## [Confab] Tiny Math Games

Jason Dyer writes a very important post highlighting Tiny Games, a listing of games you can play quickly, almost anywhere, with only limited materials. He then pivots to ask about tiny math games.

Could one make an all-mathematics variant — mathematical scrimmages, so to speak?

His post, and Tiny Games, are important because they reject an article of faith of the blended learning and flipped classroom movements, that students must learn and practice the basic skills of mathematics before they can do anything interesting with them.

For example, here’s John Sipe, senior vice president of sales at Houghton Mifflin Harcourt, talking about Fuse, their iPad textbook:

So teachers don’t have to “waste their time” on some of these things that they’ve always had to do. They can spend much more time on individualized learning, identifying specific student needs. Let students cover the basics, if you will, on their own, and let teachers delve into enrichment and individualized learning. That’s what the good teachers are telling me.

This is a bad idea. People don’t mind practicing a sport because playing the sport is fun. It’s easy to tell a tennis player to practice 100 serves from the ad side of the court, for instance, because the tennis player has mentally connected the acts of practicing tennis and playing tennis. The blended learning movement, at its worst, disconnects practice and play.

Take multiplication of one- and two-digit numbers for instance.

If you need to learn multiplication facts, one option is to watch a video and then drill away. Or we can queue up all that practice in a tiny math game that’ll have students playing as they practice:

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]

Easy money says the student who’s practicing math while playing it will practice more multiplication and enjoy that practice more than the student who is assigned to drill practice alone.

Jason Dyer helpfully highlights two examples of tiny math games, Nim and Fizz-Buzz, but he and I are both struggling to define a “tiny math game.” The success of the Tiny Game Kickstarter project indicates serious interest in these tiny games. I’d like to see a similar collection of tiny math games. Here’s how you can help with that.

1. Offer Examples of Tiny Math Games

This may be tricky. We all have games we play in math class. What distinguishes those games from “tiny math games?”

2. Help Us Define “Tiny Math Games”

This may be a better starting point. I’ll add your suggestions to this list. Here are some seeds:

• The point of the game should be concise and intuitive. You can summarize the point of these games in a few seconds or a couple of sentences. It may be complicated to continue playing the game or to win it, but it isn’t hard to start.
• They require few materials. That’s part and parcel of being “tiny.” These games don’t require a laptop or iPhone.
• They’re social, or at least they’re better when people play together.
• They offer quick, useful feedback. With the multiplication game, you know you don’t have the highest product because someone else hollers out one that’s higher than yours. With Fizz-Buzz, your fellow players give you feedback when you blow it.
• They benefit from repetition. You may access some kind of mathematical insight on individual turns but you access even greater insight over the course of the game. With Fizz-Buzz, for instance, players might count five turns and then say “Buzz,” but over time they may realize that you’ll always say “Buzz” on numbers that end in 5 or 0. That extra understanding (what we could call the “strategy” of these tiny math games) is important.
• The math should only be incidental to the larger, more fun purpose of the game. I think this may be setting the bar higher than we need to, but Jason Dyer points out that people play Fizz-Buzz as a drinking game. [Jason Dyer]

What can you add to our understanding of tiny math games?

2013 Apr 17. Nobody wanted to tackle the qualities of tiny math games, which is fine since you all threw down a number of interesting games. I’ll be compiling those on a separate domain at some point soon.

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Jason Dyer elaborates on his contribution above.

2013 Apr 24. Jason Dyer elaborates in another post.

2014 Oct 30. Eric Welch shares his thinking around tiny math games from his Masters thesis.

2014 Oct 30. Julie Reulbach lists several games in a Google doc.

Number Sense & Operations

Basically you get groups of three. Two students grab a card from a deck and without looking at them put them on their foreheads facing out. The third student multiplies the two numbers and states the product. Those holding the cards then try to guess the two numbers.

This game is played in partners. Two children share a blank 100 grid. The first partner rolls two number dice. The numbers that come up are the numbers the child uses to make an array on the 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws the array on the grid, she writes in the number sentence that describes the grid. The game ends when both players have rolled the dice and cannot put any more arrays on the grid. How close to 100 can you get?

Create a 5 x 5 grid of cards, in which every row and column adds to 31. We decided as a group that J, Q, and K were worth 10, Aces were worth 1, and all of the other cards were worth their face value.

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.

You need a special deck of cards, but it’s an easy deck to make:

ten cards with a “2” on them
ten cards with a “3” on them
ten cards with a “4” on them
two cards with a “7” on them
two cards with a “11” on them

Each player draws four cards. They multiply their hand together, and announce the only the product (!) to the group. They then play go-fish.

Write today’s date with just the number 4 and math operations.

Krypto- given 5 random numbers (use a card ddeck, 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.

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.

Taxman is one of my favorites – it can be played many times within some fraction of your class period.

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 equivilant 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.

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.

Game 1:
Players: 3
Materials: 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.

Another one is called “strike”. Each player starts with a ten pin bowling set-up, each pin numbered 1 – 10. Then 4 dice are rolled (dice don’t have to be standard 6 sided ones). The player’s goal is to “knock down” as many pins as possible. You knock down a pin by using the 4 numbers shown on the die, in any order and with any operations and grouping symbols, to arrive at the number on a pin. For example, if you rolled a 4,5,7, and 8. You could knock down pin #1 by writing (8-7)/(5-4), and pin #2 by (8-7)+(5-4), … The winner is the one who knocks down the most pins.

Graph Theory

The Game of Sprouts! This is a quick game that requires nothing more than a pen, paper and a partner. Based on graph theory the game of sprouts is easy to learn and easy to play, but also has opportunities for higher level analysis.

If students don’t know graphy theory terminology, vertex can be replaces with “dot” and edge can be replaces with “line”. The word degree can be explained as the number of lines emanating from the dot.

The rules:

Start with a finite number of vertices.
Connect two vertices with an edge, and add a new vertex to the edge you just created.
An edge cannot cross over an existing edge.
A vertex is “dead” once it has a degree of three. You can no longer play off this vertex.
The winner is the person who makes the last possible move.

Inductive Reasoning

With a deck of cards – Eleusis: http://en.wikipedia.org/wiki/Eleusis_%28card_game%29

One person thinks of a rule about what cards can be played. For example, “alternate even and odd numbers” or “only even numbers can follow a black suit and only odd numbers can follow a red suit”

Players try to discover the rule inductively, by trying to play a card. The rule thinker-upper tells them whether the card they tried to play is a legal move or not and the table keeps track of the attempts. If you make an incorrect guess, then you put your card in a row of bad guesses and draw another card. If you make a correct guess, your card is placed on the play pile, but you don’t draw another. The goal is to be the first to run out of cards.

It takes a while to explain at first, but once the game is in your repertoire it can be started and played pretty quickly. It also has the benefit of having students choose secret rules that are at a complexity level that they are comfortable with. It’s really fun.

Functions

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.

Probability

We play a quick game called “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.

Memory

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

Coordinate Plane

Phil:

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.

Estimation

Another game that can be applied to many math concepts is “Mental Math Golf”. You play 9 “holes”. Each “hole” gives you a problem (ex: What is 8% of 70?, what is square root of 90?). Using mental math/estimation strategies, each player gives their best guess. Their score on the hole is the percent error of their guess and the actual answer. Thus a perfect score on a problem would be a zero. After 9 holes, you average your percents, and the lowest score wins. You can play 9 hole courses that consist of concepts like percents, radicals, logs, missing side length of a right triangle, etc.

Factoring Trinomials

Ok, one that really is ‘tiny.’ I use it to practice skills for factoring a trinomial by grouping. Draw an X and put two numbers in the X. The rule is that the two side numbers have to add to = the bottom number and multiply to equal the top number. So, for example, -54 on top and 3 on the bottom… the students must figure out that the side numbers must be 9 and -6.

Miscellaneous

Object: Force your opponent to say “December 31″
Rules:
– The game begins with a date in January.
– Players take turns increasing either the month or the number
but not both.
– You may skip over months or numbers however you cannot
move backwards or wrap around back to the number 1.
– The player who says “December 31″ loses the game.
– Can you figure out the strategy?

