Tiny Math Games

Games culled from the comments of Dan Meyer’s Tiny Math Games post: http://blog.mrmeyer.com/?p=16386 and Jason Dyer’s Tiny Games - Mathematics Edition and follow up.

This doc at http://bit.ly/TinyMathGames

Jonah “A Tiny Math Game I used to play on the train: take the car number (usually 4 or 5 digits) and add operations between the digits and an equals sign (somewhere) to make a true equation. Try to come up with as many different solutions as possible. Use basic operations or more advanced ones as necessary; the goal is to find interesting patterns, not to conform to a particular set of rules. Sometimes the car number contains a letter (usually early in the alphabet). Ignore it, or maybe try to find an answer in hexadecimal instead?”

Dan Anderson Write today’s date with just the number 4 and math operations. Today is 4 / 4^sqrt(4) / 4+4+4+4/4

Taylor I played this with my 8th graders in Algebra I during my student teaching:

1. Class splits into teams of four. (Or whatever. I liked four.)

2. A team gives me a number which I evaluate for some function either in my head or on my graphing calculator–depending on the complexity of the function.

3. I tell them the output. (I did not write it down to encourage participation.)

4. The team that gave me the number gets the first chance to predict the function. If they pass or are incorrect, all other teams may raise their hands and volunteer an answer.

5. Proceed clockwise from the first team.

6. Correct functions score points for a team. I began at 100 points for a correct guess after one output and decreased by 10 points after each output given. Incorrect answers took away 50 points to discourage random guessing.

Jeanne Bennett Krypto- given 5 random numbers (use a card deck, krypto deck or random numbers under 16) add, subtract, multiply and/ or divide to find a 6th random number. Good for strategy development as well as fact practice. I have used it in teams and as individuals.

Yaacov Iland One Won in grade 9.

First player picks the starting whole number (greater than 10).

Second player decides who starts.

Players take turns either subtracting 1 or dividing by 2, rounding down.

Whoever reaches a result of one wins.

There is a nice strategy. Ian VanderBurgh at CEMC ( http://cemc.uwaterloo.ca/aboutus.html ) introduced me to the game.

Jessi Integers Place Game. Teacher chooses a 3,4, or 5 digit number. I usually go around the room and students make guesses about the digits in the number. I write down their guess and next to it I tell them how many digits were correct and how many place values were correct. I generally create a table and fill in. Students use logic based on previous guesses to come up with the correct answer. We usually set a class goal to try and get the number in the fewest guesses.

Marty Romero Taxman. The game consists of a set of numbers – I use 1 through 40. In the game, the numbers are represented as money. You and someone else take turns choosing numbers. If you choose a number, you get the number of points equivalent to that number. Your opponent (the Taxman) gets the factors of that number. When the Taxman chooses, you get the factors of his choice. Numbers that are chosen go to each player’s respective side of the board. Once a number has been chosen or is a factor of a chosen number, it is removed from play. Whoever has the most points (chosen numbers plus factors) after the last number is chosen, wins.

ecvulic My boys play a factoring game in the car on rides: Start with a number between 1-100, but not even. The other one can then pick a multiple of that number, or a factor. Continue, no repeating numbers, until one of them cannot take a turn. There is strategy, they do a lot of multiplying and dividing, and once they’ve done it a couple of times, they get bored with trying to win, so they help each other try to get the longest game possible.

Katie Waddle Our kids from China taught us a game: One person thinks of a number from 1 to 100, kids take turns guessing. Each time a kid guesses wrong, the person with the number uses the incorrect guess to set a new (and closer) higher or lower bound (this is where the admittedly low-level math comes in). The kid who guesses right gets a turtle drawn on their hand (I’ve never quite understood that part).

Chuck Make 24 – Pick 4 numbers (or have the student who got the last answer pick 4) and try to make 24 using all 4 numbers and any of the 4 basic operations. I.E. 4 numbers picked are 8, 2, 7, 3. (8-2)*(7-3)=6*4=24 hip hip hooorray!

Phil @liketeaching RUNNING TOTAL (not sure what its really called)

Pupil 1 picks a number between 1-5. Pupil 2 picks a number between 1-5 and adds it to pupil 1′s number. Pupil 1 picks a number between 1-5 and adds it to the previous total. The winner is the first to go over 21. (The available numbers and the target can be adjusted. Can also be done with subtraction.)

Jason Fizz-buzz (for a group): Players pick an order. The first player says the number “1″, and then the players count in turn. nn

Numbers divisible by 3 should be replaced by “fizz”. Numbers divisible by 5 should be replaced by “buzz”. Numbers divisible by both should be replaced by “fizz-buzz”. Players who make a mistake are out. Last one in wins the game.

Berry posted a variation he calls… Berry. No double digits, no multiples of 7. Substitute “Berry” instead!

