Math problem set Grade 5 Science

A Day of Flow at the Lissenden Water Reclamation Plant

A grade 5 decimal problem set following one day at a fictional wastewater plant, from the screen baskets through the settling tank to the weight of solids removed.

Grade: Grade 5
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Graph paper, Calculator, optional

Standards

5.NBT.B.7 Common Core Math

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

How this material aligns: Problems 1 through 8 add, subtract, and divide decimals to hundredths using the plant's shift weights, settling weights, and daily flow figures.

All materials for 5.NBT.B.7 →

5-PS1-2 NGSS

Measure and graph quantities to provide evidence that regardless of the type of change that occurs when heating, cooling, or mixing substances, the total weight of matter is conserved.

How this material aligns: Problem 9 graphs five daily solids weights and problem 10 uses the 96.5 and 3.5 split to show that the weight of solids is conserved when water is cleaned.

All materials for 5-PS1-2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-04.

Objectives

Students will add, subtract, and divide decimals to solve problems about one day at a treatment plant.
Students will graph five daily weights of removed solids on a labeled bar graph.
Students will explain why the weight of solids removed plus the weight left behind equals the weight that came in.

Vocabulary

Bar screen: A bar screen is a row of metal bars at the entrance of a treatment plant that catches rags, sticks, trash, and other large debris out of incoming sewage. Keeping this junk out protects the pumps and machinery further along in the process.

Also: reclamation, settling tank, solids, conserved

Teacher overview

The Lissenden Water Reclamation Plant is a fictional plant that cleans the used water from one town and returns it to the Marden River. Every problem in this set comes from a single day at that plant: the four screen baskets weighed at the end of each shift, the settling tank that pulls solids out of the water, and the total flow the pumps moved. The set is built to correct a specific misconception, which is the idea that the dirt in used water disappears when the water is cleaned. The weights in problems 4, 5, and 10 show that the solids are all still there and have only been moved into a different place, which is the same conservation idea students meet when they dissolve and evaporate a solid.

A Day of Flow at the Lissenden Water Reclamation Plant — Grade 5 Science

Name: ____________________________ Date: ______________

Problems

The plant weighs the screen basket at the end of each of four shifts. The four weights are 12.4 pounds, 9.8 pounds, 15.6 pounds, and 11.2 pounds. What is the total weight caught by the screens that day?
The heaviest basket weighed 15.6 pounds. The lightest weighed 9.8 pounds. How much heavier was the heaviest basket?
The four baskets together weighed 49.0 pounds. Divide by 4 to find the average weight of one basket.
After the screens, the water flows to the settling tank. That day, 96.5 pounds of solids settled to the bottom, and 3.5 pounds of solids stayed in the water that left the tank. How many pounds of solids reached the settling tank in all?
In that same tank, 96.5 pounds of solids settled out and 3.5 pounds stayed in the water. How many more pounds settled out than stayed in?
The pumps moved 640,000 gallons through the plant that day. The pumps ran for 8 hours and moved the same amount of water in each hour. How many gallons moved through in one hour?
The next day the plant handled 512,000 gallons. How many fewer gallons is that than the 640,000 gallons on the first day?
Over five days the plant recorded these weights of settled solids: 96.5 pounds, 88.0 pounds, 102.5 pounds, 91.0 pounds, and 97.0 pounds. What is the five-day total?
Make a bar graph of the five daily weights listed in problem 8. Label the bars Day 1 through Day 5 and number the vertical scale in pounds, counting by 10.
On day 1, a total of 100.0 pounds of solids reached the settling tank, 96.5 pounds settled out, and 3.5 pounds stayed in the water leaving the tank. Explain what these three numbers show about the weight of the solids when the plant cleans the water.

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: 49.0 pounds. Add the four shift weights in order: 12.4 + 9.8 = 22.2, then 22.2 + 15.6 = 37.8, then 37.8 + 11.2 = 49.0 pounds.
Answer: 5.8 pounds. Subtract the lightest basket from the heaviest, lining up the decimal points: 15.6 - 9.8 = 5.8 pounds.
Answer: 12.25 pounds. Divide the total by the number of shifts: 49.0 divided by 4 equals 12.25 pounds for the average basket.
Answer: 100.0 pounds. Add the solids that settled to the solids that stayed in the water: 96.5 + 3.5 = 100.0 pounds reaching the tank.
Answer: 93.0 pounds. Subtract the solids that stayed from the solids that settled: 96.5 - 3.5 = 93.0 pounds more.
Answer: 80,000 gallons. Divide the day's flow by the hours the pumps ran: 640,000 divided by 8 equals 80,000 gallons in one hour.
Answer: 128,000 gallons. Subtract the second day from the first: 640,000 - 512,000 = 128,000 fewer gallons.
Answer: 475.0 pounds. Add the five weights in order: 96.5 + 88.0 = 184.5, then 184.5 + 102.5 = 287.0, then 287.0 + 91.0 = 378.0, then 378.0 + 97.0 = 475.0 pounds.
Answer: A bar graph with five labeled bars. The vertical scale runs from 0 to at least 110 pounds and is numbered by tens. Day 3 has the tallest bar at 102.5 pounds and Day 2 has the shortest at 88.0 pounds. Accept any graph with all five bars drawn to a consistent scale and labeled.
Answer: The total weight stayed the same, 100.0 pounds. The solids did not disappear when the water was cleaned, because 96.5 pounds moved to the bottom of the tank and 3.5 pounds stayed in the water, and those two weights add back to the 100.0 pounds that came in. Accept any answer that says the total weight stayed the same and that the solids were moved rather than destroyed.

Differentiation

Support

Give these students problems 1, 2, 4, 5, and 8 with the addition and subtraction already written vertically and the decimal points aligned, so their work is the arithmetic rather than the setup. Provide graph paper for problem 9 with the vertical scale already numbered by tens and the five day labels printed under the axis.

Extension

Ask these students to find how many pounds of solids the plant would remove in a 30-day month if every day matched the five-day average from problem 8, and to state clearly what assumption they had to make for that estimate to hold.

ELL supports

Pre-teach screen, settle, and solids with a simple three-part sketch of used water passing a bar screen, resting in a tank, and leaving cleaner, with a pile of solids drawn at the bottom of the tank. Provide a sentence frame for problem 10 in the form of a total weight that came in, a weight that settled, a weight that stayed, and a closing phrase about the total staying the same.

Extensions

Have students find out where their own community's used water goes after it leaves the building, using a utility page or a printed report the teacher supplies, and write two sentences about what happens to the solids that plant removes.