Math problem set Grade 6 Engineering & Design

Kestrel Farm Buffer Strip Nutrient Runoff Problems

A grade 6 engineering set where students design a grass buffer strip that catches nitrogen and phosphorus runoff, using percent removal, unit rates, and a ratio table.

Grade: Grade 6
Subject: Engineering & Design
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Students find percent of a quantity for nutrient runoff and removal in problems 2 through 4 and 7, and complete the removal ratio table in problem 8, the percent reasoning this standard targets.

All materials for 6.RP.A.3 →

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Problems 1, 5, and 6 use unit rates such as 40 pounds of nitrogen per acre and 2 dollars per foot of buffer, the unit-rate understanding this standard develops.

All materials for 6.RP.A.2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate nutrient runoff and buffer removal using percent of a quantity.
Students will use unit rates to find total nutrient loads and the cost of a buffer strip.

Vocabulary

Key words: nutrient, runoff, buffer strip, phosphorus

Teacher overview

Kestrel Farm, in the fictional town of Mossley, is designing a grass buffer strip along Mossley Brook. Fertilizer adds nitrogen and phosphorus to the fields. These nutrients help crops grow, yet the same nutrients feed algae and harm fish when they wash into the brook. A buffer strip is a band of grass that slows runoff and traps part of the nutrients before they reach the water.

Students work out how much nitrogen and phosphorus the farm applies, how much runs off, and how much a buffer catches. A common mistake is taking the removal percent of the wrong amount. The buffer only removes a share of the nutrients that actually reach it, not a share of everything spread on the whole field.

Kestrel Farm Buffer Strip Nutrient Runoff Problems — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Use this scenario for every problem. Kestrel Farm is a fictional farm in the town of Mossley. Its fertilizer puts 40 pounds of nitrogen on each acre. The field is 15 acres.

How many pounds of nitrogen does the farm spread on the whole 15-acre field?
Without a buffer, 25 percent of the applied nitrogen runs off toward the brook. How many pounds run off?
A grass buffer removes 30 percent of the nitrogen that reaches it. If 150 pounds reach the buffer, how many pounds does it catch?
After the buffer, how many pounds of nitrogen still pass through to the brook?
The buffer strip costs $2 for each foot of length. The farm plans a 500-foot strip. What is the total cost?
The fertilizer also puts 12 pounds of phosphorus on each acre. How many pounds of phosphorus land on all 15 acres?
The buffer removes 50 percent of the phosphorus that reaches it. If 60 pounds reach the buffer, how many pounds pass through to the brook?
A wider buffer removes a larger share. Complete the table of pounds removed from the 150 pounds of nitrogen that reach the buffer.

Removal rate Pounds removed

20%

30%

40%

60%
The farm wants less than 90 pounds of nitrogen to reach the brook. From problem 4, the 30 percent buffer lets 105 pounds through. Does the design meet the goal, and by how much does it miss or clear it?
In one or two sentences, explain why nitrogen and phosphorus can be called both a resource and a pollutant.

Removal rate	Pounds removed
20%
30%
40%
60%

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

Answer Key

Answer: 600 pounds. 40 pounds per acre x 15 acres = 600 pounds of nitrogen.
Answer: 150 pounds. 25 percent of 600 is 600 x 0.25 = 150 pounds of runoff.
Answer: 45 pounds. 30 percent of 150 is 150 x 0.30 = 45 pounds caught.
Answer: 105 pounds. The buffer catches 45, so 150 - 45 = 105 pounds pass through.
Answer: $1,000. 500 feet x $2 per foot = $1,000 for the buffer strip.
Answer: 180 pounds. 12 pounds per acre x 15 acres = 180 pounds of phosphorus.
Answer: 30 pounds. The buffer catches 60 x 0.50 = 30 pounds, so 60 - 30 = 30 pounds pass through.
Answer: 30, 45, 60, 90 pounds. Multiply 150 by each rate: 0.20 gives 30; 0.30 gives 45; 0.40 gives 60; 0.60 gives 90.
Answer: No, it misses by 15 pounds. The design lets 105 pounds reach the brook, and 105 - 90 = 15 pounds over the goal.
Answer: They feed crops but also feed algae. Nitrogen and phosphorus are a resource in a field because plants need them, and a pollutant in the brook because they feed algae blooms, and when the algae die and decay they use up the oxygen fish need.

Differentiation

Support

Provide a two-step frame for the percent problems: first write the amount that reaches the buffer, then multiply by the removal rate. Give the multiplication set up for problem 2 as 600 times 0.25 so students only finish the calculation. Allow a calculator throughout.

Extension

Ask students to design a buffer that keeps nitrogen reaching the brook under 90 pounds. They must state a removal rate that works, show the calculation, and explain the trade-off between a wider, more effective strip and its higher cost per foot.

ELL supports

Pre-teach "nutrient," "runoff," and "buffer" with a simple sketch of a field, a grass strip, and a stream. Provide a sentence frame for problem 10: "Nitrogen is a resource because ___, and a pollutant because ___."