Dan Pick a number. Say 25. Now break it up into as many pieces as you want. 10, 10, and 5, maybe. Or 2 and 23. Twenty-five ones would work. Now multiply all those pieces together. What's the biggest product you can make? Pick another. What's your strategy? Will it always work? [Malcolm Swan]

Joe Boyer - Roman Goblins (for a group of 2-10)- Roman Numeral practice

Pick four random words to substitute for the roman integers of I, V, X and L. The job is just to count

upwards using roman numerals with the substitute digits. Take turns. Players who make a mistake are out, last one in wins the game.

eg, I = Cat, V = Pasta, X = Bowling, L = Flying

First student just says, “Cat” then the next has to say “Cat cat” then the next is “Cat cat cat” then “Cat Pasta” then “Pasta” then “Pasta Cat”, “Pasta Cat Cat”, “Pasta Cat Cat Cat”, “Cat Bowling” etc. The kids love it, and they love playing again trying to choose words that will result in funny outcomes.

1. Shut the Box. It’s a simple dice game for two and you can alter the rules anyway you like to make the game more “mathy”. Students of all ages love it. And you can develop strategies as you go.

2. Blind tic-tac-toe. Fill in the boxes of the board with the digits 1-9 in any order. Spend 30 seconds memorizing the pattern. Never look at the board again. Call out the position you want to place your X or O by using the numbers. You must keep track of where all previous moves have been made. Not so much math, but it’s tiny, fun, and builds your working memory

3. Break the Code (numerical variant of the classic Mastermind). One person creates a four digit code. The other tries to guess the code. Guesses are written down and the “scored” by the code maker who indicates how many digits are correct AND in the right position and how many are correct but in the wrong position.

4. Conquer the World. 2 players. Draw a grid of arbitrary size, say 10×10. Roll two dice and compute their product. Color in a rectangular area equal to that product. Alternate turns until no one player cannot color in the required area.

5. Divisimainders. First player chooses a secret number. The other tries to guess the number by asking if it is divisible by a number, x. The first player only responds with the remainder when the secret number is divided by x. Play continues until the second player successfully guesses the secret number. Goal is to get it in the fewest number of guesses.

6. Dodge’em Cars. 2 players, like a competitive Rush Hour puzzle. A square 3x3 grid starts out with 2 cars on the left top going across and two cars on the bottom right moving up. Be the first to clear off your cars. Guillermo Bautista

Jason 1-2 Nim (for two players): Start with a row of coins. Alternate turns with your opponent. On your turn you can take either 1 or 2 of the coins. The person who takes the last coin wins.

José Luis Benavente The Chinese game is that each holds in his hand 0, 1, 2 or 3 coins, without the adversary knows how many. Then try to guess the total collected from all players. If two players play what would be the amount that is more likely to appear? What if you play three players?

Variation: (John Golden) have one player guess, others guess higher/lower. 1 point if right. “Dealer” gets 2 if right, 1 if more people miss than are correct.

Shecky Riemann: There is a new carnival game in town called "Fifteen." It involves a board with the numbers 1 through 9 laid out in order (like above). You play against the carny; doesn't matter who goes first, but you will take turns back-and-forth. You each put coins down one-at-a-time on a single number and then "own" that number ('til someone wins or all 9 numbers are used up). The carny will be putting silver dollars down while you put nickels down. The object is to own any THREE numbers that add up to 15, before your opponent does (for example, 3, 5, and 7). Whoever does this gets all the money played, in cases of draws (no winner) you each take your money back. (From this post in which he explains it’s isomorphic to Tic Tac Toe.)

Large collection of counters games, including some nifty Nim variations, by Frank Tapson, found at @solvemymaths post.

J.D. Williams “Never a Six”. You need one die. We usually play half the class against the other half, or boys v. girls or something like that. I’ve had students play individually, but they don’t get as involved in the games this way. We talk about probability when playing (sometimes).

Each person gets a turn rolling the die. If they roll a 1 – 5, they add that to their turn total sum and decided to continue rolling or end their turn. If they roll a 6, their turn total is 0 and it is the other teams turn. Players can choose to stop rolling at any time and let the other team begin their turn. When students decide to stop their turn, their team gets to keep the turn total sum and add it to the group total sum. The group with the highest total group sum after everyone has had a turn wins. (Example at post) I have done this multiplying instead of adding as well.

Penney’s Game from a Burkardt & Marty column. “the game consists of two players choosing a sequence of three coin tosses, such as TTT or HTT. A coin is then tossed repeatedly and the player whose sequence appears first is the winner. For example, if the sequence of tosses was H H H T H H T H T T then HTT would have won against TTT.” Surprising is that the second player can always have a better chance of winning.

Bob Lochel “card prediction game” to get kids talking about suits, colors and possible outcomes. To start, I draw 10 cards and show them off. The class then writes what they predict the next card will be , like “8H” for eight of hearts. You earn 1 point if the card drawn is the same color as your card, 3 points if it is the same suit, 5 points if it is the same rank, and 10 points for the correct card. I will do this for the next 10 cards and high score wins. Down the road, we analyze the game and think about what fair point values should be.

Andrew Stadel 3 Players, one deck of cards.

