Project Grade 11 Math
Rowan Heights Tap Water Claims: Evaluating a Company's Report
A grade 11 project where teams evaluate a fictional bottled-water company's statistical claims against real EPA lead action levels over three sessions.
Objectives
- Students will classify a data source as a survey, an experiment, or an observational study and explain why randomization matters to each.
- Students will evaluate a claimed statistical comparison for sample size, sampling method, and potential bias.
- Students will compare a company's claimed numbers to real EPA lead action levels to assess whether its claims are statistically supported.
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: sample size, sampling method, selection bias
Teacher overview
A fictional bottled-water brand, PureSpring, has run an advertisement claiming its water is "tested and proven safer" than tap water in the fictional town of Rowan Heights, citing a small internal study. Over three sessions, teams act as statistical consultants hired by a fictional Rowan Heights consumer affairs board to evaluate whether PureSpring's claim actually holds up, comparing the company's sampling method and numbers against the real EPA lead action levels and against Rowan Heights' own compliance sampling program.
Project Brief
Driving question: Does PureSpring's ad hold up as valid statistical evidence? What would a fairer comparison look like?
Scenario: PureSpring's ad states: "In a study of 5 bottles, PureSpring water measured 0 parts per billion (ppb) lead. A single grab sample from Rowan Heights tap water measured 3 ppb lead. Proof our water is cleaner." Rowan Heights' water utility tests many household taps every year as part of its Lead and Copper Rule program. It does not rely on one grab sample. The town's fictional consumer affairs board wants a written review before it lets the ad run locally.
Handouts: Print these two sheets for each team. All values are fictional.
- PureSpring claim sheet: the ad text quoted in the Scenario above, word for word. PureSpring does not say how its 5 bottles were chosen, when they were bought, or which lab tested them.
- Rowan Heights compliance sampling summary: in the most recent round, the utility sampled 60 homes. Following Lead and Copper Rule procedures, it chose homes most likely to have lead, such as homes served by lead service lines, and collected water that had sat in the pipes unused for at least 6 hours. The 90th-percentile result was 4 ppb, and the highest single result was 12 ppb. The action level is compared with the 90th-percentile result, not with any one home's result.
Constraints:
- Use only the numbers on the two teacher-provided handouts. No outside research and no invented numbers.
- Keep the written report to 500 words or fewer. Pick your strongest statistical points instead of listing every possible objection.
- Name and explain at least three specific weaknesses in PureSpring's claim. Use unit vocabulary: sample size, sampling method, selection bias, or margin of error.
- Compare both PureSpring's 0 ppb claim and Rowan Heights' 3 ppb grab sample to the real action levels: 15 ppb now, and 10 ppb starting in 2027.
- Keep in mind that the action level is a trigger that requires a utility to act and notify the public, not a safe level. EPA's health-based goal for lead in drinking water is zero.
Final deliverable: A written report (500 words or fewer) for the town's consumer affairs board, plus a three-minute team presentation of the same findings to the class.
Milestones
- Session 1 — Classify the data sources: Read both handouts. Sort each one as a sample survey, an experiment, or an observational study. Write why randomization does, or does not, apply to each. Output: a completed classification chart for both data sources.
- Session 2 — Build the statistical critique: Compare PureSpring's 5-bottle sample to Rowan Heights' single grab sample and to the utility's much larger yearly program. Decide whether either sample looks representative, or looks picked to make a point. Compare every number to the 15 ppb and 10 ppb action levels. Output: a critique worksheet naming at least three specific weaknesses.
- Session 3 — Write and present the evaluation: Draft and finish the 500-word-or-fewer report. Prepare a three-minute presentation. Role-play as statistical consultants reporting to the consumer affairs board. Output: a final written report and a short team presentation.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Rubric
| Criterion | Emerging | Developing | Proficient | Advanced |
|---|---|---|---|---|
| Statistical critique | Report does not identify specific statistical weaknesses in PureSpring's claim | Report names a weakness but does not explain why it undermines the claim | Report names and correctly explains at least three specific weaknesses (sample size, sampling method, bias) | Report names at least three weaknesses and explains how a better-designed study could have avoided each one |
| Use of real regulatory context | Report does not reference the 15 ppb or 10 ppb action levels | Report mentions the action levels but does not compare them accurately to PureSpring's or Rowan Heights' numbers | Report accurately compares both claimed numbers to the current and 2027 action levels | Report accurately compares both numbers to both action levels and explains what those comparisons do and do not prove |
| Report length and clarity | Report is far over the 500-word limit or difficult to follow | Report stays near the word limit but reads as a disorganized list of points | Report stays within the 500-word limit and is clearly organized around the three required weaknesses | Report stays within the limit, is clearly organized, and anticipates a likely counterargument from PureSpring |
| Presentation | Presentation is incomplete or does not match the written report | Presentation covers the report's content but lacks clear delivery within the time limit | Presentation clearly and accurately summarizes the report within the three-minute limit | Presentation clearly summarizes the report and fields a follow-up question from the class with a statistically sound answer |
Differentiation
Support (below grade level)
Provide the classification chart from Session 1 partially completed, with the compliance program already labeled as a "sample survey" so teams focus their reasoning on the single grab sample and PureSpring's claim. Provide a sentence-starter template for each of the three required weaknesses in the written report.
Extension (above grade level)
Ask teams to redesign PureSpring's study so that it would actually support a valid comparison, specifying a sample size, a sampling method, and how they would handle the comparison to Rowan Heights' data, then explain what a fair advertisement based on that redesigned study could and could not claim.
ELL supports
Provide a bilingual glossary card for "sample size," "sampling method," "bias," and "action level" before Session 1. Allow the written report to include a simple labeled comparison table (PureSpring's numbers next to Rowan Heights' numbers next to the two action levels) alongside shorter explanatory sentences rather than long paragraphs.