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Lesson plan Grade 8 Health & Consumer Science

Kettle Creek Runners' Hydration: A Grade 8 Linear Function Lesson

A grade 8 health and PE lesson where students model a cross-country runner's fluid loss and water-bottle level as linear functions of practice time.

Objectives

  1. Students will convert an hourly fluid-loss rate into a per-minute rate and write it as a linear function.
  2. Students will interpret the slope and initial value of a bottle-level function in context.
  3. Students will use their function to plan how much water a runner needs for a full practice.

Vocabulary

Key words: fluid loss, slope, initial value, linear function

Teacher overview

Staying hydrated during exercise is a health skill, and the math behind it is a clean linear model. In this lesson, students imagine a cross-country runner at Kettle Creek Middle School who loses fluid through sweat at a roughly steady rate during practice, and who drinks from a water bottle to keep up. Fluid lost over time and water left in the bottle are both linear functions of the number of minutes elapsed. A common misconception is that a single bottle is always enough for a practice; building and reading the function shows students how to check that assumption instead of guessing.

Procedure

Hook (5 min): Ask students how they decide how much water to bring to a game or a long practice. Collect a few answers, then pose the question the lesson answers: can we predict, before practice starts, whether one bottle will be enough?

Direct instruction (12 min): Introduce the scenario and model the method on numbers that differ from the handout. Suppose a runner loses 18 ounces of fluid per hour. Convert to a per-minute rate, 18 divided by 60, which is 0.3 ounces per minute, and write the fluid-loss function L = 0.3t. Then model a bottle that holds 24 ounces and is sipped at 0.3 ounces per minute, giving the bottle-level function W = 24 minus 0.3t. Graph both and point out that the slope of the loss line is positive while the slope of the bottle line is negative.

Guided practice (10 min): In pairs, students complete handout items 1 through 4, building the fluid-loss rate and function and finding total loss for a full practice. Watch for students who forget to divide the hourly rate by 60.

Independent practice (10 min): Students complete handout items 5 through 7 on their own, working with the bottle-level function and interpreting its slope and initial value.

Closure and exit ticket (3 min): Students complete handout item 8, applying the same method to a runner with a different loss rate, and hand it in. Scan for the correct per-minute conversion before dismissal.

Kettle Creek Runners' Hydration: A Grade 8 Linear Function Lesson — Grade 8 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Handout

Suppose a runner on the Kettle Creek Middle School cross-country team loses about 24 ounces of fluid per hour of practice through sweat. Let t stand for the number of minutes of practice.

  1. Convert the runner's fluid-loss rate of 24 ounces per hour into ounces per minute.
  2. Write a linear function L for total fluid lost, in ounces, after t minutes at this rate.
  3. Practice lasts 90 minutes. Use your function to find how many ounces of fluid the runner loses during the full practice.
  4. The runner's bottle holds 20 ounces. Is one full bottle enough to replace the fluid lost in a 90-minute practice? Explain using your answer to item 3.
  5. Write a linear function W for the ounces of water left in the 20-ounce bottle after m minutes, if the runner sips 0.4 ounces per minute starting from a full bottle.
  6. After how many minutes would the bottle reach 0 ounces? Solve using your function from item 5.
  7. Interpret the slope and the initial value of the function W = 20 minus 0.4m in terms of the runner's bottle.
  8. A different runner loses 30 ounces of fluid per hour. Find that runner's per-minute rate, then find how many ounces that runner loses in a 90-minute practice.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 0.4 ounces per minute.
    24 ounces per hour divided by 60 minutes per hour equals 0.4 ounces per minute.
  2. Answer: L = 0.4t.
    The rate 0.4 ounces per minute is the slope, and the runner starts at 0 ounces lost, so the initial value is 0.
  3. Answer: 36 ounces.
    L = 0.4 times 90 = 36 ounces of fluid lost over the full 90-minute practice.
  4. Answer: No, one bottle is not enough.
    The runner loses 36 ounces, but a full 20-ounce bottle replaces only 20 ounces, leaving 16 ounces of loss unreplaced.
  5. Answer: W = 20 minus 0.4m.
    The bottle starts full at 20 ounces (initial value) and drops by 0.4 ounces each minute (slope of negative 0.4).
  6. Answer: 50 minutes.
    Setting 20 minus 0.4m = 0 gives 0.4m = 20, so m = 50 minutes.
  7. Answer: Slope negative 0.4 ounces per minute; initial value 20 ounces.
    The negative 0.4 slope is the rate the runner drinks the bottle down each minute, and the 20-ounce initial value is the full bottle at the start of practice.
  8. Answer: 45 ounces.
    30 ounces per hour divided by 60 is 0.5 ounces per minute, and 0.5 times 90 = 45 ounces lost over the full practice.

Differentiation

Support

Provide a two-column table of minutes and ounces already started for a few rows so students can see the linear pattern before writing the function. Give the hourly-to-minute conversion as a labeled arrow rule, "ounces per hour divided by 60 equals ounces per minute," on a printed strip.

Extension

Ask students to graph both the fluid-loss function and the bottle-level function on the same axes and identify the minute at which the water still in the bottle equals the fluid the runner has lost so far. Have them explain what that crossing point means for pacing sips during practice.

ELL supports

Pre-teach fluid loss, sweat, slope, and per minute with a simple diagram of a bottle emptying next to a clock. Provide sentence frames for item 7, such as "The slope means the runner drinks ___ each minute, and the initial value means the bottle starts with ___."

Extensions

Have students weigh a reusable bottle when full and estimate, from their own experience, how long it takes them to finish it during activity. They can then write their own bottle-level function and compare its slope with the runner's in the lesson, connecting the abstract model to their own hydration habits.