Variables

Discussion - part 2

Pupils will appreciate through discussion that sentences such as 3 + 4 = 7 and 3 + 5 = 9 communicate ideas about number, the former of these two closed sentences expressing a true statement and the latter a false statement. They are familiar from the work in earlier classes with an open sentence such as ? + 4 = 7, that is satisfied only if we put 3 in the frame. They should be told that an open sentence such as this containing the symbol = is called an equation, and that the frame is a placeholder, as it holds the place for a number.

They will see that the open sentence ? >5 will express a true statement, only if they put 6 or any greater number in the frame, and that the frame thus holds a place for any such number.

Children should get much practice in using frames and in changing verbal problems into open sentences. It should be stressed that if an open sentence contains several frames of the same shape e.g. square frames, then, whatever number a child puts in one of them, he must put the same number in all the others.

Consider for example ? X ? = 16. 4 is the only counting number that makes this a true sentence i.e. 4 X 4 = 16. ? X ? = 16 may have several solutions e.g. 2 X 8 = 16 or 1 X 16 = 16 or 8 X 2 = 16.