Mathematics: Number and Operations - Fractions
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.
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)
- 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.
- 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.
- 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?
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
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.