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2: MATHEMATICAL GAMES

Section Contents:

This section considers the elements necessary for games to be successful in providing opportunities to work with a variety of mathematical concepts. The different categories used within different age bands are described and the rationale for the choice of games and the mathematical subskills they aim to develop are outlined. A variety of ways of acquiring and/or producing a kit of games are discussed.

Principles Behind Successful Games

In his model of mathematics as an activity of our intelligence, Skemp (1989a) suggests that mathematical concepts are learned through schema building and schema testing - building up expectations of the way things behave and then testing out those ideas when new opportunities occur. Thus, we get ideas from each other which we try out against our own. We need to experience and experiment, to communicate and to discuss, and be able to use imagination and creativity to generalise and abstract, in order to determine what will remain constant.

The English National Curriculum in mathematics, in relation to 'using And Applying Mathematics', identifies ways of developing the skills necessary to tackle unfamiliar problems and processes used in mathematics (Department for Education and Employment, 1995). In this, three strands are proposed: .

The use of games and puzzles can provide the opportunities for all these relationships and skills to be developed and consolidated.

The most obvious difference between Paired Reading and Paired Maths is the availability of material. For reading there is usually a large pool of material waiting to be read. The local library is likely to be happy to help, and the school (with the support of the school library service) is usually able to provide access to a range of suitable books for home loan. With Paired Maths, however, there is no immediate source of materials ready and available for parents to borrow.

In the context of parent-child interaction, games can provide more opportunities to explore ideas and more opportunities for communication and discussion than is normally available in the classroom. As Durkin (1993) expressed it: 'the only reason a pre-school child is likely to want to know how many things there are of something is that someone else asked'. It is important that the activities are enjoyable, both in order that the parents and children can relax while engaged in a mathematical activity, and so that the motivation to continue will be high. Games also help to stimulate the use of mathematical language, especially if this is pre-structured.

Games and puzzles have a number of other advantages:

Experience showed that ideally games should meet the following criteria:

The balance between competition or co-operation is an important one. Some mathematical games are solely skills based and therefore put the child (presumed to be the one with lesser skills) at a disadvantage when playing with a parent. They might also tempt the more "able" partner to take on an overt teaching role, which is not one of the aims of the project. Therefore, the majority of games chosen can be won through luck only, but do require certain mathematical skills whilst playing. Other games pose mathematical problems which are novel to both child and partner and hence allow equal co-operation.

Beasley (1990) outlined four classes of games in mathematics:

Games kits might include games of chance (most of the dice and spinner games), games such as Yahtzee which mix chance and skill, games of skill which include many of the strategy games and puzzles, and games combining chance and strategy with an automatic element (such as Uno).

The games need to be attractively produced so that the children want to use them. If they involve as many as possible of the senses (speaking, listening, watching, touching, moving), they are likely to be accessible to more children of different abilities and cultural and linguistic backgrounds. However, they should not incorporate irrelevant distraction. They need to be durable: solidly constructed and packaged so that they are not easily broken by young, enthusiastic users. They should not have too many loose or small parts which are easy to scatter and lose, or which might be difficult to manipulate, or which might be unsafe in the hands of younger members of the family.

They should not be too big, or they will prove difficult to store and transport home. The game itself should reasonably brief - not every child can wait hours for a conclusion. Games need clear rules for play which are not too long, nor too difficult to read or follow - and the game does need to have a clear sense of purpose. Obviously, the games chosen should be appropriate to the chronological age or developmental level of the children who will be playing them. However, it is even better if they can be played at various different levels of complexity.

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Choosing The Games In The Beginning

Enjoyment is the first requirement in the choice of games. The actual activities have to encompass those elements of mathematics which can be developed further at home and yet which are robust enough to be used in many different ways. In addition the activities have to be capable of being used at various levels of development and, most importantly, have to be enjoyable.

The very first project was aimed at Key stage 1 children aged five to seven years, and used adaptations of games, each incorporating different aspects of 'number'. The English National Curriculum Level 1 description of 'number' competencies is probably fairly typical: 'Pupils count, order, add and subtract numbers when solving problems involving up to 10 objects. They read and write the numbers involved. Pupils recognise and make repeating patterns, counting the number of objects in each repeat.'

The first four basic games chosen were "Rows", "Rods", "Cards"and "Tangrams".

Tangrams is an old Chinese puzzle which involves regular shapes which can be aligned to form a square (Shape, Position and Comparison). It is available in plastic pieces which are good to handle and need just an element of competition to make into a game for two. Either a spinner for choice of pieces or 'turns' to see who is the last person to complete is required.

Rods involved a selection of coloured rods each with a regular relationship to the others, providing concrete number experience (Pattern, Size and Relationships). These were made up from old sets of wooden Cuisenaire rods (now available in plastic), provide experience of numbers in a wonderful solid form that could make many games: taking turns, making a steps or walls, copying patterns or picture outlines, perhaps using a dice or spinner to add an element of competition.

Cards involved a pack of normal playing cards with ideas for activities extending their use, including Snap, Rummy, and Pelmanism (Counting, Sorting and Groups). Parents proved to be very good at extending and devising new ideas.

Rows involved coloured counters which could be put into a frame to make both vertical and horizontal patterns. The game could be extended with the use of a dice, and further extended (e.g. 'Four in a Row') to explore wider aspects of reflection and symmetry (Matching, Orientation and Discrimination).

Each game was accompanied by a list of activities to do with the materials, a list of words to be used and a record sheet. Parents are encouraged to use all the words each session and asked to note down which were actually used.

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Development of the Games Kits

The early evaluations highlighted the need to extend the number and variety of games. Accordingly, a larger bank of suitable games was collected. Initially this was based on suggestions from parents involved in the pilot project, from colleagues in the Maths Advisory Team, from Professor Skemp who was instrumental in encouraging and supporting the development, and from catalogues and publishers who were prepared to donate possible games. Eventually over 40 different games were accumulated.

So far the mathematical element of the games has hardly been mentioned, because once the decision is made to look for the mathematics that is already there, the most interesting and enjoyable games on the toy shop shelves are the ones which are likely to have the mathematical elements to provide the experience and exploration that Paired Maths aims to encourage. Even the traditional games that grandparents remember playing before the days of television (e.g. 'Ludo', 'Snakes and Ladders', Dominoes, 'Beetle' and Draughts) all provide opportunities for meaningful counting, one to one matching and addition.

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Key Stage 1

The English National Curriculum has divided mathematics into three major fields for children in the five to seven age group (Key Stage 1):

(This fourth topic is introduced formally after children reach the age of seven, linking into Key Stage 2)

The emphasis is on flexibility and the use of a variety of resources and methods. Much of the work in mathematics is related to the real world and other curriculum topics that the children may be studying. Each aspect of the mathematics curriculum has elements that can be readily addressed through appropriate discussion of the language that directly arises from playing games, for example:

Using and applying Maths:

Number:

Shape, Space and Measure:

In order to accommodate this emphasis on language the games can be grouped under the headings of early mathematical concepts which the children will meet in class:

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Key Stage 1 Games Categories:

Matching Shape Pattern Order Counting Conservation

The six basic categories at the Key Stage 1 level relate neatly to a six-week project in which participants are asked to chose one game from a different category each week. For ease of differentiation, each category is colour coded, so participants know a red coded game has to be returned to the red coded box, and that they cannot then take another red game. This ensures that they sample a wide range of mathematical activities and avoids reinforcing a narrow conceptualisation of what maths entails and embraces. It also enables the mathematical language in play with each game to be focused on a limited set of highly relevant key words. This is more manageable for the parents, and over the whole project children are cumulatively exposed to the complete range of language. An outline of the core mathematical vocabulary covered across all categories will be found in the Appendix to this section.

Though games were chosen because they were fun and for their face validity (i.e. they had obvious mathematical elements), they were categorised by their most prominent conceptual content. However, many games actually cover more than one conceptual area of mathematics, and could be categorised in more than one. Nevertheless, in order to offer the children as wide a range of language as possible the games are placed (somewhat arbitrarily) into one of the six mathematical categories.

Well-known games with an element of luck and competition like Snakes and Ladders, Ludo, and card games are all easily accommodated under counting and matching. Other more recent commercial games were also included, alongside those which had been locally devised. An example of the latter was 'Pass the Bag' - a game that involves feeling for wooden geometrical shapes inside a bag. The shapes have then to be matched to a card where the template might be a different size or colour. Such a game obviously comes under the category of 'shape', but would also include matching, relationships and, to some extent, strategy. Pattern and relationships underpinned all the concepts that were included, since they form the basis of problem solving and as such permeate every aspect of mathematics.

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Key Stage 1 - Suggestions for Games

COUNTING

Snakes and Ladders

Ludo Shapes

Insey Winsey Spider

Scaredy Cat

Beggar my Neighbour

Blackpool card game

Leapfrog

Cat & Mouse

MATCHING

Three to Match

Huff Puff

Humpty Dumpty

Memo

Dominoes

Beetle

Snap (various forms)

Bingo

SHAPE

Pass the Bag

Tessellation

Mr. Space Game

Tangrams

Jigsaw

Attribute Bingo

Dotty Triangles

PATTERN

Ladybirds

Pick a Button

Mosaics

Happy families

3 Mens' Morris

Nine Holes

CONSERVATION

Rods

Button Box

Connect 4 (Rows)

Dogimoes

Choose a Pattern

Three At A Time

ORDERING

Rummy

Halves & Quarters

The Old Woman

100 square jigsaw

Crossing Game

Beanstalk/Dragon

Where there was a smaller number of games in a category, two of each kind were included. The number of games rather than the range within the boxes is the important element and will depend on the number of children involved. A fuller description of some of these Key Stage 1 games will be found in the Paired Maths Handbook (Topping & Bamford, 1998a).

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Key Stage 2

The categories for the next level, Key Stage 2 (children aged seven to eleven years), were somewhat different.

Key Stage 2 Games Categories:

Bonds, Shape, Strategy, Relations, Puzzles (cross-area)

The alterations in categorisation from Key Stage 1 reflect developmental patterns of mathematical growth in children, and the related difference in Key Stage 2 terminology in the National Curriculum. The early emphasis on Conservation, Matching and Counting was seen as leading to work on Number Bonds and Relationships. The early emphasis on Ordering and Pattern led toward Strategy. The Shape category remained, at a higher level of operation. Puzzles were included as examples of cross-area activities. A choice is left from any area for the sixth week.

A full listing of the titles of games included in the Paired Maths Key Stage 2 kits will be found in the Appendix.

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Key Stage 3

For Key Stage 3, the games kits were extended so that as well as being taken home they could form the basis of peer group interaction in class. The categorical structure showed further change from the kits for younger children.

Key Stage 3 Games Categories:

Number games, Space games, Strategy games, Solitaire or Co-operative Puzzles, Extension Games

Each of the boxes of games included an extended number of games in order to allow for a frequent exchange in a full class session. Given constraints of expense and storage in creating kits including large numbers of three dimensional games, a modest number of 3-D games were supplemented by a substantial quantity of two dimensional games. Many of these latter can be readily produced using card and plastic laminate. Some were based on ancient games from many world cultures, some on games of more recent origin in the public domain, and some were created for the purpose. A full listing of these will be found in the Appendix, and some examples to reproduce and use directly will be found in The Paired Maths Handbook (Topping and Bamford 1998) in Section C.

