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Project Grade 7 Math

Cutting Nitrogen at Crannock Farm: A Grade 7 Watershed Project

A five-session grade 7 math project where teams price farm practices, compute percent reductions, and pitch a nitrogen plan to a fictional watershed board.

Objectives

  1. Students will compute a farm's baseline nitrogen loss from a per-acre rate.
  2. Students will score a mix of practices as a percent reduction of that baseline.
  3. Students will defend one plan that meets both a budget and a reduction goal.

Vocabulary

Key words: nitrogen loss, baseline, cover crop, buffer strip, bioreactor, percent reduction

Teacher overview

Nitrogen that leaves a farm field in tile drainage or runoff is both a lost input and a downstream problem, so watershed districts pay farmers to adopt practices that keep more of it in the soil. Teams in this project act as consultants to a fictional district, building a plan for one fictional farm that meets a reduction goal inside a fixed yearly budget, and defending it to a board panel. The misconception the project is built to catch is applying a practice's percent cut to the whole farm when the practice covers only part of it: a team that puts cover crops on 300 of 480 acres often reports a 35 percent farm-wide reduction, when the correct figure is about 21.9 percent.

Cutting Nitrogen at Crannock Farm: A Grade 7 Watershed Project — Grade 7 Math
Name: ____________________________ Date: ______________

Project Brief

The Sedgewold Watershed District is a fictional agency. Sedge Brook runs through its area and carries too much nitrogen. The district has hired your team as consultants.

Your client is Crannock Farm, a fictional farm of 480 acres. The district estimates that the farm loses 12 pounds of nitrogen per acre each year.

Your driving question: which mix of practices cuts Crannock Farm's nitrogen loss the most for the money the district can spend?

Your plan must meet all four of these constraints.

  1. It must cut the farm's yearly nitrogen loss by at least 30 percent.
  2. It must cost no more than $24,000 in the first year.
  3. It must use at least two different practices.
  4. Every acre may receive at most one of the three acre-based practices.

The district will pay for any of these four practices.

Cover crops: $38 per acre per year. Cuts nitrogen loss on the treated acres by 35 percent.
Split fertilizer applications: $12 per acre per year. Cuts nitrogen loss on the treated acres by 15 percent.
Streamside buffer strips: $95 per acre per year. Only the 40 acres beside Sedge Brook may be used. Cuts nitrogen loss on those acres by 60 percent.
Woodchip bioreactor: $6,500 in the first year. It treats drainage from 120 acres. It cuts the nitrogen still leaving those 120 acres by 40 percent, after any acre-based practice is counted.

Your team turns in two things. The first is a written plan of about two pages with a cost table and a reduction table. The second is a five-minute pitch to a board panel, played by your teacher and two classmates. The panel will ask two questions, and one of them will be about a mix your team did not choose.

Milestones

  1. Session 1, baseline sheet: compute the farm's total nitrogen loss for one year from the per-acre rate, and state the number of pounds that a 30 percent cut represents. Turn in a single labeled page.
  2. Session 2, cost table: price each of the three acre-based practices at three different acre counts of your choosing, and list the bioreactor's fixed first-year cost. Turn in a table with columns for practice, acres, price per acre, and total cost.
  3. Session 3, comparison table: build at least two complete candidate mixes. For each mix, show the pounds of nitrogen saved, the percent of the baseline that represents, and the first-year cost. Mark which mixes meet all four constraints.
  4. Session 4, written plan: choose one mix and write the two-page plan. Include the cost table, the reduction calculation, and one paragraph on why you rejected your other candidate.
  5. Session 5, board pitch: present for five minutes and answer the panel's two questions. Turn in your slides or chart paper with the plan.

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

Rubric

Score each team on four criteria at one of four levels.

Baseline and reduction mathematics. Exceeds: every pound and percent figure is correct, and the team shows the reduction for each practice separately as well as for the whole plan. Meets: the baseline and the plan's percent reduction are correct, with minor arithmetic slips that do not change the conclusion. Approaching: the baseline is correct but a percent is applied to the wrong number of acres. Beginning: the baseline is missing or the percent reduction is copied from a single practice.

Meeting the constraints. Exceeds: the plan meets all four constraints and the team states by how much it clears the budget and the reduction goal. Meets: the plan meets all four constraints. Approaching: the plan meets three constraints and the team names the one it misses. Beginning: the plan misses two or more constraints, or the team does not check them.

Comparison of alternatives. Exceeds: two or more complete mixes are scored side by side, and the rejection paragraph cites the specific cost or reduction figure that decided it. Meets: two complete mixes are scored and the rejection paragraph names a reason. Approaching: a second mix is listed but not fully scored. Beginning: only one mix appears.

Written plan and pitch. Exceeds: tables are labeled with units, the pitch runs to time, and both panel questions receive a direct answer supported by a figure. Meets: tables are labeled, the pitch runs to time, and both questions receive an answer. Approaching: tables are missing labels or units, or the pitch runs long. Beginning: the plan or the pitch is incomplete.

Differentiation

Support

Give these teams the baseline already computed and a partially filled cost table for cover crops, so session 1 becomes a check rather than a build. Limit their comparison to two acre-based practices and drop the bioreactor, which removes the stacked-percent step. Provide a checklist of the four constraints to tick off before session 4.

Extension

Ask these teams to find the least expensive mix that reaches a 40 percent reduction rather than 30 percent, and to report the cost of each additional percentage point beyond 30. Have them add a short paragraph on why the cost of each additional point rises as the plan grows.

ELL supports

Pre-teach "acre," "baseline," "cover crop," "buffer," and "reduction" with a labeled field diagram showing a stream along one edge and shaded bands for each practice. Provide a sentence frame for the pitch: "Our plan treats ___ acres with ___, which saves ___ pounds, or ___ percent of the baseline."

Extensions

Have teams redo the plan for a second fictional farm of 260 acres whose nitrogen loss is 9 pounds per acre, using the same practice prices and the same 30 percent goal, and compare the cost of each pound saved on the two farms. Ask them to write two sentences on why the smaller farm may be harder or easier to bring under the goal.