The Pythagoras Theorum is one of the oldest and most used triangle formulas - there are literally hundreds of ways to prove that this formula is true.
Working through a proof of the Pythagorean Theorum is a great way to get a feel for the way mathemetician's show that if one thing is agreed to be true and then by working through a number of steps, you can see that something completely different must also be true.
Try and get to the point where you're not just memorising the steps but thinking to yourself that each step is a logical progression from the previous one.
We know how to find the area of squares, rectangles and triangles but how do we work out the area of a circle? Once you know how to work out the length of the perimeter, we can use that as one side of a rectangle.
Pi (the greek letter 'p' which indicates 'perimeter') is the ratio of a circle's perimeter to its diameter or more usefully if you know the diameter of a circle, you can easily find the length of the perimeter by multiplying it by pi.
Finding the area of a square or rectangle is pretty easy but how do you work out the area of a triangle?
Multiplication as repeated sets, addition jumps on the number line, and as area calculation. Use the concept of multiplication as an area calculation to break bigger numbers down into smaller numbers and then sum the parts.
Multiply and divide are 'stretch' or 'squash' on numbers shown as a distance from zero on the number line.
Introduction of the natural numbers, the number line, zero, negative numbers and finding an unknown.
Adding and subtracting are 'jumps' on the number line to the right or to the left.