Pencil And Paper Maths Games
Here are nine pencil and paper maths games which can be used in the classroom or would work well as part of a maths club. All of the games are for two players and can be played using just pencil and paper.
You can read about some of the benefits of learning mathematics through games in this
series of articles from NRICH.
The Game of 24
Both players secretly write down two whole numbers which are between 1 and 10.
The players then reveal their numbers and all four numbers are entered into the grid above.
Both players then work at the same time trying to reach 24. All four numbers must be used. Only addition, subtraction, multiplication, division, and brackets may be used. The winner is the first to reach 24.
Beware! Sometimes it will be easy to reach 24, sometimes it will be difficult and occasionally it is impossible. For example, it is impossible to make a total of 24 using 1,1,1,1.
Bulls and Cows
One pupil thinks of a four-digit number using the digits 0-9, the other pupil tries to guess the number. Repeated digits are allowed. Traditionally this game is called ‘Bulls and Cows’ but you could choose any two animals. It’s essentially a pencil and paper version of the classic board game of Mastermind, where a black scoring peg represents the correct answer in the correct position, and a white scoring peg represents a correct answer but in the wrong position.
In the example below we have used Horses and Donkeys.
Horses – The number of correct digits in the correct position.
Donkeys – The number of correct digits in an incorrect position.
If both pupils have a turn at guessing, then the winner is the pupil who uses the fewest guesses. In the example above the guesser has a had a lucky break, as it is hard to see how they could have moved from guess 4 to guess 5!
Fifteen
Write down the numbers 1-9 on a piece of paper and two boxes, one for each player.
Players take it in turns to choose a number, crossing it off as they choose it, and adding it to their box. Numbers can only be used once (so as soon as either player has used it, it can’t be chosen again).
The winner is the first one who can make a sum total of 15 with their numbers. (They don’t need to use all their numbers.)
An example of a winning total
If a pupil collects 1,6,9 then 6+9=15
(They don’t need to use the ‘1’ they have collected.)
There could also be a draw where neither pupil wins.
Nim
There are many variations of the game Nim. This version is sometimes called 1-2 Nim.
Draw a group of 7 circles. You could use counters instead of drawing.
Pupils take it in turns to take either 1 or 2 circles. (Crossing them out.)
The player who takes the last circle wins!
Questions to ask about Nim
• Would you prefer to be the 1st or 2nd player?
• What strategies work well?
• What happens if you use a different number of counters? (Try 8 and 9 counters.)
Squares
Draw a 6 X 6 grid on some squared paper.
One player chooses noughts (0) and one player chooses crosses (X).
Players take turns to add one of their symbols to an empty square.
The first player who can join up four of their symbols to form a square is the winner. There are many different sized squares to consider.
Hackenbush Game
This game was invented by the mathematician John Horton Conway.
Start off by drawing a picture which is made up of connected line segments and is attached to the ‘ground’ at one or more points. (The ground is represented by a dashed line here.)
Photo Credit: Wikipedia
Players take it in turn to erase one line segment. After each turn if there are parts of the drawing which are now unattached and floating in the air then they are erased too.
The winner is the last player to erase a line segment. (The ‘ground’ is never erased.)
Photo Credit: Wikipedia
Here is another starting picture for the game of Hackenbush. Encourage pupils to think of their own.
Sprouts
Here is another of John Horton Conway’s famous pencil and paper games.
Start off by drawing a number of dots. Three dot sprouts is a sensible number of dots to play with.
Decide who is going to go first.
The first player draws a line: The line must either connect two dots OR it can start at a dot and loop back round to join the same dot. The new line must not cross over any other lines.
The first player then adds a dot to the line they just drew.
Each dot can have a maximum of three lines coming out of it. After that it is ‘dead’ (and can’t be further connected to).
Take turns playing in this way.
The last player to make a move is the winner.
Below is a full game of Two Spot Sprouts.
Photo Credit: Wikipedia
101 You’re Out
This is a game attributed to Marilyn Burns, an American Maths Educationalist.
You will need standard six-sided dice for this game (as well as paper and pencils.)
Each player knows upfront that they will roll exactly six times. Players could take turns rolling, or they could roll simultaneously if they have one dice each.
When a player rolls, they can either add the number they roll to their total, or they can multiply the number they roll by 10 and add that number instead.
After 6 rolls, the winner is the player who is closest to 100 without going over. Getting a total of 100 after six rolls would be a perfect outcome! If both players go over 100 then nobody has won.
Example
Dots and Boxes
This is a classic Pencil and Paper game which some pupils might already be familiar with. Ask them whether they can think of any winning strategies.
Start off with a 5 X 5 grid of dots. (Pupils can just use the grid lines in their exercise books.) This is a sensible sized game board, but you could start with larger or smaller grids.
Players take turns adding a single horizontal or vertical line which joins two dots.
When a player completes a box, they get to claim that box by adding their initials to it. Importantly, they also get another go.
When the game board is full of claimed boxes, the winner is the player who has claimed the most boxes.
Below is an example game on a 3 x 3 game board. Player A is the winner.
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