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## 'Graphing Number Patterns' printed from http://nrich.maths.org/

The class were making
number patterns and then making graphs of them.

Several children had
plotted graphs of the "times tables". They made good-looking
straight lines.

Tom had started on the six
times table but had then decided to do something more interesting.
He had made the triangular numbers with counters last year. That
was a better idea, he thought.

So he started to
put them on the same graph paper as the unfinished six times
table.

"It's not a very
good straight line," he remarked to Andy who was sitting next to
him.

"I think it's going to cross the six times line," answered Tom,
"But you'll have to make a lot more of both of them. I'm going to
try square numbers, I bet the tables one will cross that!"

Does the graph
of the triangular numbers cross that of the six times table?

And if it does, where?

Does the graph
of square numbers cross those of the times tables?

And if it does, where?