Worksheet Grade 5 Health & Consumer Science

The Dorsey Family's Filter Pitcher: Dividing by Unit Fractions

A grade 5 worksheet in which students divide whole numbers by unit fractions to decide how long a fictional family's water filter cartridge will last.

Grade: Grade 5
Subject: Health & Consumer Science
Material: Worksheet
Time: 30 min
Prep: No prep
Materials: None

Standards

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: Items 1, 3, 6, and 8 ask students to divide a whole number of gallons by a unit fraction such as one half or one fourth of a gallon.

All materials for 5.NF.B.7 →

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: Items 4 and 5 have students share a whole number of gallons equally among people, interpreting the fraction as division of gallons by people.

All materials for 5.NF.B.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 divide a whole number of gallons by a unit fraction to count days or fillings.
Students will interpret a sharing situation as division and write the result as a fraction or decimal.
Students will explain why a filter cartridge is tracked by gallons and not by weeks alone.

Vocabulary

Key words: cartridge, filter, unit fraction, capacity

Teacher overview

A filter pitcher only improves the taste and quality of water while its cartridge still has capacity left, which is why manufacturers rate a cartridge by the gallons it can filter and give only an approximate replacement time, such as about two months, based on typical use. This worksheet follows the fictional Dorsey family, whose pitcher cartridge is rated for 40 gallons, and asks students to work out how long that rating lasts under different daily habits. The division work uses unit fractions of a gallon, and two items ask students to share a whole number of gallons equally among people.

The Dorsey Family's Filter Pitcher: Dividing by Unit Fractions — Grade 5 Health & Consumer Science

Name: ____________________________ Date: ______________

Student Worksheet

The Dorsey family is fictional. Their filter cartridge is rated for 40 gallons of water, and their pitcher holds 1/2 gallon when it is full.

The Dorsey family's cartridge is rated for 40 gallons. They pour 1/2 gallon of filtered water each day. How many days will one cartridge last?
During a hot week the family uses 1 gallon of filtered water each day. How many days would a 40-gallon cartridge last at that rate?
Each morning the family pours 1/4 gallon for breakfast. How many mornings does 10 gallons of cartridge capacity cover?
Six people share 3 gallons of filtered water equally. How many gallons does each person get?
Five people share 4 gallons of filtered water equally. How many gallons does each person get?
The pitcher holds 1/2 gallon when full. How many times must the family fill the pitcher to pour 6 gallons?
A cartridge is rated for 40 gallons. The family has already run 30 gallons through it. How many gallons of capacity are left?
The cartridge has 10 gallons of capacity left, and the family pours 1/2 gallon each day. How many more days will the cartridge last?
The family pours 1/2 gallon each day for 30 days. How many gallons have they used in those 30 days?
Write one or two sentences explaining why the family should keep track of gallons, not only weeks, when deciding to change the cartridge.

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: 80 days. Divide the rating by the daily amount: 40 divided by 1/2 = 80, because there are two half gallons in every gallon.
Answer: 40 days. Divide 40 by 1: 40 divided by 1 = 40.
Answer: 40 mornings. Divide 10 by 1/4 = 40, because there are four quarter gallons in every gallon.
Answer: 0.5 gallon. Sharing 3 gallons among 6 people is 3 divided by 6, which is 3/6, or 1/2 gallon each.
Answer: 0.8 gallon. Sharing 4 gallons among 5 people is 4 divided by 5, which is 4/5, or 0.8 gallon each.
Answer: 12 times. Divide 6 by 1/2 = 12, because each filling pours half a gallon.
Answer: 10 gallons. Subtract the used amount from the rating: 40 - 30 = 10.
Answer: 20 days. Divide 10 by 1/2 = 20.
Answer: 15 gallons. Multiply 30 x 1/2 = 15.
Answer: The cartridge stops working well after a set number of gallons, and a family that pours more water each day reaches that number sooner, so weeks alone do not show when it is used up. Accept any answer that ties the change to the amount of water rather than to time.

Differentiation

Support

Give these students a drawing of one gallon divided into halves and one gallon divided into fourths, and let them count the pieces for items 1, 3, 6, and 8 before writing the division sentence. Work item 1 together as a model, and provide a number line marked in halves from 0 to 5.

Extension

Ask students to write a filtering plan for a fictional household of eight people that would use up a 40-gallon cartridge in exactly 20 days, state the daily amount, and show the division that proves it. Students should then explain how the plan would change if the cartridge were rated for 60 gallons.

ELL supports

Pre-teach "cartridge," "capacity," and "rated for" with a pitcher and a labeled card showing 40 gallons. Post the sentence frame "____ gallons divided by ____ gallon each day equals ____ days," and allow students to draw the halves or fourths instead of writing a sentence for items 1 through 3.

Extensions

Students can read the capacity printed on a real filter package at home or in a store advertisement, then use their family's own pouring habit to estimate a replacement date. Bringing those estimates back to class produces a range of answers that can be compared and explained.