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.
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. 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 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 3.13.1 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.
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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: