Illuminations: Communicating about Mathematics Using Games

Communicating about Mathematics Using Games

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Playing Fraction Track

Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. In this first part, Playing Fraction Track, contains an interactive version of a game (based on the work of Akers, Tierney, Evans, and Murray [1998] that can be used in the grades 3–5 classroom to support students' learning about fractions. By working on this activity, students have opportunities to think about how fractions are related to a unit whole, compare fractional parts of a whole, and find equivalent fractions, as discussed in the Number and Operations Standard.

Materials

Computer and Internet connection

Instructional Plan

The Game

Play the Fraction Track game using the interactive board below. The first player starts by moving one or more blue markers along the tracks, either forward or backward, so that the positive and negative distances moved by all markers add to the amount shown in the fraction box. When a piece is moved, an outline is shown in its starting position for that turn. Clicking on Finish Move will either let the next player take a turn if the markers correctly add to the fraction shown on the box or display an error message if the move was not correct. When a correct move has been entered, the second player then similarly moves one or more red markers. If a player cannot complete a move, a turn can be passed by clicking on the Pass button. The first player to move all his or her markers to the right side of the Fraction Track board wins!

[How to Use the Interactive Figure]

[Stand-alone applet]

Questions for Students

Prior to playing this game, the game board itself should be explored. Teachers can help students understand the relationships among the fractions on the board by asking questions like "How was the game board constructed?" and "How are various tracks on the board related?" The Fraction Track board can be used as a visual model for comparing fractions and finding equivalent forms. For example, which fraction is larger: 2/6 or 1/4? How do the fractions 1/3 and 2/6 align on the board? Are they equivalent? How do you know?

Extensions

To extend this game, students could make their own boards with different fractions, with decimals, or with a combination of decimals and fractions.

Teacher Reflection

How can playing a game like Fraction Track help a student build understanding about the relative sizes of fractions?
How can playing a game like Fraction Track help a student build understanding about the equivalence of fractions?
What characteristics of the classroom environment would support students as they use a game like Fraction Track to help them deepen their understanding of fractions?

NCTM Standards and Expectations

Number & Operations 3-5

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
Use models, benchmarks, and equivalent forms to judge the size of fractions.
Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

References

Akers, Joan, Cornelia Tierney, Claryce Evans, and Megan Murray. "Name That Portion: Fractions, Percents, and Decimals." A unit of the curriculum Investigations in Number, Data, and Space. Parsippany, N.J.: Dale Seymour Publications, 1998.