Math problem set Grade 6 Science

Larkspur Basin Chlorine Residual: Dose, Demand, and Decay

A grade 6 problem set on a fictional system's chlorine tests, where students find chlorine demand, the mean and range of residuals, and compare them to the safe range.

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

Standards

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 1, 2, 6, and 7 subtract decimal chlorine readings to the tenth of a milligram per liter, exactly the multi-digit decimal fluency 6.NS.B.3 expects.

All materials for 6.NS.B.3 →

6.SP.B.5 Common Core Math

Summarize numerical data sets in relation to their context, reporting the number of observations, describing the attribute measured, giving quantitative measures of center and variability, and relating the choice of measures to the shape of the distribution.

How this material aligns: Problems 2, 3, and 4 report the range, mean, and median of a five-point residual data set, the summary of a numerical data set 6.SP.B.5 requires.

All materials for 6.SP.B.5 →

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 5 and 6 check each residual reading against the 0.2-to-2.0 mg/L safe range and the 4.0 mg/L MRDL, and problems 7 and 8 track the steady decay along the pipe, the water-quality monitoring method this standard asks students to reason about.

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 find chlorine demand as the dose minus the measured residual.
Students will find the range, mean, and median of chlorine residual readings and compare them to a safe range.

Vocabulary

Chlorine residual: Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.
Disinfection: Disinfection is the step that kills or disables germs in water so it is safe to drink. Water plants usually disinfect with chlorine, ultraviolet light, or ozone.

Also: chlorine demand

Teacher overview

Water plants add chlorine to kill germs. Some of the chlorine gets used up doing that job, which is the chlorine demand, and the amount left over is the residual. Operators want a small residual to stay in the water all the way to the last house, so germs cannot grow back. This set follows the fictional Larkspur Basin system as operators test the residual at points along one pipe. A common error is mixing up the dose with the residual: the dose is what goes in, the residual is what is left, and demand is the difference between them.

Larkspur Basin Chlorine Residual: Dose, Demand, and Decay — Grade 6 Science

Name: ____________________________ Date: ______________

Problems

The fictional Larkspur Basin water system measures chlorine in milligrams per liter (mg/L). Use these facts for every problem.

The plant adds a dose of 2.5 mg/L of chlorine. Just past the plant, the residual reads 2.0 mg/L.
Moving down one pipe, the residual reads 2.0, 1.7, 1.4, 1.1, and 0.8 mg/L at five test points.
The safe residual range in the pipes is 0.2 to 2.0 mg/L. The highest amount allowed, the MRDL, is 4.0 mg/L.

Chlorine demand equals the dose minus the residual. Find the demand at the plant.
Find the range of the five residual readings.
Find the mean of the five residual readings.
Find the median of the five residual readings.
Are all five readings inside the safe range of 0.2 to 2.0 mg/L?
How far below the 4.0 mg/L MRDL is the plant's 2.0 mg/L residual?
The residual drops by the same amount between each pair of test points. How much does it drop between each pair?
If that same drop keeps going, predict the residual at the next test point after 0.8 mg/L.

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: 0.5 mg/L.
Dose 2.5 mg/L minus residual 2.0 mg/L = 0.5 mg/L of chlorine demand.
Answer: 1.2 mg/L.
Highest reading 2.0 minus lowest reading 0.8 = 1.2 mg/L.
Answer: 1.4 mg/L.
2.0 plus 1.7 plus 1.4 plus 1.1 plus 0.8 = 7.0. 7.0 divided by 5 = 1.4 mg/L.
Answer: 1.4 mg/L.
In order the readings are 0.8, 1.1, 1.4, 1.7, 2.0. The middle value is 1.4 mg/L.
Answer: Yes.
Every reading falls between 0.2 and 2.0 mg/L, so all five are inside the safe range.
Answer: 2.0 mg/L.
4.0 mg/L MRDL minus the 2.0 mg/L residual = 2.0 mg/L below the limit.
Answer: 0.3 mg/L.
From 2.0 to 1.7 is 0.3, from 1.7 to 1.4 is 0.3, from 1.4 to 1.1 is 0.3, and from 1.1 to 0.8 is 0.3. Each drop is 0.3 mg/L.
Answer: 0.5 mg/L.
The last reading is 0.8 mg/L, and the steady drop is 0.3 mg/L, so 0.8 minus 0.3 = 0.5 mg/L.

Differentiation

Support

Give students the five readings already listed in order for the median, and the sum 7.0 already found for the mean, so they only divide. Write the demand rule "dose minus residual" on a card, and let students use a calculator and a number line for the subtraction steps.

Extension

Ask students to find how many more test points the residual could pass in this fictional system, dropping 0.3 mg/L each time from 0.8 mg/L, before it would fall below the safe minimum of 0.2 mg/L, and to show their reasoning.

ELL supports

Pre-teach "dose," "residual," and "demand" with a picture of chlorine going in, some being used up, and a small amount staying in the water. Provide the frame "Demand is the dose minus the ___," and let students point to the five readings in the list at the top of the problems as they answer.