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# HobbiesMath Games

These twenty-four games are fun and appropriate for a wide range of ages.

Most of the games are only for two players. These also work in a classroom with the students divided into two teams (whose members either must agree upon decisions or are lined up and take turns making decisions).

Many traditional board games involve mathematical concepts. I assume you already know these games, so this list of math games does not mention Go, Poker, Chutes and Ladders, etc.

I have also designed arithmetic worksheets (addition and subtraction, also some easy multiplication and division) to practice mental math speed. They are much more fun than flash cards.

### Build a Bug

Equipment: chalkboard or whiteboard or pencil-and-paper, either dice or cards (see below)

Divide the players into teams. Which team will be the first to finish building a bug?

A complete bugs has the parts in the diagram below.

The simplest way to play is with a die. Each team takes turn rolling the die. They get the number of points rolled. Each turn they may spend their accumulated points to buy one bug part.

There is no need to save up points. Teams may spend their points as they roll them, buying the bug part that corresponds with their die roll. But this is not always the best strategy.

Each team could keep track of their bug-in-progress on paper. Or a teacher could keep track of all the bugs by writing on a board. (The game is more exciting when all players can see and compare all the bugs-in-progress.)

For a more advanced game, replace the die with a some cards. From a normal deck of cards, take out the cards with the values one (ace) through six to form a smaller deck to play with. But do not use the same number of each card value! Adjust how many cards of each value are in the deck you use.

For example, a deck with only one each of values one through five, but all four of the cards with value six, emphasizes those "wild cards". As another example, a deck with all four ones, but only one each of the cards with value two through six, emphasizes accumulating points one at a time towards the next desired purchase.

### C-rod Tower Building Competition

Equipment: Cuisenaire rods

Divide the class into teams of two people. Which team can build the tallest tower using C-rods whose total length is fifty?

For example, it is not too difficult to build an H-shaped tower of height 21 using five orange rods. The tallest tower possible would be of height 50, but balancing this is perhaps impossible for a child.

### One Ogre, One House

Many old fairy tales had ogres. These were not friendly, green ogres. They were very scary monsters!

Why were they so scary? They ate people. They especially liked to eat children. But that's not why they were so scary. In fairy tales lots of things eat children: wolves, witches,...

Ogres were very scary because they could use magic to look like anyone. If you went into an ogre's house to rescue a child, and took the child home, it might actually be the ogre! Then poof it would turn back into its normal, big, ugly self and eat you.

This game has an ogre story. Children from two kingdoms are captured and at the ogre's house. They need rescuing!

The kings and queens from the two kingdoms went to a magician and asked, "Could you take away the ogre's power to look like anyone? Then we can be more safe when rescuing the children."

The magician said, "No. I cannot do that. The best I can do is make sure that only the last child is really the ogre. All the children you rescue before that are really children, and safe to rescue.

You are a hero from one of the two kingdoms. On your turn you can rescue one, two, or three chidren. You cannot rescue more than that because you need to get into the ogre's house and back out very quickly. And you want to leave the last "child" for the other hero because the last "child" is really the ogre!

Equipment: some objects

Players alternate taking turns.

The game begins with a single pile of objects ("the children") between the players.

A turn consists of taking one, two, or three objects away from the pile. Whichever player takes away the last object looses.

This game has a winning strategy! Part of the fun, whether you win or lose, is discovering the strategy that allows you to win all the time if the other player does not know the secret winning strategy.

Note: this game is a variant of Nim sometimes called Poison.

### One Ogre, Two Houses

So the ogre from the last game got upset. So many children were getting rescued!

He had an idea. He built another house! He would pretend to be a child, and the heroes would not know what house he was in.

Because he was trying to be tricky, he would not reveal himself when a hero was in his house. The heroes did not need to be quick any more.

You are again a hero from one of the two kingdoms. On your turn you can rescue any number of chidren. But you can only rescue children from one house at a time. And you want to leave the last "child" for the other hero because the last "child" is really the ogre!

