Graphs with Many-to-One Scales

In a pictograph the key tells you what one symbol is worth, and the work is to count the symbols on a row and multiply. With one picture standing for five books, a row of seven pictures means thirty-five books. A comparison can be done either way — thirty-five take fifteen, or four extra pictures times five, both twenty. The commonest mistake is answering with the number of pictures instead of the number of books.

A half symbol is worth half of whatever the key says. With one picture standing for ten people, four and a half pictures is forty plus five, forty-five. If the key were four, half a picture would be two. Keys are usually even numbers for exactly this reason, because half of an odd key is not a whole person. Work out the whole symbols first and then add the half, rather than trying to do it in one step.

On a column graph the first job is to work out what one gridline is worth. If the labels run nought, twenty, forty and so on, each gridline is twenty, and a bar that stops halfway between sixty and eighty is seventy. A bar that reaches ten above the eighty line is ninety. Reading a bar as three lines tall and answering three is the classic error — the answer is three times the step.

Most graph questions are two steps: read the bars, then do something with the numbers. So write the numbers down first — sixty, ninety, forty-five, seventy-five — and the question becomes ordinary arithmetic. How many more did the Bees score than the Cubs is ninety take forty-five, forty-five; how many altogether is the four added, two hundred and seventy. Reading and calculating at the same time is where mistakes creep in.

Three steps, always in the same order: find what one symbol or one gridline is worth, then read the values, then do the arithmetic the question asks for. Skipping the first step is what turns a seven into a seven when it should have been thirty-five. Quiz and exercises now.