Math Games
Math Games
p.1
Math Games
For Skills and Concepts
Other material copyright:
Investigations in Number, Data and Space , © 1998 TERC.
Connected Mathematics Project, © 1998 CMP
Original material ©2001-2006, John Golden, GVSU
permission granted for educational use
Table of Contents
Page
2
3
5
6
7
9
10
11
11
11
Game
Why games?
Tens Go Fish
Sums Game
Five in a Row
Race to 100
Close to 1000
Close to Zero
Calculator Get Down
Flip
Number Strings
Content
Teacher motivation
Addition facts
Addition, subtraction
Addition facts
Double digit addition
Place value, multidigit addition
Place value, multidigit subtraction
Multidigit operations
Reasoning
Factorization
12
13
14
15
16
17
18
Change for the Better
Product Game
Prime Time
Factor Score
Roll to 10
Triangle Game
Racin’ Robots
22
Polygon Capture
Money, two-digit arithmetic
Multiplication, factors
Prime factorization
Division facts, factors
Decimal addition, place value
Measurement, half
Motions, programming, logical
sequencing
Polygons, characteristics, geometric
vocabulary
25
25
26
27
Target Practice
Pig
Radian Race
Box Builder
Algebra, equations and graphing
Probability, strategy, expected value
Angles on the unit circle
Nets, surface area, volume
Notes
Extended teaching notes
Product Game variation
Better than bingo
Controlled die rolling
Good number sense game
Calculation practice & use
Surprisingly subtle
Can use this to discover prime
factorization
A lot of strategy, good game play
Best math game ever
Good game play value
Best with base ten blocks
Fractal geometry
Pretty involved, takes some time to
set up and to play
Can be adapted to multiple
situations where characteristics and
sorting is the content
Better the more functions kids know
Great game
Can use for probability, too
Math Games
p.2
Why use games to practice skills?
1) They are more engaging.
2) They provide more practice. Consider the product game: for each move
you are considering multiple multiplication problems.
3) They are a constructive reward for use in free time in your class, in
addition to whole class use.
4) They are more likely to involve parents and other family members with
homework. Be sure to send home the instructions or rules. Or consider
hosting a night where parents can come to play with the kids. Or pull
them out at parent-teacher conferences.
5) They can be really fun. (Duh!)
Where can you find more?
1) Best source: exemplary curricula.
o For elementary, Investigations in Number, Data, and Space (which even includes computer
games) and Everyday Math.
o For middle school, Connected Math Project and MathScape (among others).
If you are lucky enough to be in a school using these curricula, use the games! If not, you can find
copies available from your district math curriculum supervisor, from university libraries (the KCRC at
GVSU), or order them yourself from amazon.com.
o The internet, but be careful! There are a lot of useless games out there.
2) Make your own. Once you get the idea for what skill practice your students need, think of a way from
them to generate problems. This will often lead to a game structure. Or, once you are familiar with
other constructive games, adapt those to your purpose.
3) Sharing with your colleagues. In your school, from your college, at math meetings… don’t be shy. If
you write one up that you’d like to share via internet, I’d be happy to post it. If it’s original, be sure to
include a copyright with permission granted for educational use. If it’s from another source, or
closely adapted from another source, please cite that source.
How do you evaluate games?
1) Examine mathematical richness. If the game is just window dressing for drill and kill (like math
bingo) evaluate it deservingly. Look for problem solving, need for strategy, and math content
required.
2) Is speed required? The best games offer equal opportunity (or nearly so) to all your students. Games
that require computational speed to be successful will disenfranchise instead of engage your students
who need the game the most.
3) Do you find the game interesting or fun? Then your students probably will also.
Math Games
p.3
Tens Go Fish
From Number Games and Story Problems: Addition and Subtraction
Investigations in Number, Data, and Space
What Happens
In the game Tens Go Fish, students make combinations of ten with two
addends.
Introducing Tens Go Fish
If your students are familiar with the card game Go Fish, they will need just
a brief introduction to Tens Go Fish.
First explain about “making 10” with pairs of Number Cards. Draw five Number Cards in a row on the board
or on chart paper. Include one pair that makes 10. For example, you might select the cards 4, 1, 5, 7, and 9.
