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Lesson plan Grade 9 Health & Consumer Science

Reading the Prewitt Family's Tiered Water Bill in Dunbar

A grade 9 consumer-science lesson where students model a fictional tiered water bill as equations and test it against an affordability threshold.

Objectives

  1. Students will write piecewise equations that give a monthly water bill from the number of units used in each rate tier.
  2. Students will compare a monthly bill against an affordability threshold based on household income.

Vocabulary

Key words: tiered rate, service charge, affordability, unit

Teacher overview

Most water bills charge a fixed service fee plus a price per unit of water, and many use tiers that charge more once a household passes a set amount. This lesson has students model the bill of the fictional Prewitt family, served by the fictional Dunbar Water District, as a pair of equations and then check whether the bill crosses an affordability line. A common misconception is that every extra unit of water costs the same; the tiered structure shows that the last unit in a heavy month can cost more than the first, which is exactly the pricing signal utilities use to encourage conservation. A widely used rule of thumb treats combined water and sewer bills above about 4.5 percent of household income as a high burden, although EPA has no single official cutoff, which gives students a benchmark to test against.

Procedure

Hook (5 min): Project a blank bill layout with a service charge line and a usage line. Ask students to predict what happens to the per-unit price if a family uses a lot of water in a hot month. Record predictions without correcting them yet.

Direct instruction (12 min): Define the fictional Dunbar rate structure: a fixed service charge, a Tier 1 price for the first units, and a higher Tier 2 price above a set threshold. Define one unit as 1,000 gallons so the arithmetic stays clean. Model item 1 with the class, writing the Tier 1 equation and graphing it on labeled, scaled axes with units on the x-axis and dollars on the y-axis.

Guided practice (12 min): Work item 3 together, deriving the Tier 2 equation by adding the full Tier 1 charge to the higher price on the units above the threshold. Emphasize that the graph bends at the tier boundary, and have students mark that point on their axes.

Independent practice (15 min): Students finish the Student Handout, computing two months' bills, the average price per extra unit between them, the effect of a proposed rate change, and the affordability comparison. Circulate to confirm students are substituting into the correct tier equation.

Formative check and closure (6 min): Exit ticket on a slip: "In the Prewitts' heavy month, does one more unit of water cost the Tier 1 price or the Tier 2 price, and why?" Collect and scan; if more than a quarter answer Tier 1, revisit the tier boundary on the graph before the next lesson.

Reading the Prewitt Family's Tiered Water Bill in Dunbar — Grade 9 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Handout

Suppose the Prewitt family is served by the fictional Dunbar Water District. One unit equals 1,000 gallons. The bill has a fixed service charge of $18.00 per month, a Tier 1 price of $4.00 per unit for the first 5 units, and a Tier 2 price of $6.50 for each unit above 5. Use these figures for every item and show your steps.

  1. Write an equation for the monthly bill B, in dollars, when the family uses u units and u is 5 or fewer.
  2. In April the Prewitts used 4 units. Use your equation to find their April bill.
  3. Write an equation for the monthly bill B when the family uses more than 5 units, using the full Tier 1 charge plus the Tier 2 price on the units above 5.
  4. In July the Prewitts used 9 units. Use your Tier 2 equation to find their July bill.
  5. Between April (4 units) and July (9 units), what was the average increase in the bill in dollars per additional unit of water used?
  6. Suppose Dunbar raises the Tier 2 price to $7.50 per unit next year and keeps everything else the same. Recompute the July bill for 9 units under the new price.
  7. How many dollars higher is the new July bill than the old July bill?
  8. The Prewitt household income is $3,200 per month. Find 4.5 percent of that monthly income.
  9. Is the original $64 July bill above or below the amount you found in item 8, and by how many dollars?
  10. Explain, using the two prices, why using one more unit of water in July costs the Prewitts more than using one more unit in April.

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

Answer Key

The Dunbar rates below are fictional figures built into the scenario.

  1. Answer: B = 18 + 4u dollars. The $18 service charge is fixed and the first units cost $4 each, so the bill is 18 plus 4 times u.
  2. Answer: $34.00. B = 18 + 4 times 4 = 18 + 16 = $34 for 4 units.
  3. Answer: B = 38 + 6.5(u − 5) dollars. The first 5 units cost 18 + 4 times 5 = $38, and each unit above 5 adds $6.50.
  4. Answer: $64.00. B = 38 + 6.5 times (9 − 5) = 38 + 6.5 times 4 = 38 + 26 = $64.
  5. Answer: $6.00 per unit. The bill rose from $34 to $64, a change of $30 across 9 − 4 = 5 extra units, and 30 divided by 5 = $6 per unit.
  6. Answer: $68.00. With the $7.50 Tier 2 price, B = 38 + 7.5 times 4 = 38 + 30 = $68.
  7. Answer: $4.00. The new July bill of $68 minus the old $64 is $4.00 higher.
  8. Answer: $144.00. 4.5 percent of $3,200 is 0.045 times 3,200 = $144.
  9. Answer: Below, by $80.00. The $64 bill is under the $144 threshold, and 144 − 64 = $80. This bill is for water only, so the Prewitts' sewer charges would also count toward the 4.5 percent benchmark.
  10. Answer: Because July's ninth unit falls in Tier 2 at $6.50, while April's fourth unit falls in Tier 1 at $4.00, so the same extra unit of water costs $2.50 more in the heavier month.

Differentiation

Support

Provide the two tier equations already written and ask students only to substitute and evaluate. Give a filled example bill for a different unit count so students can match their steps against a model before working items 4 through 9.

Extension

Have students write a single piecewise function for the bill covering both tiers, then find the exact number of units at which a Dunbar bill would first reach the affordability threshold from item 8.

ELL supports

Pre-teach "service charge," "tier," and "threshold" with a labeled sample bill in which each term points to a line on the page. Provide a sentence frame for item 10: "The extra unit costs more in July because it is in Tier , which charges $ instead of $___."