Lesson 6-3: Comprehensive Applications

Scenario: Project Management - Apply all learned concepts to solve complex real-world problems and demonstrate mastery!

Duration: 80-95 minutesScenario: Project Management

Learning Objectives

Integrate multiple math concepts in complex problems
Apply project management principles to real-world scenarios
Demonstrate mastery of all 6th grade math concepts
Solve complex, multi-faceted real-world problems

School Science Fair Project

Comprehensive Project Management

You're managing a school science fair project that involves building a model solar system. This project requires you to apply multiple math concepts including ratios, fractions, geometry, statistics, and problem-solving strategies.

Project Requirements:
• Build a scale model of the solar system
• Use a scale of 1 cm = 10,000 km for planet diameters
• Budget: $150 for materials
• Timeline: 3 weeks (21 days)
• Team: 4 students working 2 hours per day
• Present findings with data analysis

Sun

Mercury

Earth

Mars

Jupiter

Solar system model

Comprehensive Problem-Solving Approach

Part 1: Scale Calculations (Ratios & Proportions)

Scale: 1 cm = 10,000 km
Earth diameter: 12,756 km → 12,756 ÷ 10,000 = 1.28 cm
Jupiter diameter: 142,984 km → 142,984 ÷ 10,000 = 14.30 cm
Sun diameter: 1,392,000 km → 1,392,000 ÷ 10,000 = 139.2 cm

Part 2: Budget Planning (Fractions & Decimals)

Total budget: $150
Materials: 2/3 of budget = $150 × 2/3 = $100
Tools: 1/4 of budget = $150 × 1/4 = $37.50
Contingency: Remaining = $150 - $100 - $37.50 = $12.50

Part 3: Timeline Management (Algebra & Equations)

Total time available: 4 students × 2 hours/day × 21 days = 168 hours
Planning: 20% of time = 168 × 0.20 = 33.6 hours
Building: 60% of time = 168 × 0.60 = 100.8 hours
Presentation: 20% of time = 168 × 0.20 = 33.6 hours

Part 4: Data Analysis (Statistics & Probability)

Planet size data: Mean = 6.8 cm, Median = 4.2 cm, Range = 137.9 cm
Success probability: 85% (based on team experience)
Risk factors: Weather (20%), material delays (15%), team conflicts (10%)

Project Summary: This comprehensive project successfully integrates ratios, fractions, algebra, geometry, statistics, and probability to create a realistic project management scenario.

Integration of All Math Concepts

Unit 1-2: Ratios & Fractions

• Scale calculations and proportions
• Budget allocation using fractions
• Time distribution as ratios
• Resource sharing problems

Unit 3: Algebra & Equations

• Timeline planning with variables
• Cost optimization equations
• Resource allocation formulas
• Problem-solving with unknowns

Unit 4: Geometry & Measurement

• Model construction and dimensions
• Area and volume calculations
• Spatial relationships
• Measurement conversions

Unit 5: Statistics & Probability

• Data collection and analysis
• Success probability assessment
• Risk evaluation
• Performance metrics

Real-World Mastery Applications

Engineering & Construction

• Project planning and management
• Resource allocation
• Timeline optimization
• Cost-benefit analysis

Business & Finance

• Strategic planning
• Investment analysis
• Risk management
• Performance evaluation

Science & Research

• Experimental design
• Data analysis
• Model building
• Results interpretation

Comprehensive Practice Problems

Problem 1: Community Garden Project

Design a community garden with a budget of $800. The garden is 20m × 15m. You need to allocate space for vegetables (60%), flowers (25%), and pathways (15%). Calculate material costs, create a timeline, and analyze the project's success probability.

Your comprehensive solution:

Problem 2: School Event Planning

Plan a school carnival with 200 expected attendees. You have $1,000 budget and 2 weeks to prepare. Design activities, calculate costs, manage resources, and create a success plan using all mathematical concepts.

Your comprehensive solution:

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