I'm going to show you a game called Tens Go Fish. The object is to find pairs of cards that add up to
10. Each player gets five cards to start. Let's say these cards are the cards in my hand: 4, 1, 5, 7, and 9.
Can I make 10 with two of these cards? ...OK, I could make 10 with the 1 and the 9. That's my first
pair.
Redraw the 1 and 9 cards, as a pair, to one side.
If I look at my hand when the game starts, and I have a pair that make 10, I can take them out and
then draw two more cards.
Replace the cards you have put down with two more cards; this time making sure that no pairs of cards in
your hand make 10. For example, if you have 4, 5, and 7, you might add another 4 and a 2.
Let's say I drew a 4 and a 2, so now these are my cards: 4, 2, 4, 5, and 7. Do any two of these cards
make 10?
When it's my turn, I can ask the other player for a certain card that I need to make a total of 10. For
example, suppose I wanted to make 10 using the 2 in my hand. What card would I need to add to the
2 to make 10?
So, if I was playing with Claire, I might ask, “Claire, do you have an 8!” If Claire has an 8, she gives it
to me. I put the 8 and the 2 down as a pair, and draw the top card from the deck. If Claire does not
have an 8, she says “Go Fish.” I take a card from the top of the deck.
Each time I draw a new card, I check to see if I can make 10 with that card and one already in my
hand. If I can, I put the pair aside and draw a new card. If I can't, my turn is over.
Start a demonstration game with a student volunteer. Explain that for this game, you will be showing students
your cards so that they can learn how to play. When students play in pairs, they will not show their cards to
their partners. As you play, involve students in your turn.
I have a 5, 7, 2, 1, and 4. Can I use two of these cards to make 10? No one sees away? OK, so what
could I do next?
You might decide to play an entire demonstration game, or if you think most students understand how to
play, just play for a few turns. In this case, explain that the game continues with each player trying to make
combinations of 10. The game is over when there are no more cards.
Math Games
p.4
If you never have a 10 and a 0 card in one hand during the demonstration game, find these cards and be sure
students recognize that they can make a pair with 10 and 0.
As you collect pairs that make 10, put each one in a separate pile. Explain that this is so the cards don't get
mixed up, because at the end of the game, players turn over their pairs and list all the combinations of 10 they
made, using addition notation. Model this for your students.
Rules: Tens Go Fish
Materials: Number Cards with wild cards removed (1 deck per pair); card holders (optional); unlined paper;
counters (available)
Students play in pairs or threes. Each player is dealt five cards. (Use card holders, made as described on p.
101, if the numbers show through to the back of your cards.) Players take turns asking each other for cards
that will make 10 with a card already in their hand. They place any pairs made on the table and draw a new
card from the deck at the end of each turn. If a card drawn from the deck makes a pair with a card in the
hand, the player puts that pair down and draws again.
If a player uses up all his or her cards and there are still cards left in the deck, that player draws two cards. The
game is over when there are no more cards in the deck. At the end of the game, players list the combinations
of 10 they made.
For more challenge, students can play the game in groups of three or four; with more players, it is more
difficult to remember the cards other players have asked for.
Observing the Students: Tens Go Fish
How do students decide which card to ask for? Do they use knowledge or combinations of 10? Do they use
counting strategies to find a number that goes with a card in their hand to make 10? Do they seem to ask for
cards at random?
Are students able to keep track of the cards other players have asked for? Do
they use this to reason about what cards the other player has?
Some pairs might benefit from playing cooperatively. After a player chooses
one card to use to make 10, both players figure out together which other card
is needed to finish the pair. If the other player does not have this card, the pair
can look for another way to make 10, using one card from each hand.
Variations
o Different cards will work on different skills.
o Vary the target sum for other fact practice.
o Allow more than 2 cards for a sum to ten.
o Play rummy style where you keep cards in your hand until you can lay them all down
o Keep score by counting up points on the table subtracting points in hand.
