Taking away, within twenty, twenty-four to a page. Nothing on this sheet drops below zero — a child who has not met negative numbers should not find one waiting in question nine.
Subtraction is the same fact read backwards, and that is worth saying out loud while a child works: 15 − 7 is the question “seven and what makes fifteen?”, which most children can answer a year before they can take away. If a sum stalls, turning it round is usually faster than counting back.
Negative answers are off, not absent — the engine will produce them, and the builder has the switch. They belong on the integers sheet, where the minus sign is the lesson rather than an accident of which number happened to be drawn first.
The answers were worked out when the problems were, so the key is the same page with the answers drawn in rather than a second attempt at the same questions — there is no way for the two to disagree. The number in the footer is the seed the sheet was built from: it is printed so that the identical sheet can be had again next week, rather than one that merely looks like it.
Change what is on it
This page is one sheet out of a family that can print thousands, and the settings behind it — how many problems, how big the numbers get, how they are laid out, whether there is room to work — are all switches. The builder link at the top of the page carries this sheet’s own settings, so the bench opens on exactly the sheet here rather than on a blank one.
The configuration travels in the address bar rather than on a server, so the link can be bookmarked or sent to somebody as it stands — and what they open is this sheet, down to the seed, rather than another one like it.
The same facts, on screen
The Grid drills subtraction as timed cards alongside the other three operations, so a fact that stalls on paper can be practiced on screen.