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Worksheet Grade 5 Math

Tanglebrook Water Station: A Grade 5 Unit Fraction Worksheet

A grade 5 worksheet dividing whole gallons by unit fractions and unit fractions by whole numbers at a fictional town's dry-summer water station.

Objectives

  1. Students will divide a whole number of gallons by a unit fraction to count containers.
  2. Students will divide a unit fraction by a whole number to find an equal share.
  3. Students will explain why dividing by a unit fraction produces a larger number.

Vocabulary

Key words: unit fraction, gallon, share, container

Teacher overview

Tanglebrook is a fictional town whose one well drops low during a dry summer, so the water crew opens a station in the parking lot behind the fire hall and hands out water in small containers. The crew members pour from large jugs into bottles, pitchers, and cups of different sizes, which means they are dividing all day. This worksheet uses that station to practice both directions of unit-fraction division. The misconception it targets is the assumption that dividing always makes a number smaller, which leads students to answer that 3 gallons divided into quarter-gallon bottles fills fewer than 3 bottles.

Tanglebrook Water Station: A Grade 5 Unit Fraction Worksheet — Grade 5 Math
Name: ____________________________ Date: ______________

Student Worksheet

The Tanglebrook water crew fills containers from large jugs. Use the numbers in each item.

  1. The crew fills quarter-gallon bottles from 3 gallons of water. How many bottles can they fill?
  2. The crew fills half-gallon jugs from 5 gallons of water. How many jugs can they fill?
  3. The crew fills third-gallon pitchers from 4 gallons of water. How many pitchers can they fill?
  4. A crew member pours 1/2 gallon of water evenly into 4 cups. How much water goes in each cup?
  5. A crew member pours 1/3 gallon of cleaning solution evenly into 2 buckets. How much goes in each bucket?
  6. A crew member pours 1/4 gallon of water evenly into 5 sample bottles. How much goes in each bottle?
  7. A helper fills quarter-gallon bottles from 6 gallons of water. How many bottles can the helper fill?
  8. Starting with 2 gallons, does the crew fill more half-gallon jugs or more quarter-gallon bottles?
  9. The crew fills half-gallon jugs from 8 gallons of water. How many jugs can they fill?
  10. A crew member pours 1/5 gallon of drink mix evenly into 3 cups. How much goes in each cup?
  11. Explain why 3 divided by 1/4 gives an answer greater than 3.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 12 bottles. Each gallon holds 4 quarter-gallon bottles, so 3 x 4 = 12 bottles. Written as division, 3 divided by 1/4 = 12.
  2. Answer: 10 jugs. Each gallon holds 2 half-gallon jugs, so 5 x 2 = 10 jugs. Written as division, 5 divided by 1/2 = 10.
  3. Answer: 12 pitchers. Each gallon holds 3 third-gallon pitchers, so 4 x 3 = 12 pitchers. Written as division, 4 divided by 1/3 = 12.
  4. Answer: 1/8 gallon. Splitting one half into 4 equal parts gives eighths: 1/2 divided by 4 = 1/8 gallon in each cup.
  5. Answer: 1/6 gallon. Splitting one third into 2 equal parts gives sixths: 1/3 divided by 2 = 1/6 gallon in each bucket.
  6. Answer: 1/20 gallon. Splitting one fourth into 5 equal parts gives twentieths: 1/4 divided by 5 = 1/20 gallon in each bottle.
  7. Answer: 24 bottles. Each gallon holds 4 quarter-gallon bottles, so 6 x 4 = 24 bottles.
  8. Answer: More quarter-gallon bottles. From 2 gallons the crew fills 4 half-gallon jugs but 8 quarter-gallon bottles, because smaller containers take more of them to hold the same water.
  9. Answer: 16 jugs. Each gallon holds 2 half-gallon jugs, so 8 x 2 = 16 jugs.
  10. Answer: 1/15 gallon. Splitting one fifth into 3 equal parts gives fifteenths: 1/5 divided by 3 = 1/15 gallon in each cup.
  11. Answer: Dividing 3 by 1/4 asks how many quarter-gallons fit inside 3 gallons. Because each quarter-gallon is smaller than 1 gallon, many of them fit, so the count is larger than 3.

Differentiation

Support

Give students a set of fraction circles or a paper gallon strip folded into fourths, halves, and thirds. Have them physically lay quarter pieces onto three whole strips for item 1 and count the pieces before writing the division sentence. Keep items 1 through 3 and items 4 through 6 on separate pages so the two directions of division do not blur together.

Extension

Ask students to write one problem of each type for a classmate: one that divides a whole number of gallons by a unit fraction with an answer of 20, and one that divides a unit fraction by a whole number with an answer of 1/12. Have them include the full solution on a separate page.

ELL supports

Label a real quart (quarter-gallon) container, half-gallon jug, and gallon jug at a station so students can see and hold the sizes named in the items. Pre-teach "fill," "pour," "evenly," and "share," and provide a sentence frame for item 11: "The answer is greater than 3 because ___."

Extensions

Have students plan a water station for a fictional school field day. Given 10 gallons of water and cups that hold one eighth of a gallon, they calculate how many cups they can fill, then decide how many students the station could serve if each student takes two cups.