Unit 3 · Standard 6.RP.3
Equivalent Ratios
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
3 red apples : 5 green apples
Ratio
A way to compare two amounts.
2:3 and 4:6 both mean 2 out of every 3, so 2/3 = 4/6
Equivalent ratios
Two ratios that mean the same thing.
60 miles per 1 hour
Rate
A ratio comparing two amounts with different units, like miles per hour.
2/3 = 4/6
Proportion
A math sentence saying two ratios are equal.
12:18 → divide both by 6 → 2:3
Simplify
To make a ratio smaller while keeping the same comparison.
Key Ideas & Notes
- Chef Montoya is preparing her famous tomato soup for a school banquet.
- Her original recipe serves 8 people, but tonight she needs to serve 32 guests.
- She needs your help to scale the recipe without changing the flavor!
- Chef Montoya's recipe calls for 3 cups of tomatoes for every 2 cups of broth. Complete the ratio table to help her scale the recipe.
Think About It
- What quantities are being compared in the recipe?
- What stays the same when you multiply both ingredients by the same number?
- How many times bigger is 32 than 8?
My Notes
Guided Examples
Example 1
Which ratio is equivalent to 2:5?
Solution: Multiply both parts by 2: 2×2 = 4 and 5×2 = 10, so 4:10 is equivalent to 2:5.
Answer: A. 4:10
Example 2
A recipe uses 4 eggs for every 6 cups of flour. Which ratio is equivalent?
Solution: Divide both by 2: 4÷2 = 2 and 6÷2 = 3. The ratio 2:3 is equivalent to 4:6.
Answer: A. 2:3
Example 3
Which ratio is NOT equivalent to 6:9?
Solution: 6:9 simplifies to 2:3. Check each: 2:3 ✓, 12:18 = 2:3 ✓, 18:27 = 2:3 ✓. But 3:5 does not simplify to 2:3.
Answer: A. 3:5
Write About the Math The Writing Revolution
I can explain my reasoning using the words equivalent ratios, rate, proportion, and simplify.
1. Kernel Sentence subject + verb
Model: Ratio is a way to compare two amounts.Razón es una manera de comparar dos cantidades.
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
These ratios are equal because ___.Estas razones son iguales porque ___.
I checked by ___.Lo comprobé al ___.
I would scale a recipe by ___.Ajustaría una receta al ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Marcus earns $45 for every 3 hours of work. How much does he earn in 8 hours?
- $120
- $90
- $135
- $105
2. A store sells 3 pens for $2. Another store sells 9 pens for $6. Are these equivalent ratios? If so, prove it using at least two different methods (simplifying, scaling, or cross-multiplying).
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Marcus's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A store sells 5 notebooks for $8. At this rate, how much would 15 notebooks cost?
- $24
- $18
- $20
- $40
Answer Key & Teacher Guide
- Try It 1: A. $120 — Unit rate: $45 ÷ 3 = $15/hour. In 8 hours: $15 × 8 = $120.
- Try It 2: Yes, they are equivalent. Method 1 (simplify): 9:6 ÷ 3 = 3:2, which matches 3:2. Method 2 (cross-multiply): 3 × 6 = 18 and 2 × 9 = 18. Since both cross products are equal, the ratios are equivalent.
- Exit Ticket: A. $24 — 15 is 3 times 5, so the cost is 3 × $8 = $24. The ratio 5:8 scales to 15:24.
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.
- 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).