Equipment: two piles of objects

The game begins with two piles (usually of ten to twenty objects) between the players.

Players alternate taking turns. A turn consists of taking any number of objects away from one of the piles.

The player who takes away the last object loses.

This game has a winning strategy! Part of the fun, whether you win or lose, is discovering the strategy that allows you to win all the time if the other player does not know the secret winning strategy.

Note: this game is another variant of Nim.

### Dice Targets (Subtraction)

Equipment: four six-sided dice, pencil, the target papers

All the players take turns using the four dice to try to roll the target number 20. If they are close enough, they can fill in one of the subtraction equations on their paper. For example, a player who rolls 18 could fill in 20 − 18 = 2. All of the subtraction equations need two numbers: the curent target number and a dice sum.

After each player has taken his or her turn, the target number decreases to 19. The players each try again.

Not all four dice need to be used. Once the target number has gotten smaller it will often work best to only sum two or three of the four rolled dice.

The sum of dice can exceed the target number. If the target number is 14 and the sum is 15, then the subtraction equation 15 − 14 = 1 could be filled in.

After the target number reaches 10, reverse its trend and count up back to 20.

The first player to "hit" (complete a subtraction equation) with all twelve "arrows" (places with equations) wins. If that does not happen then the player with the most "arrows hitting the targets" after the target number returns to 20 wins.

Equipment: two six-sided dice, pencil, the target papers

This is an easier version of Dice Targets that only uses addition.

### No Pigs! No Pigs!

Equipment: two six-sided dice, perhaps paper and pencil

The game always has five rounds.

For this game, the 1s on the dice are called pigs.

Each round begins with rolling both dice. If either die rolls 1, reroll how that round starts until neither die is 1. Now the players choose to either "play it safe" and keep the total of both die or "be risky" and go for a running total.

If any player chooses "be risky", the dice are rerolled. If either die is a 1, the players who chose "be risky" gain no points for that round. If neither die is a 1, the choice repeats. Those players who just picked "be risky" may "play it safe" and keep the running total so far for the round, or continue to "be risky" and attempt to gain a higher score for the round.

The round ends either when all players have "played it safe" or when either die rolls a 1.

The game ends after five rounds. Players add up their score for a grand total. The highest total wins.

Note: To practice other arithmetic use more complicated dice. How about rolling two ten-sided dice and a six-sided die, then finding the product of the ten-sided dice and subtracting the six-sided die? Similarly, younger children might need to start with only one six-sided die and then work their way up to using two dice per roll.

Note: This game is a variation of the old British game named Pig.

### Cameron's Game

Equipment: a pencil, two six-sided dice (one of which is labeled 5 to 10), the game paper below

This two-player game was invented by David V. S. and a first-grader named Cameron.

The game uses a blank five-by-five grid, like an empty bingo board. The center spot is a "wild" spot that both players can use to win.

The other twenty-four spots need a number. So before the game starts, the two players fill up those spots with numbers. They take turns writing numbers, counting from 1 up to 12 in any twelve of the empty spots. Then they do it again. Now every empty spot has a number.

The basic game is to play five-in-a-row. On your turn roll both dice. You may add or subtract, which provides a choice of two values. Hopefully one of those two values represents an unclaimed spot on the board, so you can claim a new spot. (If not, you lose your turn.)

If neither player can get five-in-a-row to win, the player that claims the most spots wins.

For a more advanced game, try four-in-a-row. Trickier!

### The Ha Ha Dice Game

Equipment: one twenty-sided die and five six-sided dice

Players take turns rolling all six dice.

The players who did not roll get to go first. They try to arrange the five six-sided dice into combinations that add up to the twenty-sided die value. Each combination scores one point.

(For example, the twenty-sided die rolled 16 and the five six-sided dice were 4, 5, 5, 1, and 6. Two different combinations are 6+4+1+5 with one of the fives and 6+4+1+5 with the other five.)

