# Playing Mathematically

```Playing
Mathematically
(Games for the Mathematics Classroom)
Jeff Trevaskis 2016
WHY GAMES?
Article by Jenni Way
http://nrich.maths.org/2489
We all know that children enjoy playing games. Experience tells us that games can be very
productive learning activities. But ...
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What should teachers say when asked to educationally justify the use of games in
mathematics lessons?
Are some games better than others?
What educational benefits are there to be gained from games?
This article supplies teachers with information that may be useful in better understanding
the nature of games and their role in teaching and learning mathematics.
What is a mathematical game?
When considering the use of games for teaching mathematics, educators should
distinguish between an 'activity' and a 'game'. Gough (1999) states that "A 'game' needs to
have two or more players, who take turns, each competing to achieve a 'winning' situation
of some kind, each able to exercise some choice about how to move at any time through
the playing". The key idea in this statement is that of 'choice'. In this sense, something like
Snakes and Ladders is NOT a game because winning relies totally on chance. The players
make no decisions, nor do that have to think further than counting. There is also no
interaction between players - nothing that one player does affects other players' turns in
any way.
Oldfield (1991) says that mathematical games are 'activities' which:
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involve a challenge, usually against one or more opponents; a
are governed by a set of rules and have a clear underlying structure;
normally have a distinct finishing point;
have specific mathematical cognitive objectives.
Benefits of Using Games
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.
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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
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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.
Few language barriers - an additional benefit becomes evident when children from nonenglish-speaking backgrounds are involved. The basic structures of some games are
common to many cultures, and the procedures of simple games can be quickly learned
through observation. Children who are reluctant to participate in other mathematical
activities because of language barriers will often join in a game, and so gain access to the
mathematical learning as well as engage in structured social interaction.
Hints for Successful Classroom Games
These tips come from Alridge & Badham (1993):
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Make sure the game matches the mathematical objective
Use games for specific purposes, not just time-fillers
Keep the number of players from two to four, so that turns come around quickly
The game should have enough of an element of chance so that it allows weaker
students to feel that they a chance of winning
Keep the game completion time short
Use five or six 'basic' game structures so the children become familiar with the rules
- vary the mathematics rather than the rules
Send an established game home with a child for homework
Invite children to create their own board games or variations of known games.
References
Aldridge, S. & Badham, V. (1993). Beyond just a game. Pamphlet Number 21 . Primary
Mathematics Association.
Davies, B. (1995). The role of games in mathematics. Square One . Vol.5. No. 2
Gough, J. (1999). Playing mathematical games: When is a game not a game? Australian
Primary Mathematics Classroom. Vol 4. No.2
Oldfield, B. (1991). Games in the learning of mathematics. Mathematics in Schools.
CONTENTS
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28
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Game
Addition War
AFL Simulation
Algebra Race
Animal Game
Battleships
Number
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Algebra
Space
Measure
Chance
Data
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Bears and Fish
Best Egg Box
Binomial War
Block or Switch
Bulls and Cows
Buzz
Cat and Mouse
Close to 50
Close to 100
Coin in the Square
Connect Three
Conway’s Army
Decimal Connect
Decimal Factors
Decimal Jigsaw
Decimal Line-up
Dice Cricket
Dicey Operations
Domino Squares
Equation War
Explain the Graph
Factor Game
Factor Grab
Factors and Multiples
Factor Triangles
FDP Bingo
First Down the Mountain
Fives a Crowd
Forbidden Words
Logic
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56
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Game
Four Digit Numbers
Fraction Wall Game
Great Expectation
Greater Than Less Than
Greedy Pig
Grid Fight
Hangman
Higher or Lower?
Horse Racing
I’m Finished
Keep your Car Going
Liars Dice
Loop Cards
Make a Moke
Make Ten
Maxi-miser
Multiples Path
Multiplication Hex
Multiplication Toss
Multo
Nim
Number Poker
1111 - 9999
One Hundred or Bust
Operation Challenge
Operation Golf
Operation Histogram
Penta Place
Place Value Dice
Polygon Capture
Pot Luck
Product Game
Quadratic Dominoes
Quad Concentration
Quadrilateral Go Fish
Quadrilateral Guess Who
Number
Algebra
Space
Measure
Chance
Data
Logic
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Game
71 Risk your Maths Skills
72 Roll a Product
73 Rolling Decimals
74 Salute the King
75 Santorini
76 Set Game
77 Shapes & Solids Bingo
78 Stop or Dare
79 Strive for the Highest
80 Sum, Difference, Product
81 Take Your Places
82 Target 100
83 Target Practice
84 Ten Thousand
85 The Decimal Game
86 The Hike
87 Thirty One
88 Tic-Tac-Toe
89 Three Cubes
90 Three Throw
91 Top Trumps
92 Total Control Bingo
93 Tricky Dice
94 Twenty Express
95 Twenty Seven
96 U Win Again
97 Ups and Downs
98 Visualising Shapes
99 Walk the Plank
100 What’s in the Bag?
101 Win at the Fair
102
103
104
105
106
107
Number
Algebra
Space
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Measure
Chance
Data
Logic
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ADDITION WAR
1. Remove the Jacks, Queens and Kings from the Deck.
2. In Addition War, Aces count as one, the rest of the cards are equal to their face values.
3. Deal an even number of cards to each player at the table. If there are three players
playing the game, discard the last card from the deck.
4. Each player flips over 2 cards, and calls out their total. The player with the highest total
adds all cards to the bottom of their deck.
5. If there is a tie between the highest totals, a WAR occurs.
6. WAR: Each player places three cards face down and flips over two additional cards face
up. The player with the higher face-up total wins the war, and takes all the cards.
7. If there is another tie, repeat turning over two more cards.
8. Continue playing rounds of Addition War until one player has all the cards. That player
is the winner.
9. If a player has not got enough cards to go to WAR, they lose.
VARIATIONS:
Advanced Addition War
Turn up 3 (or 4) cards for each battle and add them up.
Subtraction War
Everyone turns up 2 cards and subtracts them. The greatest difference wins the battle.
Product War
Turn over 2 cards and multiply.
Advanced Product War
Turn up 3 (or 4) cards and multiply.
Fraction War
Everyone turn over 2 cards and make a fraction, using the smaller card as the numerator. The highest
fraction wins the battle.
Improper Fraction War
Turn over 2 cards and make a fraction, using the larger card as the numerator. The highest fraction wins the
battle.
Integer Addition War
Black cards are positive numbers; red cards are negative. The greatest sum wins. Remember that -2 are
greater than -7.
Integer Product War
Black cards are positive numbers; red cards are negative. The greatest product wins. Remember that two
negative numbers make a positive product.
AFL SIMULATION
Players:
2 players
Equipment:
A standard 6 sided dice, scoresheet
Play:
1.
Pick an AFL team to play for and write it on the scoresheet.
2.
Take turns to roll the die twice. First roll shows goals for that quarter.
Second roll shows behinds for that quarter. Then calculate the points,
by multiplying the goals by six and adding behinds.
3.
Play a total of six games.
Extensions:
1.
Gather enough class data for a whole season.
2.
Compare your data with the data of a real AFL season. For example
use stem and leaf plots, and/or box plots.
3.
Would using an 8 sided or 10 sided die give a better result?
Team:
Team:
Goals
Behinds
Points
st
1 Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
Behinds
Points
Goals
Behinds
Points
Goals
Behinds
Points
Goals
Behinds
Points
Goals
Behinds
Points
Goals
Behinds
Points
1 Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
Team:
Team:
Goals
Behinds
Points
st
st
1 Qtr
nd
2 Qtr
rd
3 Qtr
th
4 Qtr
Total Score
1 Qtr
nd
2 Qtr
rd
3 Qtr
th
4 Qtr
Total Score
Team:
Team:
Goals
Behinds
Points
1st Qtr
2nd Qtr
3rd Qtr
th
4 Qtr
Total Score
1st Qtr
2nd Qtr
3rd Qtr
th
4 Qtr
Total Score
Team:
Team:
Goals
Behinds
Points
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
Team:
Team:
Goals
Behinds
Points
1st Qtr
2nd Qtr
rd
3 Qtr
th
4 Qtr
Total Score
1st Qtr
2nd Qtr
rd
3 Qtr
th
4 Qtr
Total Score
Team:
Team:
Goals
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
Goals
st
Behinds
Points
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
Total Score
ALGEBRA RACE
1.
Students place their counters on the start and roll the die separately.
2.
They move forward the number of spaces indicated on the die.
3.
Next turn they roll the die and substitute that number into the
expression to find out how many spaces to move. For example roll 5 on
square “3b + 2”. So move 3 x 5 + 2 = 17 spaces.
4.
Play first to make it 10, 15 or 20 times around the board.
5.
Students are expected to record their results – number rolled and
evaluation of the expression.
ANIMAL GAME
The four animals in the race are the Camel, who steadily plods
around the course, so either moves 2 or 3 paces at a time; the Cat
who is nosey and likes to look at the sights, so either sits still, 0
paces, or moves 1, 2, 3, 4, or 5 paces; the Lion who is confident
and either snoozes, 0 paces, or runs 5 paces; and the Horse who
is rather scatty and so sometimes runs backwards, -1 pace, and
sometimes forwards 6 paces. Who do you think will win?
EQUIPMENT:
Animal Game Board, 4 counters, one standard die.
BASIC RULES:
Each player chooses an animal and takes it in turn to roll a die and move
around the game board. Whoever crosses the finish line first is the winner.
Each animal moves as follows:
Camel: If the score is even, move 2 paces. If the score is odd, move 3 paces.
Cat: Subtract 1 from the number shown on the die and move that number of
paces.
Lion: If the score is even, stay still. If the score is odd, move 5 paces.
Horse: If the score is even, move 6 paces forward. If the score is odd, move
1 pace backwards.
BATTLESHIPS
Draw 5 different quadrilaterals in this grid.
They can be in any direction. Each
quadrilateral is a battleship.
Colour each ship a different colour and
label the four points of each battleship with
their co-ordinates.
If your partner guesses all four points on a
battleship, you must tell him what colour it
is.
This grid is for you to record your hits and
misses on your partner's grid. If you
successfully sink a battleship, your partner
will tell you what colour it is.
The first person to sink all the opposing
player's battleships is the winner!
BEARS AND FISH
It is winter in the arctic. An Eskimo comes across the frozen sea and
makes holes in the ice to fish through. After a few hours of fishing he
decides that he has caught enough fish and departs. Slowly the polar
bears emerge. Wary of each other they circle the abandoned fishing
holes to explore the potential for a meal.
We roll 5 dice….. and you get to figure out how many bears and how many
fish there are! Here are some examples:
We have 2 bears and 23 fish.
We have 6 bears and 16 fish.
We have 12 bears and 17 fish.
Polar Bears occur in pairs,
By holes in the ice they gather round,
How many bears can there be?
How many fish under the sea?
BEST EGG BOX
A simple probability game, that is easy to play. To analyse which is the
best egg box to choose, a lattice diagram may be used.
EQUIPMENT:
3 egg cartons as shown, 2 standard dice.
BASIC RULES:
Three half-dozen egg boxes are numbered as
below.
Working in groups of three, each player is allocated an egg box. Two dice
are rolled and their scores multiplied together. A counter is dropped into the
hole with that number. The winner is the player whose egg box gets all the
numbers covered first.
RESOURCES:
[Websites]
http://www.nzmaths.co.nz/Statistics/Probability/FairGames.aspx
BINOMIAL WAR
PLAYERS:
2
EQUIPMENT:
Deck of cards (Ace = 1) – 10, Jack = 11, Queen = 12, King = 0, one
ten sided die, paper and pen
BASIC RULES:
1.
Each player draws four cards and places them face up.
2.
Each player forms two linear binomials from their four cards.
Red cards are positive and black cards are negative.
3.
Each player calculates their sum.
4.
The die is rolled and that number is substituted into the
polynomials. The largest value wins a point.
5.
Play continues for a set period of time.
EXAMPLE:
Player One
Player Two
(5t + 4) + (3t + 5)
(-3a – 12) + (10a – 9)
= 8t + 9
= 7a – 21
ROLL 8
= 8(8) + 9
= 7(8) – 21
= 64 + 9
= 56 - 21
= 73
= 35
Player One wins this round
VARIATION:
Multiply binomials (expand brackets) and substitute dice roll.
BLOCK OR SWITCH
1. A simple card game which is best played with two players.
2. A single pack of cards is required plus 2 markers.
3. Remove the court cards (Jacks, Queens and Kings) leaving 40 cards.
4. Players sit opposite each other.
5. Cut the pack, loser deals and winner goes first. A 6 x 6 grid of cards is
dealt as shown in the picture below.
6. The yellow marker plays first. They may move to any card in the same row
or column and take that card. The highest scoring card possible is the 8H
which yellow decides to take.
7. Now blue plays. He/she decides to take either the 10Hearts for a 10 point
score.
8. Play continues in turn, but players are NOT allowed to jump over each
other in the same column or row. And so the opportunity to block your
opponent arises.
9. After all cards are taken, the cards are added up. The highest total is the
winner.
*** Original Game designed by Jeff Trevaskis ***
BULLS & COWS
Bulls and Cows is a great game to encourage logical thinking. It is
an easy game to play with the whole class on the whiteboard or
between students. Minimal equipment is needed.
BASIC RULES:
Think of a 3 digit number e.g. 419. Students try a guess – give them feed
back according to how many numbers are bulls (in the correct position) or
cows (in the wrong place value position). Here is a sample game:
179 1 bull, 1 cow
915 1b, 1c
791 2c
819 2b
419 3b
Modify the game for ability levels – 2 or 4 digits, repeated digits. Set targets to
achieve – 6 guesses. Provide example games such as above with the last
line deleted.
RESOURCES:
[Software] Bulls&Cows.xls
BUZZ
1. Sit in a circle. Choose a leader. The leader names any whole number from
3 – 9. This number is the BUZZ number. The leader may also choose a
STOP number.
2. The player to the left of the leader begins by saying “one”. Play continues
clockwise – each player saying either the next whole number or “BUZZ”.
A player must say “BUZZ” if the number is a multiple of the BUZZ number.
Example: The BUZZ number is 3. Play should proceed as follows:
1, 2, BUZZ, 4, 5, BUZZ, 7, 8, BUZZ, 10, 11, etc.
3. If a player makes an error, the next player must start again with 1.
4. Play continues until the STOP number is reached.
5. For the next round the player to the right of the leader becomes the new
leader.
BIZZ BUZZ
Bizz-Buzz is played like Buzz except the leader names two numbers; a BIZZ
number and a BUZZ number.
Example: The BIZZ number is 3 and the BUZZ number is 4. Play
should proceed as follows:
1, 2, BIZZ, BUZZ, 5, BIZZ, 7, BUZZ, BIZZ, 10, 11, BIZZ-BUZZ, 13, etc.
CAT & MOUSE
EQUIPMENT:
Cat and Mouse Game Board, one counter, one standard die.
BASIC RULES:
Put the counter in the room where the mouse is. Roll the
die. The mouse moves to the next room by the following
rules:
Move in the direction O if you roll an odd number.
Move in the direction E if you roll an even number.
Play 10 games and count your wins and losses. Is this a
fair game?
CLOSE TO 50
Rules of the game:
Each pair has 3 dice with the digits 0 – 9 on them (or one dice that they roll 3 times).
Player 1 goes first and rolls all three dice at the same time. Put the three dice in a row in
any order you want, with a decimal point after the first. If, for example, you had a 4, 7 and
a 9 you could have any of the following numbers,
4.79
9.47
4.97
9.74
7.94
7.49
Write the number down in your table, then round it to 1dp and put this number in the next
column.
Player 2 then does the same in their table. Player 1 then takes another turn and adds to
the answer from the previous one. Follow the table below. This could be an example:
Number Rounded to 1 dp
Sum
Current Total
9.47
9.5
0 + 9.5
9.5
2.45
2.5
9.5 + 2.5 = 12
12
6.72
6.7
12 + 6.7 = 18.7
18.7
3.56
3.6
18.7 + 3.6 = 22.3
22.3
After both players have had 10 goes, the winner is the player whose total is closest to 50.
Note – the game can easily be adapted for rounding to 2 decimal places by rolling the dice 4
times.
CLOSE TO 50
- Playing Tables -
Turn
Dice
Rounded
Sum
Current Total
Dice
Rounded
Sum
Current Total
1
2
3
4
5
6
7
8
9
10
Turn
1
2
3
4
5
6
7
8
9
10
CLOSE TO 100
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2 or 3 Players
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Deal out six numeral cards to each player
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Use any four cards to make two numbers. For example, a 6 and 5 could make
either a 56 or 65. Try to make the numbers that, when added; give you a total close
to 100.
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Write these numbers and their total on the Close to 100 score sheet. Your score is
the difference between your score and 100.
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Put the cards used in discard pile. Keep unused cards and get new cards to have 6
cards in your hand. Make more cards that come close to 100.
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When you run out of cards, mix up the discard pile and use them again.
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Five rounds make one game. Total your scores for the five rounds. Lowest score
wins!
COIN IN THE SQUARE
1. Draw 36mm squares on a large piece of paper.
2. Throw a 5¢ coin onto the grid. You win if the coin does not touch a line.
3. Predict how many times you would win out of 100 throws.
4. Throw the coin 100 times and record your results.
5. If you were a carnival operator, what is a reasonable prize to offer for each
winning throw?
6. What if the coin used was 10¢, 20¢, 50¢, \$1, \$2 ?
Extension:
Calculate the exact chance of winning this game.
Hint: Where must the centre of the coin finish to be in a winning position?
CONNECT THREE
PLAYERS:
2
EQUIPMENT:
Different coloured counters – one colour for each player, two six-sided
dice with numbers marked as shown below.
BASIC RULES:
1.
This is a mathematical version of noughts and crosses that
uses differently numbered dice (one with the numbers
1, 2, 3, −4, −5, −6 and the other with −1, −2, −3, 4, 5, 6).
2.
To place your counter, roll the dice and decide whether to add
or subtract the numbers.
3.
For example, three ways of landing on 4 are:
5−1=4
QUESTIONS:
2−(−2)=4
(−2)−(−6)=4
1.
Can you work out the number of different ways of achieving
each of the different totals?
2.
Can these results help you work out a strategy for
improving your chances of winning the game?
-12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11 12
CONWAY’S ARMY
There are two stages to this challenge. First position some counters below a fixed
horizontal line in a square grid. Here is an example:
The aim of the second stage is to advance one of the counters as far as possible beyond
the horizontal line. The counters are only allowed to move in a certain way. They can only
move by jumping horizontally or vertically over a neighbouring counter. If one counter
jumps over another, then the static counter underneath the jump is removed. Diagonal
jumps are disallowed. Also, the counters cannot jump over two neighbours.
Given an unlimited supply of counters, and freedom to position the counters below
the horizontal line in any way that you choose, how far beyond the horizontal line
can the counters be advanced?
CONWAY’S ARMY GRID
DECIMAL CONNECT
PLAYERS:
2 to 3
EQUIPMENT:
Different coloured counters – one colour for each player, game-board,
calculator.
BASIC RULES:
1.
Take turns to select numbers.
2.
Choose two numbers, one from the circle and one from the
rectangle and multiply them to give a number on the grid.
3.
If the calculation is accepted as correct by the other players,
cover the grid number with a counter. In case of disagreement,
use a calculator to check the answer.
4.
The winner is the first to get four counters in a line, horizontally,
vertically or diagonally to score a point.
DECIMAL FACTORS
1. Team one picks two factors by marking them with paperclips.
2. Place an “X” on their product on the grid.
3. Team two then moves one paper clip to a new factor and circles
the new product.
4. Alternate moves, one paper clip at a time, until one team has
four marks in a row.
1.2
5
.88
.011
.003
.25
100
.008
.09
.005
.006
6
3.2
.24
.48
.04
.64
16
2.4
.4
2
4.4
.15
1.21
.55
.36
.18
.3
.0001
.33
11
40
.1
8
3
.66
.3
4
.5
.01 .6
.8
10
1.1
DECIMAL JIGSAW
1.
Cut carefully along the thick lines.
2.
Turn the pieces face down on the table.
3.
Turn the pieces over one at a time and try to make the grid again.
DECIMAL LINE UP
Players:
2 players OR 2 teams
Equipment:
A deck of cards with the Tens, Queens and Kings removed.
Play:
1.
Each player or team makes a path with 10 spaces, with a
beginning and end.
2.
On your turn, flip over a card. If it’s red, flip over another
card. If it’s red, flip over another card. But you never flip more
than three. If you run out of cards, shuffle up the used cards.
3.
Arrange those cards to make a decimal number. Jacks are
the zeros. The smallest number you can make is .000, and the
largest is .999. Say your number.
4.
Fill in your decimal number somewhere on the path. But it
can’t go before a smaller number or after a bigger
number. Your path has to start small and end big. If there’s
no place to fill in your number, you don’t.
5.
Winner is the first person to completely fill in their path, with all
the numbers in order.
Examples:
1. J ♥, 3 ♣. You can make .03 or .30.
2. 5 ♥ hearts, so you flip 2 ♦, so you flip 7 ♥ hearts. (You stop because you
can’t have more than three.) You can make one of .275, .275, .527, .572,
.725 or .752. Which you want depends on your path.
Variations:
1. Simpler: Play where you always flip over 2 or 3 cards.
2. Play cooperatively. Two players work together to fill in one path.
3. More complex: Play with 10s, which fill in 2 places. So 10 ♦, 5 ♠ can be
.105 or .510.
4. More complex: Play without the three card limit. You could hit a 10 digit
long decimal or longer! (Pretty unlikely, but still…)
5. Make 12 space paths.
DICE CRICKET
EQUIPMENT:
2 different coloured dice, which score as
follows:
BATSMAN'S DIE
BOWLER'S DIE
1 = HOWZAT
2 = 2 Runs
3 = 3 Runs
4 = 4 Runs
5 = 1 Run
6 = RUN OUT
1 = NO BALL
2 = CAUGHT
3=LBW
4 = STUMPED
5 = BOWLED
6 = NOT OUT
BASIC RULES:
The two players will select who will bat first by tossing a coin.
The batsman rolls the Batsman's die and the Bowler, acting as scorer,
notes down the result of the roll. Play continues thus until the batsman
rolls HOWZAT or RUN OUT. For HOWZAT the Bowler rolls the
Bowler's die to decide the result of the appeal.
Play continues until the agreed number of batsman, usually five, have all
had an innings. The player roles are reversed with the winner being the
player who scores the most runs.
DICEY OPERATIONS
Find a partner and a 0-9 dice.
Take turns to throw the dice and decide which of your cells to fill. This can be done in two ways:
either fill in each cell as you throw the dice or collect all your numbers and then decide where to
place them. Score 1 point for a win. The first person to reach 10 wins the game.
Game 1
Game 4
Each of you uses an addition grid like this:
Each of you draws a multiplication grid like
this:
Throw the dice nine times each until all the
cells are full. Whoever has the sum closest to
1000 wins.
Throw the dice five times each until all the
cells are full. Whoever has the product
closest to 10000 wins.
Game 5
Each of you draws a division grid like this:
Game 2
Throw the dice eight times each until all the
cells are full. Whoever has the difference
closest to 1000 wins.
Throw the dice five times each until all the
cells are full. Whoever has the answer closest
to 1000 wins.
Game 6
Game 3
Each of you draws a division grid like this:
Each of you draws a multiplication grid like
this:
Throw the dice six times each until all the
cells are full. Whoever has the answer closest
to 100 wins.
Throw the dice four times each until all the
cells are full. Whoever has the product
closest to 1000 wins.
DOMINO SQUARES
*** Original Game designed by Jeff Trevaskis ***
Rules:
1. Use a standard “double six” set of dominos.
2. The caller picks one domino at a time, randomly.
3. The players place each domino horizontally or vertically in their grid.
4. Play continues until 9 dominos are called out, giving the players one
chance to discard.
5. Players calculate their total score by summing the 8 products formed in
each row and column.
6. The player/s with the largest total is the winner.
Worksheet:
1. What is the product of any number times zero?
2. What is the smallest total possible?
3. What is the largest total score possible?
4. What strategies would you use to win this game?
5. How many dominos are there in a double six set?
6. What is the sum of all the dots on a double six set?
Domino Squares
After you have placed all 9 dominos:
1.
Calculate the product of each row and column
2. Calculate the total of all the products.
The winner is the person with the highest total.
DISCARD
TOTAL
Domino Squares
After you have placed all 9 dominos:
1.
Calculate the product of each row and column
2.
Calculate the total of all the products.
The winner is the person with the highest total.
DISCARD
TOTAL
Domino Squares
After you have placed all 9 dominos:
1.
Calculate the product of each row and column
2.
Calculate the total of all the products.
The winner is the person with the highest total.
DISCARD
TOTAL
EQUATION WAR
PLAYERS:
2 to 4
EQUIPMENT:
Two, three, or four ten-sided dice, game-board, counters.
BASIC RULES:
1.
The teacher or players choose which equation to work with.
2.
Roll the ten sided dice and create a linear equation.
3.
After solving their equations, players compare answers.
4.
The player with the largest result wins a point.
5.
Play continues for a set period of time.
EXAMPLE:
Players choose game-board .
 = x + 
Player One rolls:
Player Two rolls:
9, 5, 4
8, 2, 4
9 = 5x + 4
8 = 2x + 4
5 = 5x
4 = 2x
1=x
2=x
Player two wins and scores one point.
EQUATION WAR GAMEBOARDS

x +  = 

x +  = 

x = 

x = 

x+=

x+=
 x +  = x +   x +  = x + 
𝑥
𝑥
=


 = x + 

 = x + 

x +  = x 
x +  = x



=
EXPLAIN THE GRAPH
PLAYERS:
2 to 4
EQUIPMENT:
Two ten-sided dice, graph paper, pencil.
BASIC RULES:
1.
Players take turns rolling the dice for six rounds.
2.
After each roll, ordered pairs are plotted on the graph paper.
3.
The goal is to explain the graph by choosing appropriate labels
for the axes as well as an explanation for the shape of the
graph.
EXAMPLE:
Player 1 rolls the dice six times and has the following ordered pairs:
(9, 5), (6, 8), (7, 4), (1, 5), (5, 8), (0, 3)
Player 1 chooses Age for the horizontal axis and weight for the
vertical axis with the following reasoning:
“At 0 years (birth) the dog weighed 3 kg and its weight increased until
it was 5 years old and it stayed at 8 kg for one year. The dog then
became very ill and lost 4 kg in the next year and finally died after nine
years at a weight of 5 kg.”
FACTOR GAME
Object
To be the player with the highest value of circled numbers at the completion of the game.
How to Play
1. Player 1 chooses a number (circles it) on ”The Factor Game” game board.
2. Player 2 circles all the proper factors of the number player 1 circled. (Proper factors are
any number that divides in the number evenly, but not the number itself.)
3. A number on the game board may only be circled once.
4. Player 2 then circles a new number on the game board and Player 1 circles its proper
factors.
5. Players continue taking turns until all numbers have been circled which still have un-circled
factors remaining.
Rules
1. Each player takes turns going first.
2. No number may be circled more than once.
3. If a player circles a number that has no un-circled factors, that player loses their turn and
scores no points for the number they just circled.
FACTOR GAME WORKSHEET
Complete the following table with all the first moves possible.
First Move
Proper Factors
My Score
Opponent’s Score
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
none
1
1
1,2
lose a turn
2
3
4
0
1
1
3
1. Which number seems to be the best choice for your first turn?
Explain.
______________________________________________________
______________________________________________________
______________________________________________________
2. Which number (or numbers) seems to be the worst choice for your
first turn? Explain.
______________________________________________________
______________________________________________________
______________________________________________________
3. Look for any patterns in your list. Describe any interesting patterns
you find.
______________________________________________________
______________________________________________________
4. About how many turns did it take to end a game? _______________
Is there a way to figure out the most turns possible regardless of score?
_________
How?
______________________________________________________
______________________________________________________
5. Write a strategy for playing the factor game. Is there a way to play
the game so you can win more times than you lose? (Always going first
does not count)
______________________________________________________
______________________________________________________
_____________________________________________________
FACTOR GRAB
Materials: One set of Factor Cards
2 Players
Directions:
1.
Players spread out Factor Cards face up on the table in any order.
2.
Find My Factors Cards are shuffled and kept in a pile, face down.
3.
The top card in the pile is turned over.
4.
The players grab any cards on the table that are factors of the card which was turned
over.
5.
Players may take a factor only once in a round (i.e. if the Find My Factors Card is 28, a
player can grab one only of each of the following cards if available: 1,2,4,7,14 and 28)
6.
Each player checks the other players chosen cards and may challenge any incorrect
selections.
7.
If the player is right about the other's wrong selection, that player may take any two
of the opponent's cards.
8.
Players put grabbed cards aside, as these are used to keep score.
9.
The next Find My Factors Card is turned over and players again grab factor cards
from the remaining cards on the table
10.
Play continues until all Factor Cards have been grabbed
11.
The player with the most cards is the winner
Alternate version:
Students take turns selecting the Factor Cards instead of racing to do it together. Once a
player has found all the factors he/she can, the other player may look to see if any were
missed and grab them.
Factor Card
Factor Card
Factor Card
1
1
1
Factor Card
Factor Card
Factor Card
2
2
3
Factor Card
Factor Card
Factor Card
3
4
4
Factor Card
Factor Card
Factor Card
5
5
6
Factor Card
Factor Card
Factor Card
1
1
1
Factor Card
Factor Card
Factor Card
2
2
2
Factor Card
Factor Card
Factor Card
5
7
8
Factor Card
Factor Card
Factor Card
8
9
9
Factor Card
Factor Card
Factor Card
11 11 12
Factor Card
Factor Card
Factor Card
22 2
3
Factor Card
Factor Card
Factor Card
3 13 14
Factor Card
Factor Card
Factor Card
9 27 27
Factor Card
Factor Card
Factor Card
1
2
3
Factor Card
Factor Card
Factor Card
8
9 10
Factor Card
Factor Card
Factor Card
10 6 10
Factor Card
Factor Card
Factor Card
10 5
2
Factor Card
Factor Card
Factor Card
4 21 2
Factor Card
Factor Card
Factor Card
16 16 16
Factor Card
Factor Card
Factor Card
4 22 22
Factor Card
Factor Card
Factor Card
25 36 25
Factor Card
Factor Card
Factor Card
20 2
3
Factor Card
Factor Card
Factor Card
4
6
7
Factor Card
Factor Card
Factor Card
15 3
3
Factor Card
Factor Card
Factor Card
2 13 8
Find My Factors
Find My Factors
Find My Factors
25 36 15
Find My Factors
Find My Factors
Find My Factors
20 60 24
Find My Factors
Find My Factors
Find My Factors
44 54 80
Find My Factors
Find My Factors
Find My Factors
16 42 66
Find My Factors
Find My Factors
Find My Factors
72 27 39
Find My Factors
Find My Factors
Find My Factors
91 63 12
Find My Factors
Find My Factors
Find My Factors
90 64 50
Find My Factors
Find My Factors
Find My Factors
35 21 13
FACTORS and MULTIPLES
This is a game for two players. Play on the 100 square grid below.
The first player chooses a positive even number that is less than 50, and crosses it out on the
grid.
The second player chooses a number to cross out. The number must be a factor or multi ple of the
first number.
Players continue to take it in turns to cross out numbers, at each stage choosing a number that is
a factor or multiple of the number just crossed out by the other player.
The first person who is unable to cross out a number lose s.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
FACTOR TRIANGLES A
FACTOR TRIANGLES B
FDP BINGO
1. Direct students to outline a four-by-four section anywhere on the Bingo card.
2. Call out either a fraction, decimal, or percent and keep track of your calls on
the Number Recording Sheet. Write down the specific number that you called in
order to verify the winner or just use check marks to know how many of each
value have been called.
3. Students may circle the number you called out or an equivalent fraction,
decimal, or percent.
4. Students may circle a maximum of one number each time a number is called
out. For example, if you call out 3/4 and a student has both .75 and 75% in his
section, he may only circle one.
5. The winner is the first student to get four numbers in a row (vertically,
horizontally, or diagonally).
6. Have the winner verify his numbers with you. You may want to offer a prize
to the winner.
7. There are 300 numbers on the game board, and only 16 required for each
game, so the Bingo Card should last for many games. Have students keep it to
use again at a later date.
8. You may also decide to create longer Bingo games by directing students to
choose a five-by-five (or larger) game board.
FDP BINGO
Record Sheet
FDP BINGO
FIRST DOWN THE MOUNTAIN
Ref: Maths 300 Task 4
FIVES A CROWD (1)
Group Names _____________________________________________________
State
Population
Area (square km)
Population Density
Estimate
Population Density
Population Density
Estimate
(No calculators)
Population Density
Calculation
(Calculators)
VICTORIA
 5 Minutes to pick 5 States!
 NO calculators!
 Fill in first four columns only.
DATA TABLE
State
Population
2
Area (km )
How To Score:
5 Points for each country listed in the
correct place
3 Points for each country off by 1 place
1 Point for countries off by 2 places
0 Points for countries off by 3 or more
places
SCORING CHART
Actual Order
Our List
Points
1.
1.
1.
2.
2.
2.
3.
3.
3.
4.
4.
4.
5.
5.
5.
Total Score
FIVES A CROWD (2)
Group Names _____________________________________________________
Country
Population
Area (square km)
Population Density
Estimate
Population Density
Population Density
Estimate
(No calculators)
Population Density
Calculation
(Calculators)
AUSTRALIA
 5 Minutes to pick 5 Countries!
 NO calculators!
 Fill in first four columns only.
DATA TABLE
Country
Population
Area (km2)
SCORING CHART
Actual Order
Our List
Points
1.
1.
1.
2.
2.
2.
3.
3.
3.
4.
4.
4.
5.
5.
5.
Total Score
FORBIDDEN WORDS
PLAYERS:
Whole class.
EQUIPMENT:
Forbidden word cards.
BASIC RULES:
1.
A student is given a card and has to describe an object, idea or
phrase without using certain forbidden words.
2.
The other students have to try and guess the word.
EXAMPLE:
VARIATION:
Jordan:
It’s a shape with straight sides…
Rachel:
A triangle?
Jordan:
….and it has more than three sides.
Rachel:
A pentagon?
Jordan:
It’s a quadrilateral and…
Rachel:
A square?
Jordan:
…the sides might be different lengths, but everything is
parallel.
Rachel:
A rectangle!
Supply a list of key words and ask students to make their own cards.
FOUR DIGIT NUMBERS
1.
Decide who is player A and who is player B. You each have a white box
with twenty digits.
2.
Decide in private how to arrange your twenty digits to make four-digit
numbers that fit the targets. You may use each digit only once and need
to set a time limit of 3 minutes.
3.
When the 3 minutes is up, write your numbers in the white boxes beside
the targets.
4.
Agree on who is closest to each target. Decide who wins!
FRACTION WALL GAME
1.
Each group of students needs two 10-sided dice.
2.
Each student takes it in turn to roll 2 dice.
3.
Form a proper fraction (less than or equal to 1) with the numbers thrown. For example if 3 and
5 are showing, form the fraction 3/5 and not 5/3. The student can colour in the corresponding
length on the fraction wall. The winner is the first person with three completely shaded fraction
wall strips (eg. the eighths, the quarters and the fifths).



First version: Allow students to shade only the fraction shown. So that if the fraction is 3/5,
only a section of the fifths strip can be shaded.
Second version: Allow students to shade any fraction equivalent to the one shown. So that if
the fraction is 3/5, 6 of the parts of the tenths strip can be shaded.
Third version: Allow students to shade the fraction shown in total across strips. So that if the
fraction is 3/5, 2 fifths can be shaded, along with 2 tenths.
1
1
2
1
2
1
3
1
3
1
4
1
4
1
5
1
8
1
8
1
10
1
8
1
9
1
10
1
9
1
10
1
6
1
7
1
8
1
5
1
6
1
7
1
9
1
5
1
6
1
7
1
4
1
5
1
6
1
7
1
10
1
4
1
5
1
6
1
9
1
3
1
7
1
8
1
9
1
10
1
10
1
7
1
8
1
9
1
7
1
8
1
9
1
10
1
6
1
8
1
9
1
10
1
10
1
9
1
10
What I Rolled
What I Shaded
What I Rolled
What I Shaded
GREAT EXPECTATION
The teacher has a set of six cards numbered 1 to 6 (or 1 to 9). They are placed face
down on the teacher’s desk so that the teacher can pick up one at random. Students
copy the diagram (below) showing the positioning of digits in their answer. As the
teacher selects a digit the students have to choose in which cell they will write it. They
cannot change their mind after the next digit has been called out.
Variation:
Draws may be made with or without replacement.
Game 1
The teacher draws 4 cards.
Students are successful if: The two digit number on the left should be greater than the
two digit number on the right. If the student is successful he/she scores the two digit
number on the right.
Game 2
The teacher draws 6 cards.
Game 3
The teacher draws 6 cards.
Game 4
The cards are numbered 1 to 9.
The objective is to get the largest possible value for this expression (or the smallest!)
Play online at:
http://www.transum.org/Software/Great_Expectation/default.asp
GREATER THAN > LESS THAN
1. Dominoes may be used to represent numbers. For example the domino
shown may represent 46 or 64 depending on which direction it is facing.
2. Each player is dealt three dominoes. The rest are placed face down in the
centre of the table.
3. Each player selects one domino from his/her set to place on the table. The
player placing the greatest number wins the round and scores one point.
4. Players replenish their sets by taking a new domino from the pile.
5. Continue playing until all dominoes are gone. The winner is the player with
the most points.
Variations:
1. Aim for the smallest number, rather than the largest.
2. Turn one domino up in the middle of the table and take turns placing
dominoes to the right or left of the centre domino depending on whether it is
greater or smaller than the centre domino. The winner is the last player to be
able to place a domino.
11
16
25
44
65
GREEDY PIG
Players:
2 or whole class
Equipment:
One standard dice and a score sheet.
Play:
1.
On each turn, a player rolls a die as many times as they wish, totalling the
score of the rolls until the player decides to end the turn and pass the die
to his or her opponent.
2.
However, if the player rolls a 1, they immediately lose all points
accumulated during that turn, and the die passes to the other player.
3.
The first player to reach 100 points is the winner.
Whole Class Game:
1.
At the beginning of a turn, all players stand up. One player directs play
and rolls a single die for everyone.
2.
A player holds by sitting down.
3.
At the end of each round, players call out their new scores.
4.
The winner/s are the highest scores after 5 rounds.
GREEDY PIG SCORESHEET
1.
2.
3.
4.
5.
TOTAL
GREEDY PIG SCORESHEET
1.
2.
3.
4.
5.
TOTAL
GREEDY PIG SCORESHEET
1.
2.
3.
4.
5.
TOTAL
GREEDY PIG SCORESHEET
1.
2.
3.
4.
5.
TOTAL
GRID FIGHT
A game for 2 players or teams
Objectives: multiplying integers, strategy, area of rectangles.
Materials: game sheet (see above), deck of cards with face cards removed.
Red cards are negative, black cards are positive, Ace = 1.
Goal: score the most completed rows (like Tetris).
Game play: Deal each team 3 cards. They choose one card to play. They
reveal their cards at the same time. If the product is positive, the positive team
fills in the rectangle. (For example, black 5 and black 3, they fill in a 3 x 5
rectangle) If the product is negative, the negative team fills in the rectangle. (For
example, red 7 and black 8) Each team draws a card to get back to 3. A game
is 12 rounds long.
Winner is the team with the most rows filled in.
This game is played like the word version but a mathematical equation is used
instead.
Draw one dash for every digit and symbol in the equation. This can be adjusted
to the ability level or the students.
e.g. _ _ _ _ _ _ (9 + 6 = 15) _ _ _ _ _ _ _ _ (87 – 25 = 62)
For more complex equations, players could be permitted to use a calculator.
e.g. _ _ _ _ _ _ _ _ _ _ 56 x 27 = 1512
Players take turns to say a digit or a symbol while the recorder places any
correct digits or symbols in the equation.
The recorder is the winner if the Hangman is completed or the player who gives
the final digit or symbol is the winner.
HIGHER OR LOWER?
EQUIPMENT:


A standard pack of cards (only one suit used initially) OR
Higher-Lower” flash object.
BASIC RULES:
1. Each player starts with say 10 chips.
2. Turn up the first card.
3. The player may bet any number of his chips that the next card is higher
or lower.
4. The next card is now turned up.
5. Repeat steps 3 and 4 until 9 cards have been turned over.
6. Repeat for other players. Most chips wins.
Variation: Play with the full deck of 52 cards.
RESOURCES:
[Software]
higher-lower.swf
HORSE RACING
Whether you simulate a horse race with dice, or with computer
software, there is an abundance of mathematics to be learnt!
EQUIPMENT:
Horse racing track, 2 dice, counters.
BASIC RULES:
All players place a counter on the horse of their choice (1-12). Take it in
turns to roll two dice. Add the 2 numbers on the dice and move that horse
one space along the track. The first horse to reach the end of the track
wins!
RESOURCES:
[Software]
CyberPony_v2.0_installer.exe
hrace_v114.zip
derby.swf, hounds.swf, winners.swf
[Websites]
http://lhsparent.org/horserace/horserace.html
[Document]
Horse_Race.pdf
I’M FINISHED
Players:
2 to 4
Equipment:
Five standard dice and a score sheet.
Play:
1.
Each player in turn, rolls the five dice and scores when none of the dice
thrown show a 1 or a 4.
2.
If a 1 or a 4 are not thrown, the player scores the total of the numbers
rolled.
3.
If a 1 or 4 is thrown, they score nothing and put to one side all the dice
showing a 1 or 4.
4.
These dice are finished and the player continues rolling without them.
5.
Once the final die has turned up as a 1 or 4 the player says “I’m
finished” and it is the next player's turn.
6.
Write down each players score after each round on the scoresheet. The
highest total after 5 rounds is the winner.
Example Turn:
Number’s Thrown
Thrower's Score
1, 2, 2, 4, 5
3, 5, 6
1, 3, 5
6, 2
3, 6
4, 4
0
14
0
8
9
0
Variations:
1.
Use more or less than 5 dice.
2.
Use ten sided dice.
Total Score
0
14
14
22
31
31
I’M FINISHED

Player 1
Player 2
Player 3
Player 4
SCORESHEET

Round 1
Round 1
Round 2
Round 2
Round 3
Round 3
Round 4
Round 4
Round 5
Round 5
TOTAL
TOTAL
Winner
Winner

Player 1
Player 2
Player 3
Player 4

Round 1
Round 1
Round 2
Round 2
Round 3
Round 3
Round 4
Round 4
Round 5
Round 5
TOTAL
TOTAL
Winner
Winner

Player 1
Player 2
Player 3
Player 4

Round 1
Round 1
Round 2
Round 2
Round 3
Round 3
Round 4
Round 4
Round 5
Round 5
TOTAL
TOTAL
Winner
Winner
Player 1
Player 2
Player 3
Player 4
Player 1
Player 2
Player 3
Player 4
Player 1
Player 2
Player 3
Player 4
KEEP YOUR CAR GOING
Keeping your car on the road is an expensive business! Play this game to find out how
expensive it could be.
PLAYERS:
2 to 4
EQUIPMENT:
Two six-sided dice, game-board, counters, pen, cost sheet.
BASIC RULES:
1.
To move: toss 2 dice. Move forward the difference between the
dice.
2.
You must stop on the square marked with the STOP SIGN.
3.
Follow the directions on the board. Refer to the details given
below if a space is marked with a #.
4.
Go twice around the board. Each lap corresponds to one year.
5.
Fill in your COSTS page as you go around.
6.
The winner is the player with the least costs.
COSTS:
1. You need driving lessons
\$260
3. Got your P’s
\$25
5. Pay your petrol bill. Petrol is 154.9 cents per litre.
Roll both dice. The number of litres you bought = sum
of the numbers on the dice x 20
9. Repairs: Replace a noisy muffler, move forward 2
spaces
\$235
10. Defect notice for a noisy muffler. Move back one
space.
\$150
14. Regular service:
Roll one die. Cost = \$(number on die x 100)
16. Urgent repairs: faulty brakes, oil leak.
\$600
If you had a regular service at space 14, ignore this
square and move forward 3 spaces.
19. Registration due
\$450
24. Road rule violation: You get caught doing \$296
95 km/h in a 60 km/h zone (and lose 4 points).
27. Car Insurance: You have 2 choices.
1 Take Third Party Property Insurance.
\$176
If you are at fault in an accident, you pay all the expenses for your car +
the first \$500 of any claim by the driver.
2 Take Comprehensive Insurance.
\$750
In an accident the maximum you pay is the first \$600 of any claim.
29 & 30. Car Accident: You hit another car. Your fault.
Expenses
– your car: \$2000
- other car \$4500
Cost depends on which type of insurance you have.
32. Flat tyre
- RAC member
- non-member
free
\$45
CAR RUNNING & DRIVING COSTS
Initial
Get your L’s
\$ 43
Annual
YEAR 1
Registration
Insurance
Service
Licence
RAC
Petrol
Others
Repairs
Accidents
Defect Notice
Road Rule Violation
TOTAL =
YEAR 2
AVERAGE
LIAR’S DICE
Players:
3 to 6
Equipment:
Five standard dice per player.
Play:
1.
Each round, the players roll their dice while keeping them concealed
from the other players. One player begins bidding, picking a quantity
and a face from 1 through 6. For example: four 3’s.
2.
The player may make any bid, as long as it is “higher” than the last bid.
From lowest to highest the bids are: one 1, one 2, one 3, one 4, one 5,
one 6, two 1’s, two 2’s, etc.
3.
In turn, each player must either raise the bid or challenge the previous
bid.
4.
The loser of each challenge loses one die.
5.
The last player with dice left is the winner.
LOOP CARDS (1/2)
I have
I have
I have
I have
70
0
16
80
Who has
Who has
Who has
Who has
double 0?
double 8?
double 40?
double 18?
I have
I have
I have
I have
36
2
40
15
Who has
Who has
Who has
Who has
double 1?
double 20?
half of 30?
half of 18?
I have
I have
I have
I have
9
12
90
5
Who has
Who has
Who has
Who has
double 6?
double 45?
half of 10?
double 11?
I have
I have
I have
I have
22
7
100
25
Who has
Who has
Who has
Who has
half of 14?
double 50?
half of 50?
half of 2?
LOOP CARDS (2/2)
I have
I have
I have
I have
1
60
45
6
Who has
Who has
Who has
Who has
double 30?
half of 90?
double 3?
double 13?
I have
I have
I have
I have
26
10
35
18
Who has
Who has
Who has
Who has
double 5?
half of 70?
double 9?
double 4?
I have
I have
I have
I have
8
20
3
30
Who has
Who has
Who has
Who has
half of 40?
half of 6?
double 15?
double 2?
I have
I have
I have
Doubling
4
50
14
And halving
Who has
Who has
Who has
31 cards
double 25?
double 7?
double 35?
MAKE A MOKE
EQUIPMENT:
One standard die
BASIC RULES:
Aim: Be first to complete the Moke drawing by the rules.
• You must roll a six to start. That gets you the body.
• Each time you roll one of the numbers add on that piece
• While you wait for your turn, decorate your Moke.
Is it a Beach Moke, an Army Moke, a Music Moke, a Zoo Moke, a Boat Moke,
a ... ?
6 = the body to start you off
5 = one crash bar; but you need one for each end
4 = a seat; just get one for the driver
3 = one wheel; but your drawing needs two
2 = a steering wheel for the driver
1 = a rollbar to keep your head safe
RESOURCES:
[MATHS300]
Lesson 126: Make a Moke
[Website]
http://www1.curriculum.edu.au/maths300/
MAKE A MOKE
MAKE A MOKE
MAKE TEN
INSTRUCTIONS:
1.
Remove the tens, jacks, queens and kings from a standard deck of
cards.
2.
Deal 9 cards face up in a square grid as shown in the example below.
3.
A player may capture by calling out “ten” and taking any pair of cards
that add up to 10.
4.
When no more captures are available, replace spaces with cards from
the deck.
5.
Game continues until all cards are used. Winner is the person with the
most captures.
VARIATIONS:
1.
Change capture to two or three cards that add up to 15.
2.
Change capture to three or more cards that add up to 21.
3.
Play with 10s, Jacks (11), Queens (12) and Kings (13) with a target of
15.
4.
Set your own target total.
In the layout above, possible captures are 5 + 5 and 6 + 4
MAXI-MISER
PLAYERS:
2
EQUIPMENT:
Two 0-9 dice, game-board, pencil
BASIC RULES:
1.
Players take turns rolling a die.
2.
They record the roll in a square on their game-board.
3.
Once each player has completed their math sentence, they
solve it and compare answers.
4.
Whoever has the greatest answer, wins the point for that round.
5.
Player winning the most rounds wins overall.
VARIATION:
Players take turns rolling a die but both players have to use the roll
and may place the roll in ANY math sentence. When all the sentences
are filled and solved, then answers are compared to see who wins
each round.
MAXI-MISER GAME-BOARD

 x ( - ) -  =

 +  x   =
2

 -x-=

+x=

 x ( + ) -  =

 [3 x ( - )] =

+x=

x-=
MULTIPLES PATH 1
The first player colours the square in the bottom left corner. The next player
colours a square beside or above this square but can only colour a square
that is a multiple of the starting number. Players take turns to colour a square
that joins the last square along a side. The winner is the last person who is
able to colour a square.
MULTIPLES PATH 2
The first player colours the square in the bottom left corner. The next player
colours a square beside or above this square but can only colour a square
that is a multiple of the starting number. Players take turns to colour a square
that joins the last square along a side. The winner is the last person who is
able to colour a square.
MULTIPLICATION HEX 10 - 90
MULTIPLICATION HEX 11 - 91
MULTIPLICATION TOSS
Two or more players take turns to toss 2 ten-sided dice (2 six-sided dice
could be used initially).
The result of the toss determines the region to be marked. For example, a 6
and a 4 could be recorded as 6 fours (6 rows of 4) or 4 sixes (4 rows of 6).
A border is drawn around the region and the relevant fact is recorded in the
region. The object of the game is to cover as much of the grid as possible
without overlapping.
At any time in the game a player can decide to partition or split the region. For
example, instead of 6 eights, a player may decide to enclose two separate
regions such as 5 eights and 3 eights or 4 eights and 4 eights.
MULTO
The game involves plenty of times tables practice, but this is soon
subservient to the greater challenge of finding the best Multo grid to
choose. Software aids the search. The linked assessment sheet provides
teachers with considerable assessment information.
EQUIPMENT:
100 cards marked from 0x0 to 9x9, 4x4 square grids.
BASIC RULES:
The students draw up a 4row/4column grid and enter 16 numbers which
would be answers to these cards. No repeats. The teacher draws cards one
at a time and at a regular pace announces each random times table in turn. If
they have the answer on their grid, students mark it off. Multo is either:
4 in a row horizontally
 4 in a row vertically
 4 in a row diagonally
 all four corners
RESOURCES:
[MATHS300]
Lesson 52: Multo (cards, software & assessment)
[Website]
http://www1.curriculum.edu.au/maths300/
MULTO GRIDS
NIM
Playing Nim encourages problem solving strategies such as looking ahead,
reasoning (what if?), and working backwards. This is only one version of
the famous two person strategy game.
EQUIPMENT:
Plastic counters or similar.
BASIC RULES:
Place counters in rows as follows:
On your turn, you may take any number of counters from one row. The
person who takes the last counter loses.
RESOURCES:
[Software] pearls3.swf
[Website]
http://www1.curriculum.edu.au/maths300/
NUMBER POKER
A great whole class game that helps develop thinking skills. Students love this
game – you may give an incentive for highest scores or beating the teacher!
EQUIPMENT:
One standard pack of cards
(Remove all Kings, Queens and Jacks to simplify the game).
5 x 5 square grid
BASIC RULES:
1. Get students to draw up a 5 x 5 grid (or photocopy).
2. Turn over the first 25 cards calling out the numbers clearly (Ace = 1).
3. Score each row and column (not diagonals) as follows:
1 pair
=
10 points
2 pair
=
20 points
3 alike
=
40 points
5 in a row
=
50 points
3 alike, pair
=
80 points
4 alike
points
=
160 points
4. Add the 8 row and column scores and the highest total is the winner.
One Pair
=
10 points
Two Pair
=
20 points
Three Alike
=
40 points
Straight
=
50 points
Full House
=
80 points
Four Alike
=
160 points
One Pair
=
10 points
Two Pair
=
20 points
Three Alike
=
40 points
Straight
=
50 points
Full House
=
80 points
Four Alike
=
160 points
One Pair
=
10 points
Two Pair
=
20 points
Three Alike
=
40 points
Straight
=
50 points
Full House
=
80 points
Four Alike
=
160 points
One Pair
=
10 points
Two Pair
=
20 points
Three Alike
=
40 points
Straight
=
50 points
Full House
=
80 points
Four Alike
=
160 points
1111 - 9999
Players: 2-8 with a standard 52-card deck of playing cards, the 10s, Jacks, Queens, and
Kings removed.
Arrangement of Players: In this game players must pick a side of the table to sit on,
because as you will see the side you sit on drastically changes the game's outcome.
The Deal: Pick any person to start by dealing four cards to each player. Then deal four
cards face up in a row.
Player
Player
Player
Player
Player
Player
DO NOT HAVE ANYONE PICK UP THEIR CARDS UNTIL THE FOUR CARDS ARE ALL
FLIPPED FACE UP ON THE TABLE
The way the cards are facing you is the number you must try to match (so if the cards are
4 2 3 9 for me (sitting below the table in the above diagram), the person on the other side
of the table has the number 9 3 2 4). Now everyone simply reorganizes their cards to form
a four digit number that is as close as possible to the number on the table as they see it.
Set your cards down on the table face up, and move on to scoring.
Scoring: In this game you want to avoid scoring points. A player's score is the difference
between their number and the table number - i.e. the bigger number minus the smaller
number. So in the example above if I had been dealt 5 8 7 2 and I played it so my number
became 5,278, I would take 5,278 and subtract 4,239 from it to get my score of 1,039.
After each hand the scores are recorded on paper and the deal is passed to the next
person in clockwise order.
Getting 3 of a Kind: If you are dealt three of a kind or 4 of a kind, set your hand down
immediately. If you are the first person to do this on the hand, you instantly score a 0.
Ending the Game: The game ends when one person reaches a score determined by the
number of players in the game. The winner has the lowest score.
100 or BUST
EQUIPMENT:
One die, pen and paper
BASIC RULES:
Two players take turns rolling a die. After each roll, that player must decide
whether to add the value of the roll or ten times the value of the roll to his or
her score (e.g. a 2 can be counted as a 2 or a 20). After seven rolls, the
person with the highest total less than or equal to 100 is the winner. A score
over 100 counts as 0.
VARIATION:
Play closest to 1000, rolling a die ten times, using a HTU table.
RESOURCES:
[Document]
UncoverMath_Act01.pdf
OPERATION CHALLENGE
PLAYERS:
1 or 2
EQUIPMENT:
Two thirty-sided dice, game-board, paper and pencil.
BASIC RULES:
The goal is to either fill in all of the numbers across or fill in a
column. Players take turn rolling the dice. They then identify the
numbers and record the following in the appropriate space.
QUESTIONS:
VARIATIONS:
1.
The sum of the two numbers if it fits on the forty space graph.
2.
The difference of the two numbers by subtracting the smaller
number from the larger.
3.
The product of the two numbers if it fits on the graph.
4.
The quotient if it is evenly divisible.
1.
Shade in your graph.
2.
Compare graphs for any similarities or differences.
3.
Are certain numbers more likely?
4.
Does odd and even factor into the game?
1.
Allow exponents to be used (eg. 42 = 4 x 4 = 16)
2.
OPERATION CHALLENGE
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
5
3
4
2
3
1
2
1
0
OPERATION GOLF
Can you get under par on the “18 Hole Golf Course” below? You must:
1.
use the correct order of operations (BIDMAS), with
2.
the three digits above (use in any order or quantity), to
3.
make the target number.
Your score for the “hole” is how many digits you use to make the target number.
GOLF CLUBS FOR FRONT NINE:
HOLE
1
2
3
4
5
6
7
8
9
TARGET
67
9
84
46
15
32
96
101
192
WORKING OUT
OUT
GOLF CLUBS FOR BACK NINE:
HOLE
10
11
12
13
14
15
16
17
18
TARGET
64
25
36
100
78
11
15
98
52
WORKING OUT
IN
OUT
TOTAL
1 2 8
PAR
4
3
4
5
4
4
3
5
5
37
SCORE
3 7 9
PAR
4
4
3
5
4
4
3
5
4
36
37
73
SCORE
OPERATION HISTOGRAM
PLAYERS:
2 to 4
EQUIPMENT:
Two ten-sided dice, game-board, paper and pencil.
BASIC RULES:
1.
Players take turn rolling the dice.
2.
After each roll, form an addition expression.
3.
Write the expression on the game-board in the correct column.
4.
Roll the dice a total of twenty times.
1.
Which sum is most likely?
2.
What is the most common shape for the histogram? Why?
3.
Which sum is least likely?
4.
What is the probability for each possible sum?
1.
Record the difference between the two numbers rolled.
2.
Change the number of rolls possible (30, 40) and see how it
effects the histogram.
QUESTIONS:
VARIATIONS:
3.
OPERATION HISTOGRAM
5
4
3
2
1
5
4
3
2
1
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20
PENTA PLACE
For 2, 3 or 4 players
You will need:
 A chess board.
 Stiff card (preferably marked in squares)
 Scissors
 Paper
 Pencil and thin marker pen
 Ruler
Goal: To be last person to be able to place a pentomino piece on the playing
board. To prevent your opponent(s) from finding space to place pentomino
pieces on the board.
To prepare for play:
1. Find all of the 12 pentomino shapes*, sketch them on paper.
2. Draw them using the marker pen onto card that is marked in squares the
same size as the chess board you use.
3. Don't mark the pentominoes in any way so that there is no way to tell the
top, bottom, front or back.
4. Cut out the set of pentominoes.
To Play:
 Lay out all of the pentomino pieces.
 Decide who will go first, second etc.
 The first person chooses one of the pieces, then the second person
chooses a piece etc.
 Players lay his or her chosen pieces in front of them for others to see.
 The first person to play chooses one piece and places it on the board.
 Players take turns to place pieces on the board.
 Try to decide which are the best moves to block opponents from placing
their pieces.
 The winner is the last person to place a piece on the board.
PLACE VALUE DICE
 Each player has a game sheet and takes it in turns to throw 2 ten-sided
dice.
 The numbers are used to create 2-digit numbers, e.g., a 5 and a 2
could be recorded as 25 or 52.
 Players record their numbers in the most appropriate position between
0 and 100.
 If numbers cannot be placed, the player misses his/her turn.
 The winner is the first to fill all places.
POLYGON CAPTURE
Preparation:
Each pair of players needs a set of property cards and a set of polygon cards. The polygons
go into the centre of the playing area and the side and angle property cards are separated
into two piles.
Goal:
Capture the most polygons.
Play:
1.
Randomly choose who goes first.
2.
Player 1 flips over an angle card and a side card. She captures any card which satisfies
both these properties. When finished she says: “Done”
3.
Player 2 may capture any polygons which player 1 missed.
4.
Player 2 takes a turn, turning over two new property cards and capturing the
appropriate polygons.
5.
Play continues in this manner until two or fewer polygons remain.
Notes:
If you run out of angle or side property cards, reshuffle that pile and continue.
Any player can challenge the capture of a polygon. If a player chose a polygon incorrectly, it
goes back into the centre pile and their turn is done.
If the Wild Card comes up, the player may choose any side property. For example, if the
angle card is “All angles are right angles”, she may choose “All opposite sides are equal” and
capture all rectangles.
If the Steal Card comes up, the player picks one side property and one angle property, and
steals all of the polygons the other player has captured which satisfies those properties.
Ignore the other card.
Example:
Player 1 turns up “All angles have the same measure” and “It is a quadrilateral”. She then
captures the square, the short rectangle and the right trapezoid and says “Done.” Player 2
may then capture the long rectangle. Then he begins his turn.
Source: Carroll, William M., Polygon Capture: a Geometry Game, Mathematics Teaching in the Middle School, Oct 1998. Vol. 4,
Iss. 2; p. 90
All angles are
right angles
At least one
angle is a right
angle
At least one
angle is obtuse
At least two
angles are
acute
No angle is a
right angle
At least one
angle is less
than 90o
All angles are
the same
STEAL CARD
Select a pair
of properties.
Steal all these
polygons from
your opponent
No pairs of
sides are
parallel
Exactly one
At least one
All sides are
pair of sides is pair of sides is
of equal length
parallel
perpendicular
All pairs of
opposite sides
are parallel
All pairs of
opposite sides
have equal
length
It is a
quadrilateral
WILD CARD
Pick your own
side property
POT LUCK
THE CRAYFISHING GAME
AIM: To accumulate as many assets as you can in the form of boats (value \$100 each), pots
(value \$5 each) and money.
RULES: Each player starts with 2 boats and 5 pots and can purchase new pots and boats as the
game proceeds and you can sell a boat for \$100 at any time. You have the choice of putting your
pots in-shore or out-shore and, depending on the weather, you will make money or lose the pots.
The weather is decided by the throw of a die.
INCOME
IN
OUT
Good Weather
\$2
\$6
Bad Weather
\$4
LOSE
RESTRICTION: max of 10 pots per boat
Day
Boats Pots
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2
5
IN
OUT
Weather
INCOME
1, 2, or 3 = good weather
4 = same as day before
5, 6 = bad weather
EXPENSES: new pots cost \$5, new boats cost \$100
Earned
New Pots
New Boats
Expenses
Balance
PRODUCT GAME
Read the following rules before you begin playing The Product Game.
1. Player 1 puts a counter on a number in the factor list. No square on the product grid is
marked with Player 1’s colour because only one factor has been marked; it takes two factors
to make a product.
2. Player 2 puts the other counter on any number in the factor list (including the same
number marked by Player 1) and then shades or covers the product of the two factors on the
product grid.
3. Player 1 moves either one of the counters to another number and then shades or covers
the new product.
4. Each player, in turn, moves a counter and marks a product. If a product is already marked,
the player does not get a mark for that turn. The winner is the first player to mark four
squares in a row - up and down, across, or diagonally.
1
2
3
4
5
6
7
8
9
10
12
14
15
16
18
20
21
24
25
27
28
30
32
35
36
40
42
45
48
49
54
56
63
64
72
81
1
2
3
4
5
6
7
8
9
QUADRATIC DOMINOES

Cooperative Game
Two dominoes can be placed together if they share a factor. For example,
x2 – 3x + 2 and x2 – x – 2, share a factor of (x – 2). Continue until all
possible dominoes are placed

Competitive Game
Two players start with 7 dominoes and take turns playing their dominoes into
the centre as per normal domino games. Whoever places their last domino
before the other player finishes is the winner.
x2 + 4x – 32
x2 – 10x + 16
x2 – x – 6
x2 – 2x – 3
x2 – 3x + 2
x2 – 2x – 8
x2 + 7x + 12
x2 – 2x – 15
x2 + 4x – 5
x2 - 13x + 40
x2 + 11x + 28
x2 + 6x – 7
x2 – 9x + 8
x2 – x – 2
x2 + 5x + 6
x2 + 4x + 3
x2 + 3x + 2
x2 + 5x + 4
Quadrilateral Concentration
Materials: Deck of quadrilateral cards. May want rectangles or protractors as players get
more precise. 2-4 players.
Setup: Set aside the Joker, and randomly deal the cards out into almost a rectangle. (I
prefer 6x7 with two extra on top, but choose your own.)
Gameplay: On each turn, a player turns up two cards letting everyone see. If they are the
exact same type of quadrilateral, you can collect them. If not, turn them down after all
players have had a chance to see them. Whether it is a match or not, it is the next player’s
turn. All players should agree on a match.
Winner: Player to collect the most pairs.
Quadrilateral Go Fish
Materials: Deck of Quadrilateral cards. Best with 3-5 players.
Setup: Deal 5 cards to each player. Put the rest face down in the middle, either in a neat
stack, or mixed up in a big pond.
Gameplay: Start to the left of the dealer. On a player’s turn they can ask a particular
player for a specific property. For example: “Do you have a shape with opposite angles
congruent?” You can not ask for a shape by name. (“Do you have a rectangle?”) If the
player has a card like that, they have to give it over. If they have more than one, they get
to choose which card to give away. If you have a matched pair of the same type, you can
play them down.
Winner: First winner is the first player to go out. Second winner is the player with the most
pairs.
Quadrilateral Guess Who
Materials: Quadrilateral card deck. 2 players.
Setup: Sort the quads by type. Each player puts one quadrilateral of each type face up in
front of them, and the others go face down in the middle. Each player draws a card
from the middle and keeps it hidden from the other player.
Gameplay: On your turn you can ask one question about the other player’s hidden
quadrilateral. That player answers yes or no. Turn face down the quads you have that
don’t match.
Winner: first player to guess the other player’s card.
Quadrilateral Cards (1 of 5)
Quadrilateral Cards (2 of 5)
Quadrilateral Cards (3 of 5)
Quadrilateral Cards (4 of 5)
Quadrilateral Cards (5 of 5)
YOUR ALGEBRA SKILLS 1
Name ______________________
Factor ______
Risk
Points
100
1. Write in algebra: “5 is added to a number and the result is doubled”
2. 5 - (+7) - (-8) – 9 =
3. (-1)(-2)(-3)(-4)(-5) =
4. 100 - 43+ 2(7 - 3)2 =
5. 7x + 3y when x = 4 and y = -3
6. b2 – 4ac when a =-2, b = -5, c = -3
7.
2
3
+
1
4
=
8. Expand: 3y(7 +2y)
9. Expand: (x-7)(x+4)
10. Factorize: x2 – 5x - 104
Tiebreak:
WORKING:
YOUR ALGEBRA SKILLS 2
Name ______________________
Factor ______
Risk
Points
100
1. Simplify: 6x + 17y – 8x – 19y
2. Expand 5x(x – 2)
3. Expand (x + 6)2
4. Expand (x + 4) (x – 3)
5. Factorize x2 + 6x + 8
6. Factorize x2 - 100
7. Factorize 9x2 - 225
8. The sum of the numbers in the 7th row of Pascal’s Triangle
9. Complete the following table of values:
x
-2
-1
0
1
2
X+2
(x + 2)2
(x + 2)2 - 3
10. For the graph: y = x2 – 5x – 14, state the y intercept, x intercepts
and turning point.
Tiebreak:
YOUR QUADRATIC SKILLS
Name ______________________
Factor ______
Risk
Points
100
1. y = -2x2 + 5x – 3 (State the coefficients a, b and c)
2. Expand: (x + 1)(x – 2)
3. Expand: (x - 7)2
4. Factorize: x2 – 9x - 36
5. Factorize: x2 - 81
6. Solve: x2 -6x = 27
7. Find the discriminant of:
y = 3x2 – 5x + 2
8. Solve by completing the square:
x2 + 6x -7 = 0
9. The triangle shown has an area
of 120 cm2. Find the value of x:
10. Sketch the graph of:
y = x2 -6x + 8
(clearly label axes and intercepts)
Tiebreak:
What is the longest word you can find using the letters of the
word EQUATION? (apart from “equation” of course!)
YOUR TRIGONOMETRY SKILLS
Name ______________________
Factor ______
Risk
Points
100
1. Write the 3 trigonometric ratios:
2. Use a calculator to find sin (26o) correct to 4 d.p.
3. Use a calculator to find tan-1 (1.5476) correct to
nearest degree
4. Change 46.65o to degrees and minutes
5. Find “a” to 2 d.p.
6. Find “x” to 2 d.p.
7. Find the angle “theta” to
the nearest degree.
8. Change 225o to radians
9. A plane flies S47°E at 1050 km/h after taking off at
11:15 am. How far due south of its starting point is the
plane at 2:45 pm?
10. Sketch the graph of: y = 2 sin (2x)
ROLLING DECIMALS
PLAYERS:
2 to 4
EQUIPMENT:
Four 0-9 dice, game-board, pencil
BASIC RULES:
1.
A player rolls all four dice and arranges them to create a
number that is one whole number followed by tenths,
hundredths, thousandths (eg. 3.407)
2.
After each number a running total is calculated.
3.
At the end of 5 rounds, all of the answers are totalled at the
bottom.
4.
The player (team) who's answer is closest to any whole number
wins the game.
3.316
+
+
+



4
5


=
Total


=
=
=




=
3

+

Running Total

Thousandths
0.001
2
Hundredths
0.01
+ 0.000 =
Tenths
0.1

Whole
Numbers
1
Roll
#
ROLLING DECIMALS
ROLL A PRODUCT
1.
Working in a group of 3, decide who will be players A, B, and C.
2.
Take turns rolling two dice and multiplying the numbers that land face up.
3.
Cross out the product on your hexagon.
4.
If the product is not on your hexagon or is already crossed out, miss a turn.
5.
When all numbers on a hexagon have been crossed out, that player wins.
ACTIVITY 1
a)
To help you understand whether the game is fair, fill in
record the number of times each
product occurs.
b)
Record the overall number of games A, B, and C won in
the class.
c)
Based on a) and b), do you think the game is fair?
these tables and
ACTIVITY 2
a)
What should the probability be for each player if the game is fair? Explain.
b)
Use your discoveries to create three hexagons, each of which is equally
likely to win.
SALUTE THE KING
PLAYERS:
2 to 4
EQUIPMENT:
Pack of cards with the jacks, queens, kings and aces removed.
BASIC RULES:
1.
Deal all the cards face down. It is better if everyone has the
same amount of cards, but it is not mandatory.
2.
The object of the game is to get rid all your cards. The first
person to do that is declared the winner.
3.
Every player must now, turn over the top card on their pile.
4.
Total the cards flipped over and then:
5.
A Square Number
STAND UP
A Multiple of 5
SALUTE THE KING
A Multiple of 3
HAND ON HEART
30 to 39
CLAP HANDS
Last player to perform the correct action takes all the
cards.
SANTORINI
The game: is for two players, represented by Cubes and Cylinders, which are referred
to as "men". Cube moves first.
Equipment: Each player has 2 pieces of his type, and there is an unlimited supply of
square tiles.
The object of the game is to win by either moving a man to stand on the third level
above the base of the board, or alternatively to manoeuvre so your opponent cannot
move on his turn.
Setup:
Play starts with a 5x5 grid of squares. First Cube, then Cylinder place both their men on
unoccupied squares.
Moving:
Each turn has two parts. First move one of your men to an adjacent space. The
destination space must be unoccupied, and no more than one level higher than your
starting height. If you cannot move, you lose.
Building:
The second part of each move is to place a new tile adjacent to the man which just
moved. You can place it in any unoccupied square.
Building Domes:
A square placed on level 3 (making it 4 above the base) is immediately replaced by a
dome. Domes cannot be moved onto or built upon.
Winning:
The normal way to win is to move one of your men to stand on level 3. The other way
to win is to box in your opponent so he/she cannot move.
Variation:
The basic game can be extended by adding Gods and Heroes, which alter the rules of
the game (as gods are prone to do).
SANTORINI BOARD
Take it in turns to move a man and then place a tile adjacent to it.
Whoever moves one of their men to level 3 wins.
SET GAME
An excellent game, which uses both hemispheres of the brain.
Some students will excel at this game easily beating adults or
students who usually excel in most other aspects of Maths.
EQUIPMENT:
Set Cards
BASIC RULES:
The object of the game is to identify a 'Set' of three cards from 12
cards laid on the table. Each card has a variation of four features:
(A) Colour
(B) Symbol
(C) Number
(D) Shading
A 'Set' consists of three cards in which each feature is EITHER the
same on each card OR is different on each card. That is to say, any
feature in the 'Set' of three cards is either common to all three cards
or is different on each card. Here is a “set”:
The Magic Rule
If two are... and one is not, then it is not a 'Set'.
SHAPES & SOLIDS BINGO
PLAYERS:
Whole Class
EQUIPMENT:
Set of bingo cards.
BASIC RULES:
1.
Distribute a bingo card to each student in the class.
2.
Call out the following words in random order.
3.
Winner calls out bingo when all their shapes are called.
WORD LIST:
Scalene triangle
Isosceles triangle
Equilateral triangle
Regular pentagon
Regular hexagon
Regular octagon
Irregular pentagon
Irregular hexagon
Irregular octagon
Circle
Ellipse
Annulus
Sector
Segment
Irregular quadrilateral
Trapezium
Parallelogram
Kite
Oblong
Square
Cone
Pyramid
Tetrahedron
Cylinder
Triangular prism
Hexagonal prism
STOP OR DARE
A game for two or three players. You will just need a pack of cards.
Shuffle the pack and place it face down. Set a target score for the game, for
example 100.
The first player turns over the top card and continues turning over cards,
adding together the value of each card, until they decide to stop. Jacks
score 11 and Queens score 12.
When the player stops, the total is recorded as their score.
However, if an Ace or a King is turned over, no points are scored at all,
and the turn is finished.
The second player then starts turning over cards in the same way.
Players take turns until someone reaches the target score. This player is the
winner.
If the cards are all turned over before the target is reached, just reshuffle the
pack and continue.
Play the game a few times.
Can you develop any strategies to increase your chance of winning?
Now decide on some new rules and play the game again.
You could change which cards (and how many cards) end the turn, or
introduce a card that sets your total score back to zero.
Once you have played your variant a few times, decide whether the
same strategies are best.
STRIVE FOR THE HIGHEST
PLAYERS:
2
EQUIPMENT:
Calculator, die, paper, pencil.
BASIC RULES:
1.
You have six turns to earn the highest score.
2.
When it is your turn, roll the die and circle a number on the
chart. This number cannot be used again.
3.
To calculate your score, increase the circled number by the
percentage rolled on the die.
Example:
Roll 4 on the die and circle 2350.
Add 4% to 2350
= 1.04 x 2350
= 2444
QUESTIONS:
VARIATION:
4.
Keep rolling the die and choosing a number.
5.
After six turns, add all your scores. The person with the highest
score wins.
1.
What advice would you give to a person who is going to play
this game?
2.
What is the largest possible score you can get after 6 turns, if
you were lucky?
Use a different die (eg. 10-sided, 20 sided)
Chart for Player 1
Chart for Player 2
2350
12400
2350
12400
8250
2550
8250
2550
11000
7450
11000
7450
SUM, DIFFERENCE, PRODUCT
Players:
2
Equipment:
Two standard dice
Play:
1.
Each player in turn, rolls the two dice and completes the following
calculations:
Add the numbers shown on the dice.
Find the difference between the two numbers.
Multiply the numbers shown on the dice.
2.
Add the three answers to get the score for the round.
3.
After ten rounds the player with the highest cumulative total wins.
Example: 5 & 3.
Sum(8)+Difference(2)+Product(15) = 25
Variations:
1.
Play to a set total e.g. 100
2.
Change the dice used e.g. 10 sided dice.
TAKE YOUR PLACES
Players:
Small group or whole class.
Equipment:
Counters, spinner or ten sided die to generate numerals 0-9. Do not
use repeat numerals.
Method:
1.
Generate a number. Each student must decide where to place that
number to achieve the set goal (example: highest product).
2.
Continue choosing numbers until all squares are filled.
3.
Calculate the sum, difference, product or quotient and determine the
winner.
4.
Select game format from the following pages that best suits the
current needs of your students.
1.
Use the following journal prompt:
Variations:
“What patterns or rules did you learn that helped you decide where to
place the number?”
2.
For the given set of numbers, find the min/max product, etc.
3.
Have students show all possible arrangements for a given set of
numbers in a problem and the answers that can be achieved. For
example, if you are multiplying a two-digit number times a two-digit
number on problem A, there are 24 possible problems that can be
created with four given numbers. However, they do not generate 24
different answers.
4.
Rather than maximum or minimum, set a target number. Closest to
the target is the winner.
TARGET 100
Players:
2 players
Equipment:
A deck of cards with joker, 100 number grid, tables chart, 2 counters.
Play:
One student deals cards out to his/her opponent who adds or multiplies the
cards. This continues until the student decides to stop.
The winner is the player who gets closest to 100 without going over.
Example:
Player A is going first and having cards dealt by partner.
Card 5 is dealt first so player A moves counter to 5 on number board. Card 6
is the next card dealt. This could be 5+6 and the counter is moved to 11 or it
could be 5 x 6 and counter is moved to 30. Let’s assume that Player A
decides to move to 30. The next card is a KING so the student adds 10 and
moves the counter to 40. Next card is 2. Student decides to multiply and
moves to 80. Next card is Ace. Student decides to multiply and stay on 80,
hoping that the next two cards are 10’s and he/she can hit exactly 100. Next
card is a 5. Student adds and moves to 85. Next card is 9. Student moves to
94 and decides to stop fearing that the next card flipped will be bigger than a
6 and she / he would bust.
Player B now has the cards dealt to him / her and tries to better 94 without
busting. Once this game is completed, play again but player B goes first.
100 CHART
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
TARGET PRACTICE 1
You need: 3 ten-sided dice (different colours are useful but not essential) and
a copy of the game sheet for each student.
TO PLAY:
1. Take turns to throw the dice.
2. Choose 2 of the numbers thrown to make a number as close to the target
number as possible.
3. Mentally calculate ‘how close’ and record in the space provided.
4. The winner is the player with the smallest total.
Numbers Thrown
TARGET
Number Made
74
3.5
1.9
5.7
3.5
4.7
9.3
0.8
TOTAL
How Close?
TARGET PRACTICE 2
You need: 4 ten-sided dice (different colours are useful but not essential) and
a copy of the game sheet for each student.
TO PLAY:
1. Take turns to throw the dice.
2. Choose 3 of the numbers thrown to make a number as close to the target
number as possible.
3. Mentally calculate ‘how close’ and record in the space provided.
4. The winner is the player with the smallest total.
Numbers Thrown
TARGET
567
9.45
93.6
5.7
13.8
4
627
0.81
Number Made
How Close?
10000 SCORE SHEET
Start by rolling 6 dice. Continue rolling some dice until you have at least 300 points.
5
=
50 points
5, 5, 5
=
500 points
1
=
100 points
6, 6, 6
=
600 points
2, 2, 2
=
200 points
1, 1, 1
=
1000 points
3, 3, 3
=
300 points
3 pairs
=
1500 points
4, 4, 4
=
400 points
1, 2, 3, 4, 5, 6
=
3000 points
The first player to score a total of 10,000 or above, wins the game, provided any
subsequent players, with a turn left, don't exceed their score.
THE DECIMAL GAME
1.
Divide your class into two teams who then take it in turn to choose decimal numbers
from the grid.
2.
After they choose a number, cross it off the grid.
3.
Each time they choose numbers they also write them on a whiteboard, lining them
up so they can do some column addition with them.
4.
Once all numbers have been chosen each team sums their decimal numbers and
the team with the highest total is the winner. The correct strategy is to always
choose the largest remaining decimal number on the board. When the game is over
you can look down the columns of decimal numbers that each team recorded and
they should be ordered from largest to smallest. If not, some interesting discussions
can arise and you can get a gauge as their teacher how well your pupils have
learned the skill of ordering decimal numbers.
5.
You can create variations on the game, making it a two, three or four player game
rather than a whole class game. Winner stays on etc… Who will be class
champion?!
THE HIKE
An excellent board game, which includes simple probability events to
determine a winner. Analysis of the game using tree diagrams should be
made after playing the game to find the best strategy.
EQUIPMENT:
“The Hike” game board, 2 counters, 2 standard dice, 3 coins.
BASIC RULES:
1. Roll dice to decide who goes first.
2. Starting at “Stollywood” players decide whether they will go over the
mountains or cross the river.
3. They then take turns to roll dice until they get the required target.
4. Continue making decisions (1ab, 2ab, 3ab, 4ab), rolling dice and flipping
coins.
5. The winner is the first player to reach “Finisham”.
RESOURCES:
[Game board]
The Hike.jpg
THE HIKE
GAMEBOARD
THIRTY ONE
EQUIPMENT:
Sets of 24 cards (i.e.: four of each of 1, 2, 3, 4, 5 and 6).
BASIC RULES:
1. Set up the playing cards (or number cards) as follows:
2. Players take turns to turn over a card and call out the running total.
3. The person who makes the total 31 is the winner.
REFERENCES:
[MATHS300]
Lesson 27: Game of 31
[Website]
http://www1.curriculum.edu.au/maths300/
TIC-TAC-TOE
1.
This game is played on a normal noughts and crosses grid, but numbers are used
instead of the noughts and crosses symbols.
2.
Only the digits from 1 to 9 can be used and each digit may only be used once.
3.
The winner is the first one to make three in a row add up to sixteen.
THREE CUBES
This game uses cubes in two colours, 12 in one colour for each of two
players.
They take turns to place a cube on a 3 x 3 base. As well as playing at ground
level, they may also go upwards, on top of any other cube, up to 3 cubes
high.
The winner is the first to get three cubes of their own colour in any line –
horizontally, vertically, or even diagonally through the structure.
Finally, students draw front, side and top views and submit to the teacher to
claim a prize.
THREE THROW
 Roll 3 six sided dice and multiply the numbers together. (Alternatively
roll one die three times and multiply the three numbers together.)
 Put a counter on the answer square on the Game Sheet.
 Try to get three counters in a line: horizontally, vertically or diagonally.
 If a counter already occupies a number you cannot place another one
on it.
Variation:
 Allow players to remove their opponent’s counters if they make the
same product.
1
2
3
4
5
6
8
9
10
12
15
16
18
20
24
25
27
30
32
36
40
45
48
50
54
60
64
72
75
80
90
96
100
108
120
125
144
150
180
216
TOTAL CONTROL BINGO
This maths game is designed to assist children
in developing confidence with number
calculations. It consists of a set of 15 bingo cards
for the children, and question sheets for the adult.
The children work in pairs to mark off, or cover up,
numbers on their cards which answer specific maths
problems called out.
So far so simple. This is just maths bingo. However there's a twist... the questions are
organised so that you can easily control which bingo card wins!
How does this work? The maths questions are listed on 15 separate sheets, each one is
labelled with a letter of the alphabet: "A" to "O". The bingo cards carry matching labels.
The question sheets carry 16 maths problems, 12 of which appear on one single bingo
card - making that the winner!
For example, here's card "E" and the related question sheet - 7 questions have been
called.
Four of the problems on each question sheet are
marked with an asterisk (like the second question in
the example above).
This indicates that that question does not have a
corresponding answer on the 'winning' card... so, if
time is short you can omit this question and there
will still be a winner.
This makes the question-calling quite flexible, you
can call all 16 questions, or ignore those with an
asterisk and only call 12.
The question sheets feature a wide variety of maths
functions and vocabulary, which may or may not be
appropriate for your children. However, each sheet
clearly indicates the answer too, so you can easily
rephrase, or completely alter the questions.
TRICKY DICE
A very rich game with many possibilities for further investigation. Students
can start exploring 2 dice, then 3, 4 or even 6 as shown below. They can
experiment and then draw up probability tables.
EQUIPMENT:
One set of 4 “tricky dice”
BASIC RULES:
Two players have four unusual dice. The faces of the dice are:
Red
017889
Blue
556677
Black
3 4 4 5 11 12
Green
1 2 3 9 10 11
Each player selects one of the colours. Then both players roll their dice - the
higher number wins a point. Ignoring draws, the first to 7 points wins the
game.
RESOURCES:
[MATHS300]
Lesson 59: Duelling Dice
[Websites]
http://www1.curriculum.edu.au/maths300/
TWENTY SEVEN
The first player colours a hexagon.
The second player colours a hexagon that joins to the first one.
This player adds this number to the first number and says the total.
Players take it in turns to colour a hexagon that joins to the last one coloured
and add the number to the previous total.
The first player to reach exactly 27 is the winner. If a player goes over 27 they
lose.
If a player colours a hexagon and this blocks the other player from having a
go they also lose.
U Win Again
This is a two-person game played with a
pack of 0-9 Digit Cards.
The cards are shuffled and dealt face-up in
the form of a letter ‘U’.
Children then take it in turns to choose (and
remove) a card from one of the two ‘end
cards’.
Players can only choose one of the two ‘endcards’; each time a card is removed the card
immediately next to it in the chain becomes
the new ‘end card’. When all of the cards
have been removed, the game ends, and the
players calculate their score from all of their chosen cards.
The player with the larger score is the winner.
The focus of this game is not on the calculation but on the strategy used
Notes:
The focus of this game is not on the calculation, but on the strategy used
when deciding which card to take. As with most games, the learning will be
enhanced through adult intervention. In the first instance it may be useful to
let the children simply play; observing how they take the cards and
encouraging them to discuss any strategies they seem to be using as the
games progress. After a while, children may start ‘looking ahead’ to see what
their partner may do next, for example: In the game shown here, the 7 card
seems a good starting point. However, the first player may decide to take the
6 card rather than the higher 7, since the 6 only opens up a 2 for their partner
rather than the more valuable 8.
UPS AND DOWNS
VISUALIZING SHAPES 1
Get your class to draw the figure below. You must give them only verbal instructions.
VISUALIZING SHAPES 2
Get your class to draw the figure below. You must give them only verbal instructions.
VISUALIZING SHAPES 3
Get your class to draw the figure below. You must give them only verbal instructions.
VISUALIZING SHAPES 4
Get your class to draw the figure below. You must give them only verbal instructions.
VISUALIZING SHAPES 5
Get your class to draw the figure below. You must give them only verbal instructions.
VISUALIZING SHAPES 6
Get your class to draw the figure below. You must give them only verbal instructions.
WALK THE PLANK
Ref: Maths 300 Task 32
5
4
3
2
1
M
1
2
3
4
5
Use this plank to try these challenges.
1. Start at S2 then roll this [S, B3].
End up at .......
2. Start at S1 then roll this [S, F1].
End up at .......
3. Start at B3 then roll this [B, B2].
End up at .......
4. Start at B4 then roll this [S, F3].
End up at .......
5. Start at S3 then roll this [B, B2].
End up at .......
6. Start at B5 then roll this [B, B1].
End up at .......
7. Start at M then roll this [B, B3].
End up at .......
8. Start at M then roll this [S, F3].
End up at .......
9. Start at M then roll this [S, B3].
End up at .......
Now you choose.
10. Start at .... then roll this [B, F1].
End up at .......
11. Start at .... then roll this [B, B2].
12. Start at .... then roll this [S, F3].
13. Start at .... then roll this [S, B2].
14. Find five different combinations which will finish at M.
WHAT’S IN THE BAG?
EQUIPMENT:
At least 20 mixed coloured cubes or counters and a suitable bag.
BASIC RULES:
Secretly one player puts twenty mixed coloured cubes in a bag.
Without looking in the bag, a second player is allowed to take a sample of
four cubes. The sample is put back in the bag. With due drama the bag is
shaken, and another sample of four is allowed. This is repeated one more
time. The second player now has three clues to What's In The Bag? The
object of the game is to correctly predict what’s in the bag?
RESOURCES:
[Software]
What’s in Santa’s Sack.swf
[MATHS300]
Lesson 125: What’s in the Bag?
[Websites]
http://www1.curriculum.edu.au/maths300/
WIN AT THE FAIR
I was at a school fête recently and one of the stalls was using a larger
version of this playing board. What do you notice about the board? At
the fair I saw, you had to pay \$1 to play.
EQUIPMENT:
Playing Board
1 counter or coin and 2 dice per pair
BASIC RULES:
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Pay \$1 to play.
Place your counter on the start.
Roll 2 dice and add them together.
Move your counter according to the rules at the bottom of the
board.
Continue until your counter reaches a winning hexagon.
Collect your payout.
RESOURCES:
[MATHS300]
Lesson 001: Win at the Fair
[Websites]
http://www1.curriculum.edu.au/maths300/
WIN AT THE FAIR
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