Old Math Games

These are my least successful math games. The best have been moved to my MathOER Playgrounds.

Many of these games were designed for elementary school classrooms, and are fun for young grades but not exciting for older students. In a classroom have the students play a two-player game by dividing into two teams (whose members either must agree upon decisions or are lined up and take turns making decisions).

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.

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.

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.

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.

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: 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.

Start with the object in the middle of the playing field. (Traditionally this notch is longer.)

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.

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.

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.

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.

Equipment: game board, one ten-sided die

See the game description here.

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.

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.

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.

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").

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?

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.)

Equipment: one ruler per student

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

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