The games were mainly oriented toward the lower end of Key Stage 3, but an extension category was provided. The Number category included counting, bonds, sequence, order, computation (arithmetic) and probability. There was little emphasis on measurement - games cannot (and perhaps should not try to) do everything. Strategy games involved a large element of deduction and prediction leading to the generation of strategies, in many cases requiring an algebraic understanding of the mathematical principles involved. Space games incorporated a large element of visuo-spatial perception and organisation, an appreciation of shape, pattern and geometry, in two and three dimensions and with reference to solids, and including locations and transformation in space.

Puzzles covered all areas explored in the interactive game format by the categories above. Some were very hard! The increased emphasis on individual puzzles ensured that where there is a heterogeneous group, and perhaps erratic attendance patterns, individuals can operate alone at certain times. However, many of these "solitaire" puzzles prove fascinating to others, and co-operative problem solving pairs or groups can often form spontaneously even without teacher suggestion. In these games the discussion becomes directed along the lines of why and how the puzzle works and how it could be improved.

The "extension" group was a cross-area collection of more challenging interactive games for more mathematically able or persistent pupils, preferably working in pairs of similar ability. They mainly covered Space and Strategy at a higher level. For one group of pupils the promise of answers upon application led to mass letter writing to the manufacturers, asking for the answers which had eluded even their teachers.

All five boxes required skills in data handling and the organisation of information (although not necessarily written record keeping) and skill in the application and generalisation of mathematical principles. Categories other than Strategy included activities with some strategic elements. Calculator use was suggested for some games in some categories. In relation to National Curriculum requirements, the Key Stage 3 kit was particularly strong on application and approximation, prediction and probability, strategy and spatial aspects - and especially on problem solving at speed. The kit was relatively light on written recording, decimals, fractions, percentages, measuring and working with very large numbers.

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Sources of Games

In Kirklees, the development of kits of games came about because although schools were very keen to involve parents in the extension of their children's mathematics, they sometimes struggled to immediately produce sufficient games for a whole class group to be involved. Kits were therefore made available centrally which could be borrowed by schools for an initial project, to explore whether the parents and children would be keen to be involved. These provided a means of identifying popular games in each school's catchment area and clarifying what would be needed. Once the initial project was under way, schools involved parents in fund-raising, in making games, in searching car boot sales and writing to manufacturers for sample games in order to provide their own kits for future projects.

Many games are commercially available. Some of these are for four people and can be split into two, providing two sets to borrow. However, manufacturers are constantly looking for novelty. Often the games are taken off the market or replaced with alternatives, so the basic principles of selection have to be applied each time a new kit is made up. More games will be found in commercial outlets in the months before Christmas - although it is difficult for teachers to find time for game hunting during this period. Many game suppliers have a mail order facility (although with the attendant problem of not being able to inspect the goods), and useful addresses will be found in the Appendix. A list of books including mathematical games will also be found in the Appendix.

Another source of games is the Northern Region Mathematics Council (NORMAC) publications and ideas from their conferences. Some of the games developed by Professor Richard Skemp for use in schools are also suitable for use by parents and children at home. Increasingly, maths schemes commercially produced for schools include some "games", and perhaps even take-home activities for "parental involvement", but these should be scrutinised carefully, as they often prove to be two- dimensional and rather dreary and repetitive.

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Appendices - Further Information & Resources

Details of Paired Maths Project Games: Levels 1, 2 & 3

  1. List of Suppliers of Games & other useful addresses
  2. List of other Books of Games
  3. List of Software Suppliers
  4. List of Web Sites
  5. Parents Mathematical Library - Bibliography
  6. Further Reading for Professionals
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APPENDIX 1

APPENDIX 1.a: FURTHER DETAILS OF SELECTED ITEMS IN THE KEY STAGE 1 GAMES KIT

COUNTING

  1. Snakes and Ladders (also see Ludo)

    A chance game involving counting backwards and forwards and anticipation. Age range: 4 to 12. Available from: most toy shops.

  2. Insey Winsey Spider

    Four boards with 4 spiders, a spinner and a dice. The object is to get the spider into his (her?) web at the top of the drainpipe. Age range: 3 to 8. Available from: NES/Arnold. Other information: can be split into 2 separate games.

  3. Scaredy Cat

    Set of cards with blackbirds and pieces of Scarecrow to complete. Involves counting and matching. Age range: 4 to 8. Available from: NES/Arnold.

CONSERVATION

  1. Button Box

    Collection of different buttons with instructions on different ways of sorting them. Age range: 3 to 5. Available from: Grandma's button box. Make sure there is enough variety for the suggested activities.

    Suggested Activity Card : (i) Can you sort for the same: SHAPE, or SIZE, or COLOUR or NUMBER. Which are exactly the same? (ii) Make a row of different buttons - take turns to try to copy it. (iii) Put out four different buttons. Cover and take one away - which one is missing? (iv) Put all the buttons in a row, starting with the biggest, ending with the smallest.

  2. Connect 4

    Plastic board which stands up and has rows and columns of slots to take counters of two different colours. Age range: 4 to 14. Available from: good toy shops. Other information: can also be included in Patterns.

    Suggested Activity Card : (i) Sort out the colours. How many are there? (ii) Make the wall half red and half yellow. How many ways can you do this? (iii) How many patterns can you make? (iv) Roll a dice, take turns to put in the counters (a) who is highest? (b) how many more to be equal? (v) Try to get 4 in a line, can you stop each other?

PATTERN/RELATION

  1. Pick A Button

    Set of buttons which match according to different properties.
    Object: to match the buttons according to the rules and to get rid of all the buttons. Age range: 3 to 8. Available from: Can be assembled at home. Spinner can be made out of cardboard and pencil.

    Suggested Activity Card: Rules - (i) Each player takes it in turn to choose a button from the box until each has six buttons, (ii) The king button is placed on the table, (iii) Players take it in turns to spin the spinner and must match the last button put on the table with the property displayed on the spinner, (iv) The first to get rid of all their buttons is the winner.

  2. Mosaics

    Box with different plastic shapes and a sample pattern. Object: to make up pattern in turns. The loser places the last piece. Age range: 3 to 8. Available from: Can be assembled at home from any box of different plastic shapes.

    Suggested Activity Card: (i) Can you sort the pieces for same shapes and same colours? (ii) Can you fit some of the small pieces on top of the bigger ones? (iii) Can you make a pattern? Take turns to copy each other. (iv) Can you make a picture? (v) How many pieces can you fit together without spaces?

ORDERING

  1. Cards - Rummy

    Pack of playing cards with instructions. Winner has to get 3 or more cards of the same suit in the correct order. Age range: 5 to 15. Available from: cards - most toy shops; instructions - a playing card game book (e.g. Collins Gem Card Games, Harper- Collins, Glasgow, 1991).

  2. Hundred Square Jig-saw

    Base board with numbers 1 - 100 and jig-saw pieces to fit it. The loser is the one who places the last piece on the board. Age range: 6 to 8. Available from: NORMAC.

    Suggested Activity Card: Use this an ordinary jig-saw or play the following game: (i) Share the pieces equally between you, (ii) Decide who will start, (iii) The first player places a piece on the board. The second player places another piece on the board - but only if it adjoins a yellow square, (iv) Take turns until all the pieces are on the board. The loser is the one who places the last piece on the board.

MATCHING/BONDS

  1. Humpty Dumpty

    Cards of different figures with matching base. Objective: to complete the Humpty Dumpty and gain the most men. Involves counting and matching. Age range: 3 to 6. Available from: NES/Arnold. Other information: can be split in two sets.

  2. Beetle

    Four sets of head, body, limbs, etc., plus one dice. Object: to assemble your beetle first. Age range: 3 to 8. Available from: good toy shops. Other information: can be split up into 2 games by adding another dice.

  3. Snap and Number Snap

    Eighteen pairs of cards with numbers. Object: to win all the cards. Age range: 3 to 14. Available from: good toy shops.

    Suggested Activity Cards: (i) Match the same pictures, (ii) Put a line of different pictures to copy, (iii) Put out 4 pairs face down - take turns to turn up one and find the pairs. (iv) Play SNAP, (v) How many cards are the same? (vi) How many pairs are there?

SHAPE

  1. Pass The Bag

    Four boards, 4 bags, 40 pieces to match pictures on boards. Players take turns to pick a shape from the bag without seeing it. Age range: 4 to 9. Available from: bag and board can be home-made, used with any purchased or made set of shapes. Other information: can be split into two, if one new bag is added.

    Suggested Activity Card: (i) Sorting - sort the pieces for shape, size, colour. (ii) Lotto - caller takes out one piece at a time - first full card wins. (iii) Pass the bag - take it in turns to take a shape from the bag without looking - wrong colours are put back - the first full card wins.

  2. Mr. Space Game

    Different shapes to fit a figure on a board. Dice are used to enable player to place shape on board. Winner is the one who completes figure first. Age range: 4 to 8. Available from: NES/Arnold. Other information: can be split to make two games.

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APPENDIX 1.b: KEY STAGE 2 GAMES

Strategy - Yellow Spatial - Red Number - Green Relations - Orange Puzzles - Blue
Tip It Continuo Little Professor Goldilocks Colourtair
Guess Who Crazy Connections Frog Jump Coppit Squaring the Circle
Master Mind Leap Frog Shut The Box Frustration Peg Solitaire
Number Game Car Capers Ono 99 Finders Keepers Tangrams
Battleships Mr. Space Teachers' Pet Crossing Game Playcube
Peg Game Triangulo Bingo Rods 100 Square Jigsaw
Pik a Styx Take a Train Uno Whot Outwit
Tiddley Winks White Rabbit Crazy Witch
Greed Crazy Turtle
Crazy Plane
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APPENDIX 1.c: KEY STAGE 3 GAMES

In each category, three dimensional games are above the dotted line, supplementary two dimensional games below it.

PUZZLES (blue)

  1. Disappearing Square
  2. Squaring the Circle
  3. Perfect Squares
  4. Serpent
  5. Polydron Playcube
  6. Rubik's Magic
  7. Rubik's Cube
  8. Rubik's Clock
  9. Thinkominos
  10. Tangrams
  11. Triangle Game
  12. Frogs

  13. Square Puzzles
  14. Counterfeat 1
  15. Counterfeat 2
  16. Counterfeat 3
  17. Counterpath
  18. Diviso
  19. Counterpart
  20. Dump
  21. Antisocial Puzzle
  22. Counterswitch
  23. Number Path
  24. Counterline
  25. Monster's Wardrobe
  26. Shopping on Mars
  27. United Shirts
  28. Calculation
  29. Baking on Mars
  30. Self-destruct
  31. Block saw
  32. Squares
  33. Martian Maths
  34. Hieroglyphics
  35. Rabbit Relations
  36. Endless Lines
  37. What's the Difference?
  38. Number Crozzle
  39. Stick At It
  40. Mystery Tour
  41. Treasure Map
  42. Solitaire
  43. Marvellous 26
  44. Hex Hop
  45. Card Solitaires
  46. Addition Puzzle
  47. Pentalpha
  48. Penny Solitaire
  49. Treble Interchange
  50. Vanishing Squares
  51. Magic Triangles
  52. Packing
  53. Birthdays
  54. Number Squares
  55. Number Crossword
  56. Mathword
  57. Countermore
  58. Code Wheelies
  59. Darts
  60. Number Quest
  61. Relations
  62. Stripping
  63. The Design
  64. Distort
  65. Sequences
  66. Word Symmetry
  67. Word Search
  68. Haunted House

STRAGEGY (yellow)

  1. Clash
  2. Uno
  3. 5 in a Row
  4. Othello
  5. abyrinth
  6. Tic Tac Toe
  7. Star Base
  8. Tactics
  9. Space Orbiter/Pong Hau K'i
  10. Grasshopper
  11. Entangle
  12. Encircle
  13. Enforce
  14. Enfold

