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Worksheet Grade 10 Health & Consumer Science

Cedar Hollow's Water Report: Calculating the Summary Numbers

A grade 10 worksheet in which students rebuild a fictional town's water report from raw lead, chlorine and turbidity data, then judge each result by its rule.

Objectives

  1. Students will calculate a 90th-percentile lead result, a running annual average chlorine residual, and a monthly turbidity percentage from raw monitoring data.
  2. Students will explain how each standard is judged and why a single high reading is not always a violation.
  3. Students will distinguish health-based standards from an aesthetic secondary standard in a water report.

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.
Maximum contaminant level goal (MCLG)
The level of a contaminant in drinking water below which no harm to health is expected. It is a goal, not a legal limit, and for some chemicals the goal is zero.
Turbidity
Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: Consumer Confidence Report, 90th percentile, maximum residual disinfectant level, running annual average, secondary standard

Teacher overview

The single number printed beside each item in an annual water report is usually a summary of many samples, and each federal standard is judged on a particular summary: lead on the 90th-percentile home tap result, the chlorine limit on a running annual average, and turbidity on the share of each month's readings that stay low. In this worksheet students receive a draft of the fictional Cedar Hollow utility's report with the summary cells left blank, together with the raw monitoring data behind it. They calculate each summary value, decide whether each standard was met, and explain why one high reading can appear in the data without being a violation. The lead results meet today's action level but would not meet the stricter level that takes effect in 2027, which gives students a reason to read the report closely rather than stop at "standard met."

Cedar Hollow's Water Report: Calculating the Summary Numbers — Grade 10 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Worksheet

Cedar Hollow is a fictional town whose utility treats river water at a conventional filtration plant. The utility is preparing its report on calendar year 2025 and has left several cells blank. All of the data below are invented for this exercise; the standards and the ways they are judged are the real federal rules. Use the Source packet to answer the items that follow it.

Source packet

Document 1. Draft report table, Cedar Hollow Water Utility, 2025 results. Letters (a) to (i) mark the cells you will fill in.

Item Federal standard and how it is judged Cedar Hollow summary result Detail Standard met?
Lead (ppb) Goal (MCLG): 0 ppb. Action level: 15 ppb, compared with the 90th-percentile home tap result (10 ppb starting in 2027) 90th percentile: (a) Sites above 15 ppb: (b) of 20 (c)
Chlorine residual (mg/L) Maximum residual disinfectant level (MRDL): 4.0 mg/L, judged on the running annual average of monthly averages Running annual average: (d) Range of monthly averages: (e) (f)
Turbidity (NTU) At or below 0.3 NTU in at least 95% of each month's readings; no reading above 1 NTU Lowest monthly percentage at or below 0.3 NTU: (g) Highest single reading: (h) (i)
pH (secondary standard) 6.5 to 8.5, an aesthetic guideline Average 7.3 6.9 to 7.7 Within range

Document 2. Lead results from 20 home taps sampled in 2025 (first water drawn after the water sat unused overnight).

Site Lead (ppb) Site Lead (ppb)
A1 4 A11 6
A2 1 A12 1
A3 9 A13 8
A4 2 A14 19
A5 27 A15 3
A6 5 A16 5
A7 3 A17 10
A8 7 A18 2
A9 2 A19 7
A10 11 A20 4

How Cedar Hollow finds the 90th-percentile value: list the 20 results from lowest to highest and number them 1 to 20. Multiply the number of samples by 0.9. The result at that rank is the 90th-percentile value. The action level is exceeded only when the 90th-percentile value is greater than the action level.

Document 3. Chlorine residual in the distribution system, 2025. Each value is the average of all samples taken in the pipes that month.

Month Average (mg/L) Month Average (mg/L)
January 1.0 July 2.1
February 1.1 August 2.2
March 1.2 September 1.9
April 1.3 October 1.5
May 1.5 November 1.2
June 1.8 December 1.2

How the MRDL is judged: each quarter, the utility averages the 12 most recent monthly averages. This running annual average must not exceed 4.0 mg/L. Systems using chlorine typically keep about 0.2 to 2.0 mg/L in the pipes, which is a common operating range rather than a legal limit.

Operator notes: (1) The highest single sample of the year was 4.4 mg/L, taken on August 12 at a sampling tap close to the plant. (2) On March 14, during a pump repair, the chlorine level in water leaving the plant dropped to 0.15 mg/L for 3 hours before returning to normal. The rule for water entering the pipes is that it must not stay below 0.2 mg/L for more than 4 hours.

Document 4. Turbidity of filtered water leaving the plant, 2025. The plant logs one combined reading every 4 hours, which is 6 readings a day.

Month Days Readings Readings at or below 0.3 NTU Highest reading (NTU)
January 31 186 186 0.21
February 28 168 168 0.19
March 31 186 183 0.38
April 30 180 180 0.24
May 31 186 186 0.22
June 30 180 174 0.46
July 31 186 181 0.41
August 31 186 186 0.27
September 30 180 180 0.20
October 31 186 186 0.18
November 30 180 180 0.17
December 31 186 186 0.16

Items

  1. Using Document 2, list the 20 lead results from lowest to highest and use the method described below the table to find the 90th-percentile value. Write it in cell (a). Show the rank you used.
  2. How many sites had a result above 15 ppb? Write it in cell (b). How many sites had a result above 10 ppb?
  3. Compare your 90th-percentile value with the current action level of 15 ppb and with the 2027 action level of 10 ppb. By how many ppb is it below or above each one? Fill in cell (c) for 2025, and state what would happen if results like these were judged against the 2027 level.
  4. Find the mean and the median of the 20 lead results. The lead rule uses the 90th percentile instead of either of these. Using Cedar Hollow's numbers, explain why the 90th percentile is a better quantity for this purpose.
  5. Two sites are already above 15 ppb. With 20 sites sampled, what is the smallest number of sites that would have to be above 15 ppb for the 90th-percentile value to be above 15 ppb? Explain using the ranks.
  6. The family at site A5 sees that the town met the action level and concludes that their own water is fine. Using the MCLG of 0 ppb and their own result, explain what you would tell them and what a system-wide summary can and cannot tell one household.
  7. Using Document 3, calculate the running annual average for December 2025 and write it in cell (d). Write the lowest and highest monthly averages in cell (e). What percent of the 4.0 mg/L MRDL is the running annual average? Fill in cell (f).
  8. A resident reads operator note 1 and says the utility broke the chlorine limit because 4.4 mg/L is above 4.0 mg/L. July and August were also above the typical 2.0 mg/L operating level. Is either of these a violation? Explain how the MRDL is judged.
  9. Using operator note 2, decide whether the March 14 event broke the rule for water entering the pipes. By how many mg/L was the level below 0.2 mg/L, and how long would the event have had to last to break the rule?
  10. Using Document 4, calculate the percentage of readings at or below 0.3 NTU for each month that had any readings above 0.3 NTU. Round to the nearest tenth of a percent. Write the lowest monthly percentage in cell (g) and the highest single reading of the year in cell (h). Then fill in cell (i) and explain your decision.
  11. In a 31-day month with 186 readings, what is the largest number of readings that could be above 0.3 NTU while the month still meets the 95% requirement? Show why one more reading would cause the month to fail.
  12. The report gives chlorine in mg/L and lead in ppb. In fresh water 1 mg/L is about 1 ppm, and 1 ppm equals 1,000 ppb. Convert the chlorine running annual average from item 7 to ppb. A classmate says chlorine must be the bigger health concern because its number in ppb is far larger than the lead number. Explain why that comparison is not valid.
  13. Classify each of the four rows in Document 1 as a health-based standard or an aesthetic secondary standard, and explain the difference in one or two sentences.
  14. Write a short paragraph of 3 to 4 sentences for the front page of Cedar Hollow's report that tells residents accurately how the town did in 2025. It must mention lead and the 2027 change, and it must describe at least one standard by how it is judged rather than only by its number.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

All values below refer to the fictional Cedar Hollow data in the Source packet.

  1. Answer: 11 ppb.
    Sorted: 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 19, 27. The rank is 20 × 0.9 = 18, and the 18th value is 11 ppb (site A10). Cell (a) is 11 ppb.
  2. Answer: 2 sites above 15 ppb.
    Sites A14 (19 ppb) and A5 (27 ppb) are above 15 ppb, so cell (b) is 2 of 20. Three sites are above 10 ppb: A10 (11 ppb), A14 (19 ppb) and A5 (27 ppb).
  3. Answer: 4 ppb below the current level and 1 ppb above the 2027 level.
    15 - 11 = 4 ppb below today's action level, so cell (c) is "Yes" for 2025. Against the 2027 level, 11 - 10 = 1 ppb above. Because 11 is greater than 10, results like these would be an action level exceedance under the 2027 level. An exceedance is a trigger rather than a safe-or-unsafe verdict: it requires the utility to take treatment steps and notify the public.
  4. Answer: Mean 6.8 ppb; median 5 ppb.
    The sum is 136, and 136 ÷ 20 = 6.8 ppb. The median is the average of the 10th and 11th values, (5 + 5) ÷ 2 = 5 ppb. Lead usually comes from pipes and fixtures in particular buildings, so a few homes can be much higher than the rest. The mean and median describe a typical home and would sit below even the 10 ppb level here, while the 90th percentile (11 ppb) reflects the homes near the top of the distribution, which are the ones the rule is meant to catch. Accept any explanation that connects the choice of quantity to finding high-lead homes.
  5. Answer: 3 sites.
    The 90th-percentile value is the 18th of 20 ranked results, so it is above 15 ppb only if the results ranked 18, 19 and 20 are all above 15 ppb. That requires at least 3 sites above 15 ppb. With the current 2 sites, the 18th value is 11 ppb; if one more site rose above 15 ppb, it would move into the top three and the 18th value would be above 15 ppb.
  6. Answer: Their own result of 27 ppb is 12 ppb above the 15 ppb figure, and the goal for lead is 0 ppb.
    The town's summary (11 ppb) describes the system, not one house; the action level is applied to the 90th-percentile result for the whole system, so it can be met while individual homes are well above 15 ppb. Site A5's result is 27 - 15 = 12 ppb higher than 15 ppb, and because the health goal for lead is zero, no level is considered safe. The family should follow up with the utility, use only cold water for drinking and cooking, and ask about testing again and about the material of their service line. Accept any answer that uses the household's own result and the MCLG of zero.
  7. Answer: 1.5 mg/L, which is 37.5% of the MRDL.
    The 12 monthly averages add to 18.0, and 18.0 ÷ 12 = 1.5 mg/L, so cell (d) is 1.5 mg/L. Cell (e) is 1.0 to 2.2 mg/L. The percentage is 1.5 ÷ 4.0 = 0.375, or 37.5%. Cell (f) is "Yes" because 1.5 mg/L is below 4.0 mg/L.
  8. Answer: No, neither is a violation.
    The MRDL is judged on the running annual average of monthly averages, which is 1.5 mg/L, so a single sample of 4.4 mg/L is not by itself a violation. The 0.2 to 2.0 mg/L range is a typical operating range, not a legal limit, so monthly averages of 2.1 and 2.2 mg/L in July and August do not break a rule. The 4.4 mg/L sample came from a tap close to the plant, where water arrives before much of its chlorine has been used up, which explains why that one sample was so much higher than the monthly averages.
  9. Answer: No; the level was 0.05 mg/L below 0.2 mg/L.
    The shortfall is 0.2 - 0.15 = 0.05 mg/L. The rule is broken only if the level stays below 0.2 mg/L for more than 4 hours. The event lasted 3 hours, so it would have had to last more than 4 hours, which is more than 1 hour longer than it did, to break the rule.
  10. Answer: 96.7% (June); highest reading 0.46 NTU.
    March: 183 ÷ 186 × 100 = 98.4%. June: 174 ÷ 180 × 100 = 96.7%. July: 181 ÷ 186 × 100 = 97.3%. Every other month is 100%. Cell (g) is 96.7% and cell (h) is 0.46 NTU (June). Cell (i) is "Yes," because every month had at least 95% of readings at or below 0.3 NTU and no reading went above 1 NTU. The 0.46 NTU reading was above 0.3 NTU, which the rule allows as long as the month stays at or above 95%.
  11. Answer: 9 readings.
    95% of 186 is 0.95 × 186 = 176.7, so at least 177 readings must be at or below 0.3 NTU (a month cannot have part of a reading). That leaves 186 - 177 = 9 readings that may be above 0.3 NTU. Check: 177 ÷ 186 × 100 = 95.2%, which meets the requirement. With 10 readings above 0.3 NTU, only 176 are at or below it, and 176 ÷ 186 × 100 = 94.6%, which fails.
  12. Answer: 1,500 ppb.
    A chlorine average of 1.5 mg/L is about 1.5 ppm, and 1.5 × 1,000 = 1,500 ppb. Each substance has to be compared with its own standard, not with a different substance. Chlorine is 1,500 ppb against a limit of 4,000 ppb (4.0 mg/L), while lead is 11 ppb against an action level of 15 ppb and a health goal of 0 ppb. Lead is harmful at far lower concentrations, so a smaller number can mean a larger concern.
  13. Answer: Lead, chlorine and turbidity are health-based; pH is a secondary standard.
    The lead action level, the chlorine MRDL and the turbidity requirement protect health and require the utility to act when they are not met. The pH range is an aesthetic guideline tied to taste, appearance and pipe corrosion rather than a direct health limit, and it is not federally enforceable.
  14. Answer: Accept an accurate 3 to 4 sentence paragraph.
    A full-credit paragraph says that the 90th-percentile lead result was 11 ppb, which met the current 15 ppb action level but is above the 10 ppb level that takes effect in 2027; that chlorine and turbidity met their standards; and it explains at least one standard by how it is judged (for example, that the chlorine limit applies to a yearly running average, or that 96.7% of June's turbidity readings met the 0.3 NTU target). Deduct for describing lead as "safe," since the health goal is 0 ppb, or for calling the single 4.4 mg/L chlorine sample a violation.

Differentiation

Support

Give students a rank strip numbered 1 to 20 for sorting the lead results, and work the March turbidity percentage in item 10 together as a model before students do June and July. A calculator is appropriate for items 4, 7, 10 and 11. Students may answer item 14 with a sentence frame that lists what each sentence must contain.

Extension

Suppose the fictional utility replaces the lead service line at site A5 and a retest there reads 3 ppb. Students recalculate the 90th-percentile value (it becomes 10 ppb) and decide whether that result would exceed the 2027 action level. It would not, because the action level is exceeded only when the value is greater than 10 ppb, and students should explain why a value exactly at the level is still close enough to keep watching. Students can also calculate the running annual average for March 2026 if January to March 2026 monthly averages are 1.1, 1.2 and 1.3 mg/L in this fictional scenario: replacing January to March 2025 gives (18.0 - 3.3 + 3.6) ÷ 12 = 1.525, or about 1.53 mg/L.

ELL supports

Pre-teach "percentile," "average," "residual," "turbidity," "action level" and "violation" with short definitions, and show a number line from 0 to 30 ppb with the 20 lead results marked as dots and the 10 and 15 ppb levels drawn as lines. Allow students to answer items 6, 8 and 13 with short phrases or a labeled diagram, and provide the sentence frame "The ___ standard is judged by ___, so ___" for items 8 and 14.