Solve Problems with Unit Rates
I can solve real-world problems by using unit rates to compare options.
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Launch the full HTML activity for independent practice.
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🎯 Content Objective / Objetivo de contenido
I can solve real-world problems by using unit rates to compare options.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
As supply manager you compare token deals like 500 for $60 and 350 for $38.50. You can't compare totals directly, so what does finding the cost 'per unit' let you do?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Arcade Builder Challenge
You're the new supply manager for the arcade! You need to order tokens, prizes, and snacks from different suppliers. Each supplier offers a different package deal. Your job is to find the unit rate for each deal and figure out which supplier gives you the best value for every item you need to order.
Concept Launch
💡 How do I use unit rates to find the better buy?
A unit rate is the cost for just 1 item, like the price per token. When packages have different sizes, the unit rate lets you compare them fairly.
Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy.
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 |
|---|---|---|---|
| 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. |
$2.50 per pound means $2.50 for every 1 pound | |
| Better Buy Mejor compra |
The choice that costs less for each item. La opción que cuesta menos por cada artículo. |
$0.10 each vs $0.15 each — the $0.10 option is the better buy | |
| Comparison Comparación |
Looking at numbers to see which is bigger or smaller. Mirar números para ver cuál es mayor o menor. |
$3 per game < $4 per game | |
| Per Unit Por unidad |
For each single item. Por cada artículo. |
$0.50 per token means each token costs $0.50 | |
| 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. |
120 miles in 3 hours is a rate (miles and hours are different units) | |
| 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. |
5/3 = x/12 → x = 20 |
Which Word Fits?
A rate that gives the amount for exactly one unit 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
As supply manager you compare token deals like 500 for $60 and 350 for $38.50. You can't compare totals directly, so what does finding the cost 'per unit' let you do?
👂 Listen For
Students explain the packages have different quantities, so the per-unit cost (unit rate) is needed to compare deals fairly.
Extend: Does the biggest package always have the lowest unit rate? Predict, then explain how you could be tricked by package size alone.
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
Calculate the unit rate for each supplier's deal. Then determine which is the better buy for each item.
✍️ Explore Discourse
How do you use unit rates to determine the better buy?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How did the unit rate help you decide the better buy between the two token suppliers in your table?
👂 Listen For
Students divide price by quantity for each deal (e.g., 350 for $38.50 = $0.11 each) and choose the supplier with the lower unit rate as the better buy.
Extend: One supplier had the lower price per token but a higher total. Explain why a lower unit rate, not a lower total, is what makes a deal the better buy.
Practice Check A
A machine dispenses 24 tokens in 3 minutes. At this rate, how many tokens does it dispense in 10 minutes?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A factory produces 360 widgets in 8 hours. At the same rate, how many widgets are produced in a 12-hour shift?
✍️ 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
Three friends each walked different distances in different times. Sort them from fastest to slowest.
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: "Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy." — and it works because ___.
Because Unit Rate means ___, but a tricky part is ___, so I have to ___.
A common mistake with Unit Rate is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Better Buy to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy. because ___
Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy. but ___
Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Calculate the unit rate for each supplier's deal. Then determine which is the better buy for each item.
| Item | Supplier | Deal | Unit Rate | Better Buy? |
|---|---|---|---|---|
| Tokens | Fun Supply Co. | 500 for $60 | $0.12 per token | |
| Tokens | Arcade Depot | 350 for $38.50 | ||
| Prize Rings | Fun Supply Co. | 200 for $18 | $0.09 each | |
| Prize Rings | Arcade Depot | 150 for $12 | ||
| Popcorn Bags | Fun Supply Co. | 80 for $24 | ||
| Popcorn Bags | Arcade Depot | 120 for $33.60 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Which is the better buy: 6 bouncy balls for $4.50 or 10 bouncy balls for $8.00?
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 arcade needs 600 prize tickets printed. Printer A prints 150 tickets in 5 minutes. Printer B prints 200 tickets in 8 minutes. The manager wants to use the faster printer.
✍️ Connection Reasoning
Which printer should the manager choose, and how long will it take to print all 600 tickets?
Printer A prints ___ tickets per minute. Printer B prints ___ tickets per minute. The manager should use Printer ___ because it is faster. It will take ___ minutes to print 600 tickets.
Turn & Talk — Connect
Printer A makes 150 tickets in 5 minutes and Printer B makes 200 in 8 minutes. The manager needs 600 tickets fast. How do unit rates decide the faster printer and the time needed?
👂 Listen For
Students find 30 and 25 tickets/min, choose Printer A (higher rate), and divide 600 / 30 = 20 minutes.
Extend: Here the higher unit rate is better, but for the token deals the LOWER unit rate was better. Explain why 'better' depends on what the rate measures.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A car travels 195 miles on 6 gallons of gas. What is the unit rate in miles per gallon?
Bonus Exit Check
Which is the better buy: 6 bouncy balls for $4.50 or 10 bouncy balls for $8.00?
✍️ 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 explain the packages have different quantities, so the per-unit cost (unit rate) is needed to compare deals fairly.
• Students divide price by quantity for each deal (e.g., 350 for $38.50 = $0.11 each) and choose the supplier with the lower unit rate as the better buy.
• Students find 30 and 25 tickets/min, choose Printer A (higher rate), and divide 600 / 30 = 20 minutes.
• Listen for students naming a specific strategy tied to 6.RP.3b — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Solve Problems with Unit Rates is comparing the total prices instead of the cost per item — the deal with the smaller total can still cost more per unit. Always reduce each option to its unit rate before you decide, then pick the lower one.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 80 tokens — Unit rate: 24 ÷ 3 = 8 tokens per minute. In 10 minutes: 8 × 10 = 80 tokens.
✓ Practice 2: 540 widgets — Unit rate: 360 ÷ 8 = 45 widgets per hour. In 12 hours: 45 × 12 = 540 widgets.
✓ Practice 3: 6 for $4.50 — $0.75 each — $4.50 ÷ 6 = $0.75 each. $8.00 ÷ 10 = $0.80 each. $0.75 < $0.80, so 6 for $4.50 is the better buy.
✓ Practice 4: 3 ounces per minute — 15 ÷ 5 = 3 ounces per minute.
✓ Exit ticket: 32.5 miles per gallon — 195 ÷ 6 = 32.5 miles per gallon.