makes 8? Multiply the white beads by that number.
Final answer: -
3Complete each step, then write the final answer.
A snack uses 2 crackers for every 1 slice of cheese. How many crackers go with 6 slices of cheese?
Show your workHint The scale factor is 6. Multiply the crackers by 6.
Final answer:
Lesson 3.3The Bridge Strategy (Scaling Ratios)
Apply Day · Version BCore practice
Learning target I can use a ratio table to find equivalent ratios.
-
1Circle the letter of the best answer. Show how you know.
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?
- A9:12
- B5:6
- C6:7
- D4:5
Show your work -
2Complete each step, then write the final answer.
A ratio table shows 12 pens for every 4 boxes. How many pens are in 7 boxes?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A recipe uses 3 eggs for every 2 cups of milk. How many eggs go with 10 cups of milk?
Show your workFinal answer:
Lesson 3.3The Bridge Strategy (Scaling Ratios)
Apply Day · ChallengeExtension
Learning target I can use a ratio table to find equivalent ratios.
-
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?
- A6 cups
- B8 cups
- C11 cups
- D24 cups
Show your work -
2Complete each step, then write the final answer.
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 workFinal answer: -
3Complete each step, then write the final answer.
A ratio table shows 14 red beads for every 21 blue beads. How many blue beads go with 4 red beads?
Show your workFinal answer: