🎒 Class VII Picnic Planning 🚌
An Interactive Mathematical Journey
Problem Statement
The Picnic Scenario
A picnic is being planned in a school for Class VII. Girls are 60% of the total number of students and are 18 in number.
The picnic site is 55 km from the school and the transport company is charging at the rate of ₹12 per km. The total cost of refreshments will be ₹4280.
- Number of girls = 18
- Girls = 60% of total students
- Distance to picnic site = 55 km
- Transport cost = ₹12 per km
- Refreshment cost = ₹4280
- First stop = 22 km from school
Learning Objectives
- Understand and apply percentage concepts
- Calculate ratios from percentages
- Solve real-world problems involving cost calculations
- Calculate percentages of distances
- Apply mathematical reasoning to practical scenarios
Detailed Lesson Plan (45 minutes)
1Introduction (5 minutes)
Engage: Show pictures of a school picnic or discuss students' own picnic experiences.
Connect: "Today we'll plan a picnic using mathematics! We need to figure out ratios, costs, and distances."
Concepts: Percentages, Ratios, Cost calculation, Distance percentages
2Review Prerequisites (5 minutes)
Quick Recap:
- What is a percentage? (Parts per hundred)
- What is a ratio? (Comparison of two quantities)
- How do we find a whole when we know the part and percentage?
Then, Total = given value × 100x
3Problem 1: Finding the Ratio (10 minutes)
Teach: Guide students step-by-step
Step 1: Find total students
Girls = 60% of total = 18
Total = 18 × 10060 = 180060 = 30 students
Step 2: Find number of boys
Boys = Total - Girls = 30 - 18 = 12 boys
Step 3: Find the ratio
Girls : Boys = 18 : 12 = 3 : 2 (simplified)
Practice: Ask students to verify by checking if 3:2 represents 60%:40%
4Problem 2: Cost Per Head (10 minutes)
Teach: Break down the cost calculation
Step 1: Calculate transport cost
Distance = 55 km (round trip = 55 × 2 = 110 km)
Transport cost = 110 × 12 = ₹1320
Step 2: Calculate total cost
Total = Transport + Refreshments
Total = 1320 + 4280 = ₹5600
Step 3: Find cost per head
Total people = 30 students + 2 teachers = 32
Cost per head = 560032 = ₹175
5Problem 3: Distance Percentages (10 minutes)
Teach: Apply percentage formula to distance
Part A: Percentage covered to first stop
= (22 ÷ 55) × 100 = 40%
Part B: Percentage remaining
Remaining = 100% - 40% = 60%
Or, Distance left = 55 - 22 = 33 km
Percentage = (33 ÷ 55) × 100 = 60%
6Conclusion & Assessment (5 minutes)
Summarize: Review all three solutions
Real-world connection: Discuss how these calculations help in planning events
Assessment: Use the Practice tab to test understanding
Complete Solutions
Question 1: Ratio of Girls to Boys
Given: Girls = 18, Girls = 60% of total
Solution:
If 60% = 18 students
Then 100% = (18 × 100) ÷ 60 = 30 students
Boys = 30 - 18 = 12 students
Ratio = 18 : 12 = 3 : 2
Question 2: Cost Per Head
Given: Distance = 55 km, Rate = ₹12/km, Refreshments = ₹4280
Solution:
Round trip distance = 55 × 2 = 110 km
Transport cost = 110 × 12 = ₹1320
Total cost = 1320 + 4280 = ₹5600
Total people = 30 students + 2 teachers = 32
Cost per head = 5600 ÷ 32 = ₹175
Question 3: Distance Percentages
Given: First stop = 22 km, Total distance = 55 km
Solution:
Percentage covered = (22 ÷ 55) × 100 = 40%
Distance remaining = 55 - 22 = 33 km
Percentage remaining = (33 ÷ 55) × 100 = 60%
Interactive Practice
Problem 1: Find the Ratio
Girls = 18, Boys = 12
Enter the simplified ratio:
Girls : Boys = :
Problem 2: Calculate Cost Per Head
Total cost = ₹5600, Total people = 32
Cost per head = ₹
Problem 3: Distance Percentages
Distance covered = 22 km out of 55 km
Percentage covered = %
Percentage remaining = %