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Lesson plan Grade 7 Math

Glasswing Utility Water-Loss Audit: A Grade 7 Percent Lesson

A 45-minute grade 7 lesson where students find the percent of water a fictional utility loses to leaks, then calculate a percent decrease after repairs.

Objectives

  1. Students will calculate the percent of pumped water a utility loses from pumped and billed totals.
  2. Students will find the percent decrease in lost water after leak repairs.

Vocabulary

Key words: water loss, percent, percent decrease, audit

Teacher overview

Every water utility pumps more water into its pipes than it bills its customers for, because some water leaks out along the way. Utilities call the gap non-revenue water. Leaks are usually the biggest part of it, and meters that read low and unbilled uses such as firefighting make up the rest. Utilities track the gap as a percent through a water audit. This lesson uses the fictional Glasswing Utility to teach that percent and a follow-up percent decrease. A common student error is to divide the lost water by the billed water instead of by the water pumped; the percent of loss is always measured against the total pumped into the system.

Procedure

Hook (5 min): Ask students where water might go between the treatment plant and a home. Collect ideas on the board, then name the main one: leaks in aging pipes. Tell students that the fictional Glasswing Utility wants to measure its own leaks with a water audit.

Direct instruction (12 min): Define water loss as water pumped minus water billed. For this lesson, treat the whole gap as water loss. Model one example with different numbers than the handout: a utility pumps 500,000 gallons and bills 460,000, so loss is 40,000 gallons, and 40,000 ÷ 500,000 = 0.08, or 8 percent. Stress dividing by the pumped total. Show that a percent decrease compares a drop to the earlier amount.

Guided practice (13 min): Hand out the student page. Work item 1 together so students see how to find lost gallons by subtraction. Then let pairs try item 2 and check their method before moving on. Circulate and watch for pairs dividing by the wrong total.

Independent practice (10 min): Students finish items 3 through 5 on their own. Remind them that item 5 is a percent decrease, measured against the earlier lost amount.

Closure and exit ticket (5 min): Each student answers on an index card: "A utility pumps 1,000,000 gallons and loses 120,000. What percent is lost?" Collect and check for dividing by the pumped total. A class is ready to move on when at least 80 percent divide correctly.

Glasswing Utility Water-Loss Audit: A Grade 7 Percent Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Use the fictional Glasswing Utility for every question. Last month the utility pumped 8,000,000 gallons into its pipes and billed customers for 6,800,000 gallons.

  1. How many gallons were lost last month, meaning pumped but not billed?
  2. What percent of the water pumped was lost?
  3. The utility's goal is to keep loss at or below 10 percent. By how many percentage points did last month's loss miss the goal?
  4. To meet the 10 percent goal, what is the most gallons that could be lost out of the 8,000,000 pumped?
  5. After fixing leaks, the utility cut lost water from 1,200,000 gallons to 900,000 gallons. What is the percent decrease in lost water?

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: 1,200,000 gallons. Water pumped minus water billed: 8,000,000 − 6,800,000 = 1,200,000 gallons lost.
  2. Answer: 15 percent. Divide lost by pumped: 1,200,000 ÷ 8,000,000 = 0.15, or 15 percent.
  3. Answer: 5 percentage points. The loss of 15 percent minus the goal of 10 percent is 15 − 10 = 5 percentage points over the goal.
  4. Answer: 800,000 gallons. 10 percent of the 8,000,000 pumped is 0.10 × 8,000,000 = 800,000 gallons.
  5. Answer: 25 percent. The drop is 1,200,000 − 900,000 = 300,000 gallons. Percent decrease = 300,000 ÷ 1,200,000 = 0.25, or 25 percent.

Exit ticket answer: 12 percent. 120,000 ÷ 1,000,000 = 0.12, measured against the pumped total.

Differentiation

Support

Give students the subtraction for item 1 already set up, and a printed reminder that reads "percent lost = lost gallons ÷ gallons pumped." Allow a calculator and let students round to whole percents.

Extension

Ask students to find how many gallons Glasswing would need to keep as billed water, out of the same 8,000,000 pumped, to reach exactly a 6 percent loss, and to explain the steps they used.

ELL supports

Pre-teach "pumped," "billed," and "loss" with a simple pipe drawing showing water going in, water reaching homes, and water leaking out. Provide the sentence frame "Lost gallons ÷ pumped gallons = ___ percent" for items 2 and 5.