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

1. #### Jonah

April 16, 2013 - 1:07 pm -

Tea Card Monte, from the Kickstartees (?) themselves, is a pretty good Tiny Math Game. And it’s a fun exercise to see what the optimal strategy for the Tea Keeper and Questioner are (hint: start with the first one).

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?

2. #### Jonah

April 16, 2013 - 1:12 pm -

Also, very many combinatorial games (e.g. from Winning Ways or On Numbers and Games) fit the bill besides Nim. Poison, Kayles, Chomp, Domineering, Sprouts, Brussels Sprouts (okay, maybe that one doesn’t benefit from repetition), Hackenbush, and more are all good candidates. And these ones have the interesting side effect where learning about one can lead to insights in another: start playing Kayles for a bit, say, and you’re more likely to recognize some losing positions in Nim. Solve Nim completely, and soon you can solve Kayles as well, and all impartial games!

3. #### William Carey

April 16, 2013 - 1:16 pm -

It’s not quite as tiny as the games you mention, but we play 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)
ten cards with a “4” on them (or four octopi)
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.

4. #### William Carey

April 16, 2013 - 1:19 pm -

Hmm – embarrassing – I need to edit my comment to remove the “4” cards – it’s Prime Fish after all. The real deck goes 2, 3, 5, 7, 11. Whoops.

5. #### Jonah

April 16, 2013 - 1:23 pm -

No, William, it’s great with 4! You know how many cards everyone has, so after factoring out the other primes you can figure out how many of the remaining are 2s and how many of them are 4s based on the total hand size.

6. #### William Carey

April 16, 2013 - 1:29 pm -

Interesting Jonah – that adds a nice twist to the game! I might have to mix that in for some of the older kids who’ve figured out that it’s a sneaky of practicing prime factorization.

7. #### Dan Anderson

April 16, 2013 - 1:35 pm -

Write today’s date with just the number 4 and math operations. Today is 4 / 4^sqrt(4) / 4+4+4+4/4
Can you do this with less 4’s?

8. #### Timon Piccini (@MrPicc112)

April 16, 2013 - 2:05 pm -

I am reminded first of this gem I think we called it skunk,

Any exercise in this book could be played with dice.

I also think of WAR

which as 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:

I’ve also adapted that for algebra as well (algebra-nary).

9. #### Taylor

April 16, 2013 - 2:15 pm -

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.

10. #### J.D. Williams

April 16, 2013 - 2:42 pm -

We play a quick game called “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.

I’m not sure if I’m explaining this well so I’ll go through two team turns.
Team 1 – Player A – Rolls the die and gets a 2, then a 4, then a 3 and decides to stop. His team gets 9 points from his turn.
Team 2 – Player B – Rolls the die and gets a 2, then a 5, then a 6. His team does not get any points because the 6 sets his turn total back to 0.
Team 1 – Score of 9.
Team 2 – Score of 0.

The game gets really loud. People on the same team start yelling at each other to stop, or people from opposite teams try to persuade each other to roll at least one more time. Students say “Just one more roll” a lot to their own team, and usually end up with 0 points. It’s not uncommon for teams of 15 to end with a score under 30 points. I have done this multiplying instead of adding as well.

11. #### Jonah

April 16, 2013 - 3:16 pm -

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.

12. #### Jeanne Bennett

April 16, 2013 - 4:13 pm -

Krypto- given 5 random numbers (use a card ddeck, 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.

13. #### Bob Lochel

April 16, 2013 - 4:48 pm -

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/

Another game I play is a “card predication 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.

@JD That dice game is pretty famous in stats. I was introduced to it as “Greedy Pig”, and the poison number was 2.

14. #### Yaacov Iland

April 16, 2013 - 4:55 pm -

We play 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.

15. #### Raj Shah

April 16, 2013 - 5:33 pm -

Here are few that might fit the Tiny Math Game requirements

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.

16. #### Jessi

April 16, 2013 - 5:49 pm -

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.