After those players have decided there are no more combinations, the player who rolled the dice has a chance to show any combinations that were overlooked. He or she can say "Ha ha!" if those exist. Those are worth two points!

Then the next player rolls all the dice.

Note: As appropriate to the mental arithmetic abilities of the players, allow subtraction and perhaps use ten-sided dice instead of six-sided dice.

Equipment: paper and pencil

Write the numbers one through ten on the paper. Use the side margins of the paper to keep running totals for the two players.

Players take turns crossing out one of the numbers and adding it to their running total. (Once a number is crossed out it cannot be claimed again.)

The player whose total reaches exactly 40 wins.

(Addition Picking was originally published in Five-Minute Warmups for the Middle Grades: Quick and Easy Activities to Reinforce Basic Skills (1994) by Green, Schlichting, & Thomas Publishing Company.)

### Fifteen

Equipment: pencil and paper, two sets of five matching objects

Between the players put a piece of paper with the numbers one through nine written on it. Each player has a pile of five identical objects. Players alternate taking turns. A turn consists of claiming a number on the paper by putting one of your objects on it (each number can only be claimed once). The first player who has claimed three numbers that add up to 15 wins (this winning combination need not use all of the numbers that player has claimed). If all the numbers have been claimed without either player winning, the game is a tie.

An expert at Fifteen can always force the game to be a tie. Can you rearrange the numbers one through nine on the paper to make Fifteen the same as another game you know?

### The 37 Game

Equipment: paper and pencil, an object

On the paper draw the game board: six squares labeled one through six.

The game starts with the object on the square labeled six.

Players take turns. On a turn, move the marker to a different square and add that number to the running total.

A player who gets the total to exactly 37 wins. A player who brings the total higher than 37 loses.

### Bidding War

Equipment: pencil and paper, one object

Before the game begins, pick how many points each player starts with. (For younger children 10 or 20 will suffice. For older children use 100 or 500.)

Set up the game by drawing a line with seven notches. The players sit at either end of the line.

Play begins with each player secretly writing down on a piece of paper how many points they wish to bid in the first round. These numbers are revealed, and the highest non-tying bid wins: the object moves one step in that player's direction. Each player subtracts from their point total the amount of their bid. Then repeat the bidding process. The game lasts until the object reaches the side of the playing field (that player wins the game) or no player has points left to bid.

This game works equally well with four players/teams. Use a seven-by-seven grid instead of the previous diagram, with the four players each sittting at each edge of the grid.

### Peasant Rescue

Equipment: the paper below, tokens to place on the paper

This is a version of The Factor Game for younger children. (It uses addition and subtraction, instead of multiplication and division.)

Each turn has a pattern of "move and respond". One player puts a marker on any unclaimed spot. The other player, if able, places markers on two unclaimed spots whose numbers add up to the original number. (On subseqent turns the players alternate who goes first and who responds.)

The player who is responding can only use numbers not adjacent to the original number horizontically, vertically, or diagonally.

The walls around the spots for 8 and 13 "block" adjacency. For example, the spots for 3 and 9 are not considered adjacent because the walls interrupt a line drawn between those numbers.

A player who cannot make a valid reply does nothing. (He or she does not get to pick one spot as a partial reply.)

The spots for 8 and 13 (inside the walls) cannot be picked except as replies.

The game ends when all eighteen spots outside of the walls are full. Each player adds up how many peasants are on his or her spots. The player who rescued the most peasants wins!

### Bear Battle

Equipment: six dice, two counting/sorting bears (or other objects to represent the bears), the papers below

This is an simpler but equally fun version of Robot Battle. Practice looking at several numbers to decide how they can be used together!

On your turn, move your bear up to three spaces and also do one action you pick by using your dice creatively.

Here is an image with only the map. When this is printed scaled to fill an 8.5" by 11" piece of paper the standard classroom counting/sorting bears fit in the map squares.

These bear record pages are not needed. But they help younger children keep track of their bears' powers and current oomph.

