Math problem set Grade 6 Math

Jesmond School's Aquaponics Tank: Ratios and Daily Water Loss

A grade 6 problem set on a classroom aquaponics system: students write tank-to-bed ratios, find pump turnover, and track a two percent daily water loss across a week.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Printed problem set, Calculators

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: Problem 1 asks for the ratio of fish-tank water to grow-bed water in simplest form, and problem 9 states the tank-to-fish relationship in ratio language as gallons for each fish.

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: Problems 5, 6, and 7 find a percent of the whole system volume, scale that daily loss to a week, and turn the weekly loss back into a percent.

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 2026-09-03.

Objectives

Students will write and simplify a ratio comparing two parts of one water system.
Students will find a percent of a total volume and scale that daily amount to a week.
Students will compute how many times a pump moves a system's full volume in a day.

Vocabulary

Key words: aquaponics, grow bed, turnover, ratio, percent

Teacher overview

An aquaponics system keeps fish and plants in one loop of water. A pump lifts water from the fish tank to the grow beds, where bacteria and plant roots take up the waste the fish produce, and the cleaned water drains back to the tank. The fictional Jesmond Middle School runs one in a science classroom, and the class tops it up by hand each week. The misconception this set corrects is finding the daily loss from the fish tank alone. The water that evaporates and leaves with the plants comes out of the whole system, tank and beds together, so the percent must be taken from the combined total.

Jesmond School's Aquaponics Tank: Ratios and Daily Water Loss — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

The fictional Jesmond Middle School system has a fish tank holding 240 gallons and grow beds holding 120 gallons. The pump moves 6 gallons each minute. The system loses 2 percent of its total water each day, and 30 fish live in the tank.

Write the ratio of fish-tank water to grow-bed water in simplest form.
How many gallons of water are in the whole system, tank and beds together?
The pump moves 6 gallons each minute. How many minutes does it take to move 360 gallons?
A day has 1,440 minutes. If the pump moves the full 360 gallons every 60 minutes, how many times does it move the whole system's water in one day?
The system holds 360 gallons and loses 2 percent of it each day. How many gallons is that?
The system loses 7.2 gallons each day. How many gallons does it lose in 7 days?
The system holds 360 gallons and lost 50.4 gallons over the week. What percent of the system's water is that?
The class refills the system with 5 gallon buckets. Ten full buckets are poured in to replace the 50.4 gallons lost. How many gallons short of the loss is that?
The tank holds 240 gallons and 30 fish live in it. How many gallons of tank water is that for each fish?

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: 2:1.
Both 240 and 120 divide by 120, giving 2 to 1. There are two gallons in the tank for every gallon in the beds.
Answer: 360 gallons.
240 gallons in the tank plus 120 gallons in the beds is 360 gallons.
Answer: 60 minutes.
360 gallons divided by 6 gallons per minute is 60 minutes.
Answer: 24 times.
1,440 minutes divided by 60 minutes for each full pass is 24 passes in a day.
Answer: 7.2 gallons.
2 percent of 360 is 0.02 times 360, which is 7.2 gallons.
Answer: 50.4 gallons.
7.2 gallons per day times 7 days is 50.4 gallons.
Answer: 14 percent.
50.4 divided by 360 is 0.14, which is 14 percent. This checks with 2 percent a day for 7 days.
Answer: 0.4 gallons.
Ten buckets hold 10 times 5, or 50 gallons. The loss was 50.4 gallons, so the refill is 0.4 gallons short.
Answer: 8 gallons per fish.
240 gallons divided by 30 fish is 8 gallons for each fish.

Differentiation

Support

Give these students a labeled sketch of the fictional Jesmond system with 240 and 120 already written on the tank and the beds, so problem 2 is an addition they can see. Provide a reminder that 2 percent means 0.02 as a decimal, and assign problems 1, 2, 3, 5, and 9 first.

Extension

Ask these students to find how many gallons the class at the fictional Jesmond Middle School would need to add over a 36 week school year at the same daily rate, and to decide whether a 55 gallon storage barrel in the classroom would be enough to cover a month. They should support the decision with both numbers.

ELL supports

Pre-teach tank, grow bed, and top up with a sketch showing water going up to the beds and draining back down, with an arrow for the water that leaves the loop. Provide this sentence frame for problem 7: "The system lost ___ gallons out of ___ gallons, so the loss is ___ percent."

Extensions

Have students measure a classroom aquarium or a bucket of water, mark the level, and track how much the level drops over a week. Comparing their measured loss with the 2 percent figure used for the fictional Jesmond system gives the class a real rate to substitute into every problem above.