Unit 3 · Standard 6.RP.3
Ratio and Rate Problem Solving
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
$12 for 4 pounds → dollars per pound
Rate
A ratio comparing two amounts with different units, like miles per hour.
$12 ÷ 4 = $3 per 1 pound
Unit rate
A rate for just 1 of something, like cost for 1 item.
60 miles per hour, $5 per ticket
Per
For each one. Example: 5 dollars per book.
Set up → Plan → Solve → Check
Problem solving
Using ratios and rates to find a missing amount.
3/5 = x/20 → x = 12
Proportion
A math sentence saying two ratios are equal. It helps find a missing number.
Key Ideas & Notes
- 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.
- 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.
Think About It
- What two quantities with different units are being compared?
- How could you find the cost of just 1 pound of chicken?
- How could you find the number of cupcakes frosted in 1 minute?
My Notes
Guided Examples
Example 1
A bakery makes 24 cookies in 3 batches. What is the unit rate of cookies per batch?
Solution: Unit rate: 24 cookies ÷ 3 batches = 8 cookies per batch.
Answer: A. 8 cookies per batch
Example 2
Apples cost $5 for 4 pounds. What is the cost per pound?
Solution: Unit rate: $5 ÷ 4 pounds = $1.25 per pound.
Answer: A. $1.25
Example 3
A cyclist rides 36 miles in 3 hours. At the same rate, how far will she ride in 5 hours?
Solution: Unit rate: 36 ÷ 3 = 12 miles per hour. In 5 hours: 12 × 5 = 60 miles.
Answer: A. 60 miles
Write About the Math The Writing Revolution
I can explain my solution using the words rate, unit rate, per, and proportion.
1. Kernel Sentence subject + verb
Model: Rate is a ratio comparing two amounts with different units, like miles per hour.Tasa es una razón que compara dos cantidades con unidades distintas, como millas por hora.
Write a kernel sentence about rate. Use a subject and a verb.Escribe una oración base sobre tasa. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Rate matters in mathTasa importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Rate matters in math because ___.Tasa importa en matemáticas porque ___.
Rate matters in math, but ___.Tasa importa en matemáticas, pero ___.
Rate matters in math, so ___.Tasa importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about rate.Di un hecho verdadero sobre rate.
Rate ___.
Ask a question about rate.Haz una pregunta sobre rate.
How does ___ ?¿Cómo ___ ?
Show excitement about rate.Muestra entusiasmo sobre rate.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with rate.Dile a un compañero qué hacer con rate.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
My plan was to ___.Mi plan fue ___.
The rate is ___ per ___.La tasa es ___ por ___.
Rates matter when ___.Las tasas importan cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A car travels 150 miles in 3 hours. A bus travels 200 miles in 5 hours. Which vehicle is faster?
- The car
- The bus
- Same speed
- Cannot determine
2. A factory makes 240 widgets in 8 hours. Another factory makes 200 widgets in 5 hours. Which factory is faster? If both factories work together for 10 hours, how many total widgets would they produce?
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Mia's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A printer prints 30 pages in 5 minutes. At this rate, how many pages will it print in 12 minutes?
- 72
- 60
- 36
- 42
Answer Key & Teacher Guide
- Try It 1: A. The car — Car: 150÷3 = 50 mph. Bus: 200÷5 = 40 mph. The car travels faster at 50 mph vs. 40 mph.
- Try It 2: Factory A: 240 ÷ 8 = 30 widgets/hour. Factory B: 200 ÷ 5 = 40 widgets/hour. Factory B is faster. Together: (30 + 40) × 10 = 70 × 10 = 700 widgets in 10 hours.
- Exit Ticket: A. 72 — Unit rate: 30 ÷ 5 = 6 pages per minute. In 12 minutes: 6 × 12 = 72 pages.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Rate is a ratio comparing two amounts with different units, like miles per hour.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).