## Place Value

### 101 and Out

Equipment: a six-sided die, two types of objects to represent tens and ones (see below)

The game always has six rounds. In each round, the die is rolled and each player chooses to take that number of either tens or ones.

A running total is kept for each player. After six rounds, whomever is closest to 100 withut going over wins.

Note: There are many fun ways to represent ones and tens: pennies and dimes, Base Ten Block units and tens, Cuisenaire rod ones and tens, tiles and taped strips of ten tiles, beans and popsicle sticks on which ten beans are glued, sticks and bundles of ten sticks, etc.

### Reject

Equipment: paper and pencil, one ten-sided die

Players each use a game board with empty place value spots for ones through ten-thousands, as well as an extra spot labeled "reject".

The game always has six rounds. In each round, the die is rolled and each player picks where to put the rolled number: in a unused place value spot or in the reject box. After six rolls, the player with the largest number wo can read it aloud wins.

For a "beginner" version of the game that can help teach the concept of place value, use fewer digits.

Here is a version with three digits (and the reject box) that is useful to an average first-grader that somewhat understands the concept of hundreds but is still a bit foggy about thousands. A game would involve four rounds, since there are four spots to write a number.

You can download a page with eight "beginner version" diagrams to make the game easy for younger children.

This game works equally well with more than two players/teams.

### The Caves of Wumpus and Grue

Equipment: paper and pencil, four six-sided dice

Play alone or cooperatively with friends! Roll dice to explore a cave system of 16 rooms. Hunt the wumpus! Don't get eaten by a grue.

(This game is, of course, a tribute to Hunt the Wumpus and Zork.)

## Fractions

### Fraction Bingo Twenty

Equipment: one game board per player, one twenty-sided die (percentile dice may be used instead to teach about percentages)

Each players draws a five-by-five bingo board with five "free" squares as arranged below.

Each player arranges the following twenty fractions in any order in the remaining squares of his or her bingo board.

The Twenty Fractions

1/2, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/10, 7/10, 1/25, 4/25, 7/25, 9/25, 11/25, 14/25, 16/25, 34/40, 36/40, 38/40, 124/125

Players take turn rolling a twenty-sided die. The die shows the numerator for a fraction whose denominator is always 20. With each die roll all players cross out the remaining fraction closest to the fraction produced by the die roll.

(The fractions are carefully chosen so that even different-looking pairs can be compared by "unreducing". Multiply the denominator by a number to change it to 100, then be fair by also multiplying the numerator by that number. Initially each fraction on the bingo board is within two-hundredths of a different die roll fraction. But as the game goes on the closest remaining game board fraction can grow farther in absolute value from the die roll fraction.)

One or more players win by being the first to score a five-in-a-row "bingo" using the current die roll.

The fourth and fifth grade students I work with love this game. It has just the right blend of cooperation (working together to determine which remaining fraction is closest in value to the die roll fraction) and competition (getting "bingo" first).

This game works equally well with more than two players/teams.

### Customized Deck Fraction War

Equipment: one piece of per player cut into 24 cards, a pencil

Each player makes a deck of 24 cards by writing a different counting number on each card. (Here is a handy grid of rectangles to print to cut out.) Players should make their decks distinct by using a different color pencil, intialing each card below the number, using a stamp and ink pad to decorate each card below the number, etc.

Before the game begins, both players shuffle their decks and turn over the top card. The player with the smaller number decides whether the fractions they will be making that game will be proper fractions (less than one) or improper fractions (greater than one). Both reshuffle their decks.

The game then begins. In each round, both players draw the top two cards from their deck, then place them face-up to make a fraction. There are initially no choices. Which number is numerator or denominator is forced by the earlier decision about proper or improper fractions. The player whose fraction is the larger number wins the round and "captures" his opponents two cards. Captured pairs of cards are set aside (as in Go Fish) instead of being absorbed into the victor's deck (as in War). The winner puts his or her victorious cards aside in a discard pile, which is shuffled to replace an exhausted draw pile.