Math Games
p.5
The Sums Game
10
2
3
4
5
8
6
12
10
7
9
11
14
18
13
12
16
10
17
15
6
9
5
7
10
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
Play begins with each player covering a number from 1 to 9 at the bottom. The 2nd player
then covers the sum of those two numbers on the game board. The 1st player can then select
one new number from 1 to 9 at the bottom and cover the sum of those two numbers. Play
continues until one player has covered four squares in a row, horizontally, vertically, or
diagonally.
(Adaptation of the Product Game)
Math Games
p.6
Five In a Row
Players: 2 and up
Materials: 1 Gameboard per player, counters, Number cards (1 to 10 only), chips to cover spaces.
Goal: Cover 5 spaces in a row, vertically or horizontally or diagonally.
Gameplay: Shuffle the number cards and put in a face down pile. On each turn, put the top three cards face
up. Each player can cover up any number which is the sum of any two of the revealed cards. For example, 3,
4 and 9 would mean you can cover 7, 12 and 13. Since each child has a different gameboard, this prevents
just copying the spaces covered.
Questions: Which cards do you need turned up to cover ___ or to finish a row? If a 4 is turned up, what
other numbers would you like to see turn up?
Variations:
1) Turn up five cards, cover any combination of 2. (There’s up to10 possible combinations!) Or do this
and allow students to cover only 3 of the combinations they see.
2) Have students work cooperatively on the same board. Or have students make their own boards.
Game Boards are 5 by 5 grids, with numbers from 2 to 20 distributed randomly. Use multiple 10s or other
sums of interest, and few low numbers. Kids can make up their own boards.
Sample Five In a Row -- Game Board
2
10
16
15
9
4
10
18
13
9
6
12
20
11
7
8
12
19
11
5
10
14
17
11
3
Math Games
p.7
Race to 1 0 0
Game for two players or teams.
Materials: Rolling mat, score sheet, 1 die, abacus (or hundreds chart or base ten blocks…)
How to Play: roll the die to see who goes first. That player rolls the die onto the rolling sheet. Your hand has to start from not
above the sheet. You score whatever you roll if the die is outside of the grey rectangle or off the sheet. You score your roll +10 if
the die is on the grey rectangle – even if only a little bit is on. If the die is totally within the white oval, you score your roll +20.
Keep track of your total score by moving the beads on the abacus. (Or using whatever your method is for keeping score.) The
first player to pass 100 wins. If playing again, the winner goes second and the other player goes first. Optional: record score on
paper also.
Variations: (1) rolls off the mat are subtracted from the total. (2) Start at 100, and subtract the scores to race to zero.
…
…
Score: 3
One
Two
…
Score: 13
One
Score: 23
Two
One
Two
p.8
Math Games
Roll+10
Roll+20
Roll+10
Math Games
p.9
Close To 1000
Materials
One deck of Numeral Cards
Close to 1000 Score Sheet for each player
Players: 1., 2, or 3
How to Play
1. Deal out eight Numeral Cards to each player.
2. Use any six cards to make two numbers. For example, a 6, a 5, and a 2 could make 652, 625, 526, 562,
256, or 265. Wild Cards can be used as any numeral. Try to make two numbers that, when added, give
you a total that is close to 1000.
3. Write these numbers and their total on the Close to 1000 Score Sheet. For example: 652 + 347 = 999.
4. Find your score. Your score is the difference between your total and 1000.
5. Put the cards you used in a discard pile. Keep the two cards you didn't use for the next round.
6. For the next round, deal six new cards to each player. Make more numbers that come close to 1000.
When you run out of cards, mix up the discard pile and use them again.
7. After five rounds, total your scores. Lowest score wins!
Scoring Variation
Write the score with plus and minus signs to show the direction of your total away from 1000. For example:
If your total is 999, your score is -1. If your total is 1005 , your score is +5. The total of these two scores
would be +4. Your goal is to get a total score for five rounds that is close to 0.
Score Sheet for Close To 1000
Game ___
Round 1
Round 2
Round 3
Round 4
Round 5
Score
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
Total Score
_____
Score Sheet for Close To 1000
Game ___
Round 1
Round 2
Round 3
Round 4
Round 5
Score
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
___ ___ ___
+
___ ___ ___
=
______
_____
Total Score
_____
Math Games
p.10
Close to Zero
From Mathematical Thinking in 5th Grade
Investigations in Number, Data, and Space
© 2000 TERC
This is a game that has many variations in the Investigations curriculum.
Math content: place value, mental math, estimation
Materials: a deck of number cards or playing cards with 10s, Queens and Kings removed.
Players: 2 to however many the deck supports.
Gameplay: Deal out 6 cards to each player. The goal is to arrange the cards as two 3 digit numbers whose
difference is as close to zero as possible. Arrange the 3 digit numbers for larger – smaller. After doing this
five times, the sum of the differences is taken, and the lowest score wins. All cards go to the discard pile.
When out of cards, shuffle up the discard pile to deal more cards.
Variations:
1) 2 players. Deal three cards to each player. Players take turns going first, making a three digit number.
The other player makes the 2nd number and scores the difference. Note that there is perhaps a lesser
amount of problem solving here, but the game feels more competitive.
2) Deal 4 cards to each player and make two 2 digit numbers. (Good variation for late second or third
grade.)
3) Deal an extra card so that players use all but one card to make their numbers. Makes scores much
lower.
4) The game can be adapted to addition. For example: Deal 4 cards, and make two 2 digit numbers
whose sum is as close to 100 as possible. Scoring can be: a) the difference between the sum and 100,
taken as a positive number. (i.e. 112-100 or 100-87). Play 5 times, add the distances from 100 and the
lowest score wins. Or, b) you only score if under 100. Over 100 means zero points. Play 5 times,
highest score wins. Note that some deals of four cards have no sum under 100, so the five card
variation can be used if you are scoring this way.
5) Calculators can be used at some, all or no points in this game to change the pedagogical focus.
Sample Score sheet:
___ ___ ___ – ___ ___ ___ =
___ ___ ___
___ ___ ___ – ___ ___ ___ =
___ ___ ___
___ ___ ___ – ___ ___ ___ =
___ ___ ___
___ ___ ___ – ___ ___ ___ =
___ ___ ___
___ ___ ___ – ___ ___ ___ =
___ ___ ___
Total:
___ ___ ___ ___
Math Games
p.11
Calculator Get Down
I first and last saw this game in a “calculator fun book” about 30 years ago, but long ago lost track of the
book and author. (Yes, there were calculators then. They could add, subtract, multiply and divide, and got
hot if you left them on too long.)
Math content: mental math, operations, divisibility rules.
Materials: 1 calculator
Players: 1
Gameplay: Enter a random 6 digit number with no repeats. Using only +, – , * and / perform operations
on this number to get to zero – using only 2 digit operands, and 6 or less steps! Ask students to keep a
record.
Example: 342987. (1) –37. (2)/50. (3) –59. (4) /40. (5) –85. (6) –85.
Variations: Don’t even get me started. Good order of operations practice to write down a single equation of
what they did.
Flip – a free game by James Ernest
Players: 2
Playing Time: 5 minutes
Equipment: Ten 6-sided dice
To Begin: Each player rolls five 6-sided dice. The player who rolls the lowest total goes first.
On Each Turn: You may do one of two things. You may either flip over one of your own dice, or you may
instruct your opponent to play one of his dice into the middle of the table.
Playing: When you make your opponent put a die in the middle, you choose the die. Your opponent puts it
into the middle. He may then withdraw any combination of dice from the middle which totals less than the
value of the die he put in. So, for example, if he plays a 5 into the middle, he could take out up to 4 points
worth of dice in any combination.
Winning: To win the round, you must be the last player with any dice left. To keep score over several
rounds, record the sum total of the dice you keep. In that case, play to 50 points.
Stalemate: To avoid stalemate, it is illegal to flip the same die twice without first making your opponent play.
Note: This game requires some modeling, as the reverse nature of the decisions makes it difficult for
students to get the hang of it.
Number Strings
Examples:
A) 46
2x23
Can only be broken down once, player who
started loses.
Players take turns breaking down a number by
multiplication. The first player starts with a
whole number. The next player makes a string
of two numbers that multiply to give the first.
B) 36
The next player then can break down one of the
4x9
two numbers, making a three number string.
2x2x9
The last player who can break it down is the
2x2x3x3 – loses.
loser of the game. Numbers chosen must be
able to be broken down more than once.
Players may not reuse starting numbers. 1 may not be used in the breakdown.
Math Games
p.12
Change for the Better
Materials: Real coins or play money. Enough so that each player can have 1 quarter, 2
dimes, 3 nickels and 4 pennies.
Math content: Low double digit subtraction.
Gameplay: Randomly determine who goes first. That player puts a coin in the middle. Play
goes clockwise (to the left). Each
Paid
Change
Cost
player puts in a coin, and is
allowed to take out as much
change for that coin as they can,
for any amount less than the value
they put in. For example, if you
put in a dime, you could take out
up to nine cents. The winner is
the last person to have money.
As a tutoring activity, it is
recommended that students keep
track of their change.
Variations:
1) Allow 1 dollar coin, 2 fifty
cent, 3 quarters, 4 dimes, 5
nickels and 6 pennies.
2) Have students keep track
of how much money they
have total.
Adapted from the game Fight, ©
James Earnest
Math Games
p.13
The Product Game
1
7
15
25
36
54
2
8
16
27
40
56
3
9
18
28
42
63
4
10
20
30
45
64
5
12
21
32
48
72
6
14
24
35
49
81
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
Play begins with each player covering a factor from 1 to 9 at the bottom. The 2nd player then
covers the product of those two numbers on the game board. The 1st player can then move
either one of the factor numbers and covers the new product. Play continues until a player
can cover four products in a row, horizontally, vertically or diagonally.
(From CMP)
Math Games
p.14
Prime Time
Free
50
10
6
18
15
9
27
30 105
4
70
49
35
20
8
25
14
28
42
147 21
75 175 63
45
12 125
98
Factor List
Free
Rules
2
3
5
7
2
3
5
7
2
3
5
7
Player A covers a factor and
then Player B covers a factor
and the product. Players then
take turns either changing one
factor or adding or removing a
factor chip. Play continues
until one player has covered
four in row (horizontally,
vertically or diagonally) or
neither player will be able to.
(From CMP)
Math Games
p.15
Score Factor
Game Board
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
Player A chooses a number on the game board and covers (or circles) it.
Using a different color, player B covers all of the proper factors. Player
B then circles a new number, and Player A covers all of the uncovered,
proper factors of that number. If a player circles a number with no
uncovered factors, that player scores no points and loses that turn. The
game ends when there are no numbers left that have an uncovered
proper factor. Each player scores points equal to the total of the
numbers they covered.
© Connected Mathematics Project, Prime Time
Math Games
RO
OLLLL
T
TO
O
TEEN
N
p.16
Game rules: Each group of players gets three dice – two with the same color and one that is different.
Players roll to see who goes first and the highest untied die roll plays first. On a player’s turn, they roll the two
same color dice first, and make the biggest two digit number they can from it. For example, a 4 and a 6 could
make a 46 or 64. Then the third die is rolled to determine the units: tenths, hundreds or thousandths: is it 46
tenths, 46 hundredths or 46 thousandths. Players build that amount, then add it to their total. A player is out
if their total goes over 10. The winner is the last player remaining in. Low score wins!
Unit Roll:
Tenths
Hundredths
Thousandths
Score Card:
Roll
Unit
Ones
(Blocks)
Tenths
(Flats)
Hundredths
(Sticks)
Thousandths
(cubes)
Total
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
.1
.01 .001
+
0
Math Games
p.17
A
Triangle Game
A:1,2
B:3,4
C:5,6
B
C
Game 1
Three players. Each takes a vertex. Roll dice to determine who goes first. Play proceeds counter-clockwise.
First player circles their vertex, rolls, and moves halfway towards the indicated point. Subsequent players roll a die, and move the
point halfway towards the vertex rolled. Continue until each player has rolled twice. The winner is the player whose vertex is
closest to the point at the end of the game. Players should play new games on the same board.
Game 2
Any number of players and a referee. Referee chooses a vertex (A, B or C) as a starting point and a target white triangle. Players
write down a sequence of vertex moves. Closest player to the target triangle after their sequence of moves wins and is the next
referee.
Triangle Size (edges)
Sequence Length
8
3
4
4
2
5
1
6
1 edge
triangle
Math Games
p.18
Racin’ Robots
2-3 players
Materials: Board, cards (printed two-sided or on colored paper), robot piece for each.
Goal: get your robot to his delivery spot to finish his job of transporting widgets.
Gameplay: Randomly determine who goes first. Each player draws four cards, and lays down 2 cards to program their robot.
Their robot may be placed in any direction in the home square. Note that a flipped robot has the reverse orientation of an
unflipped robot. On a player’s turn, they:
1) Lay down a third program card for their robot.
2) Turn over the front program card and make the robot do that movement. The card then goes to the discard pile.
3) Draw back up to four cards in hand.
All directions are given from the robot’s perspective. Example: forward means the direction the robot is facing. Left is the robot’s
left, etc.
If a robot moves onto another robot’s square it pushes that robot back one spot in the direction the moving robot is heading.
If a robot lands on a square with text, follow those directions.
If there are no more cards to draw, shuffle the discard pile and put it into the deck.
If the robot would be put off the board, it relocates to start.
If you play a push card on an opponent, play an additional program card on your own robot.
Turns are around the center point.
Variation: Play so that if you go off an edge you come onto the opposite side. (Less frustration this way.)
Math:
As you play, think about how the different motions combine.
How would the game be different if the motions were to some standard system instead of relative to the robot?
What new motion cards could you make?
Which motion cards were more difficult to use?
What’s the difference between a vertical flip and a 180o turn?
Inspired by the game RoboRally, designed by Richard Garfield.
Math Games
p.19
Run
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Run
Run
ROBOT
Run
Math Games
p.20
Move forward one
Move forward one
Move forward one
Flip over right hand
edge
Flip over right hand
edge
Move left one
Move left one
Move left one
Flip over left hand edge
Flip over dotted line
Move right one
Move right one
Move right one
Flip over left hand edge
Flip over dotted line
Move back one
Turn 90o right
Push forward one (this
card may be swapped
with an opponents
program)
90o
Move back one
Move back one
Move forward two
Move forward two
Move forward two
Turn
right
Push backward one
(this card may be
swapped with an
opponents program)
Move forward three
Move forward three
Move forward three
Turn 90o right
Flip over horizontal
center line
Move back two
Move back two
Move back two
Turn 90o left
Flip over vertical center
line
Turn 180o
Turn 180o
Turn 90o left
Turn 90o left
Turn 90o in a direction
of your choice.
Math Games
p.21
Race Board
ROBOT 2
START
ROBOT 1
FINISH
Rotate 90o
right around
center
Move Forward
2 spaces
Move Left 2
spaces
Rotate 90o left
around center
ROBOT 2
FINISH
R
L
R
L
Cut out Robots into two strips, fold along right hand
edge to get a robot with a front and back.
R
L
R
L
ROBOT 1
START
Math Games
Preparation:
p.22
Polygon Capture – Game Rules
Each pair of players needs a set of property cards and a set of polygon cards. The polygons go into the center
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.
If the active player believes no polygons can be captured, the other player gets a chance to capture any
matches. If there is a match, the turn is done. If not, the active player can choose to turn over one more
property card, choosing either angle or side. If they believe still no polygons can be captured, they must say,
“Done” and end their turn.
Any player can challenge the capture of a polygon. If a player chose a polygon incorrectly, it goes back into
the center 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
Math Games
p.23
Math Games
All angles are
right angles
p.24
At least one
angle is obtuse
No angle is a
right angle
At least one
angle is less than
90o
STEAL CARD
Select a pair of
properties. Steal
all these
polygons from
your opponent.
At least one
angle is a right
angle
At least two
angles are acute
All angles have
the same
measure
No pairs of sides
are parallel
All sides are of
equal length
Exactly one pair At least one pair
of sides is
of sides is
parallel
perpendicular
All pairs of
opposite sides
are parallel
It is a
quadrilateral
All pairs of
opposite sides
have equal
length
WILD CARD
Pick your own
side property
Math Games
p.25
Target Practice
Players: 2 teams.
