Mathematics: Number and Operations - Fractions

4.NF.2 / Cluster Heading:Extend understanding of fraction equivalence and ordering.
Content Standard: Compare two fractions with different numerators and different denominators.
Practice Standard: MP3 Construct viable arguments and critique the reasoning of others.
Problem/Task Suggestions / Formative Assessment Suggestions
Roll a Fraction Game
Challenge students to build the greatest fraction. Arrange students in pairs. Distribute a traditional six-sided die to each pair of students. Ask students to set up a piece of paper as shown:

  • Direct students to take turns rolling a dieand placing the number into one of the boxes. They should continue until both players’ boxes are filled in and they each have a fraction.
  • Ask students to determine the greater fraction by explaining and/or using drawings or number lines.
  • Ask students to place a greater than(>), less than (<), or equal (=)sign between the fractions
  • Have students play the game multiple times, and develop some strategies for building the greatest fraction. Have students write their strategies,and then repeat the game.
Differentiation
Supports
  • Supply fraction manipulatives, number line with fractions or grid paper and encourage students to build each fraction before comparing
  • Vary dice per student need (use sticky dots 1,2, 4,4,8, 8)
Extensions
  • Create dice with any of the following numbers, such as 1,2,3,4,5,6,8, 10, 12, 100
  • Let students decide what numbers to place on the die
  • Have a recording sheet with five empty boxes to indicate 2 fractions and a reject box. The students add the two fractions to determine which player had the largest sum.
/ Assessment
  • Check to be sure students are correctly finding the greater fraction.
  • Have students explain their reasoning.
  • Collect and read student strategies to decide which students recognized that larger numbers should go in the numerator to create a greater fraction.
Questions to Guide Student Thinking
  • Can you show me the fraction with fraction strips?
  • What does the numerator tell you?
  • What does the denominator tell you?
  • How do you know which fraction is greater?
  • What is the best roll to get? Why?
Misconceptions
Students may
  • Think that the bigger the denominator will result in the greater fraction
  • Have trouble finding the fractions on a number line
  • Have trouble with fractions like 3/1 or 5/3, which result in numbers greater than 1
  • Misunderstand fractions with the same numerator and denominator, resulting in the number 1
Vocabulary Considerations
Numerator, Denominator, Equivalent Fractions, Greater Than, Less Than, Equal, Improper Fraction
Adapted from The Comparing Game, Marilyn Burns Teaching Arithmetic: Lessons for Extending Fractions, Grade 5, MathSolutions Publications, 2003,
pp. 56–63, 145–152.