  15. Noro
  16. Achi
  17. Catch Me
  18. 3 Men's Morris
  19. 6 Men's Morris
  20. 9 Men's Morris
  21. 12 Men's Morris
  22. Poker
  23. Seega
  24. Matchin Min
  25. Trios
  26. Mosaic
  27. Crocogator
  28. Necklace
  29. Stack of Chips
  30. Trap the Pig
  31. Move Move
  32. Serpents
  33. Mu Torere
  34. Royal Game of Ur
  35. Palm Tree
  36. Ludus Latrunculorum
  37. High Jump
  38. Kono
  39. Fighting Serpents
  40. Yote
  41. Konane
  42. Go
  43. Asalto
  44. Nyout
  45. Zohn Ahl
  46. Patolli
  47. Puluc
  48. Tablan

SPACE (red)

  1. Devil's Triangle
  2. Tri-ominos
  3. Shuttles
  4. Action Replay
  5. Nine Rabbit Warren
  6. Fighting Snakes
  7. Springboard
  8. Change Over
  9. Enthrall
  10. Engage
  11. Ensnare
  12. Engender
  13. Entomb

  14. Shapes in a Row 4 x 4
  15. Shapes in a Row 5 x 5
  16. King Monster
  17. Lau Kati Kata
  18. Fox and Geese
  19. Tablut
  20. Alquerque
  21. Star Game
  22. Dara
  23. Sz' Kwa
  24. Knotty Problems
  25. Treasure
  26. Navigrid
  27. Avoid
  28. Cox's Boxes
  29. Dead End
  30. Tri-Stix
  31. Quadrangle
  32. Starslide
  33. Tri-Box
  34. Square Box
  35. Hex Box
  36. Triads
  37. Pathway

NUMBER (green)

(games 12-22 are card games)

  1. Equality
  2. Checkmath
  3. Rummikub
  4. Little Professor
  5. a Yahtzee
  6. b Yahtzee
  7. Pass the Pigs
  8. Woof Woof
  9. Gruesome Games
  10. Number Race
  11. Pirate Ludo
  12. Soccer
  13. Cheat
  14. Sweet 16
  15. Go!
  16. Blackjack
  17. 500 Rummy
  18. Product Grid
  19. What's My Rule?
  20. Multiples Rummy
  21. Twenty-Nine
  22. Tough Beans

  23. Square 15 (3 x 3)
  24. Fifteen (5 x 5)
  25. Sea Battle
  26. Digital Noughts & Crosses
  27. Guess My Number
  28. Calculator Snooker
  29. Circle Nim
  30. Rectangular Numbers
  31. Taylor's Game
  32. Number Grids
  33. Nim/Marienbad
  34. Odds On
  35. Greed
  36. Combinations
  37. Curly Combinations
  38. Sidewinder
  39. Bandits
  40. Make Ten
  41. Pirate Fight
  42. Tell Us Something New
  43. Calculator Tricks
  44. Line of Four
  45. Catch
  46. Grand National
  47. Tables Snap
  48. Multichance

EXTENSION (orange)

P = Puzzle G = Game

  1. G Rubik's Illusion
  2. G Rage
  3. G Pit
  4. G Sting
  5. P The 36 Square
  6. P Rubik's Triamid
  7. P Rubik's Dice
  8. P Rubik's Fifteen
  9. P Rubik's Tangle

  10. P Tower of Brahma
  11. P Magic Squares
  12. P Spirals
  13. P Knight's Move
  14. G Congclak (Mancala)
  15. P Prisoner's Nightmare
  16. G Tabula
  17. G Casino
  18. G Rithmomachia
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APPENDIX 2

LIST OF SUPPLIERS OF GAMES & OTHER USEFUL ADDRESSES

Toy shops, stationers and big stores

Beatties, Hamleys, The London Toy Company, John Menzies, John Lewis, Toys R' Us, etc. Many stock a particularly good selection of board games and puzzles on the run up to Christmas.

David Singmaster maintains an extensive list of European game and puzzle suppliers, and relevant magazines, societies and museums. Contact: Professor D. Singmaster, Computing Information Systems and Mathematics, South Bank University, London SE1 0AA.

Some of the following suppliers will send catalogues on request:

Beaver Books/Arrow Books, 62-65 Chandos Place, London WC2N 4NW

Big Box Games, Artstraws Ltd, Unit 3 Clarkeway, Winch Wen Industrial Estate, Swansea

Crown & Andrews UK Ltd, Wellington House, Kentwood Hill, Tilehurst, Reading

Early Learning Centre, South Marston Industrial Estate, Swindon, Wiltshire SN3 4TJ

Edprint, 234 Holyhead Road, Wellington, Telford, Shropshire TF1 2DZ. Tel 01952 48623

Falcon Games Ltd, Travellers Lane, North Mymms, Hatfield, Herts

James Galt & Co Ltd, Brookfield Road, Cheadle, Cheshire SK82PN

Gibsons Games, Greenlea Park, Prince George's Road, London

Grant Trading, 1 Morland Avenue, Croydon, Surrey CRO 6EA. Tel/fax 0181 656 8374

Harbutts Educational Services, Bretton Way, Bretton, Peterborough PE38YA

Hippo Books, Scholastic Publications, 7-9 Pratt Street, London NW1 OAE

House Martin International Ltd, Castle Gate, Oulton, Leeds LS26 8HG

Icarus Co (Toys) Ltd, Unit 1 Roundways Industrial Estate, Elliott Road, Bournemouth.

Kenner Parker Toys International, Hargrave House, Belmont Road, Maidenhead, Berkshire

Lagoon Games, P.O. Box 311, Kingston Upon Thames, KT2 5QW

The London Toy Company, Mail Order Division, Warehouse 431B, Alexandra Avenue, Harrow, Middlesex, HA2 9SG, Tel 0181 864 2186

The Longfield Press (Alan Parr), 6 Longfield Gardens, Tring, Herts HP23 4DN. Tel 01442 824173

Matchbox Toys, Swaines Industrial Estate, Ashingdon Road, Rochford, Essex SS4 1RH, Tel 01788547677

Milton Bradley Ltd, Hasbro-Bradley UK Ltd, 2 Roundwood Avenue, Stockley Park, Uxbridge, Middlesex UB11 1AZ.

