Lesson Plan: Understanding Pie Charts and Fraction Calculations
Grade Level
Primary School (Grades 4-6)
Duration
45-60 minutes
Learning Objectives
By the end of this lesson, students will be able to:
- Interpret information from pie charts
- Convert percentages to actual numbers
- Work with fractions in vertical form
- Solve multi-step word problems involving percentages and totals
Materials Needed
- Interactive web page (provided)
- Whiteboard/blackboard
- Markers/chalk
- Calculator (optional)
- Student worksheets
Lesson Structure
1. Introduction (10 minutes)
Hook Question: "How do your parents help you with homework?"
Key Concepts to Introduce:
- Pie charts represent parts of a whole
- Percentages show proportions out of 100
- The whole circle = 100% = total number surveyed
Visual Aid: Show the pie chart and identify:
- Each section represents a different time range
- Percentages must add up to 100%
2. Understanding the Problem (10 minutes)
Given Information:
- 90 parents helped for ½ hour to 1½ hours
- This 90 represents 30% of all parents surveyed
Key Question: If 90 parents = 30%, how do we find 100%?
Guided Discovery:
- 30% of total = 90 parents
- 10% of total = 90 ÷ 3 = 30 parents
- 100% of total = 30 × 10 = 300 parents
Alternative Method:
- Set up equation: 30% × Total = 90
- 0.30 × Total = 90
- Total = 90 ÷ 0.30 = 300
3. Solving Each Question (20 minutes)
Question (i): How many parents were surveyed?
Step-by-step solution:
Given: 90 parents = 30%
Find: Total parents (100%)
Method 1: Proportion
30% → 90 parents
1% → 90 ÷ 30 = 3 parents
100% → 3 × 100 = 300 parents
Method 2: Division
Total = 90 ÷ 0.30 = 300 parents
Answer: 300 parents
Question (ii): How many said they did not help?
Step-by-step solution:
Total parents = 300
Percentage who didn't help = 50%
Number who didn't help = 50% of 300
= 0.50 × 300
= 150 parents
Alternative:
50% = half
Half of 300 = 300 ÷ 2 = 150 parents
Answer: 150 parents
Question (iii): How many helped for more than 1½ hours?
Step-by-step solution:
Total parents = 300
Percentage who helped more than 1½ hours = 20%
Number = 20% of 300
= 0.20 × 300
= 60 parents
Alternative:
20% = one-fifth
One-fifth of 300 = 300 ÷ 5 = 60 parents
Answer: 60 parents
4. Verification (5 minutes)
Check: Do all categories add up to 300?
½ hour to 1½ hours: 90 parents (30%)
More than 1½ hours: 60 parents (20%)
Did not help: 150 parents (50%)
Total: 90 + 60 + 150 = 300 ✓
Percentages: 30% + 20% + 50% = 100% ✓
5. Practice Problems (10 minutes)
Problem 1: In a survey, 40% of 250 students like mathematics. How many students like mathematics?
Problem 2: If 75 people represent 25% of attendees at an event, how many people attended in total?
Problem 3: A pie chart shows: 35% chose option A, 45% chose option B, and 20% chose option C. If 60 people chose option C, how many people were surveyed?
Key Teaching Points
Working with Percentages
- 50% = ½ (half)
- 25% = ¼ (quarter)
- 20% = ⅕ (one-fifth)
- 10% = 1/10 (one-tenth)
Problem-Solving Strategy
- Identify what you know
- Identify what you need to find
- Choose a method (proportion or equation)
- Calculate carefully
- Verify your answer (check if it makes sense)
Common Mistakes to Avoid
-
Confusing the part with the whole
- 90 is NOT the total; it's 30% of the total
-
Calculation errors
- 90 ÷ 30 ≠ 30 (it equals 3)
-
Not checking if percentages add to 100%
- Always verify: 30% + 20% + 50% = 100%
-
Mixing up fraction notation
- 1½ hours means 1 hour and 30 minutes
- ½ hour means 30 minutes
Assessment Questions
Quick Check:
- What percentage of parents helped for more than 1½ hours?
- If 300 parents were surveyed and 50% didn't help, how many didn't help?
- True or False: 90 parents represent 30% of all surveyed parents.
Challenge Question: If the school surveyed 100 more parents with the same percentages, how many of these new parents would help for ½ to 1½ hours?
Extension Activities
- Create Your Own Survey: Students design a class survey and create a pie chart
- Real-World Application: Research and analyze pie charts from news articles or reports
- Digital Activity: Use the interactive web page to explore different scenarios
Answers to Practice Problems
Problem 1: 40% of 250 = 0.40 × 250 = 100 students
Problem 2: 25% = 75, so 1% = 3, so 100% = 300 attendees
Problem 3: 20% = 60, so 1% = 3, so 100% = 300 people
Challenge: 30% of 100 = 30 parents