Worksheet Grade 6 Math

Selby Lake Nitrogen and Phosphorus Ratio Worksheet

A grade 6 worksheet using ratio language, equivalent ratios, and percent to study how nitrogen and phosphorus act as both nutrients and pollution in a lake.

Grade: Grade 6
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: Calculator (optional)

Standards

6.RP.A.1 Common Core Math

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, 'The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'

How this material aligns: Items 1, 2, and 10 have students write and describe the nitrogen-to-phosphorus ratio in simplest form using for-every-there-is language, the exact ratio-language skill this standard names.

All materials for 6.RP.A.1 →

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: Items 4 through 8 use equivalent-ratio tables and finding a percent of the nutrient load, the ratio-table and percent reasoning this standard requires in real contexts.

All materials for 6.RP.A.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 write and simplify the ratio of nitrogen to phosphorus and describe it in words.
Students will use equivalent ratios and percent to plan a nutrient reduction for a lake.

Vocabulary

Key words: ratio, percent, nutrient, nitrogen, phosphorus

Teacher overview

Plants and tiny algae in a lake need nitrogen and phosphorus to grow, so these two are nutrients, not just pollution. Yet when too much washes in from lawns and farms, algae grow too fast and harm the water. This worksheet uses a fictional lake to practice ratios, equivalent ratios, and percent. As a teaching note, items 6 and 7 model how a town sets a reduction goal, and item 9 asks students to explain the "helpful yet harmful" idea in their own words.

Selby Lake Nitrogen and Phosphorus Ratio Worksheet — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

This is a fictional lake. Each summer, lawns around Selby Lake wash 400 pounds of nitrogen and 100 pounds of phosphorus into the water. Plants in the lake need small amounts of both. Too much phosphorus makes algae grow too fast.

Write the ratio of nitrogen to phosphorus (nitrogen : phosphorus) in simplest form.
Describe your ratio from item 1 in words: "for every ___ pounds of nitrogen there is ___ pound of phosphorus."
A lawn fertilizer bag has nitrogen and phosphorus in a 5 : 1 ratio. If the bag holds 20 pounds of nitrogen, how many pounds of phosphorus does it have?
Nitrogen and phosphorus together add up to 500 pounds entering the lake. What percent of that total is phosphorus?
What percent of the 500 pounds is nitrogen?
The town wants to cut the phosphorus by 30 percent. How many pounds is a 30 percent cut?
After the 30 percent cut, how many pounds of phosphorus reach the lake?
The lake's ratio stays at 4 : 1 (nitrogen : phosphorus). Complete this table of nitrogen for each amount of phosphorus.

Phosphorus (pounds) Nitrogen (pounds)

25

50

200
Explain how phosphorus can be both helpful and harmful to Selby Lake.
Suppose the nitrogen washing in drops from 400 pounds to 300 pounds while phosphorus stays at 100 pounds. Write the new nitrogen-to-phosphorus ratio in simplest form.

Phosphorus (pounds)	Nitrogen (pounds)
25
50
200

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: 4 : 1. 400 : 100 divides by 100 on both sides to give 4 : 1.
Answer: For every 4 pounds of nitrogen there is 1 pound of phosphorus. This restates the 4 : 1 ratio in words.
Answer: 4 pounds. In a 5 : 1 ratio, phosphorus is nitrogen ÷ 5, so 20 ÷ 5 = 4 pounds.
Answer: 20 percent. Phosphorus is 100 of the 500 total pounds; 100 ÷ 500 = 0.2, or 20 percent.
Answer: 80 percent. Nitrogen is 400 of 500 pounds; 400 ÷ 500 = 0.8, or 80 percent.
Answer: 30 pounds. A 30 percent cut of 100 pounds is 0.30 × 100 = 30 pounds.
Answer: 70 pounds. 100 pounds − 30 pounds cut = 70 pounds still reaching the lake.
Answer: 100; 200; 800. At 4 : 1, nitrogen is 4 times the phosphorus: 25 × 4 = 100, 50 × 4 = 200, 200 × 4 = 800 pounds.
Answer: Small amounts feed the plants and algae the lake needs, so it is helpful; too much makes algae grow too fast and harm the water, so it becomes harmful.
Answer: 3 : 1. 300 : 100 divides by 100 on both sides to give 3 : 1.

Differentiation

Support

Give students counters or square tiles so they can build the 4 : 1 ratio by grouping 4 nitrogen tiles with 1 phosphorus tile. Provide the total (500 pounds) already written for items 4 and 5, and review that "percent" means "out of 100."

Extension

Ask students to design a fertilizer with a 6 : 1 nitrogen-to-phosphorus ratio for a bag that holds 24 pounds of nitrogen, listing the phosphorus amount and the total weight, and to explain how a lower phosphorus share could help the lake.

ELL supports

Pre-teach "ratio," "nutrient," "nitrogen," and "phosphorus" with a picture of a lake, a lawn, and algae. Provide the sentence frame in item 2 for every student. Allow students to use tiles or a drawing to show the ratio in items 1 and 10.