Three-, Four- and Five-Digit Numbers

Working confidently with three-, four- and five-digit numbers is the gateway from “doing arithmetic” to “doing real math.” Once a learner can read 47,318 without flinching and can add or subtract two such numbers in a column, the rest of the elementary curriculum — multi-digit multiplication, long division, decimals, currency math — opens up. Almost every later difficulty traces back to a shaky place-value foundation.

These lessons treat large-number work as the place-value topic it actually is. We start with place value up to 1,000 so the column structure is clear before any operation runs on top of it. We move into place value for multi-digit arithmetic — the way the standard column algorithm corresponds to the underlying tens-of-tens. We cover addition of two- and three-digit numbers with carrying and subtraction with borrowing because regrouping is where most multi-digit errors originate. And we extend to addition and subtraction of four- or five-digit numbers so the same reliable column technique scales to numbers a learner will actually meet in the world (prices, populations, sports scores, distances).

Every lesson uses fully worked column-arithmetic examples — every regroup written out, every carry annotated — so the algorithm is never opaque.