Unit 3 · Standard 6.RP.3
Use Ratio Reasoning
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
2/3 = 8/12
Proportion
A math sentence saying two ratios are equal.
2/3 = 8/12 → 2×12 = 24 and 3×8 = 24 ✓
Cross-multiply
Multiplying across two ratios to check if they are equal.
5:8 × 3 → 15:24
Scale
To multiply or divide both parts of a ratio by the same number.
1/2 and 3/6 and 5/10 all equal the same amount — half
Equivalent
Having the same value.
60 miles in 3 hours → 20 miles per 1 hour
Unit rate
A rate for just 1 of something. You find it by dividing.
Key Ideas & Notes
- Chef Academy received a huge catering order — a banquet for 120 guests!
- Chef Reyes's original appetizer recipe serves 8 people and calls for 5 cups of diced tomatoes and 3 cups of mozzarella.
- The students need to use ratio reasoning to scale the recipe so every guest gets the same delicious flavor.
- Chef Reyes wrote several pairs of ratios on the board. Sort them: which pairs are equivalent ratios (proportions) and which are NOT equivalent?
Think About It
- How many times bigger is 120 compared to 8?
- What operation would help you scale both ingredients?
- What stays the same about the recipe even when the amounts change?
My Notes
Guided Examples
Example 1
A recipe uses 4 cups of broth for every 10 servings. How many cups of broth are needed for 30 servings?
Solution: Scale factor: 30 ÷ 10 = 3. Multiply broth by 3: 4 × 3 = 12 cups.
Answer: A. 12
Example 2
Are the ratios 6:9 and 2:3 equivalent?
Solution: Divide 6:9 by 3 to get 2:3. Since both ratios simplify to 2:3, they are equivalent.
Answer: A. Yes, both simplify to 2:3
Example 3
If 3 pounds of apples cost $6, how much do 7 pounds cost?
Solution: Unit rate: $6 ÷ 3 = $2 per pound. For 7 pounds: $2 × 7 = $14.
Answer: A. $14
Write About the Math The Writing Revolution
I can explain my reasoning using the words proportion, scale, equivalent, and unit rate.
1. Kernel Sentence subject + verb
Model: Scale is to multiply or divide both parts of a ratio by the same number.Escalar es multiplicar o dividir ambas partes de una razón por el mismo número.
Write a kernel sentence about scale. Use a subject and a verb.Escribe una oración base sobre escalar. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Scale matters in mathEscalar importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Scale matters in math because ___.Escalar importa en matemáticas porque ___.
Scale matters in math, but ___.Escalar importa en matemáticas, pero ___.
Scale matters in math, so ___.Escalar importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about scale.Di un hecho verdadero sobre scale.
Scale ___.
Ask a question about scale.Haz una pregunta sobre scale.
How does ___ ?¿Cómo ___ ?
Show excitement about scale.Muestra entusiasmo sobre scale.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with scale.Dile a un compañero qué hacer con scale.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I reasoned that ___.Razoné que ___.
I used the ratio to ___.Usé la razón para ___.
This helps me decide ___.Esto me ayuda a decidir ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A chef uses the proportion 3/7 = x/28 to scale a recipe. What is x?
- 12
- 14
- 9
- 21
2. A recipe serves 6 people and uses 4 cups of rice. You need to serve 15 people. Show two different methods to find how much rice you need: (1) using a scale factor and (2) using a unit rate.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Priya's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A recipe calls for 6 cups of flour for every 15 cookies. How many cups of flour are needed to make 45 cookies?
- 18
- 12
- 24
- 21
Answer Key & Teacher Guide
- Try It 1: A. 12 — Scale factor: 28 ÷ 7 = 4. Multiply: 3 × 4 = 12. So x = 12.
- Try It 2: Method 1 (scale factor): 15 ÷ 6 = 2.5. Multiply rice by 2.5: 4 × 2.5 = 10 cups. Method 2 (unit rate): 4 ÷ 6 = 2/3 cup per person. For 15 people: 2/3 × 15 = 10 cups. Both methods give 10 cups of rice.
- Exit Ticket: A. 18 — Scale factor: 45 ÷ 15 = 3. Multiply flour by 3: 6 × 3 = 18 cups of flour.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Scale is to multiply or divide both parts of a ratio by the same number.
- 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).