Use Ratio Reasoning
I can use ratio reasoning to solve problems with proportions and scaling.
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🎯 Content Objective / Objetivo de contenido
I can use ratio reasoning to solve problems with proportions and scaling.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Chef Reyes's recipe serves 8 people, but the banquet has 120 guests. How many times bigger is 120 than 8, and how does that scale factor help you adjust the tomatoes and mozzarella?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Scenario Launch
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.
Concept Launch
💡 How do we use ratio reasoning to solve problems?
Ratio reasoning means using a scale factor or a proportion to find a missing amount. A proportion is two equal ratios. You can check it by cross-multiplying.
Find the scale factor, then multiply both parts; cross-multiply to check a proportion.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Proportion Proporción |
A math sentence saying two ratios are equal. Una oración matemática que dice que dos razones son iguales. |
2/3 = 8/12 | |
| Cross-multiply Multiplicación cruzada |
Multiplying across two ratios to check if they are equal. Multiplicar en cruz dos razones para ver si son iguales. |
2/3 = 8/12 → 2×12 = 24 and 3×8 = 24 ✓ | |
| Scale Escalar |
To multiply or divide both parts of a ratio by the same number. Multiplicar o dividir ambas partes de una razón por el mismo número. |
5:8 × 3 → 15:24 | |
| Equivalent Equivalente |
Having the same value. Tener el mismo valor. |
1/2 and 3/6 and 5/10 all equal the same amount — half | |
| Unit rate Tasa unitaria |
A rate for just 1 of something. You find it by dividing. Una tasa para solo 1 de algo. La encuentras al dividir. |
60 miles in 3 hours → 20 miles per 1 hour |
Which Word Fits?
An equation that states two ratios are equal is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Chef Reyes's recipe serves 8 people, but the banquet has 120 guests. How many times bigger is 120 than 8, and how does that scale factor help you adjust the tomatoes and mozzarella?
👂 Listen For
Students find the scale factor of 15 and explain that multiplying both ingredients by 15 keeps the recipe proportional (5 cups tomatoes becomes 75, 3 cups mozzarella becomes 45).
Extend: What stays the same about the recipe even when all the amounts get bigger? Justify why scaling keeps the flavor the same.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Chef Reyes wrote several pairs of ratios on the board. Sort them: which pairs are equivalent ratios (proportions) and which are NOT equivalent?
✍️ Explore Discourse
Explain your strategy and reasoning.
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
You sorted ratio pairs into equivalent and not equivalent. How does ratio reasoning, like cross-multiplying, prove that 4:7 and 12:21 are equivalent?
👂 Listen For
Students show 4 × 21 = 84 and 7 × 12 = 84 (or that 4:7 scales by 3 to 12:21), proving the ratios are equivalent.
Extend: Two ratios cross-multiply to UNequal products. Explain what that tells you and give an example you tested.
Practice Check A
A chef uses the proportion 3/7 = x/28 to scale a recipe. What is x?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A recipe uses 4 cups of broth for every 10 servings. How many cups of broth are needed for 30 servings?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Equivalent Ratio Sort
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
For each proportion, sort whether it is set up correctly or incorrectly to solve '4 cups for 6 servings = ? cups for 18 servings'.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Find the scale factor, then multiply both parts; cross-multiply to check a proportion." — and it works because ___.
Because Proportion means ___, but a tricky part is ___, so I have to ___.
A common mistake with Proportion is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Cross-multiply to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Find the scale factor, then multiply both parts; cross-multiply to check a proportion. because ___
Find the scale factor, then multiply both parts; cross-multiply to check a proportion. but ___
Find the scale factor, then multiply both parts; cross-multiply to check a proportion. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Chef Reyes wrote several pairs of ratios on the board. Sort them: which pairs are equivalent ratios (proportions) and which are NOT equivalent?
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A recipe uses 4 cups of broth for every 10 servings. How many cups of broth are needed for 30 servings?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A school garden grows tomatoes. The gardeners know that 4 tomato plants produce about 20 tomatoes. The school wants to grow 100 tomatoes for a salsa-making event. They need to use ratio reasoning to determine how many plants to grow.
✍️ Connection Reasoning
This is like our ratio reasoning work because ___ and ___ are related by ___.
This is like our ratio reasoning work because ___ and ___ are related by ___.
Turn & Talk — Connect
Where might ratio reasoning help you make a smart choice in real life, like shopping or cooking?
👂 Listen For
Students name a real use (scaling a recipe, comparing deals, mixing paint or fuel) and explain how keeping the ratio equivalent guides the decision.
Extend: Describe a situation where ignoring the ratio would cause a real problem, and explain how proportional reasoning fixes it.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A recipe calls for 6 cups of flour for every 15 cookies. How many cups of flour are needed to make 45 cookies?
Bonus Exit Check
Are the ratios 6:9 and 2:3 equivalent?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students find the scale factor of 15 and explain that multiplying both ingredients by 15 keeps the recipe proportional (5 cups tomatoes becomes 75, 3 cups mozzarella becomes 45).
• Students show 4 × 21 = 84 and 7 × 12 = 84 (or that 4:7 scales by 3 to 12:21), proving the ratios are equivalent.
• Students name a real use (scaling a recipe, comparing deals, mixing paint or fuel) and explain how keeping the ratio equivalent guides the decision.
• Listen for students naming a specific strategy tied to 6.RP.3 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Use Ratio Reasoning is skipping the key idea: "Find the scale factor, then multiply both parts; cross-multiply to check a proportion." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 12 — Scale factor: 28 ÷ 7 = 4. Multiply: 3 × 4 = 12. So x = 12.
✓ Practice 2: 12 — Scale factor: 30 ÷ 10 = 3. Multiply broth by 3: 4 × 3 = 12 cups.
✓ Practice 3: Yes, both simplify to 2:3 — Divide 6:9 by 3 to get 2:3. Since both ratios simplify to 2:3, they are equivalent.
✓ Practice 4: $14 — Unit rate: $6 ÷ 3 = $2 per pound. For 7 pounds: $2 × 7 = $14.
✓ Exit ticket: 18 — Scale factor: 45 ÷ 15 = 3. Multiply flour by 3: 6 × 3 = 18 cups of flour.