NES Arnold Ltd, Ludlow Hill Road, West Bridgford, Nottingham NG2 6HD

Orchard Toys, Debdale Lane, Keyworth, Nottingham NG12 5HN

Polydron (UK) Ltd, Unit 11, Brackmills Industrial Estate, Scotia Close, Northampton NN4 OHR.

PUZZLES, Wallop, Hampshire. Tel 01264 781833

Ravensburger Toys, Fisher-Price Ltd, P 0 Box 100, Peterlee, County Durham DH8 2RF

Scholastic Ltd, Westfield Road, Southam, Leamington Spa, Warwickshire CV33 OJH. Tel 01926 813910, Fax 01926 817727. Photocopiable shape, space, measures and number games.

Shoptaugh Games Inc, Oakland CA 94618, USA

J W Spear & Sons plc, Richard House, Enstone Road, Enfield, Middlesex EN37TB

M. Stanfield Ltd, Murdock Road, Bicester, Oxon OX6 7RH. Tel 01869 324873

Tarquin Publications, Stradbroke, Diss, Norfolk IP21 5JP. Tel 01379 984218, Fax 01379 384 289

Taskmaster Ltd, Morris Road, Leicester LE2 6BR. Tel 0116 2704286, Fax 0116 2706992

Texas Instruments Ltd, Manton Lane, Bedford MK41 7PA

Waddingtons Games Ltd, Castle Gate, Oulton, Leeds LS26 8HG. Tel 0113 2826195

Wellingtons Ltd, Stamford, Lincolnshire (Fiendish puzzles)

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APPENDIX 3

LIST OF BOOKS OF GAMES AND PUZZLES

Allison, A. (1995) Maths From Rhymes. Birmingham : Questions Publishing Company.

Ball, J. (undated) Games From Around the World. Produced by Benn Associates for Smarties.

Barry, B. (1978) Hip Pocket Maths Games. Sydney : Harcourt Brace Jovanovich.

Barry, B. (1979) More Hip Pocket Maths Games. Sydney : Harcourt Brace Jovanovich. (Specifically for parents and children)

Bell, R. & Cornelius, M. (1988) Board Games Around The World: A Resource Book For Mathematical Investigations. Cambridge : Cambridge University Press. (ISBN 0521359244)

Bolt, B. (1984) The Amazing Mathematical Amusement Arcade. Cambridge : Cambridge University Press (ISBN 0521269806) also see: The Mathematical Funfair by Brian Bolt

Bolt, B. (1996) A Mathematical Jamboree. Cambridge : Cambridge University Press.

Brighouse, A., Godber, D. & Patilla, P. (1986) Maths Explorer. Glasgow : Collins. (six separate volumes for ages 5-11)

Bulloch, I. (1995) Action Maths. London : Watts (separate volumes for shapes, patterns, measure and games, all intended for use by parents).

Child Education (1986) Number Fun. Leamington Spa : Scholastic Publications.

Cornelius, M, & Parr, A. (1991) What's Your Game? Cambridge : Cambridge University Press

Davis, J. & Tibbatts, S. (1995) Teacher Timesavers Maths Puzzles. Leamington Spa : Scholastic.

De Bono, E. (1996) Edward De Bono's Mind Pack. London : Dorling Kindersley.

Dean, P. (1976) Commercial Games suitable for Middle and Secondary School Mathematics. In Mathematics in School, March 1976. (A list by Peter Dean of about one hundred games and their suppliers.)

Diagram Visual Information Limited (1991) Card Games. Glasgow : Harper Collins (A Collins Gem)

Diagram Visual Information Limited (1992) Games for One. Glasgow : Harper Collins (A Collins Gem)

Edwards, R., Williams, A. & Baggaley, P. (1993) Number Activities and Games. Stafford : NASEN Publications.

Erickson, T. (1989) Get It Together: Math Problems for Groups, Grades 4-12. Equals, Lawrence Hall of Science, Berkeley, California 94720. (ISBN 0912511532)

Fisher, A. & Gerster, G. The Art of the Maze. London : Weidenfeld & Nicholson.

Fraser, S. (1982) Spaces: Solving Problems of Access to Careers in Engineering and Science. Dale Seymour Publications, PO Box 10888, Palo Alto, California 94303, USA. (ISBN 0866511474)

Coghill, J. (undated) Help Your Child With Maths Games Pack. London : BBC Publications.

Golick, M. (1975) Learning Through Card Games. London : Wolfe Publishing. ISBN 723406197.

Graham, A.T. (1985) Help Your Child With Maths: A Guide For Parents. Fontana (ISBN 0006368573)

Heimann, R. (1990) Mind Bending Mazes. London : Scholastic (a Hippo book)

Heimann, R. (1991) Preposterous Puzzles. London : Scholastic (a Hippo book)

Kirkby, D. (1992) Games in the Teaching of Mathematics. Cambridge : Cambridge University Press.

Kirkby, D. (1995) Mini-Maths Series. London : Heinemann. (Separate volumes for numbers, patterns, shapes, measuring, sorting, number play.

Langdon, N. & Snape, C. (1984) A Way With Maths. Cambridge : Cambridge University Press. (ISBN 0521278833)

Langdon, N. & Cook, J. (1984) Usborne Introduction To Maths. London : Usborne.

The Mathematical Association. Fifty Per Cent Proof. Gloucester : Stanley Thornes.

