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Lesson plan Grade 7 Math

Wexbury Lead Tap Tests: A Grade 7 Probability Lesson

A 45-minute grade 7 lesson where students turn a fictional town's lead-test results into a probability between 0 and 1 and read what that risk means.

Objectives

  1. Students will write a probability as a fraction, a decimal, and a percent from test-result counts.
  2. Students will describe a probability as closer to 0 or 1 and explain the risk it shows.
  3. Students will use a probability to estimate the number of exceedances in a new set of taps.

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: probability, likelihood, sample

Teacher overview

Water systems test lead at household taps and compare each result with an action level, and the share of taps above that level is a natural setting for probability. This lesson has students turn a fictional town's test counts into a probability between 0 and 1, then read what that number says about risk. A common misconception this lesson addresses is reading "a 9 percent chance" as a promise that exactly 9 of the next 100 samples will be high; the closing discussion treats probability as a long-run share, not a guarantee about any one tap.

Procedure

Hook (5 min): Ask students how a town could decide whether its tap water is likely to have too much lead, given that testing every home is impossible. Collect a few ideas about testing a sample of homes and counting results.

Direct instruction (12 min): Define probability as a number from 0 to 1, where 0 means an event never happens and 1 means it always happens. Explain the lead action level: 15 ppb today, dropping to 10 ppb in 2027. The action level tells the utility when it must act; it is not a safe level, and EPA's health goal for lead is zero. A tap "exceeds" when its result is above the action level. Show that the probability a random tested tap exceeds is the share of tested taps that came back high.

Worked example (8 min): Suppose a fictional town tested 300 taps and 12 came back above the action level. Model finding the probability: 12 ÷ 300 = 0.04. Convert to a percent (4 percent) and place 0.04 on a 0-to-1 number line so students see it is close to 0. This example is for modeling only; students do not record it as an answer.

Guided and independent practice (15 min): Hand out the student page for the town of Wexbury and have students complete items 1 through 7, working in pairs but each recording their own answers. Circulate and check that students simplify the fraction in item 1 before converting it.

Closure and exit ticket (5 min): As a formative check, students answer item 8 on their own and hold up a thumb when done. Read three responses aloud; if fewer than two clearly separate "long-run share" from "a promise about the next 100 glasses," reteach that point before the next class.

Wexbury Lead Tap Tests: A Grade 7 Probability Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Wexbury is a fictional town used for this lesson. Last year the water system tested 200 household taps for lead. Of those, 18 taps came back above the 15 ppb action level. Use these counts for every question.

  1. What fraction of the tested taps were above the action level? Write it in lowest terms.
  2. Write that fraction as a probability in decimal form, for a randomly chosen tested tap.
  3. Write the probability from item 2 as a percent.
  4. Is that probability closer to 0 or to 1? What does that say about the chance a random tap is high?
  5. What is the probability that a randomly chosen tested tap is at or below the action level?
  6. The town plans to test 50 more taps. If the same rate holds, about how many would you expect to be above the action level?
  7. In 2027 the action level drops to 10 ppb, a stricter limit. Would the probability of a tap exceeding the level go up or down? Explain.
  8. A resident says, "A 9 percent chance means 9 of my next 100 glasses of water are unsafe." Explain why that is not what the probability means.

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: 9/100.
    18 out of 200 is 18/200, which reduces to 9/100.
  2. Answer: 0.09.
    9 ÷ 100 = 0.09, a number between 0 and 1.
  3. Answer: 9%.
    0.09 is 9 percent.
  4. Answer: Closer to 0.
    0.09 sits near 0 on the 0-to-1 line, so a random tested tap has a low, though not zero, chance of being above the level.
  5. Answer: 0.91.
    The tap is either above or not, so 1 − 0.09 = 0.91.
  6. Answer: about 4.5 taps.
    0.09 × 50 = 4.5, so expect about 4 or 5 of the 50 taps to be above the level.
  7. Answer: Up.
    A lower action level counts more results as "above," so more of the same samples would exceed it and the probability would rise.
  8. Answer: Probability is a long-run share, not a promise about the next 100.
    The 9 percent describes the share of tested taps across town that came back high. It is a long-run share, not a promise about exactly 9 of any particular 100, and it does not describe the glasses poured from one home's tap.

Differentiation

Support

Provide a 0-to-1 number line already marked at 0, 0.5, and 1 so students can place each probability. Give the fraction 18/200 with the common factor of 2 circled to start item 1, and allow a calculator for the decimal in item 2.

Extension

Ask students to find how many of the original 200 taps would need to be high for the probability to reach 0.2, and to describe what such a jump would suggest about the town's pipes.

ELL supports

Pre-teach "probability," "likely," "action level," and "exceed" with a likelihood strip labeled from "never" to "always." Provide sentence frames for items 4, 7, and 8, such as "This probability is close to ___ because ___."