If the two fractions are equivalent, neither player wins. Both players place their pairs of cards in their discard piles.

When a player has suffered four captures, he or she draws an additional card. When he or she begins each turn by drawing two cards, he or she then has three cards and may pick which two to set down.

When a player has suffered eight captures, he or she draws another additional card. When he or she begins each turn by drawing two cards, he or she then has four cards and may pick which two to set down. (This lasts until the game's final turns, when a player at risk of losing has only two cards left in his or her deck and uses them both.)

The player who captures all of the other player's cards wins.

(The pre-game selection of proper or improper fractions is vital. If only proper fractions were used, the best strategy would be to write immensely large counting numbers on each card. Then any pair of cards would make a fraction very close to one. But this strategy is not an optimal strategy because the opponent might use smaller numbers and decide to make the game about improper fractions.)

This game works best with more than two players/teams, which makes it more likely that each round one of the fractions is obviously the greatest. But there is also some potential bordeom if your deck is captured first and you are waiting for the game to end.

### Starship

Equipment: one game board per player

This is a fun version of battleship. Players can shoot "rays" instead of always targeting one board square at a time.

(In December 2013 I glanced over this WSJ article, which mentioned a game named Battleship Numberline. I misread the name as "Fraction Battleship" and was disappointed that the game was not about equivalent fractions on Battleship boards. So I invented the game I had in my mind. There is some subtlety involving the shapes of the ships and how to fit them in between the common "rays" made by equivalent fraction combinations.)

This game works equally well with more than two players/teams.

### Build and Destroy

Equipment: pattern blocks

Put a pile of pattern blocks in the middle of the table.

On a cube-shaped block, label the six sides with three sides with the letter G (for the green triangle), two sides with the letter B (for the blue parallelogram), and one side with the letter R (for the red trapezoid).

Build: Players alternate taking turns. A turn consists of rolling the "die", and if the player desires "adding" the indicated block to the blocks they have so far. If two smaller pieces in your construction can be replaced by one larger one, do so. Whichever player builds a yellow hexagon first wins.

Destroy: The same as above, but instead of building a yellow hexagon piece by piece, start with a yellow hexagon and try to get rid of it piece by piece.

This game works equally well with more than two players/teams.

## Geometry

### Take Over the Geoboard

Equipment: geoboard and rubber bands

Before play begins, each player makes one shape on the geoboard with a rubber band. These will be called obstacles.

Then players take turns claiming a corner and using a rubber band to make a triangle in this corner.

Players now take turns extending their territory by including one more peg inside their rubber band each turn. A player's territory my border but not enter an obstacle or the opponent's territory. Play until all the geoboard's area is either obstacle or a player's territory.

Whichever player's territory contains the most area at the end of the game wins.

### The Kittens of Tindalos

Equipment: the game paper below, patterns blocks (triangles, rhombuses, trapezoids, and hexagons), one eight-sided die

Start the game with "Tindalos" having one pattern block of each shape.

1. Roll an eight-sided die for which shape room you can search for a missing kitten. (1 or 2 = triangles, 3 or 4 = rhombuses, 5 or 6 = trapezoids, 7 or 8 = hexagons)
2. If you want, add one shape to Tindalos. Tindalos is a world with many rooms. Each room is one of the pattern block shapes. You can put one more shape on the paper. (Keep extra shapes off this paper to avoid loathsome confusion.)
3. If you want, either break apart one shape into smaller shapes of the same size or put together shapes into a bigger shape of the same size. (For example, you can combine three triangles into one trapezoid.)
4. Roll an eight-sided die again. If your number is equal or less than the number of rooms of the shape being searched, you have found a missing kitten!

The player that first finds six kittens wins.

### Dots and Boxes

Equipment: pencil and paper

Before play begins, the players make a rectangular grid of dots on the paper. The rectangle should be at least 6 rows long and 6 coulumns wide.

