Math problem set Grade 7 Science

Wetherby Reservoir Road-Salt Chloride: A Grade 7 Proportion Set

A grade 7 problem set tracking chloride from winter road salt in a reservoir: percent increase, proportional rates, ppm equivalence, and percent error.

Grade: Grade 7
Subject: Science
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 2, 4, and 7 have students compute percent increase, percent of a target, and percent error, the multistep percent reasoning this standard names.

All materials for 7.RP.A.3 →

7.RP.A.2 Common Core Math

Recognize and represent proportional relationships between quantities, including identifying the constant of proportionality and representing proportional relationships by equations.

How this material aligns: Problems 5 and 6 use the constant rate of chloride rise per pound of salt as a proportional relationship, the constant of proportionality this standard names.

All materials for 7.RP.A.2 →

MS-ESS3-3 NGSS

Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment.

How this material aligns: Problems 1, 2, and 8 read summer, winter, and spring-melt chloride readings as evidence of how road salt loads the reservoir, and problems 5 and 6 tie the chloride rise to the pounds of salt applied, the water pollution this standard's clarification names as an impact to monitor.

All materials for MS-ESS3-3 →

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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 compute the percent increase in a chloride reading.
Students will use a proportional rate to predict chloride from a salt amount.
Students will convert milligrams per liter to parts per million and find percent error.

Vocabulary

Parts per million (ppm): Parts per million tells how many tiny bits of a substance are mixed into a million bits of water. Scientists use it to measure very small amounts of chemicals in water.

Also: chloride, milligrams per liter, percent error

Teacher overview

Salt spread on winter roads washes into lakes and streams, where it raises the level of chloride in the water. This set follows chloride readings at the fictional Wetherby Reservoir from summer into winter and has students work with the change. A common misconception to watch for is treating the raw rise in milligrams per liter as if it were the percent increase; the two are different, and problems 1 and 2 are built to separate them. A second point to watch: in fresh water like the reservoir's, milligrams per liter and parts per million are almost exactly the same size, so no arithmetic is needed to switch between them. This shortcut does not hold for very salty water such as seawater, where a correction is needed.

Wetherby Reservoir Road-Salt Chloride: A Grade 7 Proportion Set — Grade 7 Science

Name: ____________________________ Date: ______________

Problems

Wetherby Reservoir is a fictional lake. Use the readings given in each problem.

In summer, the reservoir's chloride level is 40 mg/L. In winter it rises to 95 mg/L. How many mg/L did the chloride increase?
What is the percent increase in chloride from summer to winter? Round to the nearest whole percent.
In fresh water, 1 mg/L is about equal to 1 part per million (ppm). Write the winter chloride level of 95 mg/L in ppm.
The Wetherby water board set a local taste target of 220 mg/L for chloride. The winter level is 95 mg/L. What percent of that target is the winter level? Round to the nearest whole percent.
Chloride rises in proportion to the road salt that washes in. Suppose 500 pounds of salt raised the level by 55 mg/L. At that same rate, how many mg/L would 900 pounds raise it?
Using the rate from problem 5, how many pounds of salt would raise the level by 11 mg/L?
A lab reported the winter level as 95 mg/L, but the true value was 90 mg/L. Find the percent error. Use the absolute difference divided by the true value, times 100. Round to the nearest whole percent.
A spring melt cuts the winter level of 95 mg/L in half. What is the new level, and is it below the 220 mg/L target?

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: 55 mg/L.
95 mg/L minus 40 mg/L equals 55 mg/L of increase.
Answer: 138 percent.
The increase is 55 mg/L over the starting 40 mg/L. 55 divided by 40 equals 1.375, which is a 138 percent increase.
Answer: 95 ppm.
Because 1 mg/L is about 1 ppm in fresh water, 95 mg/L is about 95 ppm.
Answer: 43 percent.
95 divided by 220 equals about 0.432, so the winter level is about 43 percent of the taste target.
Answer: 99 mg/L.
The rate is 55 mg/L per 500 pounds, which is 0.11 mg/L per pound. Then 0.11 times 900 pounds equals 99 mg/L.
Answer: 100 pounds.
At 0.11 mg/L per pound, 11 mg/L divided by 0.11 mg/L per pound equals 100 pounds of salt.
Answer: 6 percent.
The difference is 95 minus 90, which is 5 mg/L. Then 5 divided by the true value 90 equals about 0.056, or about 6 percent error.
Answer: 47.5 mg/L, yes.
Half of 95 mg/L is 47.5 mg/L, which is well below the 220 mg/L target.

Differentiation

Support

Give students the percent formulas written out with labels (change divided by starting amount for percent increase; part divided by whole for percent of a target). Provide the salt-to-chloride rate already computed (0.11 milligrams per liter per pound) so students can focus on problems 5 and 6.

Extension

Ask students to find the summer-to-winter percent increase if the winter reading had instead reached the 220 milligrams per liter target, and to explain why the same raw increase can be a larger or smaller percent depending on the starting level.

ELL supports

Pre-teach "chloride," "increase," and "target" with a simple thermometer-style bar that fills from summer to winter. Allow students to label the parts of each percent formula before computing.