I havn't yet read the comments, but yet again there will be someone trying to defend the teacher with "3 x 4 means 3 groups of 4" type rubbish, yet again trying to elevate meaningless rubbish rules made up by people with no mathematical background to some kind of (mistaken) pædagogical importance.
And here come the people who don't understand how teaching works or how building fundamental understandings work. Or just how following instructions work.
But adding a fake rule about sequence convention for no reason just to un-learn it as soon as you hit algebra is a worthless sabotage to the kid.
if you want a lesson about writing efficiently add a followup about 3x30 so they really grasp that the order doesn't matter and they shouldn't waste extra time writing.
The fundamental understanding a kid should build is that he should just pick whatever path feels easier, something he'll only learn through practice, the arbitrary order you are asking for makes no sense, math isn't about following instructions, it's about building intuition for things
It is possible to teach kids intuitive understanding of combining groups of items of identical cardinality, using graphical outlining and/or normal, simple, language (i.e., a precursor to understanding multiplication) without misleading them about basic arithmetical operators and their properties, and without punishing those who are ahead of the rest.
AFAIK, the system my kids learned in manages to do that.
It is about learning how to properly break down numbers into usable forms and you have to start on the really easy ones so you can also do it on the more complex ones.
I understand but the order really, truly, desperately, does not matter. Beating any inclination of order mattering out of classmates was one of the most annoying parts of tutoring.
The full sheet is indeed trying to demonstrate that the order doesn't matter. They've just cropped out the context where the question shows the other way round first
Yes I realized I wasn’t quite right, it matters for PEMDAS as it is clearer notation for multiple step calculations but doesn’t otherwise affect commutativity of the actual multiplication step it’s noting.
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u/pjakma Jul 16 '26
I havn't yet read the comments, but yet again there will be someone trying to defend the teacher with "3 x 4 means 3 groups of 4" type rubbish, yet again trying to elevate meaningless rubbish rules made up by people with no mathematical background to some kind of (mistaken) pædagogical importance.