Lesson Plan
Rate & Percent Power-Up
Students will understand and apply the concepts of rates and percentages to solve real-world problems over five 10-minute sessions, with a daily intervention focus.
Understanding rates and percentages is crucial for making sense of everyday information, from calculating discounts to interpreting statistics. This lesson helps students build a strong foundation for future math concepts and real-world applications.
Audience
Small Group of 6th Grade Students
Time
5 sessions, 10 minutes each
Approach
Through focused instruction, practice, and collaborative activities.
Materials
Smartboard or Projector (optional), Markers or Whiteboard (optional), Rate & Percent Power-Up Slide Deck, Daily Warm-Up: Rate Check-in (oral questions only), Rate Practice Worksheet (select problems), Daily Warm-Up: Percent Pop Quiz (oral questions only), Percentage Application Worksheet (select problems), Daily Warm-Up: Mixed Review Mania (oral questions only), Rates & Percentages Activity Cards (select cards), Daily Warm-Up: Problem Solver Pro (one problem), Real-World Problem Solving Activity, Rates & Percentages Quick Check Quiz (shortened version), and Answer Key: Worksheets & Quiz
Prep
Review Materials & Setup
5 minutes before each session
- Review the Rate & Percent Power-Up Lesson Plan and all linked materials for each day's 10-minute session.
- Select 1-2 key slides from the Rate & Percent Power-Up Slide Deck for each session if using a projector.
- Prepare specific oral questions from the daily warm-ups.
- Select 1-2 problems from the Rate Practice Worksheet and Percentage Application Worksheet for each relevant day.
- Prepare a small set of Rates & Percentages Activity Cards for Day 3.
- Print or prepare the Real-World Problem Solving Activity for Day 4.
- Print or prepare a shortened version of the Rates & Percentages Quick Check Quiz for Day 5.
- Have the Answer Key: Worksheets & Quiz on hand for grading and review.
- Gather any necessary writing supplies for students (pencils, notebooks, etc.).
Step 1
Day 1: What's Your Rate?
10 Minutes
Quick Review & Intro to Rates (3 minutes)
- Briefly define rates with 1-2 examples, referencing Rate & Percent Power-Up Slide Deck (Slide 1).
- Ask 1-2 oral warm-up questions from Daily Warm-Up: Rate Check-in.
Guided Practice: Unit Rates (5 minutes)
- Work through one unit rate example from Rate & Percent Power-Up Slide Deck (Slide 2).
- Guide students through 1-2 problems from the Rate Practice Worksheet, providing focused support.
Quick Check & Wrap-up (2 minutes)
- Ask students to quickly share one thing they learned about rates.
- Assign one problem from Rate Practice Worksheet for optional independent practice or a quick exit ticket question.
Step 2
Day 2: Percent Power!
10 Minutes
Quick Review & Intro to Percentages (3 minutes)
- Briefly define percentages as 'parts out of 100', referencing Rate & Percent Power-Up Slide Deck (Slide 3).
- Ask 1-2 oral warm-up questions from Daily Warm-Up: Percent Pop Quiz.
Guided Practice: Percentage Conversions (5 minutes)
- Work through one example of converting fractions/decimals to percentages from Rate & Percent Power-Up Slide Deck (Slide 4).
- Guide students through 1-2 problems from the Percentage Application Worksheet, providing targeted support.
Quick Check & Wrap-up (2 minutes)
- Ask students to quickly share one common use of percentages.
- Assign one problem from Percentage Application Worksheet for optional independent practice or a quick exit ticket question.
Step 3
Day 3: Rates & Percents Together
10 Minutes
Warm-up & Connection (3 minutes)
- Ask one quick review question about rates or percents from Daily Warm-Up: Mixed Review Mania.
- Use Rate & Percent Power-Up Slide Deck (Slide 5) to connect how rates can be expressed as percentages with a simple example.
Activity: Matching Pairs (5 minutes)
- Provide each student/pair with a few Rates & Percentages Activity Cards.
- Students quickly match one rate/fraction/decimal card with its equivalent percentage card. Circulate and facilitate quick discussion.
Wrap-up (2 minutes)
- Briefly recap the connection between rates and percentages.
