Math problem set Grade 7 Math

Pelham Reach Farm Nitrogen: A Grade 7 Percent Problem Set

A grade 7 problem set tracking nitrogen on a fictional farm as both a crop resource and a runoff pollutant, using multistep percent of a changing base.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problems 1 through 7 apply percents to find crop uptake, leftover nitrogen, and runoff, the multistep ratio and percent work this standard names.

All materials for 7.RP.A.3 →

7.EE.B.3 Common Core Math

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, and assess the reasonableness of answers using mental computation and estimation strategies.

How this material aligns: Problem 7 chains a percent reduction and a percent uptake across two steps, a multistep rational-number problem whose result students check for reasonableness.

All materials for 7.EE.B.3 →

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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 use percents to find how much nitrogen a crop takes up and how much can run off.
Students will apply a second percent to a changed amount rather than the original total.

Vocabulary

Key words: nitrogen, uptake, runoff, percent

Teacher overview

Nitrogen is a resource a crop needs and a pollutant when it washes off a field into a stream. The fictional Pelham Reach Farm spreads nitrogen fertilizer, and only part of it is taken up by the corn. This set follows the nitrogen through uptake, leftover, and runoff using percents. A common error is taking the second percent from the original total: once nitrogen is left in the soil, the next percent must be found from that leftover amount, not from the starting pounds.

Pelham Reach Farm Nitrogen: A Grade 7 Percent Problem Set — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

Every problem uses the fictional Pelham Reach Farm and the same field.

The field receives 200 pounds of nitrogen. The corn takes up 60 percent of it. How many pounds does the crop use?
How many pounds are not taken up by the crop, and what percent of the 200 pounds is that?
Of the pounds not taken up, tests show 25 percent washes into a nearby stream. How many pounds reach the stream?
What percent of the original 200 pounds of nitrogen reaches the stream?
The farm switches to a split application that raises uptake to 75 percent. With the same 200 pounds, how many more pounds does the crop take up than in Problem 1?
To cut runoff, the farm lowers the total nitrogen by 15 percent, from 200 pounds. How many pounds does it apply now?
With the new lower amount from Problem 6 and 75 percent uptake, how many pounds does the crop take up?
Using your answers, explain how raising the uptake percent lowers the pounds that can run off, even when the field gets the same 200 pounds.

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: 120 pounds. 60 percent of 200 is 0.60 × 200 = 120 pounds taken up.
Answer: 80 pounds, which is 40 percent. Not taken up: 200 − 120 = 80 pounds. As a percent: 80 ÷ 200 = 0.40, or 40 percent.
Answer: 20 pounds. Find 25 percent of the 80 leftover pounds: 0.25 × 80 = 20 pounds reach the stream.
Answer: 10 percent. 20 pounds ÷ 200 pounds = 0.10, so 10 percent of the original nitrogen reaches the stream.
Answer: 30 pounds more. At 75 percent uptake, the crop uses 0.75 × 200 = 150 pounds. That is 150 − 120 = 30 pounds more than in Problem 1.
Answer: 170 pounds. A 15 percent cut means multiplying by 0.85: 200 × 0.85 = 170 pounds applied.
Answer: 127.5 pounds. 75 percent of 170 is 0.75 × 170 = 127.5 pounds taken up by the crop.
Answer: Higher uptake means the crop uses a larger share of the applied nitrogen, so fewer pounds are left in the soil to wash away. From 200 pounds, 60 percent uptake leaves 80 pounds, but 75 percent uptake leaves only 50 pounds, cutting the amount that can run off.

Differentiation

Support

Give students a two-box diagram labeled "taken up" and "left in soil" to fill in before finding runoff, so they see that the runoff percent applies to the leftover box. Allow a calculator and provide the meaning of "uptake" in plain words.

Extension

Ask students to find the uptake percent that would leave exactly 40 pounds of nitrogen in the soil from a 200-pound application, then show how much of that 40 pounds would run off at the same 25 percent rate.

ELL supports

Pre-teach "nitrogen," "uptake," and "runoff" with a simple picture of a plant taking in fertilizer and extra washing toward a stream. Provide the sentence frame "The crop uses ___ percent, so ___ pounds are left" for the early problems.