Math uses rules that are made up to determine relationships and create models. Most math teaching rarely focuses on the *understanding* of math concepts. Instead, students are taught to memorize formulas, which is very tedious. This approach is also lost if these formulas are not used often.

Math should be a way of thinking. It is a system that has developed over time and expanded as need dictates. If we look at the progress of numbers themselves, we can understand this evolution.

**Unary System**

- Very simplistic.
- You can increase a number without having to erase and rewrite it.
- Essentially you can draw lines in the sand, on a piece of paper, or scratched onto tree bark.
- Large numbers are represented inefficiently as they take up A LOT of room.

50 is |||||||||||||||||||||||||||||||||||||||||||||||||||

**Roman Numerals**

- Seven symbols were used to in combination to form all numbers:

I, V, X, L, C, D, M - The order of these symbols determined the final number represented.
- Long numbers were much easier to write, as this was a more complex math-based system.
- There are no symbols for zero or negative numbers

50 is L

**Decimal System**

- Everything is based on the number 10.
- A number is written as a row of digits, with each position in the row corresponding to a certain power of 10.
- The decimal point in the row divides it into powers of 10 equal to or greater than 0, and those less than 0, or negative powers of 10.

50 is 50 (look familiar?)

**Binary Numbers**

- All information is represented with a combination of two digits: 0 and 1
- It is based on a simple, positional system
- When spoken, it is read digit by digit, instead of as the larger number like the decimal system. 100 is read as ONE ZERO ZERO, not as ONE HUNDRED.

50 is 0011010

**Scientific Notation**

- Extremely compact and can easily gauge a number’s size and precision.
- Also known as “Standard Form.”
- It uses exponents to represent the place a numeral occurs before or after a decimal point.

50 is 5 × 10^{1}

**What is next?**

As we look at all of the different systems and how they were developed, we can only imagine which direction we will go in the future. Math IS science.

Continue reading about how to become inspired by Mathematics.