Example. Say the number is 46208
Guess. Digits. Place Values.
11111 0 0

At this point they have eliminated 1 as a possibility. It continues until they get the correct response.

17. #### Marty Romero

April 16, 2013 - 8:40 pm -

Taxman is one of my favorites – it can be played many times within some fraction of your class period.

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 equivilant 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.

18. #### ecvulic

April 16, 2013 - 9:44 pm -

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.

19. #### Andrew Stadel

April 16, 2013 - 9:58 pm -

Game 1:
Players: 3
Materials: 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.

Game 2: Taboo with math vocabulary.

20. #### Chuck

April 17, 2013 - 6:59 am -

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)=6*(7-3)=24 hip hip hooorray!

21. #### Bethany

April 17, 2013 - 7:16 am -

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.

22. #### Santosh Zachariah

April 17, 2013 - 7:21 am -

I love Krypto. I would be interested in hearing from anyone who has successfully tweaked it to include all integers (not just the positive ones).

23. #### Santosh Zachariah

April 17, 2013 - 8:16 am -

@Raj Shah, I second MasterMind-like games. It has been my favorite game of all time for the past 30 years. All it needs is a pencil and paper, and a set from which to select (colors, numerals, letters)

24. #### Jonah

April 17, 2013 - 8:21 am -

Santosh, I don’t even think it needs pencil and paper. I’ve played Word Mastermind out loud before, and while it takes many more guesses to keep everything straight in your head, it’s a great car game.

Rules: The answer and the guesses must be 5-letter English words. Guesser guesses a word, other player says how many letters it shares with the answer, ignoring position (counting multiplicity, so MELEE shares three letters with EMOTE). You can’t tell what position the letters go in, but because the answer has to be English there usually aren’t very many possibilities.

25. #### Matt McCrea

April 17, 2013 - 8:34 am -

Extend your rule on “requiring few materials” – I’d hate to see a game like your “Break 25” played with calculators. Of course, there’s still some interesting math there, but if we’re trying to accomplish the dual goal of helping students achieve computational fluency, then we should ensure that the game is structured to achieve both goals.

26. #### Phil @liketeaching

April 17, 2013 - 9:25 am -

Awesome idea for a post. There’s been some great responses already!

@John Golden: Nice one putting them all together

Anyway here are a few of my favourite games (not sure how tiny they are exactly):

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).

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.)

27. #### Max

April 17, 2013 - 11:05 pm -

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.

28. #### Bethany

April 18, 2013 - 5:26 am -

Question for everyone – how many of the games mentioned are for concepts above middle school? Any games out there for factoring or simplifying rational expressions? Am I thinking about it backwards? Do I need a game that requires the student to develop an algebraic expression that then must be factored to answer the question? So, they can’t complete the game until they learn how to factor? How does one create said game?

29. #### Lynn Spady

April 18, 2013 - 11:07 am -

I don’t know that it has a name, but I love to ask my kids questions like:

***The number of sides on a quadrilateral plus the number of days in a week minus 1.

***The number of days in a year take away the number of days in March.

***The number of ounces in a cup squared times the number of sides on a triangle.

As you can imagine, the questions are endless!

30. #### Jim Pardun

April 18, 2013 - 7:17 pm -

Object: Force your opponent to say “December 31”
Rules:
– The game begins with a date in January.
– Players take turns increasing either the month or the number
but not both.
– You may skip over months or numbers however you cannot
move backwards or wrap around back to the number 1.
– The player who says “December 31” loses the game.
– Can you figure out the strategy?

31. #### Kevin Smith

April 19, 2013 - 2:45 am -

Has “21” been mentioned yet? It’s very simple.

Players take it in turns to count. You can say one, two or three numbers and the person who gets to say “21” is the winner.

e.g. player A: 1, 2
player B: 3
A: 4,5,6
B: 7,8
A: 9
B: 10, 11, 12
A: 13, 14 (this is a losing move)
B: 15, 16, 17 (this is the required the winning move)
A: 18… oh darn it!
B: 19, 20, 21 wooo!

32. #### Bethany

April 19, 2013 - 7:06 am -

Ok, one that really is ‘tiny.’ I use it to practice skills for factoring a trinomial by grouping. Draw an X and put two numbers in the X. The rule is that the two side numbers have to add to = the bottom number and multiply to equal the top number. So, for example, -54 on top and 3 on the bottom… the students must figure out that the side numbers must be 9 and -6.

33. #### Adam Poetzel

April 19, 2013 - 9:30 pm -

Another game that can be applied to many math concepts is “Mental Math Golf”. You play 9 “holes”. Each “hole” gives you a problem (ex: What is 8% of 70?, what is square root of 90?). Using mental math/estimation strategies, each player gives their best guess. Their score on the hole is the percent error of their guess and the actual answer. Thus a perfect score on a problem would be a zero. After 9 holes, you average your percents, and the lowest score wins. You can play 9 hole courses that consist of concepts like percents, radicals, logs, missing side length of a right triangle, etc.

Another one is called “strike”. Each player starts with a ten pin bowling set-up, each pin numbered 1 – 10. Then 4 dice are rolled (dice don’t have to be standard 6 sided ones). The player’s goal is to “knock down” as many pins as possible. You knock down a pin by using the 4 numbers shown on the die, in any order and with any operations and grouping symbols, to arrive at the number on a pin. For example, if you rolled a 4,5,7, and 8. You could knock down pin #1 by writing (8-7)/(5-4), and pin #2 by (8-7)+(5-4), … The winner is the one who knocks down the most pins.

34. #### C

April 21, 2013 - 7:17 pm -

Have the class split into two teams.

One side is given a single digit number, asked to double it in their heads, and have one team member say the resulting value.

That team member is now out and no longer available. The new, resulting number gets passed to the other team, which then repeats the process.

The first team to give an incorrect answer results in the other team scoring points.

The students get really intense and focused during this game. It also allows them to show some strategic thinking in determining who is going to go first and who is going to be “saved” until later.

I have used this both as a fun game and as a way to introduce a lesson on exponential functions.

35. #### denis sheeran

April 22, 2013 - 1:17 am -

Take, at minimum, three dice. Roll them. For young kids, who can find the largest product. For older kids, allow the use of the numbers on the dice to be exponents. This can go far with the introduction of more dice, or of dice with more sides. For even older kids, use a 10 sided die, and a 6 sided. Make them find the surface area or volume of a solid with the number of sides determined by the 10 sided and the length of the side determined by the 6 sided.

36. #### Roanna Council

April 23, 2013 - 1:35 pm -

I love that other teachers think that Math should be fun and challenging. All throughout school my teachers just lectured the methods of math and never the “why”. I wanted to know what the significance of integration was and no one would tell me… Eventually (like a year later) I learned to find the volume of 3D figures by integration. That is when I loved it! The fun is in the application not the methods. I love all the games in the comments of this post! Once I begin teaching at the high school level, I will definitely be looking for game for my students to play.

37. #### Erin Gilliam

April 25, 2013 - 11:47 am -

The Game of Sprouts! This is a quick game that requires nothing more than a pen, paper and a partner. Based on graph theory the game of sprouts is easy to learn and easy to play, but also has opportunities for higher level analysis.

If students don’t know graphy theory terminology, vertex can be replaces with “dot” and edge can be replaces with “line”. The word degree can be explained as the number of lines emanating from the dot.

The rules:

• Start with a finite number of vertices.
• Connect two vertices with an edge, and add a new vertex to the edge you just created.
• An edge cannot cross over an existing edge.
• A vertex is “dead” once it has a degree of three. You can no longer play off this vertex.
• The winner is the person who makes the last possible move.

38. #### Jason Baldus

April 26, 2013 - 5:44 am -

With a deck of cards – Eleusis: http://en.wikipedia.org/wiki/Eleusis_%28card_game%29

One person thinks of a rule about what cards can be played. For example, “alternate even and odd numbers” or “only even numbers can follow a black suit and only odd numbers can follow a red suit”

Players try to discover the rule inductively, by trying to play a card. The rule thinker-upper tells them whether the card they tried to play is a legal move or not and the table keeps track of the attempts. If you make an incorrect guess, then you put your card in a row of bad guesses and draw another card. If you make a correct guess, your card is placed on the play pile, but you don’t draw another. The goal is to be the first to run out of cards.