Cards are assigned Black Jack values (aces=11).

Person1 (referee) hands one card to player1 and one card to player2 so each player can’t see the value of their own card. Without looking, each player puts the card on their forehead so their opponent can see the value. The referee adds the two visible cards and announces the sum to the two players. Each player has to figure out the value of the card on their forehead. First player to correctly state answer, wins. (*contestants can only say one number). Play a few rounds or best of three/five/seven. Switch roles and the winner is now the referee.

The game can also be used for multiplication where the referee announces the product of the two visible cards and each player has to deduct the value of their card. Increase the level of challenge for both sum and product by making the black suits positive and the red suits negative.

Phil @liketeaching VECTOR RACES

Have a basic track printed on grid paper. Pupils guess the vector they should translate their car by and then draw this vector and slide the car along it. If they hit the sides they miss this go. If they draw the vector wrong or try to cheat and their opponent notices then they also miss a go.

This also works great adapted to guessing and measuring angles (or bearings) and distances.

FACTORS AND MULTIPLES GAME

Have the numbers 1-30 written down. Pupil 1 picks a number and circles it. Pupil 2 must pick a number not previously used that is either a factor or a multiple of pupil 1′s number. Pupil 2 puts a cross on their number. Pupil 1 must now pick a number not previously used that is either a factor or a multiple of pupil 2′s number.

The winner is the one who forces the other player to get stuck (no factors or multiples not yet picked).

Matt Vaudrey - “Productivity” Each student in the pair or trio gets 4 cards (two pairs). Multiply the first pair, then the second pair, then add the two products. Students record the score on their worksheets and end by adding up all 5-7 rounds together. Teacher chooses the value of face cards on the board.

William Carey Prime fish with the sixth and seventh graders. You need a special deck of cards, but it’s an easy deck to make:

- Ten cards with a “2″ on them (or two fish)
- ten cards with a “3″ on them (or three squid)
- eight cards with a “5″ on them (or five eels)
- two cards with a “7″ on them (or seven sea-slugs)

Each player draws four cards. They multiply their hand together, and announce the only the product (!) to the group. They then play go-fish. It’s fun to watch the kids debate whether there’s a strategy to the game. It’s more fun to watch them work out that the strategy is once they decide that there is a strategy. Game has a limited life span (as there is an always-winning strategy), but fun nonetheless.

Andrew Stadel Taboo with math vocabulary.

Bethany Not sure if this qualifies as ‘tiny’ but it was fun the couple of times I did it.

7th grade algebra practice solving inequalities – I created 3 cube patterns on paper. The first one had algebraic expressions ranging in difficulty. The second had inequality symbols and the third had numbers. Each pattern is copied onto different color heavy paper. The students are split into groups of 3. They first have to cut out and create the cubes. Once the cubes are made, they each roll their own cube and create an inequality. They write the inequality on their paper and solve it. They have to solve at least 3 different inequalities.

Timon Piccini (@MrPicc112) I am reminded first of this gem I think we called it skunk, Click here Any exercise in this book could be played with dice.

I also think of WAR Click here which has been amazingly helpful. I used it the other day with ratios and helping Nana get the chocolcatiest chocolate milk!

Plus there’s my own attempt at mathematical pictionary: Click Here I’ve also adapted that for algebra as well (algebra-nary).

Jonah J.D.’s post reminds me of Reiner Knizia’s Decathlon, a series of similar push-your-luck dice games. I would not call it a single Tiny Math Game, but rather a series of ten Tiny Math Games.

Another good one is James Ernest’s Pennywise, a game about strategically making change to run your opponent out of money.

Bob Lochel I’m a big fan of the “numbers” game from the British game show Countdown. Here’s the short version:. 6 numbers are drawn, and you use the 4 operations to get as close to a “target” number as possible. It’s like “24″ on steroids. Some video examples and a link to an online applet on my blog: http://mathcoachblog.wordpress.com/2012/04/22/from-24-graduate-up-to-countdown/

Alexandre Muñiz Some of the Freeze Dried Games Pack games are of mathematical interest. Gomoku in particular swept through my group of peers when I was in middle school, and leads quickly to logical analysis of varying degrees of sophistication. (There may not be a common core standard you can point to, but there’s plenty of mathematical thinking going on.)

Nico Sprouts http://en.wikipedia.org/wiki/Sprouts_(game)

Chopsticks http://www.wikihow.com/Play-Chopsticks

Max I like a lot of the Everyday Math games, and simple old multiplication top-it and addition top-it get kids interested. The cool thing is during NCTM you can download them for free from the Apple Store.

Also, Gordon over at http://mathpickle.com has some great games that could be Tiny Math Games. My favorite is the Grade 6 $1,000,000 Unsolved Problem.

Norma If your students already like Boggle and Bananagrams…I was thinking of making math version but someone already has…

Number Boggle: http://nzmaths.co.nz/resource/number-boggle

Numenko: http://www.numenko.com/

Kind of like sudoku, but uses number sense as well as logic skills: http://www.kenken.com/