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Worksheet Grade 7 Math

Ashfold County's Private Well Screening: Probability Worksheet

A grade 7 worksheet where students turn a fictional county's 400 private well test results into probabilities, predictions, and a percent change after filters.

Objectives

  1. Students will write a probability as a fraction, a decimal, and a percent.
  2. Students will use a probability to predict results for a larger group of wells.
  3. Students will explain why a probability cannot be greater than 1.

Vocabulary

Key words: probability, private well, screening, percent, percentage point

Teacher overview

Homes on private wells are not covered by the testing schedule that public water systems follow, so counties sometimes run a free screening round to find out how widespread a contaminant is. This worksheet uses a fictional screening in Ashfold County, where 400 private wells were tested for PFOA against the federal maximum contaminant level of 4.0 parts per trillion. EPA set that level in April 2024, and water systems must meet it by April 2029. In May 2026 EPA proposed letting eligible systems apply for a two-year exemption, to April 2031, without changing the level itself; that proposal was not final as of September 2026. Two errors show up repeatedly on items like these: reporting the count of wells rather than a probability, and accepting a value greater than 1 as a probability.

Ashfold County's Private Well Screening: Probability Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Ashfold County is a fictional county. The county tested 400 private wells for PFOA. The federal limit is 4.0 parts per trillion. Of the wells tested, 52 came back above that limit.

  1. One of the 400 tested wells is picked at random. Write the probability that it was above the limit. Use a fraction in lowest terms.
  2. Write that same probability as a decimal.
  3. Write that same probability as a percent.
  4. Write the probability that a randomly picked tested well was at or below the limit. Use a decimal.
  5. Of the 400 wells, 18 tested above 8.0 parts per trillion. Write the probability that a randomly picked tested well was above 8.0 parts per trillion. Use a decimal.
  6. Next year the county will test 1,200 more wells. Use the same rate you found in item 3. How many of those wells would you predict to be above the limit?
  7. A well owner says the chance her well is above the limit is 1.3. Explain why 1.3 cannot be a probability.
  8. Put these three events in order from least likely to most likely: a well above the limit, a well above 8.0 parts per trillion, a well at or below the limit.
  9. The county put filters on 50 of the 52 wells that were above the limit. Later tests found 2 of those 50 still above the limit. What percent of the filtered wells were still above the limit?
  10. The other 2 wells never got a filter, and they are still above the limit. So 4 of the 400 tested wells are above the limit now. Write the probability that a randomly picked tested well is above the limit now. Use a decimal.
  11. By how many percentage points did the share of wells above the limit drop, from the first round to the new tests?

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: 13/100.
    Write the probability as 52 out of 400. Divide the top and the bottom by 4 to get 13/100.
  2. Answer: 0.13.
    Divide 13 by 100, or divide 52 by 400. Both give 0.13.
  3. Answer: 13 percent.
    Multiply 0.13 by 100 to get 13 percent.
  4. Answer: 0.87.
    The two events cover every tested well, so subtract: 1 minus 0.13 equals 0.87. A check is 400 minus 52, which is 348, and 348 divided by 400 equals 0.87.
  5. Answer: 0.045.
    Divide 18 by 400 to get 0.045. This is smaller than 0.13, which fits, because every well above 8.0 parts per trillion is also above the limit.
  6. Answer: 156 wells.
    Take 13 percent of 1,200. Multiply 0.13 by 1,200 to get 156 wells.
  7. Answer: A probability must be between 0 and 1.
    A probability of 1 means the event always happens, so nothing can be more likely than that. The owner may mean 1.3 times the county rate, or she may mean a test result, but neither is a probability.
  8. Answer: Above 8.0 parts per trillion, then above the limit, then at or below the limit.
    Compare the three probabilities: 0.045 is the smallest, 0.13 comes next, and 0.87 is the largest.
  9. Answer: 4 percent.
    Divide 2 by 50 to get 0.04, then multiply by 100 to get 4 percent.
  10. Answer: 0.01.
    Divide 4 by 400 to get 0.01.
  11. Answer: 12 percentage points.
    The first round was 13 percent and the new tests are 1 percent, because 0.01 equals 1 percent. Then 13 minus 1 equals 12 percentage points.

Differentiation

Support

Give these students a hundred grid with 13 squares already shaded and let them read items 1 through 4 off the grid before writing anything. Assign items 1 through 6 and item 9, and allow a calculator for the divisions.

Extension

Ask these students to find how many of the 1,200 new wells they would predict to be above 8.0 parts per trillion, using the rate from item 5, and then to explain in two sentences why a prediction from a sample may be wrong for a county whose wells draw from different depths.

ELL supports

Pre-teach "well," "limit," "above," and "at or below" with a vertical number line marked at 4.0 and 8.0, with one dot placed above each mark and one below. Provide the frame "___ out of 400 wells were above the limit, so the probability is ___" for items 1 and 2.