Mathematics: Number and Operations - Fractions
4.NF.2Cluster 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 SuggestionsFormative Assessment SuggestionsRoll a Fraction GameChallenge 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 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.DifferentiationSupports Supply fraction manipulatives, number line with fractions or grid paper and encourage students to build each fraction before comparingVary dice per student need (use sticky dots 1, 2, 4, 4, 8, 8) ExtensionsCreate dice with any of the following numbers, such as 1, 2, 3, 4, 5, 6, 8, 10, 12, 100Let students decide what numbers to place on the dieHave 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 ThinkingCan 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?MisconceptionsStudents mayThink that the bigger the denominator will result in the greater fractionHave trouble finding the fractions on a number lineHave trouble with fractions like 3/1 or 5/3, which result in numbers greater than 1Misunderstand fractions with the same numerator and denominator, resulting in the number 1Vocabulary ConsiderationsNumerator, 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, Math Solutions Publications, 2003, pp. 56–63, 145–152. ................
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