[Opening Page] [Table of Contents] [Project Overview] [Professional Development] [Number Sense Activities] [Evaluation] [Sources] [MSMME info] [Contact Author]
This idea was born out of a need for additional practice with comparing fractions and understanding fractions in different representations (particularly improper fractions).
Needed Materials: A pair of dice, a piece of paper for the team, and a writing utensil and scratch paper for each student.
Directions:
1. Students play in pairs. The teacher will need to decide if the practice is going to use proper or improper fractions. If proper, the target number is ½; if improper, 2.
2. Each player rolls the dice and records their result. One die is the numerator and the other die is the denominator, depending on the decision about proper and improper fractions. Individually, the players determine how far their fractions are from the target. All calculations are done mentally or by showing graphic representations of the quantities. Verbal explanations must accompany the calculations to signify how the students know their answers are right.
3. Each player is responsible for catching the other player’s mistakes. If a player miscalculates, the opponent automatically wins that round regardless of the magnitude of his fraction (unless they make a mistake, too, in which case that round is a “draw”). If the players roll equivalent fractions, each player earns a point as long as they each can explain how far his fraction is from the target (which requires expressing two representations of the same quantity).
4. Together the students decide which player’s quantity is closer to the target. The number comparisons and any graphic proofs are recorded on the team paper.
5. Play ends after a certain number of rounds or an allotted amount of time. (In the seventh grade we had a game equal 10 rounds.)
6. The winner is the player who was closest to the target the greatest number of times.
The mathematical goals are to think about fractions as parts of a whole, to think about the relative magnitude of fractional parts, and to practice justification of answers. After the game has been played several times, class discussion can develop the concept of probability and fairness.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
This game was well received by
my seventh graders. Winners received 2
picks from my “goody bag” (containing miniature candy bars of various kinds)
and other players got 1 pick. It seems
the older my students get, the more they appreciate playing games rather than
the “normal” lecture/homework scheme from other classes. It’s also gratifying to hear them say later
while working on other assignments, “You know, it’s like that ‘Get Close’
game…” After we played a full game, we
had an animated discussion about whether 2 was a fair target for improper
fractions that led to a great introduction to fairness in games of chance.
I noted most students explained
their fraction’s distance from the target verbally with no use of
graphics. The class was split about
half and half over use of a linear graphic model versus an area graphic model
for visual justifications when comparing the quantities. (Both had been used in prior
instruction.) If the fractions were
only one fraction unit away from the target, most students justified their
comparisons verbally by referring to the relative size of pieces when you cut
the whole.
As I circulated in the
classroom, it became apparent that virtually all the students understood
distance to the target. By listening to
student dialogues, I was able to pick out students who had trouble comparing
the fractions. I had paired the
students so as to place individuals who needed more instruction with partners
who could help them as they played (although nothing was said about the
arrangement). I did not forbid the use
of cross-products for comparing fractions, but several of the students had
demonstrated a lack of understanding in how that method works. Because the verbal explanations had to
include a graphic representation and satisfy the opponent before a point could
be awarded, peer clarification of the concept took place several times. By the end of the game I heard at least two
students comment about “now I get it” in reference to cross-product
comparisons.
_4_ Was the purpose of the activity clear to me?
_3_ Was the purpose of the activity clear to my students?
_4_ Did the activity support a range of learning styles?
_3_ Were the students engaged during this activity?
_14_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
…telling them at the beginning
we were going to play a game to practice thinking about fractions and how they
compare to each other. I told them I
would be listening to their explanations in order to assess what further work
we might need to do.
The part of the lesson that was student-centered was…
…the actual playing of the game. Students must listen to each other rather than to a teacher’s explanation and must assess each other’s work. The verbal explanations must be clear enough for a peer to understand.