Ratio and Rate Problem Solving
I can solve real-world rate problems by finding and using unit rates.
How to Use This Deck
Click Present or press F11 for fullscreen. Use arrow keys to advance.
Blue boxes show exactly what to say, ask, and how long to spend.
Text boxes, polls, and drag-sort save automatically in the browser.
Press N or click 📝 in the toolbar for pacing tips and answers.
Launch the full HTML activity for independent practice.
File → Print or the print button for handout copies.
🎯 Content Objective / Objetivo de contenido
I can solve real-world rate problems by finding and using unit rates.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Team 1 knows 3 pounds of chicken cost $18. What was your plan to find the cost of just 1 pound, and why is that unit rate useful?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Scenario Launch
It's the final day of Chef Academy — the Culinary Competition! Teams must solve ratio and rate problems to earn ingredients for their dishes. Team 1 needs to figure out how much chicken costs if 3 pounds cost $18. Team 2 must calculate how many cupcakes they can frost if they decorate 5 cupcakes every 4 minutes. The clock is ticking!
Concept Launch
💡 How do unit rates solve rate problems?
A rate compares two amounts with different units, like dollars and pounds. A unit rate is the amount for just 1. You find it by dividing, and you can use it to find any amount.
Find the unit rate by dividing, then multiply it to find the amount you need.
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 |
|---|---|---|---|
| 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. |
$12 for 4 pounds → dollars per pound | |
| Unit rate Tasa unitaria |
A rate for just 1 of something, like cost for 1 item. Una tasa para solo 1 de algo, como el precio de 1 artículo. |
$12 ÷ 4 = $3 per 1 pound | |
| Per Por |
For each one. Example: 5 dollars per book. Por cada uno. Ejemplo: 5 dólares por libro. |
60 miles per hour, $5 per ticket | |
| Problem solving Resolución de problemas |
Using ratios and rates to find a missing amount. Usar razones y tasas para encontrar una cantidad que falta. |
Set up → Plan → Solve → Check | |
| Proportion Proporción |
A math sentence saying two ratios are equal. It helps find a missing number. Una oración matemática que dice que dos razones son iguales. Ayuda a hallar un número que falta. |
3/5 = x/20 → x = 12 |
Which Word Fits?
A ratio comparing two quantities with different units 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
Team 1 knows 3 pounds of chicken cost $18. What was your plan to find the cost of just 1 pound, and why is that unit rate useful?
👂 Listen For
Students divide $18 by 3 to get $6 per pound and explain the unit rate lets them find the cost of any number of pounds.
Extend: Once you know the unit rate is $6 per pound, how can you find the cost of 7 pounds without a ratio table? Justify your shortcut.
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
Team 1 knows that 3 pounds of chicken cost $18. Complete the ratio table to find the cost for different amounts, then determine the unit rate.
✍️ 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
Team 2 frosts 5 cupcakes every 4 minutes. How did you set up a rate or proportion to find how many cupcakes they frost in a longer time?
👂 Listen For
Students state the rate (5 cupcakes per 4 minutes) and set up a proportion or unit rate (1.25 cupcakes/min) to scale to the needed time.
Extend: Would it be faster to use a unit rate or a proportion for this problem? Explain when each strategy is the better tool.
Practice Check A
A car travels 150 miles in 3 hours. A bus travels 200 miles in 5 hours. Which vehicle is faster?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A bakery makes 24 cookies in 3 batches. What is the unit rate of cookies per batch?
✍️ 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 rate problem by the strategy that works BEST to solve it.
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 unit rate by dividing, then multiply it to find the amount you need." — and it works because ___.
Because Rate means ___, but a tricky part is ___, so I have to ___.
A common mistake with Rate is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Unit rate to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Find the unit rate by dividing, then multiply it to find the amount you need. because ___
Find the unit rate by dividing, then multiply it to find the amount you need. but ___
Find the unit rate by dividing, then multiply it to find the amount you need. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Team 1 knows that 3 pounds of chicken cost $18. Complete the ratio table to find the cost for different amounts, then determine the unit rate.
| Pounds of Chicken | Cost ($) |
|---|---|
| 3 | 18 |
| 1 | |
| 5 | |
| 8 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A bakery makes 24 cookies in 3 batches. What is the unit rate of cookies per batch?
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 runner trains for a 5K race. During practice, she runs 3 miles in 27 minutes. She wants to know her pace (minutes per mile) and predict how long the full 5K (3.1 miles) will take at the same rate.
✍️ Connection Reasoning
This is like our rate problem-solving work because ___ and ___ are related by ___.
This is like our rate problem-solving work because ___ and ___ are related by ___.
Turn & Talk — Connect
Tell about a real situation where rates matter, like speed, pay, or price, and explain how the unit rate helps you.
👂 Listen For
Students give a real rate (speed, hourly pay, price per item) and explain how the unit rate lets them predict or compare.
Extend: Pick two real rates that could be compared, and explain how unit rates would let you decide which is the better choice.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A printer prints 30 pages in 5 minutes. At this rate, how many pages will it print in 12 minutes?
Bonus Exit Check
Apples cost $5 for 4 pounds. What is the cost per pound?
✍️ 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 divide $18 by 3 to get $6 per pound and explain the unit rate lets them find the cost of any number of pounds.
• Students state the rate (5 cupcakes per 4 minutes) and set up a proportion or unit rate (1.25 cupcakes/min) to scale to the needed time.
• Students give a real rate (speed, hourly pay, price per item) and explain how the unit rate lets them predict or compare.
• 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 Ratio and Rate Problem Solving is skipping the key idea: "Find the unit rate by dividing, then multiply it to find the amount you need." — 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: The car — Car: 150÷3 = 50 mph. Bus: 200÷5 = 40 mph. The car travels faster at 50 mph vs. 40 mph.
✓ Practice 2: 8 cookies per batch — Unit rate: 24 cookies ÷ 3 batches = 8 cookies per batch.
✓ Practice 3: $1.25 — Unit rate: $5 ÷ 4 pounds = $1.25 per pound.
✓ Practice 4: 60 miles — Unit rate: 36 ÷ 3 = 12 miles per hour. In 5 hours: 12 × 5 = 60 miles.
✓ Exit ticket: 72 — Unit rate: 30 ÷ 5 = 6 pages per minute. In 12 minutes: 6 × 12 = 72 pages.