Playing time: as long as you want.
Equipment: two differently colored dice, paper, graph paper.
Game play: On each turn, each team rolls the pair of dice to come up
with a set of target points. They then come up with an equation, to hit
as many of the target points in the graph of the equation as possible.
On each round, you roll the same number of targets as the round
number; ex. on round three, three targets. For each target scored, you
get the same number of points as the round; ex. If you hit two targets
on round three, you score 6 points. Play for at least five rounds.
Variations: For variety, allow teams to make any given roll positive or negative. For challenge, include (0,0)
as an extra target point in each round.
Round
1
Points
( , )
2
3
(
(
4
5
(
, ), (
Equation
Targets Hit
Score
, )
, ), ( , ), (
( , ), ( ,
( , ), ( ,
, ), ( , ), (
( , ), ( ,
, )
),
)
)
, ),
Total
Pig (Wikipedia version.)
Pig is a simple folk jeopardy dice game first described in print by John Scarne in 1945. As with many games
of folk origin, Pig is played with many rule variations.
Players: Any number.
Materials: 1 die.
Gameplay: Each turn, a player repeatedly rolls a die until either a 1 is rolled or the player holds and scores
the sum of the rolls (i.e. the turn total). At any time during a player's turn, the player is faced with two
options: roll - If the player rolls a 1: the player scores nothing and it becomes the next player's turn. 2 - 6: the
number is added to the player's turn total and the player's turn continues. Or the player may hold - The turn
total is added to the player's score and it becomes the next player's turn. Play to a total (the first player to
score 100 or more points wins) or for a set number of rounds.
Questions: The probability of this game is quite interesting, and determining the optimal strategy is such a
good problem that this is the center of an Interactive Mathematics Project unit.
Math Games
p.26
Players: Two or
Denominator
Numerator
more.
Roll Result
Roll=Result
Playing time: 5 –
1,
Thirds
1,2,3=1/4
4,5,6=2/4
10 min.
Equipment: unit circle with angles, dice, markers
2, 3 Fourths
1,2,3=1/3
4,5,6=2/3
for player position.
4, 5 Sixths
1=1/6, 2=2/6, …, 6 = 6/6
Gameplay: Roll to see who goes first. Highest
6 Twelfths 1=1/12, 2=2/12, …, 6=6/12
untied roll wins. Players roll once for the
denominator, and then for the numerator, and move that fraction of π. First player to complete the trip
around the unit circle wins.
Variations: (1) Play to get exactly to 2π. A roll that would take you past is not moved. Play for a set number
of rolls. (2) Moves may be taken clockwise or counter-clockwise, but must be moved. This is also best
played for a set number of rounds (like 6 or 10), and the closest player to 2π wins after that number of
π/2
rounds.
Radian Race
π/3
π/4
π/6
π/12
Math Games
p.27
Box Builder
2 or more players or teams
Materials: Graph paper, side cutouts (optional), die, record sheet.
Goal: Build boxes with nets to store the largest volume you can.
Play:
Roll
Piece
1
2
3
4
Players take turns rolling a die and recording the piece they got. At any
point, they can choose to use up some of their pieces to make a net for a
box. They record the net, and score 1 point for each cube of volume. Play continues until one
player/team makes a third box, or they roll their 10th piece of one type. The other team gets a last chance
to make a box out of the pieces they already have.
Example:
Team 1 has rolled the following:
X
X
One of the partners realizes they could build a box with the net
X
X
X
X
X
X
X
X
Pick from any
other number
5
So they cross off the pieces
they use and score 6 points.
X
Variations: Play for
surface area. Or you
could play until a total is
reached, like a total
volume of 10 cubes, or a
surface area of 100
squares.
6
X
Record Sheet
Score:
game1
game 2
Record rolls: X off a piece when it is rolled. Circle or cross out the X when it’s used to make a box.
Piece
game1
game2
Have players cut pieces out of a piece of graph paper as they are rolled. Keep these after the first game for playing future games.
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