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 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: Formative Assessment Suggestions 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 Direct students to take turns rolling a die and 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. Adapted from The Comparing Game, Marilyn Burns Teaching Arithmetic: Lessons for Extending Fractions, Grade 5, Math Solutions Publications, 2003, pp. 56–63, 145–152. •