Five Cards Years 1 - 8

Summary The aim of Five Cards is to make piles of cards that equal five. It is a simple game similar to adult games like 500 that require making 'tricks'. Any operation (+, - , x, ÷) may be used to combine card values to make piles worth five. Also, the starting pack may be varied, for example, all the cards from 1 to 6 or all the cards from 1 to 9. Five Cards can be played as a co-operative investigation where the aim is for both players to go 'out' in the least number of tricks, or as a competitive game in which the player with the higher number of points (see below) wins. The many variations on the basic game make it adaptable to several year levels. Its emphasis on mental arithmetic, supported by the calculator if necessary, is its mathematical strength. The connection with playing cards at home is, for many children, a feature that encourages learning. Suitable for threading. Materials One calculator per pair One pack of playing cards per pair - Royals (J, Q, K) removed

Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.

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Examples

1 - 10 Pack Ready to start. Left player will play first. Left makes a one card pile with 5. Unable to make five with the remaining 9, 9, 8 & 3, perhaps because they didn't see that 8 - 3 = 5, Left draws the top card from the deck and waits for their next turn. Right's turn, but unable to make five from 2, 2, 6, 8, 10, although some students might see (10 + 8 + 2) ÷ (6 - 2), Right asks for help from the deck and receives 1 (Ace). Right has an 'aha' moment and creates five with 10 - 2 - 2 - 1. (Left realises their first pile should have been turned over by now.) Right has finished their turn without using all cards, so takes the top card from the deck and waits for their next turn. It's Left's turn. Left might play the obvious single pile 5 card, and draw the top card because they can't think of another equation; or might play the 5 and also create 9 x 8 ÷ 9 - 3, using all their cards and gaining two piles in the process.

1 - 6 Pack Ready to start. Left player will play first. Left makes a pile with 6 + 5 - 1 - 5. Left keeps playing but can't make another pile with just a 2, so takes the top card and waits for their next turn. Right plays all their cards with 6 + 5 - 3- 1- 2 to go 'out'. Left still can't play with 2 and 1, so asks for help from the deck and receives 3. Now Left can go out. How? Care With The Calculator This activity offers opportunity to use calculators thoughtfully - in fact, to teach how to use the calculator thoughtfully. Even a machine with an algebraic operating system (designed to calculate according to order of operations conventions) can't be used blindly. Suppose a player has the cards 2, 6, 4 & 1. They might see that 2 & 6 could be an addition to make 8 and 4 & 1 could be a subtraction to make 3. Then 8 - 3 gives 5. The player would probably put their cards down and say: 2 plus 6 equals 8 take away 4 minus 1 equals 5. However, checking this on any calculator by typing in the order said, ie: 2 + 6 - 4 - 1, gives the answer 3! Children are likely to be quite sure of their answer of 5 and should be encouraged to ask why their calculator doesn't get the 'right' answer. This is the opportunity to discuss the use of brackets, which on most simple calculators is handled by using the memory buttons. The 'brackets' are likely to be indicated by the way the student has actually laid the cards down, placing the 2 and 6 together and the 4 and one together but separated from the others. See Bothering With Brackets for more discussion of this point.

Co-operative or Competitive?

• The co-operative approach is based on working together so that both players go out in the minimum number of piles. In this case, one game is, say, three rounds. Clearly the minimum possible piles for one round is two and for three rounds is six. The investigation is threaded, several times a week over several weeks and players keep a record of their piles each day. Hopefully their daily total will decrease as their mental arithmetic perception develops. Teachers might also keep a class record as an indication of the class's improving mental arithmetic skills.(Younger children are often happy just to help each other make piles without being concerned about record keeping or winning and losing.)
• The competitive game approach can be developed in two ways:
  • First person out wins the round and a game is best out of three or five rounds (agreed in advance).
  • The player who goes out first scores one point for each pile and five extra points for finishing first. The player who doesn't go out first is only allowed two more turns before the round is over. A game is three rounds and the player with the higher total score wins.

Extensions

• Cribbage is another activity rich in mental arithmetic.
• Number Game, Task 109 in the Mathematics Task Centre collection, is a similar style game with more sophisticated rules that encourage the use of place value ideas, larger numbers and division.
• Thirty-One, Task 86 in the Mathematics Task Centre collection, adds pattern, generalisation and algebra to the mental arithmetic challenge. This cameo will also lead you to the companion Maths300 Lesson 27, Game of 31, which has a further software extension challenging the children to beat the computer.

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