It takes a while to explain at first, but once the game is in your repertoire it can be started and played pretty quickly. It also has the benefit of having students choose secret rules that are at a complexity level that they are comfortable with. It’s really fun.

39. #### Jason Baldus

April 26, 2013 - 10:05 am -

I just found a great variation of Eleusis that was created by John Golden called Eleusis Express that would better fit into the category of TinyMathGames. It finishes more quickly and is slightly more fast paced. The rules are here: http://www.logicmazes.com/games/eleusis/express.html.
John first introduced me to Eleusis, but I don’t remember if we played the full version created by Robert Abbott or John’s version. Either one is fun, though.

40. #### Mark Basi

April 30, 2013 - 8:20 am -

I play a simple math game with my 6-year old. I have two pairs of place-value dice (i.e. two ten-sided dice numbered 0-9, two ten-sided dice numbered 0-90 (in increments of 10), two ten-sided dice numbered 0-900 (in increments of 100), etc.)

I also have an addition-subtraction die, and one with all four operations on it.

We roll the dice, and then do what it says. Whatever biggest dice we’re using, we’ll play to two higher powers of ten. For instance, if we play with the tens dice, we’ll play to 1000. He loves playing it, and it really gives him practice adding and subtracting.

41. #### Eric Welch

May 1, 2013 - 10:11 pm -

I’m finishing up my master’s thesis on mathematical strategy games, so I’ll take a stab at defining what makes a math game an actual game rather than a dry exercise that a teacher or curriculum writer is masquerading as a game. The last can be omitted, but without other players, you’re arguably dealing with a puzzle rather than a game.

1) Low threshold, high ceiling. You should not have to know “too much” to start playing the game, but you should be able to advance through several stages of strategy, or gain considerable fluency before the game becomes boring. The meaning of “low threshold” varies with the age of your students, but a high ceiling means that the winning strategy should not be trivial, even to an intelligent math teacher. To put it another way, the game requires you to apply existing knowledge to an interesting challenge above and beyond recall/regurgitation.

2) Clear feedback, fun failure, and a sense of agency. When you play a true game, you may not realize why your choices are good or bad at first, but it’s quickly clear that your choice had an effect — you should not think that you are winning or losing simply due to chance. Ideally, you can lose spectacularly, have a laugh, and learn from the mistake. [Credit to Jane McGonigal from her book _Reality is Broken_ for the notion of fun failure.]

3) Opportunities to consider others’ thinking. Whether or not you talk about it, you should be able to figure out why other people make the choices they do. Some people say that all of literature arises from our desire to understand other people’s motivations.

I listed these in terms of their contribution to “replay value.” Citing McGonigal again, the defining characteristics of a game seem to be (1) a goal, (2) rules, (3) a feedback system, and (4) voluntary participation. If a student doesn’t want to play, but you make them, it’s definitely not a game.

42. #### Jason Dyer

May 2, 2013 - 8:47 am -

@Eric: Will this thesis be online?

“Fun failure”: I’m wondering if McGonigal is a Dwarf Fortress fan.

If a student doesn’t want to play, but you make them, it’s definitely not a game.

Dunno, I’ve had students not want to play, say, Yahtzee. And I’m seem to remember there always being students wanting to sit out of PE class. Not that voluntary participation isn’t important, but it’s really slippery to tack on to the “game” definition.

43. #### Ms. Bains

May 2, 2013 - 1:39 pm -

I play a game called Hit Me with my middle school students

It takes 5 – 10 min and it teaches adding integers, they love it!

