Lesson 3.1Understand Ratios
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 to 5 ■■■ □□□□□ |
| 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. | apples to oranges |
| Part-to-wholeSpanish: Parte a todo | A ratio comparing one part to the whole group. | apples to all the fruit |
| 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 equal parts of apple juice beside 2 equal parts of sparkling water — 5 parts of fruit drink in all. |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
- Count each group. pens = 10 pencils = 4
- Write them in the order the question asks — pens FIRST.
- Write all three forms: 10 to 4 · 10 : 4 · 10/4
- Simplify: divide both terms by 2. 10 : 4 → 5 : 2
Answer: The ratio of pens to pencils is 5 : 2 in simplest form.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A bowl has 4 apples and 1 orange. What two amounts are we comparing?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The ratio of to is .
- This means for every , there are .
- The order matters because .
- I simplified by dividing both terms by .
Word bank ratiotermcomparefor everypartwholetotalsimplest formdivideorderfirstsecond
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 3.1Understand Ratios
Version ASupported practice
Learning target I can write and describe a ratio that compares two quantities.
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1Write the name of the correct group on each line.
Sort each statement: does it describe a ratio or NOT describe a ratio?
- 7 pencils for every 3 erasers
- 10 red beads to 4 blue beads
- There are 15 chairs in the room
- The pizza was delicious
Hint A ratio must COMPARE two amounts. Ask each card: does it mention two quantities, or just one?
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2Circle the letter of the best answer. Show how you know.
A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?
- A1:4
- B4:1
- C4:5
- D5:1
Hint Re-read the question: it asks for milk to cream, in that exact order.
Show your work -
3Circle the letter of the best answer. Show how you know.
Chef Reyes uses 6 strawberries and 2 bananas in a smoothie. What is the part-to-whole ratio of bananas to total fruit?
- A2:8
- B2:6
- C6:2
- D8:2
Hint Notice the word 'total' — this is a part-to-WHOLE ratio, not banana-to-strawberry.
Show your work -
4Circle the letter of the best answer. Show how you know.
In a class of 30 students, 18 are girls. What is the part-to-part ratio of boys to girls?
- A12:18
- B12:30
- C18:12
- D18:30
Hint The problem tells you girls (18) and the whole class (30) — but it asks about BOYS to girls.
Show your work -
5Circle the letter of the best answer. Show how you know.
A pet store has 5 dogs and 9 cats. What is the ratio of dogs to cats?
- A5:9
- B5:14
- C9:5
- D14:5
Hint Re-read: the question asks for dogs to cats, in that order.
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Spot the Mistake — Order of a Ratio
- 1Read the problemA salad bar has 5 bowls of soup and 8 sandwiches. Write the ratio of soup to sandwiches.
- 2Identify the amountsSoup = 5 and sandwiches = 8.
- 3Write the ratioA student writes the ratio of soup to sandwiches as 8:5.
- 4AnswerThe ratio of soup to sandwiches is 8:5.
Which step has the mistake? Explain what went wrong, then show the correct work.
Hint Look at Step 3. Which amount should be written first — soup or sandwiches?
Correct workCorrect answer:
Explain your thinkingWhat makes something a ratio? How did you decide which statements to sort into each group?
Sentence starter A ratio compares ___ to ___ using words like ___ or symbols like ___.
Lesson 3.1Understand Ratios
Version BCore practice
Learning target I can write and describe a ratio that compares two quantities.
-
1Write the name of the correct group on each line.
Sort each statement — is it a part-to-part ratio or a part-to-whole ratio?
- 3 boys to 5 girls in cooking class
- 5 girls out of 8 students total
- 2 cups sugar to 3 cups flour
- 4 vegetarian dishes out of 10 total dishes
- 7 savory items to 3 sweet items
- 3 sweet items out of 10 total items
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2Complete the table. Show how you found each value.
Complete the table by writing each ratio in all three forms.
Description Word Form Colon Form Fraction Form 4 cats to 7 dogs 4 to 7 4:7 4/7 9 red out of 15 total 5 wins to 3 losses Show your work
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3Circle the letter of the best answer. Show how you know.
A fruit salad has 5 pieces of melon, 3 pieces of pineapple, and 2 grapes. What is the ratio of pineapple to melon?
- A3:5
- B3:10
- C3:2
- D5:3
Show your work -
4Circle the letter of the best answer. Show how you know.
A parking lot has 10 cars and 6 trucks. What is the part-to-whole ratio of trucks to total vehicles?
- A6:16
- B6:10
- C10:6
- D16:6
Show your work
-
5Find the mistake. Explain it, then show the correct work.
Spot the Mistake — Part-to-Whole Ratio
- 1Read the problemA class has 9 boys and 6 girls. Write the part-to-whole ratio of girls to the whole class.
- 2Count the whole9 + 6 = 15 students in all.
- 3Write the ratioA student writes girls to the whole class as 6:9.
- 4AnswerThe part-to-whole ratio of girls to the whole class is 6:9.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhat makes something a ratio? How did you decide which statements to sort into each group?
Lesson 3.1Understand Ratios
ChallengeExtension
Learning target I can write and describe a ratio that compares two quantities.
-
1Write the name of the correct group on each line.
A classroom has 12 boys and 8 girls. Sort each ratio statement as either CORRECT or INCORRECT.
- Boys to girls = 12:8
- Girls to total = 8:20
- Boys to total = 12:8
- Girls to boys = 12:8
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2Find the mistake. Explain it, then show the correct work.
Find Aliya's Mistake
- 1Read the problemA trail mix has 6 almonds, 4 raisins, and 2 cashews. Write the ratio of raisins to total pieces.
- 2Count total pieces6 + 4 + 2 = 12
- 3Write the ratio4:8
- 4AnswerThe ratio of raisins to total is 4:8.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
A bag of marbles has 8 red, 6 blue, and 4 green marbles. Write three different ratios using these quantities: one part-to-part ratio, one part-to-whole ratio, and explain the difference.
Write your answer