Lineup for the quarter final of the 2018 FIFA World Cup has been decided and the World Cup Fever is at its peak. There is a lot to learn in real life from sports and it is through the watching and participation in sports, with our children, that has endless benefits for their well being and development. Research suggests that watching sports with your children can have great emotional and mental benefits too.

Soccer is a beautiful game of skill, teamwork and strategy which captivates the attention of millions around the world. You may be surprised to know that there is lot of maths and science which goes behind every aspect of this fascinating game. We will share some such fascinating facts, so that when you are bonding with your child, rooting for your favorite team during the final stages of the tournament, you can also share some of these fascinating facts with your child.

Mathematics Behind the Soccer Ball

The official soccer ball (as illustrated in the above picture) is made of a combination of 12 black pentagons and 20 white hexagons. Length of each side of the pentagon and hexagon is same to ensure that they fit together like a puzzle leaving no gaps between them. In mathematical terminology this is called Tessellation. If you are interested in knowing more about the math behind the soccer ball, you can refer: http://www.hoist-point.com/soccerball.htm. If you want to engage your child in making their own football out of paper, refer the attached youtube origami craft video https://www.youtube.com/watch?v=jfHzE3TtuaI

Science Behind the Impossible Free Kicks

Probably the most spectacular thing in soccer is seeing a player curving a soccer ball into the back of the net. Many fans almost automatically remember the Brazilian soccer player Roberto Carlos who in 1997 scored on a free kick that first went right and then curved sharply left. You would also remember the famous free kick from David Beckham, the famous England soccer player who scored on a free kick against Greece in 2001. So, how do soccer players do this? The answer lies to it in Magnus effect, a phenomenon that is commonly associated with a spinning object that drags air faster around one side, creating a difference in pressure that moves it in the direction of the lower-pressure side. A soccer ball is simply a projectile that is flying through the air with an initial velocity. The reason the ball curves is because the kicker kicks that ball at a certain angle and velocity. Once the ball is in the air, it is really the air that is curving the ball. Professional soccer players would usually kick the ball and add a little spin to it to neglect as much air resistance as possible. But in a free kick, which is usually 18 to 30 meters away from the goal, players would actually want air resistance because the air would curve and bend the ball in a way to trick the goal keeper. This all sounds easy but is extremely difficult. Players must hit the soccer ball with a precise velocity and with a particular spin. According to Bernoulli’s principles, air travels faster relative to the center of the ball where the periphery of the ball moves in the same direction as the air flow. In a normal kick, the ball would travel at roughly about 65mph. The ball would spin at around 10 revolutions per second. Once the ball travels about 10 meters, its speed would substantially drop and the drag would dramatically increase. Once the ball’s velocity drops the Magnus effect starts to increase. The Magnus effect is the reason the ball curves through the air. To know more about the magnus effect refer the Wikipedia link on the same https://en.wikipedia.org/wiki/Magnus_effect. There is a very interesting you tube video actually demonstrating the Magnus effect in football which you can also enjoy with your child https://www.youtube.com/watch?v=YIPO3W081Hw.

Maths Behind the Soccer Pitch

• The football pitch is rectangular in shape which has a length of 90m-120m and a width of 45m-90m.
• However, a rectangle is not the only 2D shape visible on a football pitch. There are also circles and semi-circles and more rectangles.
• Each of the halves of the field, divided by the Half-way Line, is symmetrical. Symmetry of the field is important to make the game fair for all
• The Half-way Line is the diameter to the Centre Circle
• All Corners of the Soccer Field are right angles
• The two penalty kick spots in the goalie box and the Centre Spot from where the ball is kicked off are coplanar
• The opposite sidelines are parallel and the opposite endlines are parallel.

Importance of Geometry in Strategising the Game

Knowledge of angles and measurements helps a soccer player improve his game significantly and goes behind every aspect of soccer strategizing.

• Knowledge of angles help in improving the accuracy of the passes
• Goal keeper relies on angles to decide where he should stand when defending. In the diagram on the left in the picture below, the goalie is standing near the goal post giving the striker a wider angle to score the goal. In the diagram on the right in the picture below, the goalie has come out of the 6 yard box narrowing the angle for the striker to score the goal.
• A striker also uses the knowledge of angles to improve their probability of scoring the goal
• Knowledge of trigonometry can be significantly useful while taking penalty kicks. The best spot to place a penalty is the top corner! So what angle would you kick the ball at to maximize your chances of scoring? Is it 30°, 45°, 77.2°?
• When you kick a soccer ball, it arcs up into the air and comes down again following the path of a parabola. Sometimes the objective is to hit the ball as far as possible. The objective is not achieved just by kicking the ball as hard as possible. Angle of the kick also plays a very important role in deciding the final distance which a ball can travel. Here is a link to a beautiful video explaining the math behind parabola https://study.com/academy/lesson/parabolic-path-definition-projectiles-quiz.html

So, next time you are watching this beautiful game of football, do engage your child into the fascinating maths and science behind the game.

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We all are aware that mathematics is a subject that deals with study of shapes, numbers and patterns. It is an abstract subject and the approach needs to be creative to solve it. As parents, somewhere deep down inside, we all want our children to be good at mathematics; meaning good at “problem solving” and “critical thinking”. But the question that immediately springs up is “How to make our children problem solvers and critical thinkers?”

Before delving into this we should first understand what is a) problem solving and b) critical thinking and why we associate it with mathematics. The simple answer is that mathematics is all about logic and logic comes from thinking i.e. exercise of mind.

When we face obstacles and challenges while executing a task and carve out a way to deal with those difficulties, we solve a problem. This is called problem solving. There are certain attributes of a task which determines whether it is a difficult one or not.

1. The task should be a new one. A person should not have done it before.
2. It should be sufficiently difficult so as to challenge the current abilities of the person.
3. The task to be executed should not have passed the stage of learning of the concerned individual.

The same can be explained through an Experiment:

Age of the sample participant : A 3 year old toddler

Skill present : Rote counting

Task : To find out sum total- addition

Level : Difficult- have never attempted addition

Experiment : First 1 yellow colored teddy bear is placed on the table and the child is asked to count. Thereafter 2 red colored teddy bears are placed on the table and the child is asked to count red ones. The toddler is then asked to find out the total number of all the teddy bears.
Execution : The toddler first looks at the bears with inquisitiveness, holds and plays with them. Thereafter places them back on the table and counts 2 reds and 1 yellow respectively. The trainer intervenes and asks probing questions like

“We see 1 yellow and 2 red teddy bears on the table but if we want to know the total number of teddy bears what shall we do?

How many teddy bears are there in all, on the table?

You counted 1 yellow teddy bear and 2 red teddy bears but if we want to know how many are there are all together what shall we do?

If we count all the teddy bears together how many they would add upto?”

The toddler once again starts counting teddy bears, slowly moves the index/pointer finger from the first teddy bear to the second one, pauses for few seconds and ponders and thereafter moves from the second teddy bear to the third one and eventually comes up with the correct answer.

Observation : Given the toddler had never counted 2 different colored manipulatives together it is posed as a challenging task. The experiment was close to introduction of addition concept. The trainer used other synonyms of the word “total” like “in all”, “together” and “add upto” to make the toddler think and understand the task.

Note : The toddler encountered with 2 different colored manipulatives for the first time and with the help of probing by the trainer could find out the total of teddy bears. The toddler was aware of the concept of rote counting and used it to find out the total. The task was ahead of the stage of learning of the toddler but by using the technique of rote counting could find out the solution.

If we conduct the above experiment with a 15 year old, it will not be problem solving scenario because the teen will not find it challenging. There would not be any struggle of thoughts to come to an answer. Also the teen would have passed this learning stage and finding total would be just an “instrumental function” of the brain now.

Also, when we develop the ability to visualise problems we are investing our time in thinking. This process of exercising our mind makes us thinkers. Thinking is a process which can be achieved only with regular practice. When we are thinking we are collating all the data in our mind, organizing it and evaluating various mathematical tools to be used for representing the same. This process is termed as “Critical Thinking”.

A problem gets solved only when we think of ways of solving it. Therefore problem solving and critical thinking is very important. It is not only crucial for mathematics but also in our day to day life. Each day unfolds with new surprises and challenges. Doing mathematics in the right way will also allow us to deal with life’s uncalled for situations and difficulties. Doing rote based learning will not make our mind prepared for the future.

Skills like a) computing fast and b) rote learning of tables and formulas, though a good skill to have, can be easily done by gadgets too. With the advancement of technology, the dependency on memory has reduced significantly and the above mentioned skills (fast computation and rote learning) constitute “Lower Order Thinking” where we are using less of human talent, i.e, our mind and treating our brain more like an instrument and performing structured tasks without much application of our mind.

Skills like

a) Reading and Understanding of a problem,

b) Filtering of relevant information and facts,

c) Visualising the facts in mind,

d) Reasoning the facts by way of analysing and evaluating the circumstances and constructing logical arguments,

e) Portraying the facts in a pictorial form,

f) Coming to the conclusion of the problem,

g) Trying out other ways to solve the same problem and

h) Expressing it verbally and in written form

constitute “Higher Order Thinking” and make our children problem solvers and critical thinkers.

Abstract art is beautiful. Even though it does not have any form, we all appreciate it because it effectively reflects fluidity in one’s thought.

Every piece of abstract art is the result of an innovative thought. When an artist sits with paint brushes and bottles of paints with an awareness that he is free – free to use any quantity, try any colour and paint whatever he desires – his mind starts constructing; and he becomes a risk taker. The absence of impediments makes the artist’s thoughts more flexible and he/she does not shy away from exploring different hues, shapes or ideas. Using paints liberally on a blank canvas helps in easy and smooth flow of thoughts.

Making an attempt to fill a blank piece of paper with colours is a struggle for many. However, regularly engaging one-self with abstract art makes one imaginative and creative.

Similarly, mathematics is an art that needs to be approached creatively. There are no fixed set of rules in mathematics with no one way to look at things. There can be various pedagogies to reach to solutions and all methods should be considered. If we always cling on to one way, our minds will become lazy and struggle to think innovatively.

When we lay emphasis on “concept building”, we help in “forming” the mind, and when mathematics is approached traditionally in the form of formula learning with set rules, we “fill” our mind. In this technology driven era we need minds that have abilities to respond to uncertainties with creative thinking. Mathematics is a wonderful tool which helps us to build our thoughts and makes us ingenious enough to work around laid information.