🧭 Math Adventurers

Focus: Functions, sequences, transformations, and quantitative modeling

Theme: High school-level math and problem solving

Materials:

  • Paper and pencil

  • Ruler or measuring tape

  • Calculator

  • Spreadsheet software such as Excel or Google Sheets

Instructions:

  1. 🔍 Explore your home, yard, or neighborhood. Look for 2D & 3D shapes, sequences, patterns, and transformations.

  2. ✏️ Record observations with sketches, photos, or diagrams. Include measurements, geometric properties, and counts.

  3. 📏 Analyze patterns using ratios, proportions, and scaling. Consider effects on area and volume.

  4. 🔄 Identify transformations (rotation, reflection, translation, scaling).

  5. 📊 Represent your data using tables, graphs, charts, or algebraic expressions.

  6. 🔣 Model observed sequences or patterns using functions (linear, quadratic, geometric, Fibonacci, etc.).

Discussion Questions

  • How can you model patterns using functions?

  • How do ratios and proportions change under scaling?

  • Can you use algebraic or geometric formulas to describe your observations?

  • How do transformations affect area, volume, or symmetry in real-life objects?

  • Can natural patterns be described mathematically (fractals, spirals, symmetry)?

Optional Extensions

  1. 🔣 Pattern Analysis: Predict patterns using functions or sequences.

  2. 📊 Data Visualization: Use spreadsheets or graphs to analyze complex data from shapes and patterns.

  3. 📐 Ratios & Proportions: Calculate scaled areas, perimeters, or volumes and compare ratios.

  4. 🧩 Challenge Problem: Create a challenge problem for a friend using real-world measurements and transformations.