How to Play
• Players do not pick up their cards! Each player may peek at his own face down card as often as he likes, but it remains hidden from the other players until the end of the round. The card that is face up remains visible to all players.
• Each player mentally calculates the sum of the numbers on his cards. Aces count as 1. Black cards (positive numbers) are added to the total; red cards (negative numbers) are subtracted. A player’s score may go below zero.
• When all players have had a chance to check their cards, the dealer asks each in turn whether he wants a hit — an extra card, also dealt face up so everyone can see it. If the player wants the extra card, he says, “Hit me!” Last of all, the dealer may take a hit, if he wishes.
• Then each player in turn has a chance to ask for a second hit, and then a third, and so forth.
• Players may take up to 3 hits, for a maximum of 5 cards, or they may hold (stick with the cards they already have) at any time.
Endgame
The round is over when all the players have either taken their maximum number of hits or refused any more cards. At the end of the round, each player turns his hidden card face up and announces his score.
The player with the lowest absolute value (the sum closest to zero, whether positive or negative) wins the round. When every player has had a chance to deal, whoever has won the most rounds is the champion.

Pasted from

44. #### Dan Meyer

May 6, 2013 - 2:30 pm -

Nat Highstein posts a game. Just adding it to the pile here, though it might be too mathy and not gamey enough, depending on who’s asking.

45. #### Aaron F.

June 5, 2013 - 8:31 am -

“MacGuffin Roulette” is not so tiny, but I think it could be a lot of fun. With luck, I’ll be trying it out on some high school students in July!

You, the croupier, have a THING in a box. You also have several packets of betting slips, which look like this:

__ ===== PRICE ========>
The THING has four doors
<======= PAYOUT ===== 10

Betting slips are dangerous. Any players who find themselves on the left end of one when the THING is revealed must pay the PRICE to the players on the right. The players on the right, on the other hand, must hand over the PAYOUT to the players on the left if the words in the middle turn out to be true.

All the betting slips have the same payout printed on them; the prices are blank for now. The payout conditions in a full packet might look something like this:

* … has two doors
* … has three doors
* … has four doors
* … has at least three doors
* … is a hatchback
* … is not a hatchback
* … is a two-door hatchback
* TRUE FACTS
* VICIOUS LIES

For more experienced players, betting slips can also include conditions which need to be met in order for any money to change hands:

The THING has two doors
(void unless the THING is a hatchback)

The players get in teams, which face each other in pairs. Each team fills in the prices on a packet of betting slips. Then, their opponents get to decide which way the slips are facing.

Like “Prime Fish,” this game is pretty boring once you figure out the winning (er, not-losing) strategy, but the strategy is cool enough to be worth it. ^_^

46. #### Aaron F.

June 5, 2013 - 8:56 am -

@Kevin Smith: We played 21 in my 3rd or 4th grade math class, with increments of one or two. Working out the strategy was a lot of fun! ^_^

In your example, isn’t “1, 2” the losing move? ~_^

47. #### Aaron F.

June 5, 2013 - 11:47 am -

@Yaacov Iland: Holy crap, “One Won” is a great game! It took me nearly three hours to solve. ^_^

48. #### Jonah

June 5, 2013 - 12:22 pm -

Aaron, Yaacov, wow! That’s really good.

I programmed SAGE to tell me the winning and losing positions up to n=200, but it’s really not at all obvious what the pattern is just from looking at the data. I got it eventually, but only because of instincts that I never would have had if it weren’t for Nim and its ilk.

49. #### Phil D

June 5, 2013 - 5:11 pm -

I have played a game called ‘The Date Game’ for years. Using the digits from that day’s date. E.g. for June 5th you would use 5,6,20,13 the students have to try to make the digits from 1 to 10. They cannot use a number more than once.

To make it more challenging, I stipulate that they must use 3 or more numbers each time.

It’s a great starter, different every day and the students genuinely enjoy it. I have students who I taught many years ago who still talk about it!

I love (and the students really love) to play Nim on the IWB. I like a slightly different alternative called Pick It. Place dots around a polygon, students take it in turns to pick one or two dost, the winner taking the last dot. However, two dots can only be taken if they lie on the same edge. It’s an interesting game for students to analyse and come up with optimal strategies.

50. #### Dan Requa

June 6, 2013 - 9:24 am -

Just to clarify…

The date game, they create an expression using those numbers to try and create the numbers 1-9?

Ex. 5,6,20,13

6-5=1, so one is taken care of

51. #### Phil D

June 6, 2013 - 4:03 pm -