Players take turns connecting adjacent dots with a vertical or horizontal line. If such a move completes a box, that player initials the box and gets to move again. The game ends when no more moves can be made, at which time the winner is the player who made the most boxes.

Note: Normally a "box" means a suqare of the smallest possible size. What changes if larger squares also are allowed to count as "boxes"?

### Greatest Degree

Equipment: paper and pencil, sometimes a protractor

Before play begins, the players take turns drawning some dots on the paper. The total number of dots should be a multiple of six. Do not just draw dots in rows and columns.

The players take turns connecting three dots with two straight lines to make an angle. The lines drawn may not cross or touch previously drawn lines; in particular, each dot can only be used once. Play until no more angles can be legally drawn. The player whose angles sum to the largest number of degrees wins.

### Sprouts

Equipment: paper and pencil

Start sprouts with two or more hollow dots on the paper. Players take turns. A turn is drawing a curve connecting two hollow dots (the curve can start and end at the same dot), and then adding a hollow dot to the middle of this new curve.

Curves are not allowed to cross each other. A single dot is only allowed to have three paths coming into it; fill in dots that have three paths to avoid confusion.

The last player that is able to move wins.

## Multiplication and Division

### The Most Special Snowflake

Equipment: game board, one ten-sided die

See the game description here.

### The Factor Game

Equipment: pencil and paper, two sets of tokens (to claim squares)

Two players claim squares numbered 1 through 30, trying to get the highest total.

The players use distinct markers to mark which squares become theirs. (Use two kinds of coins or beads, or write X or O).

Each turn has a pattern of “move, respond, counter-respond”. The first turn goes like this:

1. Player One claims any unclaimed square.
2. Player Two gets to claim all the unclaimed factors of Player One's number.
3. If Player Two did not notice any factors, Player One gets to say "ha ha!" and claim them.

The next turn is similar except the players switch who goes first. Turns repeat until every square is claimed.

I have made an .png image file and a .svg vector-graphics file with both the instructions and a larger grid (1 through 36).

### Twenty-Four

Equipment: four ten-sided dice

The classic game Twenty Four was the basis for my board game Robot Battle (below) and its simplification Bear Battle (above).

Four numbers are supplied by a moderator, dice, or cards. Players or teams race to use these numbers along with any arithmetic operation, parenthesis, or fraction bars to get to 24.

Each of the four provided numbers must be used once and only once. Two answers are considered the same solution if they only differ by having terms rearranged.

Example of Twenty-Four Game

Consider these four provided numbers: 2, 3, 4, and 6

Possible answers include (2 × 4) × (6 − 3) and 6 × 4 × (3 − 2).

Can you find any of the other answers? There are at least seven more!

Note that (6 − 3) × (2 × 4) is not a new answer because that is merely the first of our answers with terms swapped.

This game works equally well with more than two players/teams.

In the classroom it works well to divide the class into three teams that earn points by finding correct answers. Most sets of four numbers provided will have many possible answers, so do not stop just because other teams have found some answers.

Here are more examples of four provided numbers, with each set having many answers.

Play the Twenty Four Game with these numbers: 1, 2, 3, and 5

Play the Twenty Four Game with these numbers: 1, 2, 4, and 12

Play the Twenty Four Game with these numbers: 2, 3, 5, and 11

Play the Twenty Four Game with these numbers: 3, 3, 6, and 9

### The Invisible Fairy Race

Equipment: four six-sided dice are shared, each player needs one gameboard, a pawn or other marker, and book to hide those before

This game is my simpler way to make Twenty-Four more fun. Having multiple target numbers makes the game fun even when students have different amounts of arithmetic proficiency.

Each player moves a pawn along the path, racing to get to the end first. But the players do not know where each other's pawns are.

On your first turn, roll 1 die and move that many spaces forward.

On later turns, roll 4 dice and try to use all four numbers and basic arithmetic to make a certain number.

