Missing Number Sentences

The box stands for a number, and your job is to work out which one. Eight plus box equals fifteen. Draw it as a whole and two parts: fifteen is the whole, eight is one part, and the box is the other part. To find a missing part, take the part you know from the whole — fifteen take eight is seven. Then put it back in and check: eight plus seven is fifteen. It works, so seven is right.

When the box is at the front of a take-away, it is the whole, not a part. Box take seven equals twelve — so seven came out of the box and twelve was left. To get the whole back, put the seven in again: twelve plus seven is nineteen. Check: nineteen take seven is twelve. Taking away is undone by adding. And notice the answer is bigger than both numbers in the sentence, which is a useful sign you have done it the right way round.

This is the one that catches people out. Twenty take box equals thirteen. Twenty is the whole and thirteen is what is left, so the box is the gap between them: twenty take thirteen is seven. Check by putting it back: twenty take seven is thirteen. It works. The safe habit here is always to ask what the whole is before you do anything, because the whole is the biggest number in the sentence, and everything else fits inside it.

Boxes work the same way with times and share. Six times box equals thirty: times is undone by sharing, so thirty divided by six is five. Check — six times five is thirty. Box divided by four equals three: sharing is undone by times, so three times four is twelve. Check — twelve divided by four is three. Every operation has one that undoes it. Add and take away undo each other, times and share undo each other. Use the opposite one on the box, then put your answer back in.

Some questions ask for the number sentence rather than the answer. Twelve pizzas with four on each tray — twelve times four is forty-eight, which is far too many trays, and twelve plus four is sixteen, which makes no sense because you cannot add pizzas to trays. Twelve divided by four is three, and three trays is right. The trick is to work out the answer in your head first, then find the sentence that gives it. That is the whole lesson: add and take away undo each other, times and share undo each other, and always check by putting your answer back. Quiz and exercises now.