## Thursday, January 9, 2014

### Homeschool Math: Pascal's Triangle for Addition Review

Will's Math Mammoth text asked her to complete a Pascal's Triangle the other day--

--and the Pascal's Triangle has since become one of my favorite mathematics concepts. First of all, it's just a great addition review or test for kids who've mastered addition with carrying and/or mental addition, since building the triangle requires lots of great addition. You start with a 1 at the top of the triangle; to build the triangle downwards, add the two numbers in the two boxes above to arrive at the sum in the box below; if there is no second box above (as with the sides of the triangle), then that spot counts as 0. That's how the sides of the triangle build as the same number as the top box--they're all that number + 0.

Because you can put any number at the top, the Pascal's Triangle is a good enrichment activity to use when learning the multiplication table (see the 2x table hiding down there in that triangle?)--

--but we'll be able to keep revisiting just that simple Pascal's Triangle with the 1 at the top as the girls move into more advanced math, since there are a lot of interesting patterns and calculations hidden in there. But even with just the math that the kiddos know now, there are some really cool math games to play, based on this triangle:
• Quincux: It's a probability engine, with the pegs set up in the same triangular formation as Pascal's triangle. It's also PLINKO, which Will and I studied for her History of Video Games unit study.
• Worksheets: You don't have to build your own Pascal's Triangle boxes!
• Pascal's Triangle on Scratch: The kiddos haven't shown a ton of interest in making their own programs on Scratch (yet), but I love searching it for other users' programs related to ideas that we're studying. There's actually an entire studio on Scratch dedicated to Pascal's Triangle!
• 3D Pascal's Triangle: This LEGO model illustrates the multiplication table, but could just as easily (with the addition of many more LEGOs, of course...) build Pascal's Triangle.
Hmmm... that 3D LEGO model may actually happen next week. Stay tuned!