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Lesson plan Grade 7 Engineering & Design

Ballantry School Taps: A Lead Sampling and Retrofit Plan

A grade 7 lesson where students build a proportional sampling plan for a fictional school's drinking taps, infer how many exceed the action level, and size a retrofit.

Objectives

  1. Students will build a proportional sampling plan across three groups of taps in a building.
  2. Students will explain why a convenience sample does not represent a whole population.
  3. Students will use a sample result to estimate how many taps in the full population exceed a limit.

Vocabulary

Action level
A trigger number in lead and copper testing. If too many homes test above this level, the utility must take steps like improving treatment and telling the public.

Also: representative sample, retrofit, parts per billion, constraint

Teacher overview

Ballantry Middle School is a fictional building with sixty drinking taps of three kinds: classroom sinks, hallway fountains, and kitchen and staff-room taps. Older plumbing fittings and solder can release lead into water that has been sitting in the pipes overnight, and the district can afford to test only a quarter of the taps this year. This lesson asks students to design the sampling plan first and the fix second, which is the order a real engineering team works in, because the size of the retrofit depends on how many taps turn out to be above the limit. A common misconception here is that testing the taps most likely to be bad gives the truest picture of the building, when a sample chosen that way overstates the problem just as testing only the new wing would understate it.

Procedure

Hook (5 min): Tell the class that the fictional Ballantry district has money to test 15 of its 60 school taps this year. Ask students to write down, privately, which 15 they would pick. Collect three or four strategies aloud without judging them, and note on the board which strategies pick taps from every part of the building and which do not.

Direct instruction (12 min): Define action level as the concentration that triggers required action rather than a line between safe and unsafe water. State the current federal figure of 15 ppb and the drop to 10 ppb in 2027 under the Lead and Copper Rule Improvements, and note that these are utility-wide triggers while schools often follow their own state or district thresholds. Then define a representative sample: one whose parts mirror the population's parts. Model the arithmetic on a group students will not be asked to key. In a wing holding 40 taps where 10 may be tested, one quarter of the taps are sampled, so a proportional plan tests one quarter of each kind.

Guided practice (13 min): Distribute the student handout and work questions 1 and 2 together. Make the sampling fraction explicit on the board as a single number that then multiplies each group. Ask the class to predict whether the three group answers should add back to 15 before anyone computes questions 3 and 4, which surfaces students who are treating each group as a separate problem.

Independent practice (20 min): Students complete handout questions 3 through 10 in pairs. Circulate and press pairs on question 5 to say what the newest wing sample would miss rather than simply calling it unfair. For questions 7 and 8, check that pairs are comparing the measured value against each stated action level separately instead of averaging the two.

Closure and formative check (5 min): Collect the handouts and scan question 6 only. If fewer than three quarters of the class scaled the sample result to 12 taps, open the next session by drawing 15 boxes with 3 shaded and asking the class to extend the pattern to 60 boxes. Close by having two pairs read their question 10 constraint aloud.

Ballantry School Taps: A Lead Sampling and Retrofit Plan — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

Suppose your team is planning the tap testing at the fictional Ballantry Middle School. Use the figures below for every question.

The school has 60 drinking taps in all: 24 classroom sinks, 20 hallway fountains, and 16 kitchen and staff-room taps. The district can pay for 15 tests this year. Lead in water is measured in parts per billion, written ppb. The federal action level today is 15 ppb, and it drops to 10 ppb in 2027.

  1. The district can test 15 of the 60 taps. What percent of the school's taps is that?

  2. Your plan tests the same share of every group. How many of the 24 classroom sinks should be tested?

  3. How many of the 20 hallway fountains should be tested?

  4. How many of the 16 kitchen and staff-room taps should be tested?

  5. A staff member suggests testing 15 taps in the newest wing instead, because they are easy to reach. Explain why that sample would not represent the whole school.

  6. The results come back, and 3 of the 15 tested taps are above the action level. Based on that sample, about how many of the school's 60 taps would you expect to be above it?

  7. One tested tap measured 12 ppb. The action level today is 15 ppb. Is that tap above today's action level?

  8. The action level drops to 10 ppb in 2027. Would that same 12 ppb tap be above the 2027 action level?

  9. A filtered bottle-filling station costs $1,200 to buy and install. The district has $18,000 for this retrofit. How many stations can it pay for?

  10. Cost is one constraint on the retrofit. Name one other constraint the team must respect, and explain in one sentence why it limits the plan.

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: 25 percent.
    15 tests divided by 60 taps = 0.25, which is 25 percent of the taps.

  2. Answer: 6 taps.
    24 classroom sinks x 0.25 = 6 sinks tested.

  3. Answer: 5 taps.
    20 hallway fountains x 0.25 = 5 fountains tested.

  4. Answer: 4 taps.
    16 kitchen and staff-room taps x 0.25 = 4 taps tested. Check: 6 + 5 + 4 = 15, which matches the number of tests the district can pay for.

  5. Answer: The newest wing is not representative.
    Accept any answer explaining that the newest wing's plumbing differs from the rest of the building, so the sample would leave out the older fittings and solder most likely to release lead. Strong answers add that a sample must include every kind of tap in roughly the share it makes up, and that a sample from one part of the building can only describe that part.

  6. Answer: 12 taps.
    3 of 15 tested taps is 3 divided by 15, or 0.2. 0.2 x 60 taps = 12 taps expected above the action level across the school.

  7. Answer: No.
    12 ppb is less than the current action level of 15 ppb, so this tap is not above today's action level.

  8. Answer: Yes.
    12 ppb is greater than 10 ppb, so the same tap would be above the action level once it drops in 2027. This is why the team should plan the retrofit against the future figure rather than the current one.

  9. Answer: 15 stations.
    $18,000 divided by $1,200 per station = 15 stations. That is three more than the 12 taps question 6 expects to be above the action level, which gives the team a small margin.

  10. Answer: One valid constraint with a reason.
    Accept any genuine limit with an explanation attached. Common correct answers include the installation window, since plumbing work has to happen when the building is empty; the need for a drain and a water line at each chosen spot; the recurring cost and schedule of replacing filter cartridges; the requirement that a station be reachable by students in wheelchairs; and the time the testing lab needs to return results. Do not accept the target of lowering lead, which is a criterion rather than a constraint.

Differentiation

Support

Give these students a handout copy with question 1 already answered and the sampling fraction printed in a box at the top of the page, so questions 2 through 4 become one multiplication each. Provide a strip of 60 squares grouped in three colors by tap type for question 6, so the inference can be shaded rather than computed. Offer a word bank of six possible constraints for question 10.

Extension

Ask students to redesign the sampling plan for a year when the district can pay for only 9 tests, then explain in writing what the smaller sample costs them in confidence. Have them propose which tap group they would oversample if forced to choose, and defend that choice against the representativeness argument they made in question 5.

ELL supports

Pre-teach action level, sample, and retrofit using a drawing of the building split into three labeled tap groups with the tested taps circled. Provide the sentence frame "The sample is not representative because it leaves out ___" for question 5, and the frame "This is a constraint because ___" for question 10. Allow yes-or-no answers on questions 7 and 8 without a written explanation.

Extensions

Have students draft a one-page notice to families explaining the testing plan, what the action level means, and what the district will do next. Ask them to state plainly that the action level is a trigger for action rather than a bright line between safe and unsafe water, which is one of the hardest ideas to communicate honestly in a public notice. Students can then trade drafts and mark any sentence a worried reader might misread.