Lesson 3.13.1 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can write and describe a ratio that compares two quantities, explain what each part stands for, and build one for a situation I have not seen before.
Why This Matters This is your challenge small group for Lesson 3.1. 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 |
|---|---|---|
| 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.
A shelf has 6 math books and 9 reading books. Write reading to math, then math to all books.
- Reading first: 9 : 6.
- All books: 6 + 9 = 15, so math to all is 6 : 15.
- Divide both terms by 3: 6 : 15 = 2 : 5.
Answer: 9 : 6 and 2 : 5
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. Write the ratio of apples to oranges and the ratio of apples to all the fruit.
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 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 3.13.1 Small Group · Group 2
Group 2Challenge practice
Learning target I can write and describe a ratio that compares two quantities, explain what each part stands for, and build one for a situation I have not seen before.
Why This Matters This is your challenge small group for Lesson 3.1. 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.
The first column is one batch. A smoothie uses 2 cups of mango for every 5 cups of yogurt. Jen makes 28 cups of smoothie. How many cups of mango does she use?
- 1One batch has 2 cups of mango and 5 of yogurt. How many cups of smoothie?
- 2What scale factor takes 7 cups to 28 cups?
- 3Multiply the mango by 4. How many cups of mango?
Final answer: -
2Complete each step, then write the final answer.
The first column is the ratio 4:5. The ratio of boys to girls in a chorus is 4:5. There are 20 girls. How many students are in the chorus?
- 1What scale factor takes 5 girls to 20 girls?
- 2Multiply the 4 boys by 4. How many boys?
- 3Multiply all 9 students by 4. How many students?
- 4Why is the answer not 4 + 5 = 9 students?
Final answer: -
3Complete 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: -
4Complete each step, then write the final answer.
Chef Reyes uses 3 cups of apple juice for every 2 cups of sparkling water. She used 21 cups of apple juice. How many cups of fruit drink did she make?
Show your workFinal answer: -
5Complete each step, then write the final answer.
A school club has 40 members. The ratio of 6th graders to 7th graders is 3:5. How many more 7th graders than 6th graders are in the club?
Show your workFinal answer: -
6Complete 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: