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Lesson plan Grade 11 Math

Grover Mill Lead Sampling: Ranking Taps to the 90th Percentile

A grade 11 lesson where students rank a fictional district's tap lead results, find the 90th-percentile value, and test it against the current and 2027 action levels.

Objectives

  1. Students will rank a set of lead-sample results and find the 90th-percentile value using the Lead and Copper Rule method.
  2. Students will compare a district's 90th-percentile lead level to the current and 2027 action levels and judge compliance.

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.
Lead service line
A lead service line is an old water pipe made of lead metal that connects a house to the water main. Lead can get into the drinking water, so these pipes are being dug up and replaced across the country.

Also: percentile, sample

Teacher overview

Water systems do not test every tap for lead; they sample a set of higher-risk homes and use the results to decide whether the whole system must take further action to control lead. The Lead and Copper Rule bases that judgment on the 90th percentile of the samples rather than the average, because the average would hide the most-exposed homes. This lesson uses a fictional dataset from the Grover Mill Water District so students can rank results, find the 90th-percentile value, and compare it to the action level. A common misconception is that the mean tells the compliance story; the lesson corrects that by showing the mean and the 90th percentile side by side.

Procedure

Hook (5 min): Ask students how a district could decide whether it needs to take action on lead if it can only test a handful of the thousands of homes it serves. Collect a few ideas about sampling and worst-case homes without resolving them yet. Note that the Grover Mill district in this fictional lesson tested ten homes.

Direct instruction (12 min): Explain that lead reaches tap water mainly from old lead service lines and plumbing, so systems sample higher-risk homes. Introduce the current lead action level of 15 ppb and the reduced level of 10 ppb taking effect in 2027 under the Lead and Copper Rule Improvements. Note that EPA's health-based goal for lead is zero; the action level triggers treatment and public notification and is not a safe level. Model the rule's method on a small made-up set: rank the results low to high, multiply the sample count by 0.9 to find the rank of the 90th-percentile sample, and read off that value. This worked example is for teacher modeling and is not part of the graded handout.

Guided practice (10 min): Hand out the ten Grover Mill results. As a class, rank them low to high and plot them as a dot plot on graph paper. Together compute the median and the mean so students can compare them later to the 90th percentile.

Independent practice (15 min): Students complete the Student Handout, finding the 90th-percentile value and testing it against both action levels. Circulate and check that students multiply the sample count by 0.9 correctly rather than taking 90 percent of the largest value.

Closure and exit ticket (8 min): As an exit ticket, students answer one question in writing: "If a district's 90th-percentile lead value is 11 ppb, is it in compliance today, and will it be in 2027? Explain." Collect and scan for correct comparison against both the 15 ppb and 10 ppb levels before dismissal; aim for at least 80 percent of the class comparing to both.

Grover Mill Lead Sampling: Ranking Taps to the 90th Percentile — Grade 11 Math
Name: ____________________________ Date: ______________

Student Handout

The Grover Mill Water District (a fictional district used for this lesson) tested tap water at ten homes for lead. The results, in parts per billion (ppb), came back in this order:

8, 3, 21, 5, 12, 2, 14, 6, 9, 4

  1. Rank the ten results from lowest to highest.
  2. Find the median lead level of the ten homes.
  3. Find the mean lead level of the ten homes.
  4. Multiply the number of samples by 0.9 to find the rank of the 90th-percentile sample, then state that ranked value.
  5. The lead action level is 15 ppb today. Does the district's 90th-percentile value exceed it?
  6. The action level drops to 10 ppb in 2027. Would the same 90th-percentile value exceed the 2027 level?
  7. Explain why the rule uses the 90th percentile instead of the mean, using your answers to items 3 and 4.

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: 2, 3, 4, 5, 6, 8, 9, 12, 14, 21 ppb. The ten values placed in order from lowest to highest.
  2. Answer: 7 ppb. With ten values, the median is the average of the 5th and 6th ranked values: (6 + 8) / 2 = 7 ppb.
  3. Answer: 8.4 ppb. The ten values sum to 84, and 84 / 10 = 8.4 ppb.
  4. Answer: 14 ppb. 0.9 x 10 samples = 9, so the 9th value in the ranked list is the 90th percentile, which is 14 ppb.
  5. Answer: No. The 90th-percentile value, 14 ppb, is below the current action level of 15 ppb, so the district does not exceed it today.
  6. Answer: Yes. The same 14 ppb value is above the 2027 action level of 10 ppb, so under the reduced level the district would exceed the action level.
  7. Answer: The mean of 8.4 ppb sits well below the 90th-percentile value of 14 ppb because a few high homes are averaged in with many lower ones. Using the 90th percentile focuses attention on the higher-exposure homes, which is what a lead rule is meant to protect.

Differentiation

Support

Provide the ten values already ranked so students can begin at item 2, and give a filled example of the 90th-percentile method on a different five-value set. Allow calculators for the mean.

Extension

Ask students to determine the smallest single change to one home's result that would push the district's 90th-percentile value above the current 15 ppb action level, and to explain which ranked home matters for that decision.

ELL supports

Pre-teach "rank," "percentile," "action level," and "exceed" with a simple number line showing the ranked values and a marked cutoff. Provide sentence frames for items 5 and 6: "The 90th-percentile value is ___, which is ___ the ___ ppb action level."