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Lesson plan Grade 8 Engineering & Design

Pellstock School Rooftop Condensate: A Recovery Design Lesson

A 55-minute grade 8 lesson where students set criteria and constraints for capturing air conditioner condensate, then model the storage tank with a linear function.

Objectives

  1. Students will separate design criteria from design constraints for a condensate capture system.
  2. Students will construct a linear function for the volume of water in a storage tank over time.
  3. Students will interpret the rate of change and initial value of that function in terms of the building.

Vocabulary

Key words: condensate, criteria, constraint, rate of change, initial value

Teacher overview

Air conditioners pull water vapor out of warm indoor air, and that vapor condenses on the cold coils and drips away as condensate. It is the same phase change that forms dew on grass and cloud droplets in the atmosphere, happening on a metal coil instead. Pellstock Middle School is a fictional school whose rooftop units send that water straight to a storm drain, and the facilities committee wants to know whether it could water the courtyard garden instead. This lesson has students state the design criteria and constraints first, then build a linear function for the storage tank so they can answer sizing questions with numbers rather than guesses. Students often name 45 gallons as the rate of change because it is the larger of the two numbers, so the modeling step is built to separate the starting amount from the per-day amount.

Procedure

Framing the problem (7 min): Describe the situation at Pellstock Middle School. Four rooftop air conditioning units drip condensate into a pipe that runs to a storm drain. The courtyard garden is watered from a hose bib on the building. Ask students what question the facilities committee actually needs answered, and steer the discussion toward a sizing question rather than a yes-or-no question.

Criteria and constraints (12 min): On chart paper, build two labeled lists with the class. Criteria are the qualities that make a design better, such as collecting more water, needing less maintenance, and being easy to inspect. Constraints are the limits a design must respect. Supply these three constraints if students do not raise them: the roof structure allows no tank above the units, the courtyard has room for a tank no larger than 400 gallons, and any open water must be screened so mosquitoes cannot breed in it. Press students to state each constraint with a number or a testable condition rather than a general phrase.

Modeling the tank together (10 min): Tell the class that on a hot day the four units together produce 30 gallons of condensate, and that the tank already holds 45 gallons on Monday morning. Build the table for days 0, 1, and 2 on the board, then write V = 30d + 45 with the class. Label 30 as the rate of change and 45 as the initial value, and mark on the table where each one appears.

Formative check (3 min): Ask every student to hold up one finger for 30 or two fingers for 45 in answer to the question, "Which number is the rate of change?" If more than a third of the class holds up two fingers, rebuild the table for days 3 and 4 and point to the repeated addition of 30 before moving on.

Student handout (18 min): Students work the handout individually or in pairs. Circulate and check that item 6 subtracts the garden's daily use from the daily collection rather than from the starting amount.

Close and collect (5 min): Collect the handouts. Ask two students to read their answer to item 9 aloud, and record those constraints on the class chart before dismissal.

Pellstock School Rooftop Condensate: A Recovery Design Lesson — Grade 8 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

Pellstock Middle School is a fictional school with a courtyard garden. On a hot day its four rooftop air conditioning units together produce 30 gallons of condensate. The storage tank holds 45 gallons on Monday morning, before any collection begins.

  1. Write a function for V, the number of gallons in the tank after d hot days, assuming no water is taken out.
  2. What is the rate of change in your function, and what does it stand for at this school?
  3. What is the initial value in your function, and what does it stand for at this school?
  4. How many gallons are in the tank after 7 hot days with no water taken out?
  5. The tank holds 400 gallons. After how many whole hot days does the tank first hold more than 400 gallons?
  6. The courtyard garden uses 18 gallons every day. Write a function for W, the gallons in the tank after d days when the units collect and the garden waters on the same day.
  7. Using your function from item 6, how many gallons are in the tank after 7 days?
  8. On cool days the units produce no condensate, but the garden still uses 18 gallons a day. Starting from 129 gallons, how many full days of watering can the garden get before the tank is empty?
  9. Name one constraint from the class list that could keep this design from working, and explain in one sentence why it matters.

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: V = 30d + 45.
    The tank gains 30 gallons for each hot day, and it starts with 45 gallons already in it.
  2. Answer: 30 gallons per day.
    The rate of change is the daily condensate production of the four rooftop units.
  3. Answer: 45 gallons.
    The initial value is the water already in the tank on Monday morning, before day 1 of collection.
  4. Answer: 255 gallons.
    V = 30(7) + 45 = 210 + 45 = 255 gallons.
  5. Answer: 12 days.
    After 11 days the tank holds 30(11) + 45 = 375 gallons, which is still under the limit. After 12 days it holds 30(12) + 45 = 405 gallons, which is the first whole day above 400.
  6. Answer: W = 12d + 45.
    The tank gains 30 gallons and loses 18 gallons on the same day, so the daily change is 30 - 18 = 12 gallons. The starting amount of 45 gallons does not change.
  7. Answer: 129 gallons.
    W = 12(7) + 45 = 84 + 45 = 129 gallons.
  8. Answer: 7 days.
    Seven days of watering use 7 × 18 = 126 gallons, which leaves 3 gallons in the tank. An eighth full day would need 144 gallons, which the tank does not hold.
  9. Answer: Accept any constraint from the class list with a matching reason.
    Strong responses name the 400-gallon tank limit and explain that extra water would overflow during a long hot stretch, the roof load limit and explain that the tank has to sit on the ground, or the mosquito screening requirement and explain that open standing water would breed insects between waterings.

Differentiation

Support

Give these students the day 0 through day 3 table already filled in for item 1 and a printed reminder that a function of the form y = mx + b pairs the rate of change with m and the starting amount with b. For item 5, allow a guess-and-check table rather than solving the inequality.

Extension

Ask students to write and graph a third function for a summer week in which the units run only half the day and produce 18 gallons daily while the garden still uses 18 gallons. Have them explain what a horizontal line means for the tank and what it would mean for the design.

ELL supports

Provide a labeled diagram of the roof, the drip pipe, the tank, and the garden, with each part named in both English and the student's first language. Give sentence frames for items 2, 3, and 9, such as "The rate of change is ___ gallons per day, which is the water the units make each day."