Math problem set Grade 6 Math

Danforth Farm Fertilizer Runoff: Ratios, Percents, and Decimals

A grade 6 math problem set on a fictional farm's fertilizer, where students use ratios, percents, and decimal changes to study nutrient runoff into a creek.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

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: Problems 1, 2, and 7 have students scale a 4-to-1 nutrient ratio and find a percent used and a percent decrease, the ratio and percent reasoning this standard targets.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 4 and 5 have students subtract multi-digit decimal nitrate and oxygen readings, the exact decimal computation this standard expects.

All materials for 6.NS.B.3 →

Download Word file

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 scale a nutrient ratio and find what percent of applied fertilizer crops use versus what could run off.
Students will subtract decimal water-quality readings and compare an oxygen reading to a fish safety level.

Vocabulary

Key words: nutrient, ratio, runoff, percent decrease

Teacher overview

Fertilizer feeds crops with nutrients such as nitrogen and phosphorus, but the nutrients that crops do not take up can wash into nearby water. In a creek, that extra nutrient load feeds heavy algae growth, and when the algae later break down they pull oxygen out of the water that fish need. This set treats nutrients as both a resource and a pollutant, depending on where they end up. Danforth is a fictional farm created for this problem set. A common misconception is that nutrients are simply harmful; the real issue is the extra amount that runs off, and students should keep the crop share and the runoff share as two parts of the same whole.

Danforth Farm Fertilizer Runoff: Ratios, Percents, and Decimals — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Suppose the fictional Danforth farm sits next to Muddy Fork Creek. The farmer spreads fertilizer on the fields. The crops take up some of the nutrients. Extra nutrients wash into the creek. Use the numbers in each problem.

A fertilizer bag mixes nitrogen to phosphorus in a 4-to-1 ratio. If it holds 20 pounds of nitrogen, how many pounds of phosphorus does it hold?
The farmer spreads 200 pounds of fertilizer. The crops take up 150 pounds. What percent did the crops use?
What percent of the 200 pounds was not used and could run off?
Before a storm the creek's nitrate reading is 2.5 mg/L. After the storm it is 6.0 mg/L. Find the increase.
The creek's oxygen was 8.0 mg/L. After the algae die and break down, the oxygen drops to 4.5 mg/L. Find the decrease.
Fish need oxygen above 5 mg/L. Is the creek's 4.5 mg/L reading safe for fish?
The next season the farmer cuts fertilizer from 200 pounds to 170 pounds. Find the percent decrease.
Explain how nutrients can be both a resource and a pollutant.

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: 5 pounds. In a 4-to-1 ratio, phosphorus is one fourth of the nitrogen: 20 ÷ 4 = 5 pounds.
Answer: 75%. The crops used 150 of 200 pounds: 150 ÷ 200 = 0.75, or 75 percent.
Answer: 25%. The unused part is 200 − 150 = 50 pounds, and 50 ÷ 200 = 0.25, or 25 percent.
Answer: 3.5 mg/L. The nitrate rose from 2.5 to 6.0, and 6.0 − 2.5 = 3.5 mg/L.
Answer: 3.5 mg/L. The oxygen fell from 8.0 to 4.5, and 8.0 − 4.5 = 3.5 mg/L.
Answer: No. The reading 4.5 mg/L is below the 5 mg/L that fish need, so it is not safe.
Answer: 15%. The cut is 200 − 170 = 30 pounds on a start of 200, and 30 ÷ 200 = 0.15, or 15 percent.
Answer: It depends on where the nutrients go. On the field they feed crops, which is useful; in the creek the extra feeds algae and lowers oxygen, which is harmful.

Differentiation

Support

Provide a bar model labeled 200 pounds for item 2, with 150 shaded for crop use, so students can see the used part and the unused part before they divide. Work item 4 together as a decimal subtraction lined up by the decimal point, and allow a calculator for the percent problems.

Extension

Ask students to find how much lower the after-storm nitrate reading would have been if the farmer had cut fertilizer to 170 pounds first, assuming the runoff share stays the same percent, and explain their reasoning.

ELL supports

Pre-teach nutrient, runoff, nitrate, and oxygen with a simple picture of a field beside a creek. Provide a sentence frame for item 8: "Nutrients are a resource when ___, and a pollutant when ___." Allow labeled number sentences in place of full sentences.