Estimating Areas Quickly

Mental Math · Axiom Academy

The room picks the trick for you A room is two numbers multiplied together, and the two numbers tell you how to do it. One side on a whole ten? Shift it. Both sides the same distance from an easy middle number? Difference of squares. A twenty-five in there? A quarter of a hundred. Otherwise split the bigger side into tens and ones and add. Drag the walls and watch the method change. Which way is your estimate wrong? Nobody paces a room and gets 13 by 17 — they call it 15 by 15 and move on. Round both walls up and the estimate is bigger than the room, always. Round both down and it is smaller, always. But round one up and the other down and there is no rule: you have gained one strip of floor and lost another, and only the bigger strip decides. The figure shades both. From square feet to what is in the trolley The area is only half the job. Add the tenth you will waste on cuts and mistakes, divide by whatever one box, one yard, one pound or one gallon covers, and then round up — because no shop sells you 8.47 boxes, and a second trip costs more than a spare box.

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