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Worksheet Grade 8 Health & Consumer Science

Ferris Home Water Filter Test: A Grade 8 Removal-Efficiency Worksheet

A grade 8 consumer-science worksheet where students compute a home filter's removal efficiency for lead and PFAS and compare tiny concentrations in scientific notation.

Objectives

  1. Students will compute a filter's removal efficiency from before and after concentrations.
  2. Students will express parts-per-billion and parts-per-trillion levels in scientific notation.
  3. Students will compare two contaminants' removal and explain why home testing is useful.

Vocabulary

Parts per trillion
A unit for measuring extremely small amounts of a chemical in water. PFAS limits are set in parts per trillion because these chemicals matter even in tiny doses.
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: removal efficiency, parts per billion

Teacher overview

A home water filter is a consumer product, and its usefulness can be measured. This worksheet has students read a fictional household's before-and-after filter test for lead and for PFAS, compute how much of each contaminant the filter removed, and write these very small concentrations in scientific notation. Removal efficiency is found as the before level minus the after level, divided by the before level, times 100.

Ferris Home Water Filter Test: A Grade 8 Removal-Efficiency Worksheet — Grade 8 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Worksheet

Suppose the Ferris household, in the fictional town of Cindermill, tested their tap water before and after installing a filter. The results are below. Today's lead action level is 15 ppb, dropping to 10 ppb in 2027. The action level tells a utility when it must act; it is not a safe level, because EPA's health goal for lead is zero. The federal limit for PFOA is 4.0 ppt (PFOS has its own 4.0 ppt limit).

Contaminant Before filter After filter
Lead 18 ppb 3 ppb
PFOA 8 ppt 1 ppt
  1. Before the filter, the lead level was 18 ppb. Is that above or below today's lead action level of 15 ppb, and by how much?
  2. Find the filter's lead removal efficiency. Use (before minus after) divided by before, times 100, with 18 ppb and 3 ppb. Round to the nearest whole percent.
  3. In 2027 the lead action level drops to 10 ppb. Was the 18 ppb before-filter level above that 2027 level too, and by how much?
  4. Find the filter's PFAS removal efficiency, using 8 ppt before and 1 ppt after.
  5. The PFOA limit is 4.0 ppt. Did the 8 ppt before-filter level exceed the limit, and by how much?
  6. Write the after-filter PFAS level of 1 ppt as a decimal fraction (1 out of one trillion), then in scientific notation.
  7. Write the after-filter lead level of 3 ppb as a decimal fraction (3 out of one billion), then in scientific notation.
  8. Using your scientific-notation answers to items 6 and 7, how many times larger is 3 ppb than 1 ppt?
  9. Which contaminant did the filter remove more effectively, lead or PFAS? Use your two removal-efficiency percents to justify your choice.
  10. Explain why a family might test their water both before and after installing a filter, rather than trusting the filter's advertised removal rate.

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: 3 ppb above the action level.
    18 ppb minus the 15 ppb action level equals 3 ppb above today's level.
  2. Answer: 83 percent.
    (18 minus 3) divided by 18, times 100, equals 15 divided by 18 times 100, which is about 83 percent.
  3. Answer: 8 ppb above the 2027 level.
    18 ppb minus the 10 ppb level equals 8 ppb above the tighter 2027 action level.
  4. Answer: 87.5 percent.
    (8 minus 1) divided by 8, times 100, equals 7 divided by 8 times 100, which is 87.5 percent.
  5. Answer: Yes, 4 ppt above the limit.
    8 ppt minus the 4.0 ppt limit equals 4 ppt above the PFOA limit.
  6. Answer: 0.000000000001; 1.0 times ten to the negative twelfth.
    1 part per trillion is 1 out of 1,000,000,000,000, which is 0.000000000001, or 1.0 times ten to the negative twelfth power.
  7. Answer: 0.000000003; 3.0 times ten to the negative ninth.
    3 parts per billion is 3 out of 1,000,000,000, which is 0.000000003, or 3.0 times ten to the negative ninth power.
  8. Answer: 3,000 times larger.
    Dividing 3.0 times ten to the negative ninth by 1.0 times ten to the negative twelfth gives 3.0 times ten to the third, which equals 3,000.
  9. Answer: PFAS, removed more effectively.
    The filter removed 87.5 percent of the PFAS but about 83 percent of the lead, so it took out a higher share of the PFAS.
  10. Answer: Testing checks the real result at this tap.
    Advertised rates come from lab conditions, so testing before and after shows how well the filter actually performs on this household's own water and whether it is being maintained.

Differentiation

Support

Work one removal-efficiency calculation as a model with different numbers before students try items 2 and 4, and provide a place-value chart for parts per billion and parts per trillion to support items 6 and 7. Allow calculator use throughout.

Extension

Ask students to suppose the filter's cartridge wears out and lead removal drops to 60 percent, and to find the new after-filter lead level from an 18 ppb before level. Have them state whether that worn-cartridge result would still be below today's 15 ppb action level, and why a family would still want the level as low as possible.

ELL supports

Pre-teach removal efficiency, action level, and before and after with a simple diagram of water passing through a filter. Allow items 1, 3, and 5 to be answered by circling the higher number and writing the difference rather than a full sentence.