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Math problem set Grade 3 Math

Marigold Lane's Well Jugs: A Grade 3 Fraction-of-a-Gallon Problem Set

A grade 3 problem set where volunteers fill quarter-marked jugs from a community garden's well, building and comparing fractions of a whole gallon.

Objectives

  1. Students will identify a unit fraction of a gallon based on equal sections of a jug.
  2. Students will build and compare fractions of a gallon made from several quarter-gallon sections.

Vocabulary

Key words: unit fraction, section, whole, gallon

Teacher overview

At the fictional Marigold Lane Community Garden, volunteers fill water jugs from a hand-pump well to water new seedlings. Each jug holds 1 gallon and is marked into 4 equal sections, and volunteers fill jugs to different marks depending on how much water a row of seedlings needs. This problem set uses those marked jugs to build and compare fractions of a whole gallon. A common misconception is comparing fractions by looking only at the numerator, assuming that because 2 is a smaller number than 3, a jug filled to 2 sections must always hold less than a jug filled to a different fraction; problem 5 asks students to justify a comparison using the actual number of equal sections filled, since both jugs here are divided the same way.

Marigold Lane's Well Jugs: A Grade 3 Fraction-of-a-Gallon Problem Set — Grade 3 Math
Name: ____________________________ Date: ______________

Problems

  1. A 1-gallon jug is marked into 4 equal sections. Each section holds the same amount. What fraction of the gallon does 1 section hold?

  2. A volunteer fills 3 of the 4 sections with water. What fraction of the gallon has been filled?

  3. A second jug is filled all the way, all 4 of its 4 sections. What fraction is that? Why does that fraction equal one whole gallon?

  4. A volunteer fills a third jug to 2 of its 4 sections. Write this amount as a fraction of a gallon.

  5. Look at the jug from problem 2 (3 sections filled) and the jug from problem 4 (2 sections filled). Which jug has more water? Use the number of sections to explain.

  6. Five seedlings each need 1 section of water, so 5 sections of water are needed in all. Each jug holds only 4 sections. Volunteers fill one jug completely before starting the next. How many jugs get filled all the way to the top, and how many sections are left over to put in the next jug?

  7. A fourth jug has 2 of its 4 sections filled with water. The rest of the jug is empty. What fraction of the jug is empty?

  8. At the end of the morning, one jug has 3 filled sections. Another jug has 1 filled section. Which jug has more water? By how many sections is it more?

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: 1/4 gallon.
    The jug is divided into 4 equal sections, so 1 section is 1 part of 4 equal parts, or 1/4 gallon.

  2. Answer: 3/4 gallon.
    Filling 3 of the 4 equal sections means 3 parts of size 1/4, which is written as 3/4 gallon.

  3. Answer: 4/4 gallon, which equals one whole gallon.
    Filling all 4 of the jug's 4 equal sections means every part of the whole is filled, so 4/4 gallon is the same amount as 1 whole gallon.

  4. Answer: 2/4 gallon.
    Filling 2 of the 4 equal sections means 2 parts of size 1/4, which is written as 2/4 gallon.

  5. Answer: The jug from problem 2 has more water.
    Both jugs are divided into the same 4 equal sections, so the jug with 3 sections filled (problem 2) has more water than the jug with 2 sections filled (problem 4), since 3 sections is a greater number of equal parts than 2 sections.

  6. Answer: 1 full jug, with 1 section left over.
    Five sections of 1/4 gallon each are needed. One jug holds 4 sections, using up 4 of the 5 needed sections, which leaves 1 more section to fill in a second jug.

  7. Answer: 2/4 of the jug (which is 2/4 gallon, since the jug holds 1 gallon).
    Since 2 of the 4 equal sections are filled, the other 2 of the 4 equal sections are empty, which is 2/4 gallon of empty space.

  8. Answer: The jug with 3 sections has more, by 2 sections.
    3 filled sections compared to 1 filled section: 3 − 1 = 2 more sections, which is 2/4 gallon more water.

Differentiation

Support (below grade level)

Provide a printed picture of a jug already divided into 4 equal sections with shading options, so students color in the correct number of sections instead of imagining the divisions. Allow students to answer using the section count alone ("2 sections filled") before writing the matching fraction.

Extension (above grade level)

Ask students to design a jug divided into 8 equal sections instead of 4, and find how many of the 8 sections would need to be filled to hold the same amount of water as 2 of the 4 sections in the original jug, explaining their reasoning.

ELL supports

Pre-teach "section," "whole," and "fraction" using a physical measuring cup or jug divided into fourths, with the words labeled directly on the container. Allow students to answer items 3 and 5 by pointing to and counting sections on a printed picture instead of writing a full sentence.