## Real Mathematics – Numbers #10

A game for kids who would like to get better at arithmetic operations, decimal system and numbers in overall:

European Championship

• Only materials needed for this game are a twelve-faced dice, pen/pencil and a piece of paper.
• Game consists of encounters between two players.
• In each encounter players roll the dice four times in order.
• Outcome of a rolled twelve-faced dice is like the following:
• For every player only ambition is to write the biggest possible four-digit number.
• Difference of players’ four-digit numbers decides the winner.

Scoring of the game

Player with the bigger number would get:

• 4 points if the difference is a four-digit number.
• 3 points if the difference is a three-digit number.
• 2 points if the difference is a two-digit number.
• 1 point if the difference is a single-digit number.

If the difference is zero; meaning that the numbers are equal to one another, then both players get no points.

Every encounter finishes when one of the players gets to 7 points.

League

In case there is enough number of students, it is possible to construct a league version of the game that finishes after playoffs. For instance if there were 20 students we could divide them into 4 groups with 5 teams. In each group every player would play 4 games and after the group stage group leaders would go onto the playoffs where the champion can be decided after semi-final and final games.

World Cup

In this version of the game players would roll the dice three times and write the biggest possible three-digit number. Although this time winner gets to be decided like following:

• If the difference is odd, biggest number wins.
• If the difference is even, smallest number wins.
• Winner gets 3 points as loser gets nothing. Differences are kept as averages.
• If numbers are the same, players get 1 point each.

M. Serkan Kalaycıoğlu

## Real Mathematics: Pattern #4

Leonardo Pisano

Italian town Pisa was the home of an ingenious person named Leonardo Pisano, which means Leonardo from Pisa. He was not only essential to history of mathematics, but he was also influential for the birth of scientific revolution. It is not a surprised that Leonardo Pisano was from Italy as Italians were involved with Arabs through trading.

Arabs knew an amazing way of counting and calculating, which were done with a system called decimal system. I’ll talk about that story in another article.

Leonardo Pisano was the first known person who brought modern numbers Western Europe. Although this was an amazing accomplishment, his importance comes even more fascinating if you look at what he did for patterns.

The Rabbit Problem

If I wrote his name as Fibonacci, then majority of you would understand what problem I’ll mention in the following:

In a farm, there is one couple of baby rabbits. A rabbit couple can give birth to baby rabbits only after their 2nd month and they can continue giving birth each month after that. Leonardo Pisano tried to find out the number of rabbit couples after one year.

Solution

First month there is a baby couple. This couple will be adult in the second month and they will give birth to one couple baby rabbits in the third month.

In the fourth month first couple reproduces as the second couple becomes an adult.

In the fifth month first and second couples have new babies as third couple becomes an adult.

In the sixth month first, second and third couples have new babies as the fourth and fifth couples become an adult.

At this point we can point out a pattern in the number of rabbit couples. After second month, total of previous two months gives the number of rabbits in the next month. For example number of rabbit couples in the third month becomes the summation of first and second months, which is 1+1=2.

Fourth month = Second month + Third month = 1 + 2 = 3… and so on.

Then number of rabbit couples after one year (twelve months) is:

Beauty of Fibonacci

This number sequence is known as the Fibonacci sequence and it is visible to us in nature on so many occasions. I’ll be talking about the most popular examples of Fibonacci sequence in the following articles.

Real life examples of math subjects are crucial, especially the ones from nature itself. But most of the population lives in the cities and this force us math teachers to find out examples from modern life.

Stairs and Fibonacci

Imagine that you have to climb up from stairs inside your apartment.

1. How many ways are there to climb 3 steps?
2. How many ways are there for 5 steps, 6 steps, 8 steps and n steps?
3. What is the relationship of this question and Fibonacci numbers?

M. Serkan Kalaycıoğlu

## Real Mathematics: Numbers #8

Dotted Tic-Tac-Toe

Almost everyone knows how to play tic-tac-toe. Dotted tic-tac-toe is a multiplayer game to teach kids about number systems.

Rules:

• Players throw a dice in turns.
• Each square in the board has the capacity of 9 dots.
• Players should put dots into one of the boxes as many as their dice shows.
• While putting down dots, players must be careful not to exceed the capacity of the box. In such situations they have to put dots to another box that has capacity.
• Whoever gets right to left, upside-down or diagonal three boxes will be the winner.

Beauty of this game is although it is competitive, it requires help of your opponent.

An example:

In the first three rounds players get 5, 6 and 3 from the dice:

Fourth dice is 1 which gives second player a chance to complete a box.

In the next four rounds players get 5, 5, 6 and 4 which gives again second player to complete another box.

Game resolves in the next rounds as shown in the following:

Binary Tic-Tac-Toe

In this version of the game, use a coin instead of a dice.

Tails: 0

• Consider that a box can have either of the following: A head & tail (tail & head is the same) or a tail & tail.
• This means that every box is either 1+0=0+1=1 or 0+0=0.
• So in this version of the game, x-o-x turns into 1-0-1. Right to left, upside-down or diagonal 1s or 0s wins the game.

Once again, although the game is competitive, you’ll need your opponent’s help.

An Example:

First two coin tosses are both tails.

Then four consecutive heads are tossed.

Game resolved after three consecutive tails.

M. Serkan Kalaycıoğlu

## Real Mathematics: Game #1

Circle of Numbers

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Most of the countries in the world use these symbols for the remarkable decimal system. The system was designed so perfect, even though symbols might change in some regions, logic of the system is conserved all around the world. Decimal system is one of those things that are “universal”.

If you are willing to participate in today’s modern world, you’d better know how to use numbers. You could go on and try to live a day without using any numbers: You’d see that it is impossible to finish even one single day. Actually, using numbers is not enough: you should be able to understand what a given number represents.

Understanding Numbers

What do I mean by “understanding numbers”?

If I show you 2125555555, can you associate it with anything?

How about 212 555 55 55?

Now most of you realize that 212 555 55 55 is a telephone number. Using three blank spaces inside the number 2125555555 changed the way you look at it.

Numbers take too much space in our daily lives. I think this is a great reason to work and develop a good understanding of them. Circle of Numbers is a game that helps children cultivate the ability of using numbers.

In order to play Circle of Numbers, all you need is a pencil and a pen. This game can have various numbers of versions.

Circle of Numbers 1.0.0

Draw a circle.

Place four boxes on the circle.

You have to place the numbers 0, 1, 2 and 3 inside the boxes such that difference of two adjacent boxes will be an odd number.

Example

Circle of Numbers 1.0.1

Again draw a circle with four boxes on it.

This time each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 should be used.

In order to do that, you will need ten boxes which means you will have to add six more boxes on the circle.

Difference of two adjacent boxes should be odd.

Example

Let’s assume 4 and 7 are placed as following.

Player knows no matter which number is chosen, there will be number pairs that will not have odd difference. For instance if 5 is chosen, even though 5-4=1 is odd, 7-5=2 will be even. Player should add a new box to avoid this problem. Following will show you a working strategy step-by-step.

Circle of Numbers 2.0.0

Assume that there are five boxes on the circle and you are allowed to use the numbers 1, 3, 5, 8, 9. Can you construct a valid circle?

Check it out

I just gave three different versions for the game Circle of Numbers with three different names: Circle of Numbers 1.0.0, Circle of Numbers 1.0.1 and Circle of Numbers 2.0.0. What do these numbers remind you? What would Circle of Numbers 2.0.1 look like?

M. Serkan Kalaycıoğlu