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Math problem set Grade 5 Math

Dellwood Water System's Shared Supply: A Grade 5 Fraction Set

Grade 5 students interpret division as a fraction, sharing whole gallons of test solution equally among sample bottles and tanks at a fictional small water system.

Objectives

  1. Students will write a whole-number division as a fraction or mixed number.
  2. Students will solve sharing word problems that give fractional answers.

Vocabulary

Key words: fraction, division, mixed number, share

Teacher overview

The Dellwood Water System is a fictional small utility that serves a few streets. An operator there shares test solution equally among sample bottles and tanks. This set shows students that a fraction is really a division: sharing 3 gallons among 4 bottles gives 3/4 of a gallon each. Seeing division this way now prepares students for the sharing and rate problems they will meet in later grades, where the same fraction can stand for a division, a part of a whole, or a ratio. A common student error is writing the larger number on top out of habit, so remind students that the amount being shared is the numerator and the number of groups is the denominator. A quick sense check helps: when the number of groups is larger than the amount shared, each share must be less than one whole.

Dellwood Water System's Shared Supply: A Grade 5 Fraction Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

Every problem shares a whole number of gallons equally. Write each answer as a fraction or a mixed number of a gallon.

  1. Share 3 gallons of test solution equally among 4 sample bottles. How much goes in each bottle?
  2. Share 5 gallons equally among 4 bottles. How much goes in each bottle?
  3. Share 7 gallons equally among 8 groups. How much does each group get?
  4. Share 9 gallons equally among 4 tanks. How much goes in each tank?
  5. The operator writes the amount 3/4 of a gallon. What division does 3/4 stand for?
  6. Share 2 gallons equally among 3 buckets. How much goes in each bucket?
  7. Six groups share 4 gallons equally. How much does each group get?
  8. Explain in one or two sentences why sharing 3 gallons among 4 bottles gives less than 1 gallon in each bottle.

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: 3/4 gallon. 3 gallons divided by 4 bottles is 3 ÷ 4 = 3/4 gallon each.
  2. Answer: 1 1/4 gallons. 5 ÷ 4 = 5/4, which is the mixed number 1 1/4 gallons each.
  3. Answer: 7/8 gallon. 7 ÷ 8 = 7/8 gallon for each group.
  4. Answer: 2 1/4 gallons. 9 ÷ 4 = 9/4, which is the mixed number 2 1/4 gallons each.
  5. Answer: 3 ÷ 4. The fraction 3/4 means 3 divided by 4, the numerator over the denominator.
  6. Answer: 2/3 gallon. 2 ÷ 3 = 2/3 gallon for each bucket.
  7. Answer: 2/3 gallon. 4 ÷ 6 = 4/6, which simplifies to 2/3 gallon for each group.
  8. Answer: Sharing 3 gallons among 4 bottles gives less than 1 gallon because there are more bottles than gallons, so each bottle gets only part of a gallon.

Differentiation

Support

Give students a picture of the gallons as rectangles being cut into equal parts for each problem. Model problem 1 by drawing 3 rectangles split into 4 equal shares before students try problem 2.

Extension

Ask students to write a new sharing problem whose answer is exactly 1 1/2 gallons, then show the division that proves it. Have them trade problems with a partner to solve.

ELL supports

Pre-teach "share," "equally," "each," and "left over" with a picture of pouring water into bottles. Provide a sentence frame for problem 8: "Each bottle gets less than 1 gallon because ___."