Learning Math Visually

Many students find learning math boring from a very early age, when they move to higher grades this boredom will make them hate or fear math. This is true of many students. Many of us consider math as not a creative subject, we believe that math could be mastered only by someone with a so-called “mathematical brain”

But in reality, math is a creative subject if it is taught in the right way.

Let us take the example of fractions.

In the early stages, many students find it difficult to understand fractions..and many learn it the wrong way…

For example what is ½ +¾ = (3+1)/(2+4) =4/6 =⅔ <THIS IS COMPLETELY WRONG..>

WHY?

Here the student did the sum of the numerator and divided it with the sum of the denominator..which is not the whole idea of what fractions are all about FRACTIONS

It is defined as the part of a whole

Fractions are always taught with the help of pizzas…..since I also like pizza  a lot let’s consider the classic example of pizza

We can say that this is “a pizza” or you can call it “one pizza” or “1 pizza” or (1/1 pizza)

Here if you look at the numerator and the denominator we have “1” in both numerator and denominator.

Now one of your friends came home and you wanted to share the pizza with your friend …so how can you do that ..you have to divide your pizza into two equal parts

This is how your pizza will look like …so if we are asked what portion of pizza you had, can you say that you ate the whole pizza….no…you can’t say that because you haven’t eaten one pizza..

so what can you say?

You can say that I divided the pizza into 2 equal parts …out of which I ate only one part …or I ate the PART OF THE WHOLE pizza..so how can you mathematically represent the division of one pizza into two equal parts….you can say 1 divide by 2 or you can write mathematically….. ½

This is called a fraction

Now coming back to our specific question of adding ½  with ¼   

So to make you understand better, imagine that you visited two of your friends’ houses on a single day ..in the first house you and your friend were there..but only one pizza …so you divided the pizza into two and ate one portion….

Now you went to your second friend’s house and there were 3 of your  friends .but unfortunately ..there was only one pizza..so you all decided to divide the pizza equally among all the four friends including you…so now you divided one pizza to four pieces 

Or ¼…is how you mathematically write it…

And visually

Now you got home, at night and thought of how many pizzas you had on that particular day. you did not eat one pizza. you ate half of the pizza from the first friend’s house ..so definitely you ate more than half a pizza  but 

You did not eat one pizza either….so you thought of thinking about the problem visually  …

Let’s see

How we divided the pizza

First friends house

Second friends house 

This is what you ate

First House

Second house

But how are you going to add both of them?

HERE  if we just look the first one is ½ and the second one represents ¼ 

But does the 1 represent the same quantity in both cases, no.  why?  The first portion is bigger than the second portion.

So mathematically we cant add both of them….so how can we make them equal mathematically…

If you closely look into it we can see that

The first pizza can be also divided into 4 equal parts

Now if you compare we can see that the first portion(in the pizza which has been divided into two) is equal to the 2 portions in the second pizza which was divided into 4.

So in the first pizza ½ = 2/4 

So now our equation

½ + ¼ 

Becomes

2/4 + ¼ 

So now, since we have made our base the same(no: of pieces divided), or rather we have the same denominator, we can add up the numerator(WE CAN ADD ONLY THE UNITS WITH SAME SIZE)

So (2+1)/4=¾

Now we know that ½ +¼  is not equal to 2/6….but

It’s equal to ¾ ..

By understanding the concept visually ..the child’s perspective towards fractions will be more sound…. it’s all about the ‘why’ of math rather than the ‘what ‘of math 

Now mathematically how can we make the base the same, just by taking the least common multiple of the denominators

Here, for example,½+¼ ….

The LCM of 2 and 4 is 4…

So we have to multiply the numerator and denominator of ½ by 2 to make the base the same…so ½ becomes 2/4 … now since we have the same base we can add them up

So 2/4 +¼ = ¾