Playzone discount

Game

This game has two mathematical features: the calculation of a percentage discount and the use of a winning strategy to get four in a row on a 5 by 5 array.

If the students are familiar with finding percentages, they can play the game as a percentages maintenance activity and focus on working out a winning strategy. The player who goes first could choose the centre square and try to get a line of three in a row with both ends unblocked. Once the player has this, victory is assured.

The player who goes second should use their turn to defend immediately by trying to block the first player until the first player makes a mistake. If both players do not make any mistakes, either the player going first will win or the game will end in a draw.

If the strategy for winning is the learning outcome you want the students to focus on, you may let them do their discount calculation on a calculator.

If the main purpose of the game is to introduce percentage calculations to the students, they should not use a calculator because the intention is to develop mental strategies for doing these.

Make sure that the students understand that percentage means “out of 100”. One interesting way to do this is to explain the origins of the percentage symbol, %. The backward slash symbol (/) represents “out of” or division and the two small zeros on either side of the backward slash symbol (/)  represents the zeros in 100. So the symbol represents “out of 100”.

The students could make a chart or a double number line showing the equivalent values of the percentages as fractions.

Have the students develop and discuss strategies for estimating and calculating a percentage amount, starting with the 50 percent coupon, then the 25 percent, and then the 10 percent. Do these first because they are equivalent to unit fractions, and so they allow the students to get used to dividing the amount by the denominator of the unit fraction before they move on to looking at the more complex calculations involved with the improper fractions.

With 75 percent (3/4) and 30 percent (3/10), the students need to see these as “three lots of a quarter” and “three lots of one-tenth” respectively to develop a suitable strategy for calculating the percentage amounts.

The students could make a chart showing the discount amounts for each of the Playzone games.

The students could then use this chart as they try to win the game. However, you could challenge them to use mental strategies to work out the percentages instead of using the chart.

If estimation is the main purpose of the game, the students should definitely not make the chart above. It would be better to explore strategies for estimating. Begin by asking the students:

• Which Playzone game would be the easiest to look at in terms of estimating the discounts?

The Sound Barrier Playzone game is probably the easiest as its price rounds to $100 and therefore the percentage gives a one-to-one indication of the discount. The discount for this game can then be used as a guide for other games. Team Pro will be twice as much. Lightning will be half as much again as Sound Barrier. Exotic Raiders will be just under half as much as Sound Barrier.

After the students have played the game a few times, discuss the best strategies for winning. The students could compare the 5 by 5 board strategies with the common game of noughts and crosses, which uses a 3 by 3 board or grid.

A game estimating percentages.