# Math Games For Skills and Concepts

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5 Math Games p.5 The Sums Game Play begins with each player covering a number from 1 to 9 at the bottom. The 2 nd player then covers the sum of those two numbers on the game board. The 1 st 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)

6 Math Games p.6 Players: 2 and up Five In a Row 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

7 Math Games p.7 Race to 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 Score: 13 Score: 23 One Two One Two One Two

8 Math Games p.8 Roll+10 Roll+20 Roll+10

10 Math Games p.10 Close to Zero From Mathematical Thinking in 5 th 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 2 nd 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 or ). 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:

11 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: (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 Players take turns breaking down a number by Can only be broken down once, player who multiplication. The first player starts with a started loses. 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.

12 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

13 Math Games p.13 The Product Game Play begins with each player covering a factor from 1 to 9 at the bottom. The 2 nd player then covers the product of those two numbers on the game board. The 1 st 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)

14 Math Games p.14 Prime Time Free Free Factor List Rules 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)

15 Math Games p.15 Score Factor Game Board 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

16 Math Games p.16 Game rules: Each group of players gets three dice two with the same color and one that is different. ROLL TO TEN 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) 0 Total

17 Math Games p.17 Triangle Game A A:1,2 B:3,4 C:5,6 C B 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 edge triangle

18 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 180 o turn? Inspired by the game RoboRally, designed by Richard Garfield.

19 Math Games p.19

20 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 Move back one Move back one Turn 90 o right Push forward one (this card may be swapped with an opponents program) Move forward two Move forward two Move forward two Turn 90 o right Push backward one (this card may be swapped with an opponents program) Move forward three Move forward three Move forward three Turn 90 o right Flip over horizontal center line Move back two Move back two Move back two Turn 90 o left Flip over vertical center line Turn 180 o Turn 180 o Turn 90 o left Turn 90 o left Turn 90 o in a direction of your choice.

21 Math Games p.21 Race Board 2 START Rotate 90 o right around center 1 FINISH Move Forward 2 spaces Move Left 2 spaces 1 START Rotate 90 o left around center 2 FINISH L R R L Cut out Robots into two strips, fold along right hand edge to get a robot with a front and back. L R R L

22 Math Games p.22 Polygon Capture Game Rules Preparation: 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 Vol. 4, Iss. 2; p. 90

23 Math Games p.23

24 Math Games p.24 All angles are right angles At least one angle is obtuse No angle is a right angle At least one angle is less than 90 o At least one angle is a right angle At least two angles are acute All angles have the same measure STEAL CARD Select a pair of properties. Steal all these polygons from your opponent. No pairs of sides are parallel All sides are of equal length Exactly one pair of sides is parallel At least one pair of sides is 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

25 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 Points Equation Targets Hit Score 1 (, ) 2 (, ), (, ) 3 (, ), (, ), (, ) 4 5 (, ), (, ), (, ), (, ) (, ), (, ), (, ), (, ), (, ) Total Pig (Wikipedia version.) Pig is a simple folk jeopardy dice game first described in print by John Scarne in 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.

26 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

27 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 1 2 Piece 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 10 th piece of one type. The other team gets a last chance to make a box out of the pieces they already have. 3 Example: Team 1 has rolled the following: X X 4 One of the partners realizes they could build a box with the net X X X X 5 Pick from any other number So they cross off the pieces they use and score 6 points. X X X X X 6 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. 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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