Objective

By the end of this lesson, the student will be able to apply algebraic concepts to solve problems related to running, such as calculating speed, distance, and time.

Materials and Prep

• Pencil and paper
• Calculator (optional)
• Basic knowledge of algebraic operations

Activities

1. Warm-up: Calculate Average Speed

   Ask the student to think about their running routine. Let's say they run 5 miles in 40 minutes. Have them calculate their average speed in miles per hour. Remind them to use the formula: speed = distance / time.

2. Running Time Calculation

   Provide the student with a scenario: "You want to run a 10k race in under 50 minutes. You have already run 5k in 25 minutes. How fast do you need to run the second 5k to achieve your goal?" Instruct them to use algebra to solve for the unknown variable, which represents the required speed for the second 5k.

3. Distance Calculation

   Give the student another scenario: "You are planning to participate in a marathon. You know that the average speed of the fastest marathon runner is 12 miles per hour. How long does it take for the fastest runner to complete the marathon distance of 26.2 miles?" Encourage the student to set up an equation using the formula: speed = distance / time, and solve for time.

Eighth Grade Talking Points

• "Algebra is a branch of mathematics that uses letters and symbols to represent unknown values."
• "In algebra, we can use equations to solve problems and find the value of unknown variables."
• "Algebraic operations, such as addition, subtraction, multiplication, and division, are used to manipulate equations and solve for unknowns."
• "The formula for speed is speed = distance / time. This formula helps us calculate how fast an object is moving."
• "We can use algebraic equations to solve problems related to running, such as calculating average speed, finding required speed to achieve a goal, and determining time taken to cover a certain distance."