Mathematical Games

Mathematical Games Monken Hadley Friday 8th March 2013

Why play games? • Develops turn taking, sharing & collaborative skills • Develops thinking, memory skills & concentration • Develops speaking and listening and vocabulary • Develops problem solving, logical & strategic thinking • Improves mental calculation • Competitive • Can be affordable (Cards from 50p) • Structured images aid learning and promotes abstract understanding • Fun!

Research • The advantages of using games in a mathematical programme have been summarised in an article by Davies (1995) who researched the literature available at the time. • Meaningful situations - for the application of mathematical skills are created by games • Motivation - children freely choose to participate and enjoy playing • Positive attitude - Games provide opportunities for building self-concept and developing positive attitudes towards mathematics, through reducing the fear of failure and error; • Increased learning - in comparison to more formal activities, greater learning can occur through games due to the increased interaction between children, opportunities to test intuitive ideas and problem solving strategies • Different levels - Games can allow children to operate at different levels of thinking and to learn from each other. In a group of children playing a game, one child might be encountering a concept for the first time, another may be developing his/her understanding of the concept, a third consolidating previously learned concepts • Assessment - children's thinking often becomes apparent through the actions and decisions they make during a game, so the teacher has the opportunity to carry out diagnosis and assessment of learning in a non-threatening situation • Home and school - Games provide 'hands-on' interactive tasks for both school and home • Independence - Children can work independently of the teacher. The rules of the game and the children's motivation usually keep them on task.

Dice, Dominoes & Cards

Dice Odds & Evens Two people –one is odd and one is even! Roll one dice each. Add the two numbers together Work out whether it is odd or even If odd, odd person wins and scores a point/takes a counter If even, even person wins and scores a point/takes a counter Variations - score the total – winner is 1st to 50. Start from 50 and subtract total. Is this game fair? Why? What scores are possible?

Dice - Aim for 50 • 1 v 1 (or 2 v 2) • Roll four 0-6 dice each • Use any operation - add, subtract, multiply & divide (and brackets!) • Closet to 50 wins • E.g. roll 4, 6, 6, 1 • Could make ((6+6) x 4 ) + 1 = 49

Killer - Closest to 50 T U T U Up to 4 players 1 v 1 or 2v2 Aim of game – to make a number that is a closest to 50 as possible Have dice 0 to 9 or pile of cards face down - Ace (1) up to 9 - all 4 suits Player/Team 1 - roll dice and decide where to put on grid – the tens column or the units column. Player/Team 2 - roll dice and decide where to put on grid – the tens column or the units column. Player/Team 1 - roll dice and complete your number Player/Team 2 - roll dice and complete your number Closest to 50 is the winneer. • Use <, > or = symbols • Difference calculated • Link to probability • Extend to HTU – Closest to 500

Super Killer - Closest to 50T U T U Rules as killer only when you roll your dice you can choose whether to place in your tens and units column or your opponents!

Dice Wars ! • Players roll 2 dice and multiply • Greatest total (product) wins!

Dice coordinates • Draw a co-ordinates grid 0 to 6 • Roll 2 dice e.g. 3 & 6 • Decide which coordinates you will make e.g. (3,6) or (6,3) • Place a counter or colour in the position you land on. • The first person to get 3 in a line is the winner.

Factors A factor is any number which divides exactly into another number. For example the factors of 8 are 1, 2, 4 & 8. Roll a 1 – 20 dice twice. Choose which number will be your multiple number Work out all the factors of your multiple number Add them together - this is your score. First to 100 is the winner

Classic Dominoes Lay all dominoes face down. Each player takes 7 dominoes The player with the highest double starts. Take it in turns to lay dominoes that match If you cannot go, pick up another domino. The first player to lay all of their dominoes is the winner.

Fifteen • Spread dominoes face down • Each player chooses two dominoes • Count the spots and find the total • Below 15 - collect 1 cube • Exactly Fifteen - Collect 2 cubes • Above 15 - NO CUBES – BUST!

Fractions • Remove dominoes with blanks! • Place rest face down. • Both players choose one domino each. • Make a fraction by turning the domino vertically, placing the smaller number on top) • Whose fraction is the greatest. • (Convert by making common denominators)

Card Games

Why use cards? • Inexpensive (cheap – about 50p) • Improves mental calculation • Structured images aid learning and promotes abstract understanding • Develops turn taking, sharing & collaborative skills • Develops thinking and memory skills • Develops speaking and listening • Develops vocabulary • Competitive • Fun!

Sorting Individual or small groups – All Cards • Children given the 52 cards (or 13 etc) and asked to put them in an order. How will they sort them? (Colour, number, suits, odd, even?) Can they be sorted in any other way? • Can they sort them ace to king in the 4 separate suits? Variation • Give out 51 cards or 12 from same suit. Which card is missing? • Give out 5 cards each from 1 suit. Who can order them the quickest? • Use with Carroll or Venn diagrams

Snap Individual - 2 to 3 players – all cards • Deal out all of the cards • Each player takes it in turn to lay a card on the ‘pile’ (do not look at your cards first) • When 2 similar cards appear (2 fours etc) put your hand on the pile and say snap • The winner is the first person to collect all of the cards.

1 More Snap Individual - 2 to 3 players – all cards Similar rules as snap, only…. Snap can only be said when one card which is 1 more is laid on top of another card. E.g. when a 4 is lid on top of a 3. Variation Play 2 more snap, 1 less snap or 2 less snap

Pairs (Pelmanism) Individual, 2v2 or 4 individual players – All Cards • Lay all 52 cards face down in a grid/array e.g. 13 rows of 4 • Take it turns to turn two cards over at a time. • If they are similar (e.g. 2 kings) keep them and have another go. • If they are not similar, turn them back over so they are face down. • Play passes on to the next person. • The winner is the person (or team) that collect the most pairs. Variation Reduce the number of cards used at the beginning.

1 More Pairs (Pelmanism) Individual, 2v2 or 2 - 4 individual players – Ace to 10 4 Suits • Use ace to 9 of one suit and 2 to 10 of another suit (ace worth 1) • Similar rules to pairs, only… • When two cards are turned over, one of them needs to be worth 1 more than the other. e.g.. a 4 and a 5. Variation • Play 1 less (technically the same game!) • Play 2 more snap/2 less • Use jack (11), queen (12) & king (13)

Bonds to 10 Pairs (Pelmanism) Individual, 1 v 1 or 2v2 Two suites ace up to 9. Two additional 5s from the remaining two suits. Ace worth 1 Similar to pairs Turn over 2 cards If they total 10, keep them If they do not, turn them back over (face down) Variation Reduce number of cards - use 1 suit ace to 9 and one additional 5 Play bonds to 9, etc NB – cards used will have to be adjusted.

Higher or Lower Individual, 2v2 or 1 v 1 9 Cards in a grid - from whole pack • Turn first card over • Predict of next card will be higher or lower • You get nothing for a pair! • Ace is worth 1, Jack 11, Queen 12 & King 13. Variation • Can children work out the probability of the card being higher, lower, the same?

2 Cards Total 2 to 3 Individual Players or 2 to 3 groups of pairs – All Cards Deal out 2 cards to each player Calculate your total The person with the largest amount is a winner and receives a cube. Variation Use 3 Cards Only use cards Ace to 6 Play for 2p or 5p (to promote coin equivalences e.g. 2 x 1p or 1 x 2p

Pontoon - 21 (Black Jack) 2-6 Individual Players – All Cards Ace = 1 or 11, Picture cards =10 Aim: To get a score as close to 21 as possible Deal out 2 cards to each player face down Dealer turns their 2nd card over so that everyone can see. Players add the total of their 2 cards Players decide if they want another card (twist) to get closer to 21 Re- add scores & repeat Can stick (no more cards) or bust (go over 21) 5 cards totalling 21 or under can only be beaten by pontoon (Ace and Picture card = 21) Variation Can children predict probability/chances of getting a card that will not make them go bust? Have a rule where you can not ‘stick’ below 16.

Adding & Subtracting 1 v 1 or 2v2 Using Cards Ace to 5 Use a number line 0-30 Place counter on number 15 Turn over card. If red, subtract that number, if black, add that number. Calculate where you will land mentally before moving counter One player needs to get to 0, the other 30, whoever gets there first is the winner. Variation Use number line 0 – 100 Use cards Ace - 10

Pyramids Individual or pairs - All 4 suits - Ace to 10 • Lay out 5 different value cards in a row • The remainder of the card are placed in a pack • Turn over every 3rd card. • If it is the answer to the sum or difference to two cards below, place it above them! • If not, place to the bottom of the pack. • Repeat with every 3rd card. • Aim – to complete the pyramid. Variation Children make their own pyramid - they are allowed to just sort through the cards

Avoid multiples of 7 Individual or pairs against each other Ace to 10 all 4 suits except 7s Deal out 5 cards each. First player lays card 2nd player lays card, The total of the last 2 cards or 3 cards must not be a multiple of 7 Variation The total of the last card, last 4 o 5 cards etc must not be a multiple of 7 Avoid multiples of other numbers

Multiplication Individual - Ace (1) to 10 of all 4 suits (even amount of cards) Aim to collect all pairs of cards in as quick a time as possible. • Turn 2 cards over at time e.g. 10 and 6 • Say the multiplication 10 x 6 and calculate answer = 60 • If correct keep • If incorrect place at bottom of pack (therefore will reappear later) Variation Use 2 suits Ace (1-10 only) Use cards Ace to 6 only Play against another person – whoever answers first keeps cards

Multiplication Individual Ace to 10 – all 4 suits • Choose a times table to practise e.g. 5 • Place cards in a pack face down • Turn over 1 card at a time e.g. possibly a 4 • Multiply the card (4) by the table agreed (5) and give answer - so 4 x 5 = 20 • If correct keep, if incorrect, place at bottom of pack. Variation • Time yourself – can you beat your own time? • Use 1 suit • Use Ace (1) to 5 or 6 to 10 • Play 1 v 1, as cards are turned over, the person who correctly answers the quickest keeps the card. Winner is the person with most cards at end.

Rummy 2 to 4 players – all cards • Objective of Game – To be the first to collect a set of 4 and a set of 3 cards. • A set could be a run of cards of the same suit, e.g. 3, 4, 5/6 or similar cards e.g. 3 kings • Each player needs 7 cards. Dealer gets 8. • Remainder of cards are stacked in a pile – face down • Dealer discards one of his cards - starting a new pile of cards face up wards. • The next player chooses a card from either pile. They may keep it and discard a different card or just discard it. • Play continues until someone gets a set of 3 or 4 cards, Variations • Runs could be of mixed suits

Thirty Six • Use 2, 3, 4, 5, 6, 7, 8,9 & 10 of all 4 suits • Arrange the cards so that the total of each row is 36 and the total of each column is 36. • No two cards of the same number are in the same row, column or diagonal • Each row and column has three red and three black cards. • One diagonal is made up of red cards only, the other of black cards only!

Any Questions?

Mathematical Games