Equivalent Ratios
I can find and check equivalent ratios using multiplication and division.
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🎯 Content Objective / Objetivo de contenido
I can find and check equivalent ratios using multiplication and division.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Chef Montoya's soup serves 8 people, but she needs to serve 32. How many times bigger is the recipe, and what must she do to BOTH ingredients to keep the flavor?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Scenario Launch
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!
Concept Launch
💡 What are equivalent ratios?
Equivalent ratios are ratios that mean the same thing. You make one by multiplying or dividing BOTH numbers by the same amount.
Multiply or divide both numbers by the same amount to make an equivalent ratio.
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 |
|---|---|---|---|
| Ratio Razón |
A way to compare two amounts. Una manera de comparar dos cantidades. |
3 red apples : 5 green apples | |
| Equivalent ratios Razones equivalentes |
Two ratios that mean the same thing. Dos razones que significan lo mismo. |
2:3 and 4:6 both mean 2 out of every 3, so 2/3 = 4/6 | |
| Rate Tasa |
A ratio comparing two amounts with different units, like miles per hour. Una razón que compara dos cantidades con unidades distintas, como millas por hora. |
60 miles per 1 hour | |
| Proportion Proporción |
A math sentence saying two ratios are equal. Una oración matemática que dice que dos razones son iguales. |
2/3 = 4/6 | |
| Simplify Simplificar |
To make a ratio smaller while keeping the same comparison. Hacer una razón más pequeña sin cambiar la comparación. |
12:18 → divide both by 6 → 2:3 |
Vocabulary — True or False?
Which statements correctly use Equivalent ratios?
Fix the False One
Which Word Fits?
A comparison of two quantities 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 Montoya's soup serves 8 people, but she needs to serve 32. How many times bigger is the recipe, and what must she do to BOTH ingredients to keep the flavor?
👂 Listen For
A strong answer finds the scale factor 4 (32 ÷ 8) and explains both ingredients must be multiplied by 4 to make equivalent ratios.
Extend: Chef Montoya now needs to scale DOWN to serve only 4 people. Explain what scale factor she uses and why dividing keeps the ratios equivalent.
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 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.
✍️ 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
Looking at the tomatoes-to-broth table (3:2, 6:4, 9:6, 12:8), how can you PROVE these ratios are all equivalent?
👂 Listen For
Listen for proof by simplifying (all reduce to 3:2) or scaling (each multiplied by the same factor), not just 'they look similar.'
Extend: A student says 6:4 and 9:6 are equivalent because 'you add 3 and 2 each time.' Critique this reasoning even though the rows happen to be correct.
Practice Check A
Marcus earns $45 for every 3 hours of work. How much does he earn in 8 hours?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which ratio is equivalent to 2:5?
✍️ 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
Sort these ratios — which are equivalent to 3:4 and which are not?
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: "Multiply or divide both numbers by the same amount to make an equivalent ratio." — and it works because ___.
Because Ratio means ___, but a tricky part is ___, so I have to ___.
A common mistake with Ratio is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Equivalent ratios to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Multiply or divide both numbers by the same amount to make an equivalent ratio. because ___
Multiply or divide both numbers by the same amount to make an equivalent ratio. but ___
Multiply or divide both numbers by the same amount to make an equivalent ratio. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
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.
| Servings | Cups of Tomatoes | Cups of Broth |
|---|---|---|
| 8 (original) | 3 | 2 |
| 16 | ||
| 24 | ||
| 32 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Which ratio is equivalent to 2:5?
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 local smoothie shop sells a Berry Blast smoothie. The recipe calls for 2 cups of strawberries for every 3 cups of yogurt. Today they need to make 15 cups of yogurt worth of smoothies for a catering order.
✍️ Connection Reasoning
Find the scale factor (15 ÷ 3) and use it to figure out how many cups of strawberries the shop needs. Show your steps and explain why multiplying both ingredients by the same factor keeps the smoothie tasting the same.
Find the scale factor (15 ÷ 3) and use it to figure out how many cups of strawberries the shop needs. Show your steps and explain why multiplying both ingredients by the same factor keeps the smoothie tasting the same.
Turn & Talk — Connect
The smoothie shop uses 2 cups of strawberries for every 3 cups of yogurt and needs 15 cups of yogurt. How is this the same as scaling Chef Montoya's soup?
👂 Listen For
A strong answer uses the scale factor 5 (15 ÷ 3) to find 10 cups of strawberries and names this as making an equivalent ratio / proportion.
Extend: Set up this smoothie situation as a proportion (2/3 = ?/15) and explain how cross-multiplying confirms your strawberry amount.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A store sells 5 notebooks for $8. At this rate, how much would 15 notebooks cost?
Bonus Exit Check
A recipe uses 4 eggs for every 6 cups of flour. Which ratio is 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
• A strong answer finds the scale factor 4 (32 ÷ 8) and explains both ingredients must be multiplied by 4 to make equivalent ratios.
• Listen for proof by simplifying (all reduce to 3:2) or scaling (each multiplied by the same factor), not just 'they look similar.'
• A strong answer uses the scale factor 5 (15 ÷ 3) to find 10 cups of strawberries and names this as making an equivalent ratio / proportion.
• 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 Equivalent Ratios is skipping the key idea: "Multiply or divide both numbers by the same amount to make an equivalent ratio." — 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: $120 — Unit rate: $45 ÷ 3 = $15/hour. In 8 hours: $15 × 8 = $120.
✓ Practice 2: 4:10 — Multiply both parts by 2: 2×2 = 4 and 5×2 = 10, so 4:10 is equivalent to 2:5.
✓ Practice 3: 2:3 — Divide both by 2: 4÷2 = 2 and 6÷2 = 3. The ratio 2:3 is equivalent to 4:6.
✓ Practice 4: 3:5 — 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.
✓ Exit ticket: $24 — 15 is 3 times 5, so the cost is 3 × $8 = $24. The ratio 5:8 scales to 15:24.