Arithmetic
What are the four operations on whole numbers and decimals, and what rules do they obey?
Where you are 5 inside
What this area is about
Arithmetic is adding, subtracting, multiplying and dividing. Here the numbers are whole numbers and decimals: what each operation means, the facts and written methods that carry it out, the rules that let a calculation be rearranged, and the agreed order for reading a line with several operations in it.
How these fit together
The operations. Addition and subtraction put together and take apart: adding finds a whole, subtracting finds a part. Multiplication and division do the same for equal groups. Decimal arithmetic runs all four with a decimal point, where the new question is where the point goes.
A convention. The order of operations fixes how to read a line such as 3 + 4 \times 5: grouping first, then powers, then multiplying and dividing, then adding and subtracting, each pair from left to right.
A habit. Estimation and mental math gets close quickly, checks whether an exact answer is the right size, and reshapes a problem into an easier one with the same answer.
A path through it
Addition and subtraction first, then multiplication and division. Decimal arithmetic and the order of operations both come after multiplication and division. Estimation and mental math run alongside the operations rather than after them: parts of it use adding or multiplying, and parts of those areas use estimates.
Next come fractions and algebra, which writes the rules of arithmetic with letters.