If you can, make the number of your pawn's space. That allows you to secretly roll 1 die and move that many spaces forward. If you cannot, make any other number. Then any players whose pawns are on the space with that number must (each separately) roll 1 die and move that many spaces backward.

Finally, you can always decide to skip rolling dice, and simply move forward 1 space on your turn. That can help you get past spaces whose numbers are difficult to make (such as 17 and 23).

### Contig

Equipment: three six-sided dice, pencil and paper, two sets of tokens (to claim squares)

Contig (and Contig Jr.) are nicely enhanced versions of Twenty-Four by MathWire. These games are available here.

As with The Invisible Fairy Race, multiple target numbers allow the game to be fun even when students have different amounts of arithmetic proficiency.

This game works equally well with more than two players/teams.

### Robot Battle

Equipment: game board, four ten-sided dice, pencil and paper, tokens to use as crates and robots

This game is my complicated version of Twenty-Four. I have had students really enjoy modifying the game and playing other versions. Some kids love killer hammer robots with lasers.

If you want to only print the map so it fits larger onto one sheet of paper, use this image.

This game could work equally well with more than two players/teams, but you would want to draw a different game board. The pace of the game slows down with more players, but the fourth and fifth grades with whom I have play-tested this did not mind.

### SubDivvy

Equipment: none

Before you begin, decide on a counting number greater than 1. Players take turns. One each turn, subtract from the current number a factor of the current number (which is less than the current number) to create a new number. The player which creates a new number equal to 1 wins.

(SubDivvy was created by Daniel Fendel and Diane Resek, and was originally published in Foundations of Higher Mathematics: Explortion and Proof (1990) by Addison-Wesley Publishing Company.)

### Octahedral Roulette

Equipment: game board, one eight-sided die, pencil and paper, three tokens per player

Each player has three tokens. For the "easy mode" version of this game the tokens are numbered 1, 2, and 3.

On each turn all players put their tokens on the game board squares. One 8-sided die is rolled. All game board squares appropriate to the rolled number win.

For each winning game board square, divide the reward by the total of the tokens on the board. Drop any remainder. That answer (the quotient, always rounded down) is how many points are recevied by all players with a token on that game board square. For example, if the reward was 50 and tokens totaled 12, each player with a token on that square would receive 4 points.

Play until at least one player has a certain total score. For the "easy mode" the goal is to get 500 points or more.

For "easy mode" using fake paper money might help students divide a winning game board square's reward among the winning players.

The "medium mode" uses slightly larger numbers. The tokens change to 1, 5, and 10. The game board square rewards are also larger, and the goal changes to 2,000 points or more.

The "hard mode" uses fractions. The tokens change to one-eighth, one-quarter, and one-half. The game board square rewards are smaller, and the goal changes to 100 points or more.

For "hard mode" using pattern blocks might help students divide a winning game board square's reward among the winning players.

## Set Theory

### Difference Trains

Equipment: attribute blocks

Play in groups of four. Each group as a set of attribute blocks. The group is assigned 1 or 2 and a starting block.

Students take turns adding one block to the "train" of blocks. Each new block must differ from the previous block in one/two ways, as assigned. (Attribute blocks can differ in color, shape, size, or thickness.) Keep taking turns until every block is used.

The group wins if the completed train is a loop: going from the last block to the first block is also a valid step.

### The Bomb Game

Equipment: the diagram below, scissors, pencil and paper

This game has proven to be a favorite among first- and second-graders.

Play in groups of two to four people. Each group of players uses a set of the twenty-four Bomb Clue Cards below, and a large paper on which is drawn a three-circle Venn diagram.

One player is "it" and secretly labels each of the Venn diagram circles. Each circle is assigned one of the nine possible characteristics of the Bomb Clue Cards (round, square, pentagon, 1, 2, 3, 4, A, B).

It works well to write a characteristic on a small piece of paper, then fold it a few times before setting it next to the appropriate circle.

The other player(s) look through the bomb cards. They give the player who is "it" any card they want. The player who is "it" places the card on the appropriate part of Venn diagram. Then more cards are given, to gain more clues.

