Dice, dominoes and cards – there’s maths in that game!

    Published: 23 June 2020

    The following set of six games involve little equipment and, as well as being fun and revealing the odd competitive streak here and there, they are stocked full of maths.

    When using dice and dominoes, children will become familiar with dot patterns and will eventually be able to recognise them on sight. The children may notice (or be guided to notice) that the patterns are linked.

    For example, on the dice,

    1 dice spot

     

    This is '1'

     

    Two dice

     

    3 is '2 and 1 more'

     

    2 dice

     

    5 is '4 and 1 more'

     

     

    Recognising a quantity without counting is called ‘subitising’ and this is one of the skills that underpins addition and subtraction going forward.

    The domino tiles have the same layout of dots (pips) for each number as the dice but they have a potential two numbers on one tile (one on each half). For some games, children may need to take into account one of these numbers on each turn and for some, they may need to combine them. This further supports with understanding parts and wholes.

    Playing cards offer something different and potentially less familiar in terms of patterns. When playing games, challenge children to see ‘numbers within numbers’. For example, in the Winner Takes the Difference game later in the blog, the example uses the following cards with counters to match:

     

    Cards and spots

     

    Can children identify ‘the five’ and ‘the three’ on the eight card? Is there only one way?

     

    Dice

    Dotzi

    1 or more players, you will need:

    • 6 dotty dice
    6 dice

    Optional equipment:

    • A container  (if you wish to contain the dice!)
    • A timer (for timed games)

    How to play

    • Player 1 rolls all 6 dice (or shakes the dice in the container for tidier play!) and keeps any dice that show the number 5.

     

    Dice

     

     

    • Player 2 rolls the remaining dice and keeps any dice that show the number 5.

     

    Dice

     

    • Continue taking it in turns to roll the remaining dice. If there are no dice that show the number 5, the next player rolls. When all of the dice have been taken, the player with the most dice wins!

    For single players, keep any dice that show the number 5 on each roll. Either count how many rolls it takes or use a timer to see how long it takes. Then try to beat that number of rolls or time on your next go!

    Changing it up!

    Try one of the following…

    • Change the target number for keeping dice, e.g. take all of the dice that show a number 6.
    • Keep any matching pairs or seats, e.g.

     

    Dice

     

    Player 1: I have rolled two threes, a six, a five, a two and a four. I can keep the threes because there are two of them. They are a pair.

     

    Dice

     

    Player 2: I have rolled three sixes and a one. I can keep the sixes because there are three of them. They are a set.

    • Keep any odd numbers.
    • Keep any even numbers.
    • Keep any numbers that add to total 7 (pairs or sets), eg.

     

    Dice

     

    Player 1: I can keep the three and the four because 3 more than 4 is 7.

     

    Dice

     

    Player 2: I can keep the five, the one and the one because the sum of 5, 1 and 1 is 7.

    Note: Players can keep more than one pair or set from a throw, e.g.

     

    Dice

     

    I can keep the six and the one because 1 plus 6 is 7. I can also keep the two twos and the three because double 2 equals 4. 4 and 3 make 7 altogether.

    • Change the target total, e.g. keep any numbers that add to total 10.
    • Keep any consecutive numbers.
    • Keep any dice that show a number that is less than 3.
    • Keep any dice with a difference of 2, e.g. 1 and 3, 2 and 4, 3 and 5 or 4 and 6.
    • Make the winner the player with the highest total number of dots won. e.g. in a round of ‘keep the dice that show odd numbers’:

     

    Dice

     

    Player 1 won four dice and Player 2 won two but Player 2 is the overall winner because 5 + 5 = 10 which is worth more than 1 + 3 + 1 + 1 = 6.

    Note: Keep the dice the same way up as when they were won so that the total can be counted or draw a picture of the dice combinations won each time.

    • Single players could keep rolling until the numbers 1 to 6 have been collected.

    Questions to consider:

    Can you explain why you are allowed to take the dice in a different way?

    For example, in a game where the target total is 6,

    I can take these two dice because…

     

    Dice

     

    •  

     

    • The sum of 2 and 4 is 6.
    • 4 plus 2 equals 6.
    • 6 is 4 more than 2.
    • 4 and 2 total 6 altogether.
    • If 2 and 4 are the parts, the whole equals 6.
    • 4 add 2 is 6.

    When using each rule to play, is it possible to get a draw?

    What is the highest / lowest possible number of dots you could win when playing each rule?

    Will all of the dice be used in each game? If not, why not?

    Can you make up your own rule?

     

    Make 10

    2 or more players

    You will need:

    • A dotty dice
    • A 3x3 grid drawn on a piece of paper
    • A pen / pencil

    How to play:

    • Take it in turns to roll the dice and record the number of dots rolled  in a square on the grid, e.g.

     

    Table

     

    • On each turn, a player may choose to add to a square that already contains dots or to start a new square, e.g.

     

    Dice

     

    • The player that completes a square with exactly 10 dots wins that square. The player may initial that square or outline it in their colour pen, e.g. for Player 2 above.
    • Squares are not allowed to contain more than 10 dots so if a player rolls a number that cannot fit in any squares, the next player takes their turn.
    • When all of the squares have been won, the player with the most squares overall wins!

    Changing it up!

    • All squares must contain at least one dot before dots can be added to other dots.
    • Allow players to split the dots on their dice between more than one square. Any square that’s filled during the turn can be claimed.
    • Change the game to ‘Make 100%’ where each dot is worth 10%. Explain what is in the square you add to each time, e.g. There were 3 dots here so that’s 30%. I added 5 dots so now it is 80% complete. 2 more dots are needed to make the final 20%.

    Questions to consider:

    • In which boxes is it easier to see how many dots there are? Why is that?
    • Which numbers are you more likely to be able to fit in a box? Why?
    • Can there ever be a draw?
    • How many different combinations of dots are there that make 10? How will you know if you have them all?
    • Can a player with less dots overall still be the winner?

     

    Dominoes

    Twelve Pips

    1 or more players

    You will need:

    • A set of dominoes

    How to play:

    • Place the dominoes face down, shuffle them and lay in rows to make a grid.
    • Take it in turns to turn over two domino tiles.
    • If the dots on both tiles total 12 altogether, keep the tiles. If not, turn them back over. Try to remember where they are!
    • The player with the most dominoes at the end wins!

    For single players, see how many pairs you can make before you turn over the ‘double five’ domino.

    Changing it up!

    • Allow players to turn over a third domino if the dots on the pair don’t yet total 12. If the set of 3 total 12, the player takes them all.
    • If the player before you doesn’t make it to 12, you can choose to keep their tiles turned over and begin your turn from there.
    • Players get a bonus point if they use a ‘double domino’.
    • If a player turns over double 3 and then doesn’t find a tile to make 12, the other player gets two turns in a row.

    Questions to consider:

    • Is it possible to match all of the domino tiles in pairs to make 12 without having any left over?
    • Is it easier to remember the location of certain dominoes? Why is that?

    Make it a Multiple

    2 or more players

    You will need:

    • A set of dominoes

    Optional equipment:

    • Domino racks

    How to play:

    • Place the dominoes face down and shuffle them.
    • If there are 2 players, each player takes 7 tiles (6 tiles each for 3 players and 5 tiles each for 4 players).
    • Any remaining tiles are left face down to be taken during the game.
    • Player 1 lays down a domino to start the game. It doesn’t have to be a double. However, the first double played is the only double that can be played off of all four sides (see below).
    • Players in turn then lay tiles on the open ends of the domino layout. Domino ends must connect with a matching number of pips (dots on the domino), e.g. if the double six started the game:

     

    Dominoes

     

    • Any player who does not hold a tile in their hand with the correct number of pips must take a tile from the overturned dominoes.
    • Players score when they play a tile on the layout and the pips on all the open ends add up to equal a multiple of 5.
      • 1 point is earned if the total is 5
      • 2 points are earned if the total is 10
      • 3 points are earned if the total is 15 etc
    • Continue to play until one player gets rid of all of their tiles. That player is the winner!
    • If play is blocked and no player can add a tile to the layout then the game is over and the player who earned the most points through scoring for making multiples of 5 wins!

    Changing it up!

    • Change the multiples that score points.
    • Score points for totalling a specific amount on the ends of the lines, e.g. 12.

    Questions to consider:

    • If you don’t start with a double (and therefore only have 2 ‘branches’, how does this affect your chances of making a multiple of 5 on the ends?
    • How many different ways can the multiples of 5 be made using domino tiles? Are there more ways to make 20 than there are to make 15? Can you prove it?

     

    Cards

    Winner Takes the Difference

    2 Players

    You will need:

    • A pack of playing cards with the picture cards and jokers removed
    • A bowl of counters (or suitable alternative small objects for counting)

    How to play:

    • The card pack is placed face down as a deck.
    • Players each take a card and take that number of counters.

     

    Cards

     

    • Identify who has the most and what the difference is

     

    Dots

     

    Player 1 has the most and the difference between 8 and 3 is 5.

    • The player who picked the largest number keeps the difference between their counters and the other player’s counters (5 in the example above) and returns the other counters to the bowl.
    • The first player to 25 counters wins!

    For single players, take two cards, make the lines of counters and play as above. Count how many turns it takes to make the total of 25. Have another go and see if you can do it in less turns.

    Changing it up!

    • Keep the picture cards in the pack and give them values, e.g. Jack = 11, Queen = 12 and King = 13.
    • Each player starts on 50 points and adds their counters from there. The first player to reach 75 is the winner.
    • Each player starts on 25 points and subtracts the difference each time. The first player to reach 0 is the winner.

    Questions to consider:

    • What is the smallest possible difference you could have?
    • What is the largest possible difference you could have?
    • What are the possible odd / even differences? Which numbers could they be between?

    Risky

    2 players

    You will need:

    • A pack of playing cards with the jokers removed
    • Pen and paper

    How to play:

    • Shuffle the cards and place the deck face down.
    • Cards 2 to 10 are worth their face value; Jacks = 9; Queens = 11; King or Ace = no score for that turn
    • Player 1 turns over as many cards as they dare, adding to a running total as they go. If a King or Ace is turned, all cards must be returned to the bottom of the deck. If Player 1 stops before that happens, the total can be noted down, e.g. 3, 7, J (9), 1, 5, “stop” = 25 points
    • Player 2 takes their turn. 6, 9, Q (11), 5, 7, 8, 2, J (9), K = put all cards back – 0 points
    • Each time a player takes a turn, they start adding to their previous total. In this example, Player 1 would start from 25 and Player 2 from 0.
    • If a player then turns over a King or an Ace, they return only to the last recorded total rather than to 0 (unless no totals have yet been recorded – then it’s back to 0), e.g. for Player 1: 5, 1, 2, Ace = put these cards back – 0 points added – stay at 25
    • The first to reach 100 wins!

    For single players, can you reach 100 in less than 5 turns? Can you make it in 1 turn without turning over an Ace or a King? Is it possible?

    Changing it up!

    • Lower the target total for a game with more than 2 players.
    • Start from a different total, e.g. 300. First to 400 wins!
    • Start from 100 and subtract the value of each card. First to 0 wins!
    • Change the value of the Jack and Queen.
    • If you stop and your score is a multiple of 8 during the game, your score is doubled.
    • Prime numbers can be doubled before adding to the running total.

    Questions to consider:

    • What is the highest possible total you could reach if all of the Kings and Aces were at the bottom of the pack?
    • Does it become more or less risky to carry on turning over cards the further into the game you get? Why?

    Do Tweet us @hertsmaths to let us know which games you’ve been playing, especially if children have come up with their own rules.

    Further games to try can be found on our Herts for Learning YouTube channel where there are videos of the games being played and lots of ideas for adaptations.

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