More than One-Half:
Materials: one game sheet (sheet A), one pair of number cubes, two different colored crayons or pencils for each pair of players. Also give students pattern blocks to use as a way to explain their reasoning.
Objective: This game is best played as a two-person game. The objective of the
game is to own more circles than one’s opponent. A player owns a
circle when more than one-half of the circle has been colored with his/her color.
Purpose:This math game will activate grade 7 students’ prior knowledge of fractions in an engaging and fun way. It can be used as a formative assessment activity prior to starting Chapter 2 of Mathematics 7: Focus on Understanding to help the teacher determine what students know about fractions. The observation chart that is provided can be used to record the student’s ability to
use related math language
relate a fraction to a visual representation
create equivalent fractions
model his/her knowledge with a manipulative
explain his/her reasoning
The observation chart may be used in two ways. The entire chart may be used for teacher observation or part of the chart may be used for peer evaluation (columns 1-3) and the rest of the chart (columns 4-5) for teacher observation.
Questions to ask when observing students:
What strategy did you use to shade in your circle or circles?
How did you decide how many sections to color?
Please explain your thinking using (indicate a manipulative such as Fraction Factory)
Why did you decide to shade in parts of 2 circles? How did you decide which part of each circle to shade in?
Could you have shaded a different way?
More examples of effective questioning can be found in Mathematics Grade 7: A Teaching Resource, pages 115-117.
It is important to make“why?”, “how do you know?”,“convince me”,“explain that please”
part of yourregular classroom routine.
Other possible ways to play this game:
When students are comfortable with percents use sheet B, or more complicated fractions use sheet C.
In grade 8, where fractions are done in more depth you might
- work with improper fractions as well as proper fractions
introduce a third number cube that can represent the whole number to multiply a fraction by a whole number
use four number cubes and have students find and shade in the sum
use number cubes with more than 6 sides and alter the game board
Directions for the Basic Game: (Sheet A)
(Adapted by Mary Altieri from The Fraction Game--Open Court Publishing)
• Players roll one number cube to see who becomes “Player One”.
• Player One rolls the pair of number cubes. The lower number representsthe numerator, and the larger number represents thedenominator. For example, if a 3 and a 5 are rolled, the numberrolled is the fraction .Player One then says the name of the fraction ("three-fifths"), selects a circle(the circle divided into fifths) and colors in the correct parts of the circle(three).
• Player Two then rolls the number cubes, states the fraction, selects a circle and colors in the parts of the circle thatrepresent his/her roll.
• The players may use an equivalent fraction and shade in the appropriate sections for the equivalent fraction. For example, if the fraction is, they may use or etc.
• The players take turns rolling the number cubes and naming and coloringeach fraction that is rolled.
• Each player must use all of his/her roll. If he/she cannot use the wholeroll, then he/she loses a turn.
• On each turn a player may color all of his/her roll on one circle, orsplit it among two or more circles.
• When a player has more than one-half of any circle in his/her color, thenhe/she puts initials next to that circle. (This initialing makescounting circles at the end easier, but does not mean that blankparts of the circle can’t be used when necessary to complete aperson’s roll. This, of course, does not affect ownership.)
• If a circle is colored equally by two players, each having half,then neither player may claim the circle.
• Play continues until all circles have been claimed or neutralized,or when it becomes obvious that one player must win.
Characteristics of Really Good Math Games
• Students like to play them.
• They are games that have mathematical content at their core.
• Playing the game encourages and/or provides skill practice and concept development.
• The games involve a combination of chance, content skills/concepts, and strategic possibilities.
• The games vary in complexity for different players depending upon their level of skill and understanding of content and strategy.
• After initial teaching, the games can be played relatively independently with readily available and inexpensivematerials.
• They can be “morphed” to meet the needs of students, thus providing an opportunity for differentiatinginstruction.
Generally a really good math game is one that provides fun and learning at the same time. A player can improve his/herchance of winning by content knowledge and by strategy. However the chance factor always plays a role and sometimesallows a less able player to win. Playing the game provides practice and/or allows opportunities to see math relationshipsin a different way. Because it is available to students, and because they like to play it, the game becomes part of thestudents’ math resource materials, helping them to become better math students.