Lesson 3.1Ratios with Tape Diagrams
Start hereWords, worked example, and sentence starters
Learning target I can write and describe a ratio that compares two quantities.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| RatioSpanish: Razón | A way to compare two amounts, like 3 to 2. | 3 cups flour to 2 cups sugar → 3:2 |
| ComparisonSpanish: Comparación | Looking at two or more amounts to see how they are related. | 5 eggs vs. 3 eggs — which recipe uses more? |
| Part-to-partSpanish: Parte a parte | A ratio comparing one part of a group to another part. | 3 teal counters to 5 amber counters → 3:5 |
| Part-to-wholeSpanish: Parte a todo | A ratio comparing one part to the whole group. | 3 teal counters out of 8 counters in all → 3:8 |
| Colon notationSpanish: Notación con dos puntos | Writing a ratio with two dots between the numbers, like 3:2. | 3 to 2 can be written as 3:2 |
| Tape diagramSpanish: Diagrama de cintas | A bar cut into equal parts that shows how two amounts in a ratio compare, and how they make up the whole. | 3 : 1 ▭▭▭ | ▭ |
How it worksWorked examplesharing a total using a ratio
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Paint mixes 3 cups blue for every 1 cup white. The painter needs 24 cups in all.
- Add the terms to find total parts. 3 + 1 = 4 parts
- Divide the total by the parts. 24 ÷ 4 = 6 cups in each box
- Multiply each row by 6. blue: 3 × 6 = 18 white: 1 × 6 = 6
- Check by adding. 18 + 6 = 24 ✓
Answer: The painter needs 18 cups blue and 6 cups white.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A dish uses 2 cups rice for every 1 cup beans. The cook makes 21 cups in all.
- Add the terms. + = total parts
- Divide the total by the parts. 21 ÷ = in each box
- Multiply each row. rice: 2 × = beans: 1 × =
- Check by adding. + = 21 ?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- There are total parts because + = .
- Each box is worth because ÷ = .
- I multiplied by to get .
- I checked my answer by .
Word bank tape diagramunitparttotalequaldividemultiplyaddfor everyin alleachcheck
Watch outA common mistake
A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.
Lesson 3.1Ratios with Tape Diagrams
Apply Day · Version ASupported practice
Learning target I can write and describe a ratio that compares two quantities.
-
1Complete each step, then write the final answer.
A pencil box has 9 pencils and 2 erasers. The ratio of erasers to pencils is ? : 9. What is the missing number?
Show your workHint Erasers come first in this ratio.
Final answer: -
2Complete each step, then write the final answer.
A vase has 5 red flowers and 4 yellow flowers. The ratio of red flowers to all the flowers is 5 to ?. What is the missing number?
Show your workHint All the flowers means red and yellow together.
Final answer: -
3Complete each step, then write the final answer.
A team has 7 players on the field and 4 players on the bench. The ratio of bench players to all the players is 4 to ?. What is the missing number?
Show your workHint All the players means the field and the bench together.
Final answer:
Lesson 3.1Ratios with Tape Diagrams
Apply Day · Version BCore practice
Learning target I can write and describe a ratio that compares two quantities.
-
1Circle the letter of the best answer. Show how you know.
Lily has 3 cats and 4 dogs. Ben says the ratio of dogs to cats is 3:4. Which ratio of dogs to cats is correct?
- A4:3
- B3:4
- C4:7
- D3:7
Show your work -
2Complete each step, then write the final answer.
A paint mix uses red paint and blue paint in a ratio of 1:3. A can holds 24 cups of the mix. How many cups of blue paint are in it?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A plate has 6 cookies and 1 muffin. The ratio of cookies to all the treats is 6 to ?. What is the missing number?
Show your workFinal answer:
Lesson 3.1Ratios with Tape Diagrams
Apply Day · ChallengeExtension
Learning target I can write and describe a ratio that compares two quantities.
-
1Circle the letter of the best answer. Show how you know.
A class has 12 sixth graders and 18 seventh graders. What is the ratio of sixth graders to the TOTAL number of students, written in simplest form?
- A2 : 5
- B2 : 3
- C3 : 5
- D12 : 18
Show your work -
2Complete each step, then write the final answer.
A trail mix uses 2 cups of nuts for every 3 cups of raisins. Leo makes 20 cups of trail mix. He says 20 ÷ 2 = 10, so he needs 10 cups of nuts. How many cups of nuts does he really need?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A punch uses 1 cup of lemon juice for every 4 cups of water. Tom makes 30 cups of punch. How many cups of water does he use?
Show your workFinal answer: