Unit 3 · Standard 6.RP.3
Compare Ratios
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
$3 per 1 pound → unit rate is $3/lb
Unit rate
A rate for just 1 of something, like cost for 1 item.
4:6 and 2:3 are equivalent (both simplify to 2:3)
Equivalent ratio
Two ratios that mean the same thing.
3:4 vs. 2:5 — which has more of the first ingredient per unit?
Compare
To look at ratios and see which is bigger, smaller, or equal.
8:12 → divide both by 4 → 2:3
Simplify
To make a ratio as small as possible while keeping the same comparison.
To compare 3/5 and 4/7, use LCD 35: 21/35 vs 20/35
Common denominator
A bottom number that two fractions can share so you can compare them.
Key Ideas & Notes
- Chef Academy is holding a Flavor Challenge!
- Chef Reyes's hot cocoa recipe uses 3 tablespoons of cocoa for every 5 ounces of milk.
- Chef Tran's recipe uses 4 tablespoons of cocoa for every 7 ounces of milk.
- The students need to figure out whose hot cocoa is more chocolatey.
- Build equivalent ratios for each chef's recipe so you can compare them fairly. Chef Reyes: 3 tbsp cocoa per 5 oz milk. Chef Tran: 4 tbsp cocoa per 7 oz milk.
Think About It
- What quantities are being compared in each recipe?
- Can you tell just by looking which recipe has more cocoa per ounce?
- What would make the comparison fair?
My Notes
Guided Examples
Example 1
Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?
Solution: Chef A: 2÷8 = 0.25 cups per cracker. Chef B: 3÷9 ≈ 0.33 cups per cracker. Chef B uses more cheese per cracker.
Answer: A. Chef B
Example 2
Which ratio is greater: 3:4 or 5:8?
Solution: Convert to the same denominator: 3:4 = 6:8. Since 6:8 > 5:8, the ratio 3:4 is greater.
Answer: A. 3:4
Example 3
Which lemonade recipe is more lemony? Recipe A: 2 lemons for 6 cups of water. Recipe B: 3 lemons for 7 cups of water.
Solution: Recipe A: 2÷6 ≈ 0.33 lemons per cup. Recipe B: 3÷7 ≈ 0.43 lemons per cup. Since 0.43 > 0.33, Recipe B is more lemony.
Answer: A. Recipe B
Write About the Math The Writing Revolution
I can explain my comparison using the words unit rate, equivalent ratio, compare, and common denominator.
1. Kernel Sentence subject + verb
Model: Compare is to look at ratios and see which is bigger, smaller, or equal.Comparar es mirar razones para ver cuál es mayor, menor o igual.
Write a kernel sentence about compare. Use a subject and a verb.Escribe una oración base sobre comparar. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Compare matters in mathComparar importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Compare matters in math because ___.Comparar importa en matemáticas porque ___.
Compare matters in math, but ___.Comparar importa en matemáticas, pero ___.
Compare matters in math, so ___.Comparar importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about compare.Di un hecho verdadero sobre compare.
Compare ___.
Ask a question about compare.Haz una pregunta sobre compare.
How does ___ ?¿Cómo ___ ?
Show excitement about compare.Muestra entusiasmo sobre compare.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with compare.Dile a un compañero qué hacer con compare.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I compared by ___.Comparé al ___.
___ is bigger because ___.___ es mayor porque ___.
The better deal is ___ because ___.La mejor oferta es ___ porque ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Store A sells 3 mangoes for $6. Store B sells 5 mangoes for $9. Which store offers a better price per mango?
- Store B
- Store A
- Same price
- Cannot determine
2. Store A sells 5 notebooks for $12. Store B sells 8 notebooks for $20. Without calculating, a student says Store B must be cheaper because you get more notebooks. Is the student's reasoning valid? Find the unit rates to prove your answer.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Kai's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A bakery sells 4 muffins for $10 and another bakery sells 6 muffins for $14. Which bakery has the lower price per muffin?
- The second bakery
- The first bakery
- Same price
- Cannot determine
Answer Key & Teacher Guide
- Try It 1: A. Store B — Store A: $6÷3 = $2.00 per mango. Store B: $9÷5 = $1.80 per mango. Store B has the better (lower) price per mango.
- Try It 2: The student's reasoning is not valid — getting more items does not mean a lower price per item. Store A: $12 ÷ 5 = $2.40 per notebook. Store B: $20 ÷ 8 = $2.50 per notebook. Store A is actually cheaper per notebook, even though Store B offers more notebooks per purchase.
- Exit Ticket: A. The second bakery — First bakery: $10÷4 = $2.50 per muffin. Second bakery: $14÷6 ≈ $2.33 per muffin. The second bakery has the lower price.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Compare is to look at ratios and see which is bigger, smaller, or equal.
- 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).