1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and they form a very interesting pattern when graphed.
Can you guess the next triangular number? Can you guess the shape of the graph of the triangular numbers? Can you explain that graph?
This is one of those math puzzles that come up in contests but which turn out to be quite interesting mathematically. Imagine a long hallway with lights in the ceiling, all on and each controlled by its own chain. A long line of people (as many as there are lights) walk down the hallway. The first one pulls every chain, the second one every other chain, the 3rd pulls every 3rd chain and so on. When all the people have walked down the hallway, what lights, if any, will still be lit? What more can you learn from this puzzle about multiplication?
Spreadsheets always automatically perform the operations you ask them to do. But sometimes we want to see the process. We can make spreadsheets show us that in several ways. Here we show the factors and have students build a times table showing the factors by using a special formula called Concatenate which means join together. This enables us to create a table of factors that we can see with a single rule. Concatenate has a wide variety of uses and it is worth playing with both to visualize factors and to build interesting spreadsheets.
