# Five Cards Years 2 - 8

This is a game for two players ... Younger learners will need to play with an adult or older child.

### Preparation

• One calculator per pair (there's one on your phone)
• One pack of playing cards per pair - Royals (J, Q, K) removed and Ace is worth 1
• Write the title of this challenge and today's date on a fresh page in your maths journal.
The activity emphasises mental arithmetic, supported by the calculator if necessary.

### How To Play Five Cards

The aim is to make piles of cards that equal five (5).
• It is similar to adult games like 500 that require making 'tricks'.
• Any operation (+, -, x or ÷) may be used to combine card values to make piles worth five.
• The starting pack may be varied, for example, all the cards from 1 to 6 or all the cards from 1 to 9.

In the beginning, play the game as a co-operative investigation where the aim is for both players to go 'out' in the least number of tricks. A few days later you can make it a competitive game if you really want to. (See Co-operation or Competition below.)

Have fun exploring Five Cards.

### How To Play

• Choose the appropriate card pack.
• The first example uses a 1-10 pack and the second a 1-6 pack.
• Shuffle the cards.
• Younger children can spread the cards out on the table face down, swirl them around and push them back into a pile.
• Place the shuffled pack between the two players.

• Players take turns to select cards and place them face up in front of themselves until they have five cards.

• Player A tries to use any combination of +, -, x or ÷ to make their cards into a pile worth five. A calculator may be used to help.
• A pile, called a 'trick', can be any number of cards, including just one card.
• If a player has cards left after making a trick they try to make more tricks.
• If a player can't make any tricks they can ask the pack for help and pick up the top card.
• Asking for help can only be done once each turn.
• A 'help' card can be used straight away or the player can choose to stop and wait for their next turn.
• If a player decides not to use the 'help' card and wait for their next turn, their turn is over.
• If Player A uses all their cards to make tricks, they go 'out' and don't play again until Player B has also gone 'out'.

• If Player A doesn't use all their cards to make tricks they take the top card from the deck and wait for their next turn.

• Now it's Player B's turn.

• Play keeps going until both Players are out.

• The game is over when both players are 'out'. When it's over:
• Count the number of tricks that were made.
• Record the number of 'tricks' in each game.
• You can record the total number of 'tricks' between you or just your own number.
• Choose one of your tricks and quickly sketch its cards.
• Write the equation you created from these cards.
• Shuffle the cards and begin another game.
• ### Co-operation or Competition?

• Co-operation
Work together so that both players go out in the smallest number of tricks. Play three games and record the total number of tricks. Do this at least three times in a week and do it for at least three weeks. In your journal keep a table of results and draw a graph from the table.

• Competition
Here are two ways to make the game competitive.
1. First person out wins the game. Agree before starting that the winner will be the person who wins most out either three or five games.
2. The player who goes out first scores one point for each trick and five (5) extra points for finishing first. The player who doesn't go out first is allowed two more turns before the game is over. Play three games and the player with the higher total score wins.

### Care With The Calculator

This activity offers opportunity to use calculators thoughtfully - in fact, to teach how to use the calculator thoughtfully.

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. What?

The player is likely to be quite sure the answer is 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 player has actually laid the cards down, placing the 2 and 6 together and the 4 and 1 together but separated from the others.

### What Happens If...?

• What happens if you play the same rules but Jack, Queen and King are included in the pack with values of 11, 12 and 13?
• What happens if the rules are the same but the tricks have to equal seven (7) ... or 8 or 11 or any number up to 20 that you choose?
• What happens if you are allowed to take one rule out of the game (or add one new rule to the game)?

### Just Before You Finish

• Draw an oval in your journal.
Change it into a face that shows how you feel about Five Cards.
Add a speech bubble if you wish.

• What do you know now that you didn't know when you started Five Cards?

### Example

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 (it was another 5)
and decides to wait for their next turn.

NB: If playing a co-operative game the other
player would tell Left player about the 8 - 3 before
the deck card was drawn. Why? Because they are working
together to end the game in the lowest total number of tricks.

Right's turn, but unable to make five from 2, 2, 6, 8, 10,
although some players 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 trick should have been turned over by now.)

Right has finished their turn without using all cards,
so takes the top card from the deck (6 H) 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 by making two more tricks and going out.

### Example

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?

### Answers & Discussion

These notes were originally written for teachers. They have been shared from the Members section of Calculating Changes, which is a division of Mathematics Centre.

Send any comments or photos about this activity and we can start a gallery here.

Maths At Home is a division of Mathematics Centre