Only ten cards may be placed on the Venn diagram. (But usually it does not take that many.)

Then the players who are not "it" agree on what they deduce must be each label for each of the three Venn diagram circles. If they are correct, they win and defuse the bomb! If not, the person who is "it" shouts "Boom!".

Note: Before teaching kids the rules to this game, it is recommended that you prepare the mood by asking about what skills secret agents need, and allowing the kids to act like secret agents while playing the Mission Impossible theme song in the background. That helps get their wiggles out, so they are ready to hear about "a game about diffusing a bomb" and focus on a logic game while sitting in small groups.

### Venn Diagram Game

Equipment: attribute cards (see below), pencil and paper

This is a more complicated version of The Bomb Game (above).

Note One: This game can be used to teach the set theory vocabulary Venn Diagram, Union, and Intersection. But there is no need to use these words when playing the game.

Note Two: Attribute cards are special cards you can make from index cards. The cards each have symbols on them that vary in four different ways: shape (circle, square, triangle), color (red, yellow, blue), shading (hollow, solid, striped), and number of symbols (one, two, three). This makes a total of 3 × 3 × 3 × 3 = 81 different cards.

Before the game begins draw a three-circle Venn Diagram on the paper large enough that an attribute card can be placed in any section. By each of the three circles draw a blank label (a box).

One player is It. This player leaves the room and on a piece of paper makes a smaller, similar diagram but with the labels filled in. Labels can be any of the Attribute card attributes (as examples: triangle, square, red, striped, three). Then the player who is It returns to the room.

The other player makes guesses. For each guess, he or she picks an attribute card and hands it to the playe who is It. The player who is It then puts the card on the three-circle diagram inside any circle that describes that card's picture. Then the guessing player guesses what all three labels are. The player who is It then says if the guess about all three labels is correct. Do not guess what labels are individually. When guessing, point to the blank labels as you say your guesses.

Note that some cards will be put "outside" the three-circle diagram, because they belonging to any of the three categories. For example, if this game the labels are circle, red, and yellow, then the card with one red solid circle goes in the section that is both in the circle circle and the red circle (but not in the yellow circle). But the card with three blue shaded triangles goes outside all three circles.

When a player correctly guesses all three labels, he or she becomes the new It.

This game works equally well with more than two players/teams. The players take turns guessing, and receiving feedback from the player who is It.

Note Three: To make this game more difficult, you can allow "negative labels" (such as "not red" or "not squares"). Or you can allow more than one adjective in each label (such as "red circles" or "blue twos").

## Algebra

### Diffy the Subtractor

Equipment: pencil and paper

This shape is caled Diffy.

Start with the number 5, 3, 11, and 12 in the outer corners. Then subtract along the lines (larger number minus smaller number) to fill in the circles. What happens?

Try for other starting numbers. Can you explain the trick?

## Miscellaneous Challenges

### Stack the Counting Cards

Equipment: ten index cards labeled 1 through 10

Challenge A: Stack the cards so that the first card turned over is 1, then the top card is put on the bottom of the stack, then the next card turned over is 2, then the top card is put on the bottom of the stack, then the next card turned over is 3, etc. (Cards that are turned over are removed from the stack.)

Challenge B: Stack the cards so that the first card turned over is 1, then one top card is put on the bottom of the stack, then the next card turned over is 2, then two top cards are put on the bottom of the stack, then the next card turned over is 3, then three top cards are put on the bottom of the stack, etc. (Cards that are turned over are removed from the stack.)

### Measurement Challenges

Equipment: one ruler per student

Students race to complete a Treasure Hunt of measurement tasks. Here is one example.

1. Find something exactly one foot long (that is not a ruler).
2. Find something less than six inches long.
3. Find something more than one meter long.
4. Find something that is less than one-quarter inch wide.
5. Find something more than ten centimeters wide.
6. Find something less than one-half an inch thick.
7. Find something more than two centimeters thick.