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Lesson 6-2: Cross-Topic Integration

School Fair Planning

Learning Objectives

By the end of this lesson, you will:

  • Combine concepts from multiple math topics
  • Make connections between different mathematical ideas
  • Use complex reasoning to solve integrated problems
  • Synthesize information from multiple sources

Topics You'll Integrate:

FractionsDecimalsAlgebraGeometryData AnalysisProblem Solving

School Fair Challenge

Your school is organizing an annual fair with games, food, and activities. You need to help plan the fair by combining knowledge from all your math topics: fractions for recipes, decimals for money, algebra for planning, geometry for layout, and data analysis for success measurement.

Food & Recipes

Use fractions to scale recipes and decimals for pricing

Layout & Space

Apply geometry for booth placement and area calculations

Data & Analysis

Use data analysis to predict attendance and profits

Problem 1: Food Booth Planning

The Challenge:

You're planning a pizza booth. The original recipe makes 8 slices, but you need to make 120 slices. Each slice costs $0.75 to make and sells for $2.50. The booth space is a 6 ft × 8 ft rectangle. Calculate the profit per square foot of booth space.

Step 1: Recipe Scaling (Fractions)

Scale the recipe from 8 slices to 120 slices.

Scale factor = 120 ÷ 8 = 15
You need to make 15 times the original recipe

Step 2: Cost Calculation (Decimals)

Calculate total cost and revenue using decimal operations.

Total cost = 120 slices × $0.75 = $90.00
Total revenue = 120 slices × $2.50 = $300.00
Profit = $300.00 - $90.00 = $210.00

Step 3: Area Calculation (Geometry)

Find the area of the booth space.

Booth area = 6 ft × 8 ft = 48 square feet

Step 4: Profit per Square Foot

Divide total profit by booth area.

Profit per sq ft = $210.00 ÷ 48 sq ft = $4.375 per sq ft

Answer:

The pizza booth generates $4.38 per square foot of profit.

Problem 2: Game Booth Layout

The Challenge:

You need to arrange game booths in a 20 ft × 30 ft area. Each booth is 4 ft × 6 ft. You want to leave 2 ft walkways between booths and around the edges. If each booth charges $3.00 per game and averages 25 games per hour, what's the hourly revenue per square foot of the entire area?

Step 1: Calculate Available Space (Geometry)

Find how much space is available for booths after accounting for walkways.

Total area = 20 ft × 30 ft = 600 sq ft
Walkway area = 2 ft around all edges = 2 × (20 + 30) × 2 = 200 sq ft
Available for booths = 600 - 200 = 400 sq ft

Step 2: Calculate Number of Booths (Algebra)

Determine how many booths can fit in the available space.

Booth area = 4 ft × 6 ft = 24 sq ft
Number of booths = 400 sq ft ÷ 24 sq ft = 16.67
Maximum booths = 16 (can't have partial booths)

Step 3: Calculate Hourly Revenue (Decimals)

Find the total hourly revenue from all booths.

Revenue per booth per hour = 25 games × $3.00 = $75.00
Total hourly revenue = 16 booths × $75.00 = $1,200.00

Step 4: Revenue per Square Foot

Calculate revenue per square foot of the entire area.

Revenue per sq ft = $1,200.00 ÷ 600 sq ft = $2.00 per sq ft

Answer:

The game booth area generates $2.00 per square foot per hour.

Problem 3: Attendance Prediction & Analysis

The Challenge:

Based on past data, 60% of the school's 400 students attend the fair. Of those who attend, 3/4 buy food, 1/2 play games, and 1/3 buy souvenirs. If food averages $8.50 per person, games average $5.00 per person, and souvenirs average $12.00 per person, what's the total expected revenue?

Step 1: Calculate Attendance (Fractions & Decimals)

Find how many students will attend the fair.

Attendance = 400 students × 0.60 = 240 students

Step 2: Calculate Activity Participation (Fractions)

Find how many students participate in each activity.

Food buyers = 240 × 3/4 = 180 students
Game players = 240 × 1/2 = 120 students
Souvenir buyers = 240 × 1/3 = 80 students

Step 3: Calculate Revenue by Category (Decimals)

Calculate revenue from each activity category.

Food revenue = 180 × $8.50 = $1,530.00
Game revenue = 120 × $5.00 = $600.00
Souvenir revenue = 80 × $12.00 = $960.00

Step 4: Calculate Total Revenue

Add up all revenue sources.

Total revenue = $1,530.00 + $600.00 + $960.00 = $3,090.00

Answer:

The expected total revenue for the school fair is $3,090.00.

Cross-Topic Integration Strategies

Making Connections

  • • Look for relationships between different math concepts
  • • Use one topic to solve problems in another
  • • Recognize when multiple approaches are needed

Complex Reasoning

  • • Break problems into multiple mathematical components
  • • Apply different strategies for different parts
  • • Synthesize information from multiple sources

Real-World Application

  • • Connect abstract concepts to practical situations
  • • Use multiple math skills to solve authentic problems
  • • Consider how different topics work together

Verification

  • • Check each step using different methods
  • • Ensure all parts of the problem are addressed
  • • Verify that the solution makes sense overall

Practice Problems

Practice 1: Art Project

An art class is making a mural. The design is 3/4 the size of the wall (12 ft × 8 ft). Each student can paint 2.5 square feet per hour. If 15 students work for 3 hours, what fraction of the mural will be completed?

Topics: Geometry (area), Fractions (scaling), Decimals (rate), Algebra (time calculation)

Practice 2: Science Experiment

A science class is growing plants. Each plant needs 1/3 cup of water daily. The class has 24 plants and a 2-gallon water container. If 1 gallon = 16 cups, how many days will the water last? What percentage of the container is used per day?

Topics: Fractions (water per plant), Decimals (conversion), Algebra (time), Percentages (usage)

Practice 3: Sports Tournament

A basketball tournament has 8 teams. Each game lasts 1.5 hours, and there are 2 courts. If each team plays every other team once, how many total games are there? If the tournament runs for 6 hours per day, how many days will it take?

Topics: Algebra (combinations), Decimals (time), Geometry (scheduling), Data Analysis (organization)

Excellent Work!

You've learned how to integrate concepts from different math topics to solve complex, real-world problems. This skill helps you see how all math concepts work together!