Step 4
Day 4: Real-World Problem Solving
10 Minutes
Warm-up & Problem Introduction (3 minutes)
- Pose a real-world problem involving both rates and percentages, drawing from Daily Warm-Up: Problem Solver Pro or the Real-World Problem Solving Activity. You may use Rate & Percent Power-Up Slide Deck (Slide 6) to display the problem.
Guided Problem Solving (5 minutes)
- Work through the problem as a small group, guiding students to identify the rate and percentage components and solve step-by-step.
Discussion & Wrap-up (2 minutes)
- Discuss the steps taken to solve the problem and its real-world relevance. Briefly address any lingering questions.
Step 5
Day 5: Quick Check & Review
10 Minutes
Quick Assessment (7 minutes)
- Distribute a shortened version of the Rates & Percentages Quick Check Quiz (2-3 questions).
- Students complete the quiz independently, focusing on showing their work.
Brief Review & Reflection (3 minutes)
- Quickly review the quiz answers as a group using the Answer Key: Worksheets & Quiz.
- Ask students one quick question: "What was the most challenging or easiest concept for you this week?"
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Slide Deck
Rates: Comparing Different Things
A rate compares two quantities with different units (e.g., miles per hour). A unit rate has a 1 as the second quantity.
Example: A baker made 60 cookies in 30 minutes. What is the rate of cookies per minute?
Welcome students. Briefly define rate and unit rate with an example. Ask students to share other rates they know. Guide them to solve the example: 60 cookies / 30 minutes = 2 cookies per minute.
Quick Rate Check!
A car travels 120 miles in 2 hours. What is its speed in miles per hour?
Present this problem for a quick individual attempt or group discussion. Use it to gauge understanding of unit rates. (Answer: 120 miles / 2 hours = 60 miles per hour)
Percentages: Parts of 100
A percentage is a part of a whole, expressed as 'out of 100.' The '%' symbol means 'percent.'
Example: Convert the fraction 1/2 to a percentage.
Define percentage as 'parts out of 100'. Connect it to fractions and decimals. Guide students to solve the example: 1/2 = 0.5 = 50%.
Quick Percent Conversion!
Convert the decimal 0.75 to a percentage.
Present this conversion for a quick individual attempt or group discussion. (Answer: 0.75 x 100% = 75%)
Rates & Percents: Buddy System!
Rates can often be expressed as percentages!
Example: A basketball player made 8 out of 10 free throws. What is their success rate as a percentage?
Explain how rates can be expressed as percentages. Guide students through calculating the percentage for the example. (Answer: 8/10 = 0.8 = 80%)
Problem Solver Pro!
A shirt originally costs $20. It's on sale for 25% off. What is the discount in dollars, and what is the new price?
Present this real-world problem. Guide the small group through solving it step-by-step, emphasizing how both rates (price) and percentages (discount) are involved. (Answer: Discount = $20 * 0.25 = $5. New Price = $20 - $5 = $15)
Power-Up: Mission Complete!
We've reviewed Rates (unit rates!) and Percentages (parts of 100!), and seen how they work together in the real world. You're becoming a Rate & Percent Pro!
Use this slide to briefly recap the main concepts covered during the week. Reinforce student learning and build confidence before the quick quiz.
Warm Up
Daily Warm-Up: Rate Check-in
Name: _________________________
Date: _________________________
Instructions: Answer the following questions to the best of your ability.
-
What is a rate? Give an example.
-
A baker made 60 cookies in 30 minutes. What is the rate of cookies per minute?
-
You read 40 pages in 20 minutes. How many pages per minute did you read?
Worksheet
Rate Practice Worksheet
Name: _________________________
Date: _________________________
Instructions: Read each problem carefully and calculate the unit rate. Show your work!
-
A car travels 240 miles in 4 hours. How many miles per hour did it travel?
-
A store sells 12 apples for $3. What is the cost per apple?
-
A printer prints 75 pages in 5 minutes. How many pages per minute can it print?
-
You can type 400 words in 8 minutes. What is your typing rate in words per minute?
-
A recipe calls for 2 cups of flour for 30 cookies. How much flour is needed per cookie?
Warm Up
Daily Warm-Up: Percent Pop Quiz
Name: _________________________
Date: _________________________
Instructions: Answer the following questions about percentages.
-
What does the word "percent" mean?
-
Convert 1/2 to a percentage.
-
Convert 0.25 to a percentage.
