It continues to be really hard to set a level for Beast Academy. So far the difficulty has not been entirely what I’d hoped for – although I recognize that we did do multiplication already in MEP before covering it again in BA, which has meant a lot of review. (Which did at least get Alex to the point of automaticity with her times tables. By previous arrangement, she is being rewarded for this with a toy of her choice
Anyway, there will be days of fairly simple and straightforward problems, and then suddenly those will be followed by this:
…in which Alex learned a stunning mental math trick for squaring numbers that end in five, accompanied (at greater length in the text than you see here) by an elegant geometrical proof of why it works. And now we’ve moved on from there to finding the difference between two adjacent perfect squares. Neither of these is all that difficult to do, if you follow the Beast Academy method – but neither one feels like “third grade math,” either.
So, I don’t know. Is BA normal third grade math, or is it breathtakingly advanced? Sometimes it’s one. Sometimes it’s the other.
?
It’s sure not anything like I got in 3rd grade math. But from what I’ve seen of it, it’s great.
From my experience, math curricula for early grades don’t do a good job of fostering “mathematical thinking”. It sounds like BA does this, which is great. I think you see it in the enrichment section of textbooks, which are often skipped by teachers who are pressed for time and forced to emphasize algorithmic skills to make their kids do well on standardized tests. So maybe it is just that you are teaching the whole chapter!
The big thing I’ve noticed in grades 6-8, when kids are being asked to transfer their earlier concrete math skills to the abstract thinking of algebra, is that kids who have good approaches to “word problems” and other problem solving not involving rote application of an algorithm will do much better. So becoming aware of graphical and geometric equivalents or logical consequences of “3rd grade math” standard fare, e.g. multiplication, is developmentally appropriate (related to why manipulatives help kids at early ages learn math, I think) but not so common in practice.
I don’t know about 3rd grade, but I’m contemplate ordering that for myself at this point. I was “good at math” as a kid, but the underlying concepts (and heaven help me, the proofs) were never clearly handled. I’d like a shot at getting them into my head.
Suddenly struck me and I’m not sure why (few weeks after reading this) but isn’t this squaring method actually preparing them for quadratic equations? (a + b) squared = a squared plus 2ab plus b squared?
So it doesn’t work only for numbers that end in 5. It could be any number. (62 squared = 3600 + 2 x 120 + 4.)
Dredging up really rusty math skills, but the square thing somehow clicked. Cool cool cool.
Deb
Oh my gosh, Deb, you’re totally right!
I figured it was in the curriculum because it’s a neat trick, and because the company and community that produced BA is very involved in preparing kids for math competitions. I figured that this is the kind of shortcut that would give kids an advantage in a competition where others might be using long multiplication. But you’re right, visualizing and dividing those squares is absolutely preparation for (a + b)^2.
When Alex was solving them, she liked to actually draw and divide the square. That was really helpful for showing her where she was leaving out a term – I’d shade in the boxes she had accounted for, and she could visually see what she’d left out.
Thanks for sharing that insight!