Unit 3 · Standard 6.RP.1
Understand Ratios
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
3 cups flour to 2 cups sugar → 3:2
Ratio
A way to compare two amounts, like 3 to 2.
5 eggs vs. 3 eggs — which recipe uses more?
Comparison
Looking at two or more amounts to see how they are related.
3 cups flour : 2 cups sugar (ingredient to ingredient)
Part-to-part
A ratio comparing one part of a group to another part.
3 cups flour out of 5 cups total → 3:5
Part-to-whole
A ratio comparing one part to the whole group.
3 to 2 can be written as 3:2
Colon notation
Writing a ratio with two dots between the numbers, like 3:2.
Key Ideas & Notes
- Welcome to Chef Academy!
- Head Chef Reyes is teaching new students how to read recipes like a pro.
- Her signature cookie recipe calls for 3 cups of flour for every 2 cups of sugar.
- Before the students can start baking, they need to understand how these ingredient amounts compare to each other.
- Chef Reyes wrote several comparisons on the board. Sort them into two groups: statements that ARE ratios and statements that are NOT ratios.
Think About It
- What two ingredients are being compared in the recipe?
- How could you describe the relationship between flour and sugar?
- Is the amount of flour more than, less than, or equal to the amount of sugar?
My Notes
Guided Examples
Example 1
A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?
Solution: A ratio compares quantities in the order given. Milk to cream = 4 to 1, or 4:1.
Answer: A. 4:1
Example 2
Chef Reyes uses 6 strawberries and 2 bananas in a smoothie. What is the part-to-whole ratio of bananas to total fruit?
Solution: Total fruit = 6 + 2 = 8. The part-to-whole ratio of bananas to total fruit is 2:8.
Answer: A. 2:8
Example 3
In a class of 30 students, 18 are girls. What is the part-to-part ratio of boys to girls?
Solution: Boys = 30 − 18 = 12. Part-to-part ratio of boys to girls = 12:18. (Order matters!)
Answer: A. 12:18
Write About the Math The Writing Revolution
I can explain a comparison using the words ratio, part-to-part, part-to-whole, and colon notation.
1. Kernel Sentence subject + verb
Model: Ratio is a way to compare two amounts, like 3 to 2.Razón es una manera de comparar dos cantidades, como 3 a 2.
Write a kernel sentence about ratio. Use a subject and a verb.Escribe una oración base sobre razón. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Ratio matters in mathRazón importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Ratio matters in math because ___.Razón importa en matemáticas porque ___.
Ratio matters in math, but ___.Razón importa en matemáticas, pero ___.
Ratio matters in math, so ___.Razón importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about ratio.Di un hecho verdadero sobre ratio.
Ratio ___.
Ask a question about ratio.Haz una pregunta sobre ratio.
How does ___ ?¿Cómo ___ ?
Show excitement about ratio.Muestra entusiasmo sobre ratio.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with ratio.Dile a un compañero qué hacer con ratio.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The ratio of ___ to ___ is ___.La razón de ___ a ___ es ___.
This means for every ___ there are ___.Esto significa que por cada ___ hay ___.
I see ratios when ___.Veo razones cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A parking lot has 10 cars and 6 trucks. What is the part-to-whole ratio of trucks to total vehicles?
- 6:16
- 10:6
- 6:10
- 16:6
2. 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.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Aliya's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A bag of trail mix contains 8 peanuts and 5 raisins. What is the ratio of raisins to total pieces?
- 5:13
- 8:5
- 5:8
- 13:5
Answer Key & Teacher Guide
- Try It 1: A. 6:16 — Total vehicles = 10 + 6 = 16. The ratio of trucks to total is 6:16.
- Try It 2: Part-to-part: red to blue = 8:6. Part-to-whole: green to total = 4:18. The difference is that part-to-part compares two individual groups, while part-to-whole compares one group to the entire collection (8 + 6 + 4 = 18).
- Exit Ticket: A. 5:13 — Total pieces = 8 + 5 = 13. The ratio of raisins to total is 5:13.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Ratio is a way to compare two amounts, like 3 to 2.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).