The Mathematical Association (1987). Sharing Mathematics With Parents: Planning School-Based Events. Stanley Thornes, Old Station Drive, Leckhampton, Cheltenham GL53 ODN. (ISBN 0859506959)

Merttens, R. (1987) More Monster Maths. London : Octopus.

Merttens, R. (1987) Numbers Time and Money. London : Octopus. (The two items above are examples from the Parent and Child Programme, which includes a range of activity books and workbooks in mathematics).

Merttens, R. & Leather, R. (1995) Impact: Holiday Activities. Leamington Spa : Scholastic

Merttens, R. & Leather, R. (1995) Impact: Early Years Activities. Leamington Spa : Scholastic

Merttens, R. & Leather, R. (1995) Impact: Shape - Key Stages 1 and 2. Leamington Spa : Scholastic (Many other Impact books exist, some fearsomely titled "Impact Maths Homework")

Moscovich, I. (1984) Supergames. Hutchinson (ISBN 0091563814)

Moscovich, I. (1986) Mind Benders: Games of Chance. Penguin ISBN 0140098240. Also see: Games of Shape ISBN 0140098259.

NES Arnold (see 'Suppliers') (undated): Multilink Traditional Games Pack. (Ref SY 562/1).

Owen, A. (1995) Everyday Maths. London : Wayland. (separate volumes for At Home, Ourselves, Fun With Food, Out and About)

Pappas, T. (1989) The Joy of Mathematics: Discovering Mathematics All Around You (second edition). from Wide World Publishing or John Bibby books, 1 Straylands Grove, York YO3 0EB. (ISBN 0933174659)

Parr, A. Twenty-Five Mathematical Card Games. Longfield Press (see 'Suppliers')

QED Books, 1 Straylands Grove, York Y03 OEB supply many mathematical titles

Rice, T. (1973) Mathematical Games and Puzzles. B & T Batsford. A book explaining more than forty types of puzzles and games. The final section deals with games for one or more players. Attractively set out. For primary school pupils upwards.

Sheppard, R. & Wilkinson, J. (1989) The Strategy Games File. Tarquin Publications, Stradbroke, Diss, Norfolk IP21 5JP. (ISBN 0906212707)

Sheppard, R. & Wilkinson, J. (1994) Strategy Games. Diss : Tarquin Publications

Skemp, R.R. (1989) Structured Activities for Primary Mathematics: How To Enjoy Real Mathematics. London : Routledge. Volume 1 for the early years, volume 2 for the later years, volume 1a photomasters, volume 2b photomasters. (Designed for teacher use).

Smullyan, R. (1978) What Is The Name of This Book? London : Pelican. Smullyan, R. (1990) The Riddle of Dracula And Other Logical Puzzles. London : Penguin. (ISBN 0140135111)

Snape, C. & Scott, H. (1996) How Many? Cambridge : Cambridge University Press.

Snape, C. & Scott, H. (1996) Puzzles, Mazes and Numbers. Cambridge : Cambridge University Press.

Stenmark, J. K., Thompson, V. and Cossey, R. (1986) Family Math. Equals, Lawrence Hall of Science, Berkeley, California 94720 (ISBN 0912511060)

Tapson, F. & Parr, A. (1979) Pick A Pair. London : A. & C. Black

Tyler, J. & Round, G. (1980) Picture Puzzles. London : Usborne. (ISBN 0860204332)

Tyler, J. & Round, G. (1980) Number Puzzles. London : Usborne. (ISBN 0860204359)

Williams, M. & Somerwill, H. (1982) Forty Maths Games To Make and Play, Macmillan Education. (ISBN 0333317300).

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APPENDIX 4

LIST OF SOFTWARE SUPPLIERS

(much of this will be almost instantly outdated)

In addition to regional centres supported by LEAs, the following are suppliers of software suitable for home use in the UK for various hardware platforms. Many will send catalogues on request.

ABLAC gives free telephone advice to parents and encourages home-school learning links - also has a catalogue - tel 01626 332233

AVP, School Hill Centre, Chepstow, Monmouthshire NP6 5PH, tel 01291 625439, fax 629671, email 100441.130@compuserve.com (primary catalogue and special needs catalogue)

Brilliant Computing tel 01274 497617

The British Library offers a catalogue of CDROMs. tel 0171 412 7797, email education@bl.uk

Creative Curriculum Software tel 01422 340524

Don Johnston tel 01925 241642

Lander Software, 1 Atlantic Quay, Glasgow G2 8JE, freefone 0800 403040 or 0141 226 5611, fax 5622, email Lander@cix.compulink.co.uk

The National Centre for Educational Technology (tel 01203 416994) also has much relevant information and are very helpful (email enquiry_desk@ncet.org.uk; also see their homepage at http://www.ncet.org.uk/). They produce a (long!) updated information sheeet on Educational Software Suppliers and a guide for parents called "Children's Software and Where To Get It". They review CD-ROMs including those for mathematics and have a searchable software database.

New Media tel 0171 916 9999

New Vision (CDROM only) tel 0181 964 3334

Parents and Computers is a magazine for parents with children between 3 and 11 years old, tel 01625 878888

Parents' Information Network, PO Box 1577, London W7 3ZT, 0181 248 4666.

Rickitts Educational Media (REM), Great Western House, Langport, Somerset TA10 9YU, tel 01458 253636, fax 253646, email 100647.3472@compuserve.com (Educational Software Yearbook, Special Needs Catalogue and CDROM catalogue)

NW SEMERC tel 0161 627 4469

Sherston Software tel 01666 840433

Software Production Associates (SPA), PO Box 59, Tewkesbury GL20 6AB, tel 01684 833700, fax 833718, email sales@spasoft.demon.co.uk

Tag Developments Ltd tel 01474 357350

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APPENDIX 5

LIST OF WEBSITES

The Internet is constantly changing, and readers are advised to conduct their own up-to-date search with the usual search engines. Listed below are some of the more enduring current websites, but even these may change.

