Numbers.

When we learn math, we usually start by learning the names of numbers like “one”, “two”, “three”, and “four”. Then we learn how to match those names with groups of objects that have the same number of things. For example, if we say “one ♠”, we mean “one spade”. If we say “two ♣♣”, we mean “two clubs”. If we say “three ♥♥♥”, we mean “three hearts”. And if we say “four ♦♦♦♦”, we mean “four diamonds”. Finally, we learn how to write the numbers using special symbols like “1” for “one”, “2” for “two”, “3” for “three”, and “4” for “four”.

As we get better at math, we learn how to count bigger and bigger numbers like “ten”, “twenty”, “thirty”, and so on. But sometimes it’s hard to count really big numbers like a hundred or a thousand. That’s why we use special symbols like “100” for one hundred and “1000” for one thousand. These symbols make it easier to do math with really big numbers.

Please note, it took humans a really long time to figure out how to count numbers and how to write them down. They had to come up with a special system that everyone could use so that they could talk about numbers and do math together. So if you’re learning math and it seems hard, don’t worry! It’s okay to take your time and be patient with yourself.

Number Sense.

At a very basic level, it seems that many animals, including humans, are born with a sense of numbers that allows them to guess how many things are in a group. They also have an ability to tell if two groups have more or less things in them when compared to each other. In math, we can compare numbers to see which one is bigger or smaller or if they are the same. We use special symbols to show this. The symbol “<” means “less-than”, the symbol “>” means “more-than”, and the symbol “=” means “equal-to”.

So if you see “1 < 2”, it means that “1 is less than 2”.

If you see “2 > 1”, it means that “2 is more than 1”.

And if you see “3 = 3”, it means that “3 is equal to 3”.

Arithmetic.

As we progress in math we learn to add numbers together like :

“1 + 2 = 3”. This is called addition.

But sometimes we need to take numbers away from each other like :

“3 - 2 = 1”. This is called subtraction.

When we add or subtract numbers, we can use a special line with numbers on it called “the number line” to help us understand what’s happening. The number line helps us see how adding and taking away numbers changes them.

Grids.

To help us understand harder problems, like multiplication, we can use two number lines that cross each other to make a picture with boxes inside it, called “a grid”.

Fractions and Decimals.

A “fraction” is a special way of writing numbers that shows us how many parts of something we have.

When we multiply a number by a fraction, the effect is like division.

When we divide a number by a larger number using a calculator, we get a special kind of fraction called a “decimal”. For example, “5 ÷ 10 = 0.5”.

We can use number-lines to convert between fractions and decimals, and percentages as well:

Final Thought...

Links.

Videos.