# Abstract Confusions

Complexity is not a cause of confusion. It is a result of it.

## Math Games for Children

Games are the sure shot fun way to teach some thing. And math is one of the top-notch skills one needs to own for being successful in any career. Imagine if playing games hone your mathematical skills. As a kid I grew up learning few board games which helped me to understand the most basic math operations – counting, addition and division (subtraction and multiplication thereof).

Very recently, I tried teaching math principles to my nephew but found difficult without the help of games. The most important thing I did was to run to a store to get him a board game. So, if you don’t want to spend those long boring hours and make teaching fun, try few of these games.

This is a simple game. Most of adults would have played it. Two or more players can play this game. This board game has hundred squares numbered from 1 through 100. And a player wins if he starts from 1 and reach 100. Each player has to toss a die and move their playing piece according to the output of the die.

Snakes and Ladders - A Chance game in 100 squares

##### Mathematical Concepts

Start by playing with the kid. Toss the die and ask him to count as he moves from one square to another. Like if the die lands with 5, let him count from square 12 to 17 and move the pieces. You can improvise by asking the kid to move from one square to another without counting each them. Also make sure the kid moves the pieces for both of you.

Also ask questions like, how much you need to climb a ladder? or what number you avoid from getting bitten by snake? How many squares are one ahead/trailing of/from other?

A kid can learn counting, adding, subtraction by playing snake and ladder. Try your luck on probability. Engage him on throwing the die at random and ask for what’s the chance of 6 or 4 appearing? Some how the kid can imagine the number line.

For bigger guys, snake and ladders can be represented as a Markov chain. Surprised? Check “The Chutes and Ladders” for more details. And graph theory also: one can also think of each square linked to others as a mixed graph, an edge from $i$ to $i+1$, with few directed edges for ladders and snakes connecting distant squares.

### Pallanguli

Pallanguli is a strategical board game. It is a two player game (and there is a single person game version too). You need 14 cups arranged as 7 cups each in a row. Most of them time the setup is made in wood, with elaborate carving. It is filled with seeds equally. The aim of the game is to accumulate as much seeds as possible and eventually ending up robbing all seeds from your opponent. Check for rules of the pallanguli.

Pallanguli - A strategy game.

##### Mathematical Concepts

As you start playing, let and make obvious that you count the seeds before you distribute one each in the cups. Encourage the kid to count before he could play his turn. The kid has to distribute with aim to win the seeds in the cup after the empty ones. By letting him to count, you are encouraging him to learn division.

Ask questions like, how much seeds the kid should divide equally to win the treasure? Encourage him to learn counting. In advance levels, ask the kid the keep track of seeds in the cup in mind and play without counting them. This will help his memory skills.

The kid will learn, counting, adding, dividing by playing pallanguli.

Aadu Puli Aattam or “Goat-Tiger game” is yet another strategy game. A detailed information on playing aadu puli aatam. This game is very famous in Indian villages and played in several regions with many other names.

Two players are needed to play this game. One player will play as aadu (goat) and the opponent as puli (tiger). There are 15 goats and 3 tigers. Each player takes turns to place one piece at a time in the nodes. Tiger and goats can move across the edges. A tiger can also jump over a goat, note: it can jump just one goat, but not two. When a tiger jumps over a goat to move from one node to another, the goat is considered as caught (or dead, eaten up by tiger). The goat is moved outside the board. The aim of the game is to catch all tigers from making a legal move.

Adu puli aattam or Goat-Tiger game, another strategy game.

##### Mathematical Concepts

This game is slightly advanced. But it involves a lot of strategy. a graduate level math student can start trying to answer, whether there is any winning strategy for tiger or goat? How about trying to understand the possible legal move by depth first search or breadth first search? Backtracking? There could be hidden connections to game theory, combinatorics and graph theory.

I can sense, this game is worth atleast one technical paper publication.

You can also play aadu puli attam online.

### Comparison of Board Games

Following is a small comparison on mathematical natures of board games.

 Game # of players Genre Difficult Group Concepts Snakes and ladders 2 or more Chance Beginner Age: 5 + Counting, addition, subtraction, chance Pallanguli 2 or more Strategy Beginner Age: 5 + Counting, addition, division Aadu puli attam 2 Strategy Intermediate Age: 10+ Search, combinations Chess 2 Strategy Intermediate Age: 10+ Search, combinations

Update: I have missed to mention few simple games.

Book Cricket: In a country like India, cricket frenzy leads to innovative way to play the game. Apart from street cricket, students also play “book cricket”. Two or several players, some times, a book cricket tournament will have as many as ten players participating. A book, numbered properly.  Paper to score. Player should open a page from book at random, the page number from the even pages will be taken for scoring. Page numbers ending with 2, 4 and 6 are considered as possible scores. Numbers ending with 0 is considered as out. 8 sometimes considered as out, or dot, or sometimes modulo 6 addition.

Math concepts: Players are encouraged to open book pages fast, there by aiding fast addition. Modulo 6 could help to introduce modular addition. When books get used to the game, opening of the pages are no more random. Observe the occurrence of bias, with players as well as books.

Dots and squares: This game also doesn’t need elaborate settings. A plain paper, color pencils, two or more players. A column of dots (matrices) of 10 x 10 or some number to start with. Each player will choose a letter, either from name or initial, the game starts by connecting two dots. When you form a closed loop, you can fill it with your initial. At the end of the game, the one with maximum number of boxes filled in with his initial wins the game.

Math concepts: Graph theory concepts. Vertices and edges. The game is also know famously as packing graphs. A detailed study is available on the strategies to follow to win “dots and squares”. There are detailed theorems and interesting open problems on this.

Warning: Be careful in introducing these games to children. These games are highly captive and needs nothing less than study book or plain paper to play. Young people could waste their time and other’s, in classes as well as in tuitions.

### 10 responses to “Math Games for Children”

1. Santhosh M K Swamy June 4, 2010 at 11:05 AM

Excellent piece of Information and Advice to teach kids …

its “Abstract Clarifications”

• SREE GURUPARAN June 4, 2010 at 7:01 PM

Hey mams, Thanks! And good to see you around. Hope you have good time teaching this, as I had teaching this to Tanuj. Ushhhh!!! It was really difficult, but he picked up adding when I played with him recently. 😀

2. metin2 yang June 17, 2010 at 1:13 PM

nice blog, great.

3. aali@aurora June 28, 2010 at 4:25 PM

I havent played snakes and ladder in many many years it was so much fun

4. Muthu October 10, 2010 at 2:30 AM

Boss.. Kalakkaringa!

“I can sense, this game is worth atleast one technical paper publication.”
-Like

5. SarahJ January 20, 2011 at 8:30 AM

An interesting post! Children can learn so much math through math. So much more fun than the endless worksheets seen in many classrooms.

6. Prabhakaran January 27, 2013 at 8:26 AM

I am planning to collect the priceless [less prices 😉 ] games that we played during childhood… Looking for pics and links that describes the game… Can I use the images in this site and link ?

Thanks and Regards,
Prabhakaran R.