There is a large number of locations dealing with mathematics, but most deal with teacher-directed mathematics in school, college or university. There are also websites which enable parents and children to rehearse major national mathematics tests (e.g. SATs). There are also sites which offer commercial profit making services to parents (e.g. Water Street, The Digital Education Network). Additionally, there are scores of email listservs and newsgroups for those interested in mathematics, but rarely for parents and children together. None of the above are listed below.

US Department of Education: Helping Your Child Learn Math
(in addition to a number of detailed activities, includes a listing of US resources for parents, books for children, and maths magazines and periodicals for adults and children)
http://www.ed.gov/pubs/parents/Math/index.html

Doing Mathematics With Your Child
(M. Hartog & P. Brosnan, 1994: ERIC Digest)
(US-based, brief general information, mentions some resources and projects, useful lists of and references to other parent guides and activities)
http://www.stemworks.org/digests/dse94-3.html

PRIME: Parent Resources in Mathematics Education
(M. Hartog & M. Reed: ERIC publication)
(a more extensive US-based annotated bibliography of parent guides, activities and programmes)
http://www.stemworks.org/Bulletins/SEB94-3.html

Family Math (The Berkeley EQUALS Programme)
(describes the programme, its email Newsletter, gives access to back issues of the newsletter, and contact details)
http://www.lhs.berkeley.edu/equals/FMnetwork.htm

Figure This!
http://www.figurethis.org/

Math Forum
http://mathforum.org/

Mathematical Resources (Math Links by Bruno Kevius)
http://mathres.kevius.com/problem.html

Mathematics for Parents
(a series of newsletters for parents from the University of Wisconsin Center for Educational Research, each dealing with a specific area of maths)
http://www.wcer.wisc.edu/archive/mims/Parent_Newsletters/

Mathematics Resources for Parents
(brief list with price, contact details; some emphasis on materials also in Spanish)
http://www.iusd.k12.ca.us/curriculum/mathrsrc.htm

Ask Dr. Math
(provides a solving service for K-12 maths problems, among other things)
http://forum.swarthmore.edu/dr.math/

Think like a Computer! A Guide to Number Sequence Puzzles
http://www.barcodediscount.com/articles/think-like-a-computer-a-guide-to-number-sequence-puzzles.htm

Also see the Parents In Education web site at
http://www.dundee.ac.uk/eswce/research/projects/ParentsInEducation

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APPENDIX 6

PARENTS MATHEMATICAL LIBRARY - BIBLIOGRAPHY

Bright Ideas - Maths Games Rosemarie Brewer and Marion Cranmer (1988) Scholastic Publications Ltd, Marlborough House, Holly Walk, Leamington Spa, Warwickshire CV32 4LS. (ISBN 0590708740) Pages: 127

Maths and Me Avelyn Davidson (1983) Shortland Publications Ltd, republished 1988 by NES Arnold (see 'suppliers') (ISBN 0560091001) Pages: 40

Parent and Child Programme Ruth Merttens Octopus Publishing Group Ltd, Michelin House, 81 Fulham Road, London SW3 6RB. a) Counting On - 1987 (ISBN 1852700092) 32 pages b) Beqinninq to Count (1) - 1987 (ISBN 1852700084) 32 pages c) Beginning to Count (2) - 1988 (ISBN 1852700645) 32 pages d) Parents' Guide to Your Child's Maths - 1988 (ISBN 1852700599) 32 pages e) Fun With Shape - 1987 (ISBN 1852700203) 32 pages

Help Your Child With Maths - BBC TV Series Angela Walsh (ed.) (1988) BBC Books, BBC Enterprises Ltd, Woodlands, 80 Wood Lane, London W12 OTT. (ISBN 0563214449) Pages: 128

Maths Through Play Rose Griffiths (1988) MacDonald & Co (Publishers) Ltd, Greater London House, Hampstead Road, London NW1 7QX (ISBN: 0356134601). Pages: 96

Help Your Child Learn Number Skills Frances Mosley and Susan Meredith (1989) Usborne Publishing, 20 Garrick Street, London WC2E 9BJ (ISBN 0746003145) Pages: 48

Parents And Maths ACE Information Sheet (4 pages) Advisory Centre for Education, 18 Victoria Park Square, London E2 9PB

Graham, A.T. (1985) Help Your Child With Maths: A Guide for Parents. London : Fontana.

GEMS (1991) A Parent's Guide to Great Explorations in Math and Science. Berkeley CA : Lawrence Hall of Science.

Further Reading for Parents of Pre-school Children:

Ready for Maths C Heald and V Eustice (1988) Hippo Books, Scholastic Publications (ISBN 0590709534)

Parents as Playmates J Millman and P Behrmann (1979) Human Sciences Press, 3 Henrietta Street, London WC2E 8LU (ISBN 0877054045)

Let Me Count Dorothy M. Jeffree (1989) London : Souvenir Press (ISBN 0285650815)

Mokros, J. (1996) Beyond Facts and Flashcards: Exploring Math with Your Kids. Portsmouth NH: Heinemann.

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APPENDIX 7

FURTHER READING FOR PROFESSIONALS

Campbell, P.B. (1992) Maths, Science and Your Daughter: What can parents do? Washington DC : US Department of Education (ERIC ED350172).

Centre for Mathematics Education (1995) An ABC of Number. Milton Keynes : Open University Press.

O'Connell, S.R. (1992) Math Pairs: Parents as Partners. Arithmetic Teacher, 40 (1), 10-12.

Struggle: Mathematics for Low Attainers. Journal for teachers produced by the Mathematical Association, 259 London Road, Leicester LE2 3BE, Tel 703877.

Neil, M.S. (1994) Parent-Teacher Partnerships: Enhancing Learning in Mathematics. Georgia. ERIC ED377054.

Apelman, M. & King, J. (1989) Pizzas, Pennies and Pumpkin Seeds: Mathematical Activities for Parents and Children. Denver CO : State Department of Education. ERIC ED327395.

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