Lesson 3.33.3 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can use a ratio table to find equivalent ratios, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 3.3. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
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. | 5, 10, 15 / 2, 4, 6 |
| 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 mix uses 5 scoops of powder for every 2 cups of water. How much water for 15 scoops?
- Find the factor: 15 ÷ 5 = 3.
- Multiply the water by 3 too: 2 × 3 = 6.
- Check: 15 : 6 ÷ 3 = 5 : 2.
Answer: 15 scoops go with 6 cups 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 drink uses 1 cup of juice for every 4 cups of water. Double the recipe.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I multiplied both terms by .
- and are equivalent because .
- Adding does not work because .
- The factor is because × = .
Word bank equivalentratio tablefactormultiplydividebothsamescale upscale downfor everyrowpattern
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
Lesson 3.33.3 Small Group · Group 2
Group 2Challenge practice
Learning target I can use a ratio table to find equivalent ratios, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 3.3. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
-
1Complete each step, then write the final answer.
Divide first, then multiply. A recipe uses 8 cups of flour for every 12 cups of water. How many cups of water go with 6 cups of flour?
- 1What do we divide 8 by to get 2?
- 2Divide 12 by 4 too. How much water goes with 2 cups of flour?
- 3What scale factor takes 2 cups of flour to 6 cups?
- 4Multiply 3 cups of water by 3. How much water?
Final answer: -
2Complete each step, then write the final answer.
A party plan uses 6 bags of chips for every 15 juice boxes. How many juice boxes go with 10 bags of chips?
- 1Divide both numbers by 3. What is the smaller ratio?
- 2Multiply both by 5. How many juice boxes go with 10 bags?
- 3Ben adds 4 to both numbers and gets 10:19. Why is that wrong?
Final answer: -
3Complete 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: -
4Complete each step, then write the final answer.
A smoothie uses 15 strawberries for every 6 bananas. How many strawberries go with 8 bananas?
Show your workFinal answer: -
5Complete each step, then write the final answer.
A food truck sells 9 burritos for $24. At that rate, how much do 6 burritos cost?
Show your workFinal answer: -
6Complete 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: