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1 FUN + GAMES = MATHS Sue Fine Linn Maskell Teachers are often concerned that there isn t enough time to play games in maths classes. But actually there is time to play games and we need to make sure that we choose quality games that reinforce concepts taught in the classroom and that challenge students to think and extend themselves. What do we hope students will achieve in maths by the end of Primary school? A flexible understanding and working knowledge of numbers and number relationships e.g. 1,2,4,8,16 is doubling, 5 is 3 more than 2, 2 is 3 less than 5 and 2 is 2 / 5 of 5 and 2 and 1 / 2 2 equals 5. An understanding of addition, subtraction, multiplication and division. Basic number facts to 100 including times tables. Place value and the importance of zero as a place holder. Understand the concept of fractions, that they are a number and that there are many different ways of expressing fractions (proper, decimal, percentage). Good problem solving strategies. Be confident to have a go and reflect on the answer. And most important of all, a positive attitude towards mathematics. We use games to experience maths in a non-threatening context. There are certain general requirements to facilitate effective learning and to ensure that we are using a quality game. It must have an aim. This can develop insight into a mathematical concept or develop or reinforce a mathematical skill e.g. Automatic recall of multiplication tables, identifying counting patterns. 64

2 Sue Fine and Linn Maskell There should only be a few simple rules. It should be engaging. All maths lessons should begin with a quick 5-minute game that motivates students and, gets their head into a maths space. Sooly An example of a quick game Material: two 6-sided dice, game board Game board. 1. Children fill the grid with numbers, which they think will be thrown when two dice are rolled and the two numbers are added together. They can use each number more than once. 2. The teacher throws two dice. The two numbers thrown are called out, e.g. 3 and 5 these are written on the board. 3. The students total the numbers called and if they have the total they mark it off their grid. 4. The winner is the first person to have all their numbers marked off. 5. The winner calls out the answers and the numbers are checked off the board, e.g. 3 and 5 is written on the board, when the answer 8 is called out, 3 and 5 are ticked off. Sooly 2 is an extension of Sooly 1 1. Each student has 12 counters that are placed anywhere on the grid with no more that 4 counters against any one number. 2. Two six sided dice are rolled and their total added. 3. If there is a counter against that total then one counter only is removed. 4. The first person to remove all their counters is the winner. 65

3 KEYNOTE: Fun + Games = Maths Game board. After the game has been played a few times ask the students what they have discovered. Repeat the game using one 12-sided dice. Will the results be the same? Ask the students what they have learnt from these games. How do we know what is likely to be the most frequently rolled number? Write down and discuss the pattern 12 = 6,6 11 = 6,5 5,6 10 = 5,5, 6,4, 4,6, 9 = 6,3, 3,6, 5,4, 4,5 and the pattern starts to emerge. Covered Numbers Materials: game board, two lots of 20 colored counters (2 colors only) and 2 six sided dice. 1. Two players each with 20 coloured counters and a game board. 66

4 Sue Fine and Linn Maskell 2. Each player takes it in turn to roll the dice, e.g. Player A rolls a 9, and then has the choice of either placing 1 counter on 9 or counters on a combination that total 9, e.g. 6 and 2 and 1, or 5 and Player B has their turn and rolls a 7, they are able to place one counter on 7 or on both 2 and 2 and 3, or counters on 6 and There is a limit of 3 counters on any one number. This forces players to rethink combinations for the number they have rolled. 5. Once a player can no longer make a move, the game ends. The scores are totalled, i.e. each player adds up their total of the numbers that their counters have covered. 6. Extension of this game is to have more numbers on the grid, e.g and use a 12-sided dice and an 8-sided dice. Fish to Ten Materials: a pack of cards with the picture cards removed. This game is used to consolidate number combinations to 10. This can be played by up to 4 players. 1. The aim of the game is to make pairs to ten. 2. Each player is dealt 5 cards. If you have a six in your hand you must ask another player if they have a 4 i.e = A player must always have a minimum of 5 cards in their hand. They need to pick up from the pack of cards in the centre if a pair is made. 4. If the player you ask does not have your card, you pick a card up from the centre pack. 5. The player with the most pairs is the winner. 6. Extension to this game is to include the picture cards and make a higher total e.g. 15 or 20 using a combination of 3 or 4 cards to make the total. Partner Numbers to 10 Materials: Each child has a sheet with MAB longs drawn on it, plus one ten sided dice. 1. The dice is rolled and the number rolled is colored in e.g. 7 is rolled then 4 then 1 so the longs will look like this: 67

5 KEYNOTE: Fun + Games = Maths 2. Students then write the number sentence that equals ten e.g. 7+3=10, 4+6=10, 1+9= After the page is completed students can then cut out each long and order them from = 10, = 10, = 10 etc. to consolidate patterning and number facts to 10. An extension activity is to join two longs together to make 20 so patterns extend to = 20, = 20, = 20. Compatible numbers This is from Alistair McIntosh s Think Mathematically Materials: a card for each student with 8 or 10 pairs of numbers, arranged randomly, and such that each pair adds to say 10 or 100. A sample of each of these is shown. 1. Ask children to list as many pairs of compatible numbers as they can in a certain time e.g. 1 minute. 2. As a class check the different answers e.g. 33 and 67, 40 and 60 etc. 3. Repeat step 2 the next day to see whether they can beat the amount of compatible numbers they listed yesterday. 68

6 Sue Fine and Linn Maskell 4. Variation is to ask children to use three numbers that total e.g Ask children to make up their own boxes with 10 to 20 pairs of compatible numbers. Jessica s Game Material: Game board, tiles with numbers 0 to 9 on them, 10-sided die for the extension. 1. Each player places a set of number tiles face down in front of him/herself. The tiles should not be in order. 2. Each player takes one tile at a time and places it on any one of the squares on his/her game board. This step is repeated until the board is filled. 3. Numbers must be placed as drawn, and once placed cannot be moved or changed. 4. The last tile of each player will not be used. 5. The students add the numbers in the columns. The object of the game is to get as close to 1000 as possible without going over A player is out if they go over e.g. Player A puts these tiles in these spaces: hundreds tens ones Total 928 Game board This game reinforces place value, probability of numbers coming up and addition of 3-digit numbers. 69

7 KEYNOTE: Fun + Games = Maths An extension of this is by using a 10-sided die. Now the same numbers can keep recurring. An easier version of this game is one from FAMPA called: Ninety Nine or bust This is a game for two or more players. Material: Die, calculator 1. Players take turns to roll the die and key in either the number rolled OR ten times that number, e.g. if 3 is rolled the player may key in either 3 or The number keyed in is added to that player s total. 3. After seven rounds, the player whose total is closest to, but less than 100 wins. Game board Pattern Block P 2 Fraction Game Materials: Pattern blocks hexagons, trapeziums, rhombi and triangles and fraction dice 1 / 4, 1 / 2, 1 / 3, 1 / 6.) 1. Each student begins with two hexagon shapes. The rest of the shapes are in the middle. 2. Place the dice in an opaque container. 70

8 Sue Fine and Linn Maskell 3. Player 1 takes a die from the container and selects an appropriate shape, e.g. 1 / 2 = a trapezium. The die is replaced after each turn. 4. The next player has their turn etc. 5. The first player to have both hexagons covered is the winner. An extension to this activity is to have 6 hexagonal shapes. Each shape must be covered in a different way from the previous shape. The following is a great Fraction activity for the upper grades which students find fun, and non-threatening. 1. In large print write a proper fraction between 0 and 1 on a piece of paper. 2. Order yourselves from the smallest to the largest fraction. 3. Write down everything you know about the fraction. 4. Represent the fraction on a number line. 5. Write down the decimal equivalent. 6. Find and draw three other fractions equivalent to your fraction. Daring ducks This is a game of chance where you predict when you think the number 4 will be rolled. Rules: 1. All stand up. 2. The die is rolled and the number is called. Everyone should write that number in the Game 1 row. As the die is rolled again and additional numbers are called they must also be written down in that row. Your point score is the total of all those numbers. 3. Now you must decide whether to sit down and retain that number of points OR to remain standing and chance that a 4 will not be called. If the dice is rolled and a 4 is called, all those standing will lose all the points they have accumulated for this game. All those who have sat down may add the numbers for this game and write the total in the last column. 71

9 KEYNOTE: Fun + Games = Maths 4. Continue throwing the die and calling the number until a 4 is thrown. 5. Play 5 games and then total the scores. 6. The person with the highest score is the winner. Game board We enjoy Maths, and we enjoy games. Let us join the two and have fun with maths. References McIntosh, A. (1994) Think Mathematically, Melbourne: Longman/Cheshire. 72

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