Worksheet
Percentage Application Worksheet
Name: _________________________
Date: _________________________
Instructions: Convert between fractions, decimals, and percentages. Show your work!
Part 1: Convert to Percentage
-
1/4 =
-
0.7 =
-
3/5 =
Part 2: Convert to Decimal
-
20% =
-
85% =
Part 3: Convert to Fraction (simplify if possible)
-
50% =
-
75% =
Warm Up
Daily Warm-Up: Mixed Review Mania
Name: _________________________
Date: _________________________
Instructions: Solve the following problems.
-
A cyclist rode 60 miles in 3 hours. What was their average speed in miles per hour?
-
What is 25% written as a decimal?
-
If a shirt is on sale for 30% off, what fraction of the original price are you paying?
Activity
Rates & Percentages Activity Cards
Instructions: Cut out the cards below. Work with your group to match each 'Rate/Fraction/Decimal' card with its equivalent 'Percentage' card. Some cards may have more than one match!
Card Set 1: Rates & Fractions
| Card A |
|---|
| 1/2 |
| Card B |
|---|
| 3 out of 4 |
| Card C |
|---|
| 10 errors per 100 questions |
| Card D |
|---|
| 15 correct answers out of 20 |
| Card E |
|---|
| 0.75 |
| Card F |
|---|
| 20 students per 100 students |
| Card G |
|---|
| 0.5 |
| Card H |
|---|
| 1/4 |
Card Set 2: Percentages
| Card 1 |
| :------ |\n| 50% |
| Card 2 |
|---|
| 75% |
| Card 3 |
|---|
| 10% |
| Card 4 |
|---|
| 25% |
| Card 5 |
|---|
| 20% |
(Teacher Note: You might want to print these on different colored paper for easier sorting.)
Challenge: Create 2 new matching pairs of your own!
Warm Up
Daily Warm-Up: Problem Solver Pro
Name: _________________________
Date: _________________________
Instructions: Solve the following problem, showing your work.
- A store has a sale: "Buy any item and get 20% off the original price!" If a toy car originally costs $15, how much is the discount in dollars? How much will you pay for the toy car?
Activity
Real-World Problem Solving Activity
Name: _________________________
Date: _________________________
Instructions: Read the problem carefully and solve it, showing all your work.
- A store is having a "Buy One, Get One 50% Off" sale on all t-shirts. Each t-shirt originally costs $12. If you buy two t-shirts, what is the total cost, and what is your overall discount percentage for both shirts combined?
Quiz
Rates & Percentages Quick Check Quiz
Answer Key
Answer Key: Worksheets & Quiz
Daily Warm-Up: Rate Check-in
-
What is a rate? Give an example.
- Thought Process: A rate compares two quantities measured in different units.
- Answer: A rate is a comparison of two different quantities with different units. Example: 60 miles per hour.
-
A baker made 60 cookies in 30 minutes. What is the rate of cookies per minute?
- Thought Process: To find the rate, divide the number of cookies by the time in minutes.
- Answer: 60 cookies / 30 minutes = 2 cookies per minute.
-
You read 40 pages in 20 minutes. How many pages per minute did you read?
- Thought Process: Divide the number of pages by the time in minutes.
- Answer: 40 pages / 20 minutes = 2 pages per minute.
Rate Practice Worksheet
-
A car travels 240 miles in 4 hours. How many miles per hour did it travel?
- Thought Process: Divide total miles by total hours.
- Answer: 240 miles / 4 hours = 60 miles per hour.
-
A store sells 12 apples for $3. What is the cost per apple?
- Thought Process: Divide total cost by total number of apples.
- Answer: $3 / 12 apples = $0.25 per apple.
-
A printer prints 75 pages in 5 minutes. How many pages per minute can it print?
- Thought Process: Divide total pages by total minutes.
- Answer: 75 pages / 5 minutes = 15 pages per minute.
-
You can type 400 words in 8 minutes. What is your typing rate in words per minute?
- Thought Process: Divide total words by total minutes.
- Answer: 400 words / 8 minutes = 50 words per minute.
-
A recipe calls for 2 cups of flour for 30 cookies. How much flour is needed per cookie?
Thought Process: Divide total flour by total cookies.- Answer: 2 cups / 30 cookies = 1/15 cup of flour per cookie (approximately 0.067 cups).
Daily Warm-Up: Percent Pop Quiz
-
What does the word "percent" mean?
