Pascal’s triangle with routes

Pascal's Triangle

Pascal’s triangle is one of my favourite mathematical concepts. It shows how lots of maths links together and that makes it exciting! Today I am starting a series on Pascal’s triangle to show you how great it is so you can be excited about maths too!

 Pascal's triangle spiderweb

We’re starting with a spider on a web. Can you see him? Sorry if he is creeping you out a bit. He is starting at the top of the web. He is only allowed to travel down the web, not back up again. We need to work out how many routes there are to each node (those are the circles where the lines meet) and we will write them on as we go. If you want to do this discovery activity with your child or students please feel free to print the picture and use it.

 Pascal's triangle spiderweb letter labelled

Let’s imagine that Fly lands on node a. There is only one route down from where Spider is to a, and it is the same if Fly lands on b, with only one route down to b. So write a 1 in both nodes a and b.

The next row has c, d and e on it. If Fly lands on c, Spider can only go there by going down to a, then to c, so we can write a 1 in there. If Fly lands on e, Spider can only get to e by going down to b then to e. It is a little different if Fly lands on d, Spider can get there from the start by going to a, then d, or from the start to b, then d. This has two routes, so we will write a 2 in there.

The next row has f, g, h and i on it. For Spider starting at the top, if Fly lands on f or i then there is only one possible route to f, and only one possible route to i. Now we can look at what happens if Fly lands on g.

Pascal's triangle spiderweb route to g

Spider could go from start to a, then c, then g. Or Spider could go from start to a, then d, then g. Or Spider could go from start to b, then d, then g. Three ways. There are three routes to h as well. If you carry it on, you get to see even more of Pascal’s triangle! Thanks to Spider 🙂

Stop by again next week to find out more about Pascal’s triangle, that’s where it starts to get exciting! And I promise no more spiders.


Pascal’s Triangle series:

Pascal’s Triangle with Routes

Pascal’s Triangle with Probability

Pascal’s Triangle Sequences part 1

Pascal’s Triangle Sequences Part 2

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