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Graphic organizer Grade 7 Engineering & Design

Pentarrow PFAS Options: A Treatment Decision Matrix

A grade 7 organizer pairing a pass-or-fail constraint screen with a weighted scoring matrix for three PFAS treatment options at a fictional water district.

Objectives

  1. Students will sort a design requirement into a pass-or-fail constraint or a scored criterion.
  2. Students will score three treatment options against weighted criteria and total each column.
  3. Students will justify a recommendation from the matrix total rather than from one criterion alone.

Vocabulary

Granular activated carbon
Small black grains of specially treated carbon that grab contaminants as water flows through them. Utilities use big tanks of it to remove PFAS, bad tastes, and odors.
Ion exchange
A water treatment method that swaps unwanted charged particles in the water for harmless ones held on tiny resin beads. It is used to remove PFAS and to soften hard water.

Also: criterion, constraint, decision matrix, weight, reject stream

Teacher overview

This organizer has two stacked parts. The first is a pass-or-fail constraint screen, a short table where each option is checked against a limit the district cannot move. The second is a weighted decision matrix, a grid where the surviving options are scored from 1 to 5 on criteria that carry different weights. The fictional Pentarrow Water District uses it to choose among three ways of removing PFAS. The misconception worth naming out loud is that the option removing the most contaminant automatically wins. Students who believe that will score the deepest-treating option highest on every row and stop there, when in practice an option can be ruled out before scoring because it produces a waste stream the district has nowhere to send. Point out that a constraint eliminates, while a criterion only earns points.

Pentarrow PFAS Options: A Treatment Decision Matrix — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Organizer

Design file for the fictional Pentarrow Water District. Raw well water carries 21 parts per trillion of PFOA and PFOS combined. The federal limit is 4.0 parts per trillion for each of the two compounds. The district has one open building pad of 2,000 square feet, six operator hours per week to spare, and no approved place to send a liquid reject stream.

Option What it is Finished water, pilot test Waste it makes Footprint Operator hours per week Yearly operating cost
A Granular activated carbon vessels 0.8 parts per trillion combined Spent carbon hauled off site 1,600 square feet 4 78,000 dollars
B Ion exchange resin vessels 1.6 parts per trillion combined Spent resin hauled off site 900 square feet 3 61,000 dollars
C Reverse osmosis skid 0.4 parts per trillion combined Liquid reject equal to one fifth of the flow 2,400 square feet 9 96,000 dollars

Part 1. Constraint screen. Write pass or fail in each cell.

Constraint Stated limit Option A Option B Option C
Liquid reject stream
Building footprint
Operator hours per week
Options still in the running →

Part 2. Weighted matrix. Score each surviving option from 1 to 5, then multiply by the weight.

Criterion Weight Score A Weight × A Score B Weight × B
Margin below the limit 4
Yearly operating cost 3
Operator hours 2
Footprint 1
Column total

Part 3. Recommendation. Finish both sentences.

  1. The district should build Option ____ because its weighted total is ____ .
  2. Option ____ was removed before scoring because it failed the constraint on ____ .

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

Completed Exemplar

Part 1. Constraint screen.

Constraint Stated limit Option A Option B Option C
Liquid reject stream No approved disposal, so none allowed Pass, waste is a solid Pass, waste is a solid Fail, reject is one fifth of flow
Building footprint 2,000 square feet available Pass at 1,600 Pass at 900 Fail at 2,400
Operator hours per week 6 hours available Pass at 4 Pass at 3 Fail at 9
Options still in the running → A B removed

Part 2. Weighted matrix. Scores below come from the fictional pilot data in the design file.

Criterion Weight Score A Weight × A Score B Weight × B
Margin below the limit 4 5 20 4 16
Yearly operating cost 3 3 9 5 15
Operator hours 2 4 8 5 10
Footprint 1 3 3 5 5
Column total 40 46

Part 3. Recommendation.

  1. The district should build Option B because its weighted total is 46, which is higher than the 40 earned by Option A.
  2. Option C was removed before scoring because it failed the constraint on liquid reject disposal, and it also failed on footprint and operator hours.

Teachers should accept scores one point away from the exemplar in either direction as long as the ranking within each row matches the data, since the 1 to 5 scale is a judgment. What should not vary is the constraint screen, which follows directly from the stated limits, or the finding that the option treating deepest is not the one the matrix recommends.

Differentiation

Support

Give these students the constraint screen already filled in, so the lesson starts at the scoring grid. Provide a scoring rule written out in words, such as five points for the lowest cost, three for the middle, and one for the highest, so the judgment step becomes a ranking step. Fill the weight column in advance and mark the multiplication with a worked first row.

Extension

Have students redo Part 2 after the fictional district doubles the weight on operating cost, then write two sentences on whether the recommendation changed and why. Ask a second group to argue for a different weight set and defend it to the class, which shows that weights are a choice the district makes rather than a fact about the options.

ELL supports

Pre-teach criterion and constraint with a pair of everyday examples, such as a shoe that must fit compared with a shoe that should be comfortable. Provide the sentence frames "Option ____ fails because ____" and "Option ____ scores higher on ____." Allow students to write pass or fail as a check mark and a cross rather than in words.

Extensions

Ask students to add a fifth criterion of their own to the matrix, assign it a weight out of the same total, and explain in a short paragraph what evidence the fictional district would have to collect before that row could be scored honestly. This asks students to consider what evidence each score in the grid depends on.