These are all great investigations/rich problems with plenty of practice working with square numbers  a little more interesting than fifteen questions out of a textbook. If pupils have to learn facts, such as the squares to 15, I think it's better to embed them into something a little mathematically rich than just drill.
Five ideas for square numbers25/2/2016 Post 25/29 in the Staffrm #29daysofwriting challenge: Lesson ideas for exploring square numbers As we've got two squares in today's date, I thought I'd go for a square themed post. Also I've just realised that this year contains 25/04/16, and 25/09/16, both even better excuses for a lesson on square numbers.
These are all great investigations/rich problems with plenty of practice working with square numbers  a little more interesting than fifteen questions out of a textbook. If pupils have to learn facts, such as the squares to 15, I think it's better to embed them into something a little mathematically rich than just drill. I thought Christmas was over...?4/2/2016 Mental squares23/2/2015 Thank you, Internet, for wasting my evening. I don't know how I found this on YouTube  one of my random clickathons searching for goodies, and I'm a sucker for "magic maths" tricks. This one is how to square any (twodigit) number mentally. If you don't want to watch the video, here's the basic idea with 33² as an example:
And here's my workings: So I did this one...then tried another. Cute? Convoluted, really, and not particularly workable in the curriculum (I'd much prefer a sensible approach with proper multiplication), but then I got one of those "oh now how does that work?" moments. I could see how it was kinda linked to quadratics and square areas, so I did some doodling. After many aborted attempts, I came up with this: Take a square with side length 33(cm if you insist on units). You can then chop a rectangle off the edge of length 3 (making an easier multiplication of 30 x something) and whack that on the bottom. So then you've got a 30 x 36 rectangle, and the little square left over to add on. Then, because I'm a mathematician and I like doing things properly, I tried to make it work with algebra: Typical quadratic expansion, but we think about a as the tens digit and b as the units, because we're trying to change the square into a rectangle with length a (so we have a multiple of 10 to calculate with). Then: So we've changed the problem from (a + b)² (difficult) to a(a + 2b) + b² (messy but easier mentally). I was quite pleased with this! Just thought this might be a nice challenge problem to give to pupils when working with quadratics (or square numbers for that matter)  show them the video, then get them to explain why it works  numerical or algebraic approach. I do think this lends itself to an exploration of the link between square numbers, area and quadratics, which I think is often overlooked. Growing squares29/1/2015
Square differences28/1/2015
Happy numbers28/1/2015

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