Understand Ratios
I can write and describe a ratio that compares two quantities.
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🎯 Content Objective / Objetivo de contenido
I can write and describe a ratio that compares two quantities.
Today's Flow
Total pacing: ~50 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Chef Reyes's signature cookie recipe uses 3 cups of flour for every 2 cups of sugar. How would you describe how these two ingredient amounts compare?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Chef Academy Ratio Rookie
Welcome to Chef Academy! Head Chef Reyes is teaching new students how to read recipes like a pro. Her signature cookie recipe calls for 3 cups of flour for every 2 cups of sugar. Before the students can start baking, they need to understand how these ingredient amounts compare to each other.
Concept Launch
💡 What is a ratio?
A ratio compares two amounts. It tells how much of one thing there is for another thing.
A ratio compares two quantities, and the order you write them in matters.
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, like 3 to 2. Una manera de comparar dos cantidades, como 3 a 2. |
3 cups flour to 2 cups sugar → 3:2 | |
| Comparison Comparación |
Looking at two or more amounts to see how they are related. Mirar dos o más cantidades para ver cómo se relacionan. |
5 eggs vs. 3 eggs — which recipe uses more? | |
| Part-to-part Parte a parte |
A ratio comparing one part of a group to another part. Una razón que compara una parte de un grupo con otra parte. |
3 cups flour : 2 cups sugar (ingredient to ingredient) | |
| Part-to-whole Parte a todo |
A ratio comparing one part to the whole group. Una razón que compara una parte con todo el grupo. |
3 cups flour out of 5 cups total → 3:5 | |
| Colon notation Notación con dos puntos |
Writing a ratio with two dots between the numbers, like 3:2. Escribir una razón con dos puntos entre los números, como 3:2. |
3 to 2 can be written as 3:2 |
Which Word Fits?
A comparison of two quantities, like 3 to 5, 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 signature cookie recipe uses 3 cups of flour for every 2 cups of sugar. How would you describe how these two ingredient amounts compare?
👂 Listen For
A strong answer names that flour and sugar are being compared and states the relationship as 3 to 2 (or 'for every 3 flour, 2 sugar'), not just that there is more flour.
Extend: Would the ratio still describe the same recipe if you wrote it as sugar to flour instead of flour to sugar? Justify why the order changes the ratio but not the recipe.
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 comparisons on the board. Sort them into two groups: statements that ARE ratios and statements that are NOT ratios.
✍️ Explore Discourse
What makes something a ratio? How did you decide which statements to sort into each group?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
At the Prep Station you sorted the chef's statements. What made something a ratio instead of NOT a ratio (like '12 cookies on the tray')?
👂 Listen For
Listen for the idea that a ratio must compare two quantities (using 'to', 'for every', 'out of', or a colon), while a single count or a description is not a comparison.
Extend: Critique this claim: 'The oven is set to 350°F is a ratio because it has the word to in it.' Is the student right? Defend your answer.
Practice Check A
A fruit salad has 5 pieces of melon, 3 pieces of pineapple, and 2 grapes. What is the ratio of pineapple to melon?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A parking lot has 10 cars and 6 trucks. What is the part-to-whole ratio of trucks to total vehicles?
✍️ 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 each statement — is it a part-to-part ratio or a part-to-whole ratio?
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: "A ratio compares two quantities, and the order you write them in matters." — 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 Comparison to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
A ratio compares two quantities, and the order you write them in matters. because ___
A ratio compares two quantities, and the order you write them in matters. but ___
A ratio compares two quantities, and the order you write them in matters. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Chef Reyes wrote several comparisons on the board. Sort them into two groups: statements that ARE ratios and statements that are NOT ratios.
| 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 milk and 1 cup of cream. What is the ratio of milk to cream?
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
The school cafeteria is planning a new lunch menu. They want to offer 3 main dishes for every 2 side dishes. If they have 10 side dishes, the cafeteria manager needs to figure out how many main dishes to prepare.
✍️ Connection Reasoning
This is like our ratio work because ___ and ___ are related by ___.
This is like our ratio work because ___ and ___ are related by ___.
Turn & Talk — Connect
In Menu Planning the cafeteria wants 3 main dishes for every 2 side dishes. How is this the same kind of thinking as Chef Reyes's flour-to-sugar ratio?
👂 Listen For
A strong answer identifies the 3:2 part-to-part ratio and explains that the cafeteria keeps that comparison the same even when amounts grow, just like the recipe.
Extend: If the cafeteria has 10 side dishes, generalize how you could figure out the main dishes — and explain why simply 'adding 1 more main than side' would NOT work.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A bag of trail mix contains 8 peanuts and 5 raisins. What is the ratio of raisins to total pieces?
Bonus Exit Check
A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?
✍️ 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: ~50 min
🎯 Listen For · Common Errors
• A strong answer names that flour and sugar are being compared and states the relationship as 3 to 2 (or 'for every 3 flour, 2 sugar'), not just that there is more flour.
• Listen for the idea that a ratio must compare two quantities (using 'to', 'for every', 'out of', or a colon), while a single count or a description is not a comparison.
• A strong answer identifies the 3:2 part-to-part ratio and explains that the cafeteria keeps that comparison the same even when amounts grow, just like the recipe.
• Listen for students naming a specific strategy tied to 6.RP.1 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Understand Ratios is skipping the key idea: "A ratio compares two quantities, and the order you write them in matters." — 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: 3:5 — The ratio of pineapple to melon compares pineapple (3) to melon (5), so the ratio is 3:5.
✓ Practice 2: 6:16 — Total vehicles = 10 + 6 = 16. The ratio of trucks to total is 6:16.
✓ Practice 3: 4:1 — A ratio compares quantities in the order given. Milk to cream = 4 to 1, or 4:1.
✓ Practice 4: 2:8 — Total fruit = 6 + 2 = 8. The part-to-whole ratio of bananas to total fruit is 2:8.
✓ Exit ticket: 5:13 — Total pieces = 8 + 5 = 13. The ratio of raisins to total is 5:13.