Objective

By the end of this lesson, you will be able to apply algebraic concepts to solve real-life problems related to hiking.

Materials and Prep

• Paper
• Pencil
• Calculator (optional)

No prior knowledge is required for this lesson.

Activities

1. Activity: Calculating Distance

   Measure the distance of a hiking trail you are interested in. Use the formula d = rt, where d is the distance, r is the rate, and t is the time taken. Choose a reasonable rate and calculate the time it would take to complete the trail.

2. Activity: Budgeting for a Hiking Trip

   Plan a hiking trip, including transportation, accommodation, and food expenses. Use algebraic equations to determine how much money you need to save for the trip. Consider variables such as the number of days, cost per day, and any additional expenses.

3. Activity: Elevation Gain

   Research a hiking trail that involves significant elevation gain. Use the formula y = mx + b, where y is the elevation gain, x is the distance hiked, m is the slope, and b is the initial elevation. Calculate the elevation gain at different distances along the trail and plot them on a graph.

Tenth Grade Talking Points

• "Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols."
• "In hiking, algebra can be used to solve various problems, such as calculating distance, budgeting for a trip, and analyzing elevation gain."
• "The formula d = rt, where d is the distance, r is the rate, and t is the time, helps us determine how long it would take to complete a hiking trail at a given speed."
• "To budget for a hiking trip, we can use algebraic equations to calculate the total cost based on variables like the number of days, cost per day, and additional expenses."
• "When analyzing elevation gain, the formula y = mx + b can be used, where y is the elevation gain, x is the distance hiked, m is the slope, and b is the initial elevation. This allows us to calculate the elevation gain at different points along a trail."