Objective

By the end of this lesson, you will be able to apply geometric concepts to real-life hiking scenarios, such as calculating distances, angles, and elevations.

Materials and Prep

• Pen/pencil
• Graph paper
• Ruler
• Calculator
• Compass
• Printed maps of hiking trails

Prior knowledge required: Basic understanding of geometry concepts such as angles, triangles, and Pythagorean theorem.

Activities

1. Map Reading: Start by examining the printed maps of hiking trails. Identify key landmarks, such as peaks, valleys, and lakes. Discuss how these can be represented using geometric shapes.
2. Distance Calculation: Select a specific hiking trail and determine the distance between two points using the scale provided on the map. Show the steps involved in calculating the distance using the Pythagorean theorem.
3. Elevation Change: Choose a trail with varying elevations. Using the contour lines on the map, calculate the change in elevation between two points. Discuss how this can be represented using a slope or gradient.
4. Angle Measurement: Identify angles formed by intersecting trails or when changing direction on a trail. Use a compass and protractor to measure these angles accurately.
5. Real-Life Application: Discuss the importance of understanding geometry in hiking. Explore how hikers use geometric concepts to plan routes, estimate travel times, and navigate through challenging terrains.

Twelfth Grade Talking Points

• "Geometry plays a crucial role in real-life scenarios, such as hiking, where understanding distances, angles, and elevations is essential."
• "By applying geometric concepts, we can accurately calculate distances between points on a map, allowing us to plan our hiking routes effectively."
• "The Pythagorean theorem helps us determine the straight-line distance between two points, even if the path is not a straight line."
• "Contour lines on a map provide valuable information about changes in elevation, allowing us to assess the difficulty of a hiking trail."
• "Angles on a hiking trail can indicate changes in direction, intersections, or even the steepness of a slope. Measuring these angles helps us navigate safely."
• "Understanding geometry in hiking is vital for hikers to make informed decisions, estimate travel times, and ensure their safety in challenging terrains."