Lesson plan Grade 6 Math
Hollowgate's Rebate: Solving One-Step Water-Conservation Equations
A grade 6 math lesson where students write and solve one-step equations to spend a fictional apartment complex's low-flow showerhead rebate budget.
Objectives
- Students will write and solve one-step equations of the form px = q for a fixed budget and unit price.
- Students will write and solve one-step equations of the form x + p = q for a remaining amount.
- Students will explain what the solution to each equation represents in the water-conservation scenario.
Vocabulary
- WaterSense
- An EPA label on toilets, showerheads, faucets, and irrigation controllers that meet water-saving standards. It works like the ENERGY STAR label, but for water.
Also: equation, variable
Teacher overview
A standard showerhead flows at 2.5 gallons per minute, while a WaterSense-labeled showerhead uses 2.0 gallons per minute or less. This lesson uses a fictional apartment complex's rebate program for WaterSense showerheads as the context for writing and solving one-step equations, giving students a real budget decision instead of an abstract "solve for x" problem.
A common misconception is trying to solve px = q and x + p = q the same way, by always dividing. The direct instruction step names the two equation forms explicitly and asks students to notice which operation undoes each one.
Procedure
Hook (5 min): Show the two showerhead flow rates side by side: 2.5 gallons per minute for a standard showerhead, 2.0 gallons per minute or less for a WaterSense-labeled one. Ask why a building manager might want to switch every showerhead in a building.
Direct instruction (10 min): Introduce Hollowgate Apartments (a fictional apartment complex used for this lesson), which has a $480 rebate to spend on WaterSense showerheads priced at $24 each. Model writing the equation 24x = 480, where x is the number of showerheads the rebate buys, and solving it by dividing both sides by 24 to get x = 20. Name this equation form as px = q, where p is the price and q is the total budget.
Guided practice (15 min): In pairs, students solve two more one-step equations. First, a smaller building in the complex gets a $216 rebate at the same $24 price per showerhead: 24x = 216. Second, after buying 15 showerheads at $24 each ($360 total) from a $500 budget, students write and solve x + 360 = 500 to find how much of the budget remains. Circulate and check that pairs correctly identify which operation undoes each equation.
Independent practice (10 min): Each student solves two equations on the handout:
- 24x = 432 (showerheads bought from a $432 budget at $24 each)
- x + 275 = 400 (remaining budget after $275 is already spent from a $400 budget)
Closure / exit ticket (5 min): Students solve one equation on an index card: 24x = 600. Collect and scan for correct division before dismissal.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 18 showerheads.
24x = 432. Dividing both sides by 24 gives x = 432 ÷ 24 = 18.Answer: $125. x + 275 = 400. Subtracting 275 from both sides gives x = 400 − 275 = 125.
Exit ticket answer: 25 showerheads.
24x = 600. Dividing both sides by 24 gives x = 600 ÷ 24 = 25.
Differentiation
Support (below grade level)
Provide a labeled reference card showing "px = q: divide both sides by p" and "x + p = q: subtract p from both sides," and let students use a calculator for the division and subtraction steps so they can focus on choosing the correct operation.
Extension (above grade level)
Ask students to write a single two-step equation for a fictional scenario where Hollowgate buys some showerheads at $24 each and also spends a fixed $60 on installation tools, given a total budget of $540, and to explain why this equation needs two operations to solve instead of one.
ELL supports
Pre-teach "equation," "variable," and "budget" using a simple balance-scale picture showing both sides of an equation staying equal. Allow students to show their equation-solving steps with numbers and arrows instead of a written explanation for the guided and independent practice.