Q:

How to explain fractions to 7 year old kid

I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out of the 2. 
Any ideas or any books I can buy which can help me to explain this?

A:

Comparing fractions only works when the whole is the same size.
Here's a few examples to get help the 7 year old understand what happens when things aren't the same size:

1/2 will be greater than 2/4 when you compare 1/2 of a watermelon
and 2/4 of an apple.
1/2 will be less than 2/4 when you compare 2/4 of a watermelon and
1/2 of an apple.
If you take 1/2 of 4 pieces of candy, you will take 1 from the first
2 and 1 from the second 2 which is the same 2 out of 4 or 2/4.
Furthermore 1/2 of 6 pieces of candy is 3 candies and 2/4 of 4
candies is 2 candies.  In this case 1/2 is greater than 2/4.

By showing the examples the 7 year old will start to understand that comparing fractions is can only work if the wholes that you take the fraction of are identical.
My suggestion is to show all these examples, and then explain that since 1/2 is sometimes greater than 2/4 (see 1 and 4), sometimes equal to (see 3), and sometimes less than  2/4 (see 2)- the mathematicians decided we would only compare 1/2 and 2/4 (or any fractions) when we are taking 1/2 and 2/4 of the same thing.

A:

Typically, it is better to introduce mathematical ideas after the need for that new idea is obvious. For example:

How should 2 children share 8 pieces of licorice?
How should 4 children share 8 pieces of licorice?
How should 3 children share 15 pieces of licorice?
How should 3 children share 2 pieces of licorice? And why is this different from the prior cases?
How should 5 children share 4 pieces of licorice?
How should 4 children share 5 pieces of licorice?
etc.

Challenge them to show and assess all of their work according to three main criteria:

Everyone must have the same amount.
There should be no leftovers.
They can name the amount everyone has. [This is where formal fractional language comes in handy.]

Ensure you compare and contrast whole numbers vs fractional numbers. That is really the heart of the matter - that fractions are numbers, most of which are used to name quantities between consecutive whole numbers.
Bonus criteria and tasks can include:

How can you do the sharing with as few cuts as possible?
Is there some other way you can name the amount everyone received?
Is there a systematic way to solve all of these problems?
Generate some sharing examples that do require fractions, then generate some sharing examples that do not require fractions. How do you know when fractions are necessary?

Eventually you can guide them toward the situations of 2 kids sharing one unit of food vs 4 kids sharing 2 units of food. When they have to name the amounts, you can show them the amount of food is exactly the same and then show them that even the cuts can be the same.
You can also show them counting by fractions on a number line to show that 1/2 and 2/4 occupy the same point on a number line.

A:

7? I work in the math dept at a local high school, and students 14-18 struggle with fractions. 
I've found 2 things that help. 

Money Math

Somehow, the same student struggling to take 1/2 of 2-1/2 can easily tell me that half of \$2.50 is \$1.25. For your son, 1/2 of a dollar is 50 cents. No need to stack the pennies, he knows (right?) that 50 cents is 2 quarters. But wait, we just said two quarters, 2/4. Half of a dollar is literally 2 quarters, assuming, of course, that your currency works this way. I am in the US. After this discussion, ask him what half of \$4 is, and then what 2 fourths of that same \$4 is. Further on, you can show how this all changes if the second item, the thing we're multiplying, changes. Of course, he'd prefer to have 1/4 of \$10 than half of \$1. 

Pizza/food Math

I'm a fan of the circular pizza cut into 8 equal sectors. It makes discussing fractions easy for any student, as the fractions 1/2, 1/4, 1/8 are right there. Similar to the money discussion, you can start with what 1/2 means, and how 1/2 of 1/2 is 1/4, and then go into the above explanation of how the whole is our 8 slice pizza. When we ask "how much pizza would you like?" it's essential to know how much is there to begin with. 1/4 of one pizza is not the same as 1/4 of the 10 pizzas I bought to treat the class at year end. As far as 1/2 vs 2/4 is concerned, the answer is right there, they are both the same 4 slices of our standard 8 slice pizza. 
In both cases, money and food lend themselves to divisibility. And having them right there avoids the issue with things being too abstract. Even in high school, I find that numbers and variables create a struggle for some students, and the faster I can move the conversation to solid objects or real life examples, the easier they get it. 

