Math problem set Grade 5 Math

Cattail Marsh Nature Center's Test Kit: Fraction Division Problems

A grade 5 problem set where a fictional nature center's water-testing club divides gallons and cups of testing supplies among wetland monitoring stations.

Grade: Grade 5
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

5.NF.B.3 Common Core Math

Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

How this material aligns: Students interpret whole-number division problems, such as splitting 3 gallons of solution among 4 stations, as fractions in problems 1 and 4.

All materials for 5.NF.B.3 →

5.NF.B.7 Common Core Math

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

How this material aligns: Students divide unit fractions by whole numbers and whole numbers by unit fractions across problems 2, 3, 5, 6, and 8 to split test solutions.

All materials for 5.NF.B.7 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will interpret a fraction as the division of a whole number by another whole number.
Students will divide a unit fraction by a whole number and a whole number by a unit fraction.
Students will compare two fractional shares to decide which is greater.

Vocabulary

Key words: unit fraction, constructed wetland, monitoring station

Teacher overview

Cattail Marsh Nature Center, a fictional nature center used for this problem set, maintains a constructed wetland that filters runoff before it reaches a nearby creek. A student water-testing club monitors the wetland at several sample stations, and each visit starts with dividing a fixed amount of testing solution evenly among those stations. This set follows the club through one monitoring day, using fraction division to split gallons, cups, and dye among stations and containers. A common misconception in this math is treating "dividing by a fraction" the same as "dividing by the fraction's denominator alone"; problem 3 is built to surface that error, since dividing 6 cups by 1/3 gives more tests, not fewer, than dividing by 3 would.

Cattail Marsh Nature Center's Test Kit: Fraction Division Problems — Grade 5 Math

Name: ____________________________ Date: ______________

Problems

The club has 3 gallons of cleaning solution. They split it evenly among 4 stations. How much solution does each station get? Write your answer as a fraction of a gallon.
The club has 1/2 gallon of buffer solution. They split it evenly among 4 containers. How much does each container get?
A box of powder holds 6 cups. Each water test uses 1/3 cup of powder. How many tests can the club run with one box?
The club has 2 gallons of dye. They split it evenly among 5 stations. How much dye does each station get? Write your answer as a fraction of a gallon.
One station's sample container holds 1/4 gallon. The club splits that sample evenly between 2 test tubes. How much sample is in each tube?
The club has 4 gallons of clean water for rinsing tools. Each rinse uses 1/6 gallon. How many rinses can the club do with the whole jug?
In problem 1, the club split 3 gallons among 4 stations. In problem 4, the club split 2 gallons among 5 stations. Which split gives each station more solution, 3/4 gallon or 2/5 gallon? Explain how you know without doing more math.
Challenge. The club has 5 gallons of test liquid. They want each station to get exactly 1/4 gallon. How many stations can get that much?

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: 3/4 gal.
3 gallons divided by 4 stations equals 3/4 gallon per station.
Answer: 1/8 gal.
1/2 gallon divided by 4 containers equals 1/2 x 1/4 = 1/8 gallon per container.
Answer: 18 tests.
6 cups divided by 1/3 cup per test equals 6 x 3 = 18 tests.
Answer: 2/5 gal.
2 gallons divided by 5 stations equals 2/5 gallon per station.
Answer: 1/8 gal.
1/4 gallon divided by 2 test tubes equals 1/4 x 1/2 = 1/8 gallon per tube.
Answer: 24 rinses.
4 gallons divided by 1/6 gallon per rinse equals 4 x 6 = 24 rinses.
Answer: problem 1's split gives more.
3/4 is greater than 1/2, while 2/5 is less than 1/2, so 3/4 must be greater than 2/5. Each station in problem 1 receives more solution than each station in problem 4.
Answer: 20 stations.
5 gallons divided by 1/4 gallon per station equals 5 x 4 = 20 stations.

Differentiation

Support (below grade level)

Provide a printed fraction strip or visual model for problems 2, 5, and 6 showing the whole divided into the given unit fraction, and allow students to draw circles or bars to check problems 1 and 4 before writing the fraction answer.

Extension (above grade level)

Ask students to find how many stations problem 8's 5 gallons could supply if each station instead received 1/6 gallon, and explain why that number is larger than the answer to problem 8 even though the total amount of solution did not change.

ELL supports

Pre-teach "divide evenly," "unit fraction," and "solution" using a simple picture of one gallon jug being poured into several equal-sized cups. Provide a sentence frame for problem 1: "3 gallons divided among 4 stations means each station gets ___ gallon."