- Thought Process: Recall the definition of percent.
- Answer: "Percent" means "per hundred" or "out of one hundred."
-
Convert 1/2 to a percentage.
- Thought Process: Convert fraction to decimal (1 ÷ 2 = 0.5), then multiply by 100.
- Answer: 0.5 x 100% = 50%.
-
Convert 0.25 to a percentage.
- Thought Process: Multiply decimal by 100.
- Answer: 0.25 x 100% = 25%.
Percentage Application Worksheet
Part 1: Convert to Percentage
-
1/4 =
- Thought Process: 1 ÷ 4 = 0.25; 0.25 x 100 = 25
- Answer: 25%
-
0.7 =
- Thought Process: 0.7 x 100 = 70
- Answer: 70%
-
3/5 =
- Thought Process: 3 ÷ 5 = 0.6; 0.6 x 100 = 60
- Answer: 60%
Part 2: Convert to Decimal
-
20% =
- Thought Process: 20 ÷ 100 = 0.2
- Answer: 0.2
-
85% =
- Thought Process: 85 ÷ 100 = 0.85
- Answer: 0.85
Part 3: Convert to Fraction (simplify if possible)
-
50% =
- Thought Process: 50/100 = 1/2
- Answer: 1/2
-
75% =
- Thought Process: 75/100 = 3/4
- Answer: 3/4
Daily Warm-Up: Mixed Review Mania
-
A cyclist rode 60 miles in 3 hours. What was their average speed in miles per hour?
- Thought Process: Divide total miles by total hours.
- Answer: 60 miles / 3 hours = 20 miles per hour.
-
What is 25% written as a decimal?
- Thought Process: Divide percentage by 100.
- Answer: 25 / 100 = 0.25.
-
If a shirt is on sale for 30% off, what fraction of the original price are you paying?
- Thought Process: If 30% is off, 70% is being paid. Convert 70% to a fraction.
- Answer: 70% = 70/100 = 7/10.
Daily Warm-Up: Problem Solver Pro
- A store has a sale: "Buy any item and get 20% off the original price!" If a toy car originally costs $15, how much is the discount in dollars? How much will you pay for the toy car?
- Thought Process: Calculate 20% of $15. Then subtract the discount from the original price.
- Answer:
- Discount: 0.20 * $15 = $3.00
- Amount paid: $15.00 - $3.00 = $12.00
Real-World Problem Solving Activity
- A store is having a "Buy One, Get One 50% Off" sale on all t-shirts. Each t-shirt originally costs $12. If you buy two t-shirts, what is the total cost, and what is your overall discount percentage for both shirts combined?
- Thought Process: Calculate the cost of the first shirt ($12). Calculate the cost of the second shirt (50% of $12 = $6). Add these for the total cost. Calculate the total original price ($12 + $12 = $24). Find the total discount ($24 - $18 = $6). Calculate the overall discount percentage ($6 / $24 * 100%).
- Answer:
- Cost of first t-shirt: $12
- Cost of second t-shirt (50% off): $12 * 0.50 = $6
- Total cost for two t-shirts: $12 + $6 = $18
- Total original price for two t-shirts: $12 + $12 = $24
- Total discount: $24 - $18 = $6
- Overall discount percentage: ($6 / $24) * 100% = 0.25 * 100% = 25%
Rates & Percentages Activity Cards
- Card A (1/2) matches Card 1 (50%)
- Card B (3 out of 4) matches Card 2 (75%)
- Card C (10 errors per 100 questions) matches Card 3 (10%)
- Card D (15 correct answers out of 20) matches Card 2 (75%)
- Card E (0.75) matches Card 2 (75%)
- Card F (20 students per 100 students) matches Card 5 (20%)
- Card G (0.5) matches Card 1 (50%)
- Card H (1/4) matches Card 4 (25%)
Rates & Percentages Quick Check Quiz
-
Which of the following is an example of a unit rate?
- Thought Process: A unit rate has a denominator of 1.
- Answer: C. 60 miles per hour
-
A runner completed 10 miles in 2 hours. What was their average speed in miles per hour? Show your work.
- Thought Process: Divide total miles by total hours.
- Answer: 10 miles / 2 hours = 5 miles per hour.
-
What does 75% mean?
- Thought Process: Recall the definition of percent.
- Answer: C. 75 parts out of 100