Foundation Skills Summary

Mental Math · Axiom Academy

SUMMARY Foundation Skills Summary Let's review the number sense, place value, and estimation skills that make every calculation easier. Every number is a sum of its places — 537 = 500 + 30 + 7 — and reading those places on sight unlocks every other shortcut. Numbers relate to each other: near-doubles, partners that make ten, halving-and-doubling, and distance on a line each turn an unfamiliar fact into one you already know. Breaking a number apart — by place value or into a friendly round number — turns one hard calculation into a couple of easy ones you recombine at the end. Rounding to a friendly number (10, 25, 50, or 100) is a loan: whatever you borrow to make the numbers easy, you pay back before you're done. Estimating before and after a calculation — by rounding or by front-end digits — catches mistakes and builds confidence that an answer is reasonable. Every number is really a sum of its places — a digit's value depends on where it sits, not just what it says. Slide a digit one place to the left and its value multiplies by ten (5 → 50 → 500); split a number into its places and you can add tens to tens and ones to ones instead of the whole number at once: 34 + 52 = (30+50)+(4+2) = 86 . When to use: any time you want to see why a number behaves the way it does, or before adding or subtracting by place. Watch out for: face value and place value are different — the 3 in 537 is worth 30, not 3. Core Concept Number Relationships

This is the written version of the interactive lesson above. See the full Mental Math course.