Basic Arithmetic

Basic arithmetic is the load-bearing layer of everything that comes after. Multiplication is repeated addition; division is repeated subtraction; long multiplication and long division are addition and subtraction with bookkeeping. Fluency in the four basic operations on whole numbers — and an honest understanding of why the algorithms work — turns the rest of K-8 math from a hill into a flight of stairs.

These lessons cover addition and subtraction at every level: single digits, two-digit numbers with and without carrying, three-digit numbers with regrouping and borrowing, four- and five-digit numbers when the bookkeeping starts to bite. We treat place value as a topic of its own (because if a learner doesn’t see why “37” means three tens and seven ones, addition with carrying never quite makes sense). We cover estimation and rounding because mental math is a real-world skill — knowing that 487 + 312 is “about 800” before you compute the exact answer prevents most arithmetic errors. And we cover the properties of addition and subtraction — commutativity, associativity, identity — early, because they make later algebra readable.

Every lesson opens with a plain definition, walks through worked examples on tangible quantities (apples, balloons, blocks), and finishes with practice problems whose full reasoning is shown — not just the answer.