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 example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Ana and Ben share 28 stickers in the ratio 3 : 4. Find each share.
- Total parts: 3 + 4 = 7.
- One box: 28 ÷ 7 = 4.
- Ana 3 × 4 = 12; Ben 4 × 4 = 16. Check: 12 + 16 = 28.
Answer: Ana 12, Ben 16
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 out!A 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
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: