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Back to Unit 6

Lesson 6-3: Comprehensive Applications

Scenario: Community Service - Apply all 7th grade math concepts to solve real-world problems!

Duration: 75-90 minutesScenario: Community Service

Learning Objectives

  • Apply all 7th grade math concepts to one comprehensive problem
  • Solve real-world community and environmental problems
  • Integrate multiple mathematical skills and concepts
  • Make informed decisions based on mathematical analysis

Community Service Scenario

The Problem

Your school is organizing a community service project to create a sustainable garden and recycling program. You need to plan the entire project using mathematical analysis. The project includes: designing a garden layout, calculating costs, analyzing recycling data, and planning volunteer schedules.

Community Challenge:
Create a comprehensive plan that applies all your 7th grade math skills to make this project successful.

Project Components

Garden Design:

  • • Rectangular garden: 20m × 15m
  • • Vegetable plots: 4m × 3m each
  • • Flower beds: circular, radius 2m
  • • Paths: 1m wide around plots

Recycling Program:

  • • 500 students participate
  • • Average 2kg waste per student/week
  • • 60% recyclable, 40% compostable
  • • Recycling saves $0.50/kg

Part 1: Garden Design (Geometry & Measurement)

Calculate Garden Areas

Total Garden Area: 20m × 15m = 300 m²

Vegetable Plot Area: 4m × 3m = 12 m² per plot

Flower Bed Area: π × (2m)² = 12.57 m² per bed

Maximum Plots: Can fit 6 vegetable plots and 4 flower beds with paths

Part 2: Cost Analysis (Algebra & Ratios)

Budget Planning

Seeds: $5 per plot × 6 plots = $30

Flower Plants: $8 per bed × 4 beds = $32

Soil & Fertilizer: $2 per m² × 300 m² = $600

Tools & Equipment: $150

Total Garden Cost: $30 + $32 + $600 + $150 = $812

Part 3: Recycling Analysis (Statistics & Probability)

Waste Analysis

Total Weekly Waste: 500 students × 2kg = 1,000 kg

Recyclable Waste: 1,000 kg × 60% = 600 kg

Compostable Waste: 1,000 kg × 40% = 400 kg

Weekly Savings: 600 kg × $0.50 = $300

Annual Savings: $300 × 36 weeks = $10,800

Part 4: Volunteer Scheduling (Rational Numbers)

Time Management

Garden Setup Time: 40 hours total

Available Volunteers: 20 students

Hours per Volunteer: 40 ÷ 20 = 2 hours each

Daily Maintenance: 1.5 hours per day, 3 volunteers needed

Comprehensive Project Analysis

Project Summary

Total Investment: $812 (one-time garden setup)
Annual Savings: $10,800 (from recycling program)
Net Benefit: $9,988 per year
ROI (Return on Investment): 1,230% in the first year!

Environmental Impact: Diverts 1,000 kg of waste weekly from landfills

Educational Value: 500 students learn about sustainability

Community Benefit: Fresh produce for school cafeteria

Practice Problems

Problem 1: School Fundraiser

Plan a school fundraiser selling homemade cookies. You can make 200 cookies per day for 5 days. Each cookie costs $0.50 to make and sells for $2.00. You need to raise $1,500 for new computers. Will you meet your goal? If not, how should you adjust your plan?

Your comprehensive analysis:

Problem 2: Community Park Design

Design a community park with a playground, basketball court, and picnic area. The total area is 1,200 m². The basketball court is 28m × 15m, the playground is circular with radius 8m, and the picnic area is rectangular. If the picnic area should be 20% of the total area, what are its possible dimensions?

Your design solution: