Maths curriculum workings y4-6

[Guest55]

My year 8 niece recently had some homework to do that she asked for my help with. One part of this was doing long multiplication (3 or 4 digit numbers, from memory) and her teacher had recommended using a grid which had diagonal lines across the squares, and allocating numbers to these then adding up them diagonally at the end.
She had no understanding of why this worked. It did not encourage her to get a proper understanding of place value, just "follow this formula and it will come out in the end". In this sense it was arcane, mysterious, secret. Like a conjuror's trick along the lines of "think of a number, now double it, then reverse the digits... etc... etc ... you are now thinking of the number 11!" (every time the same end result)

I could see that the diagonal lines were effectively the same as carrying "tens" across to the next column where there were added to the units of that column. Once this was explained she understood why the method worked, and was much more comfortable with it as it was no longer mysterious.

The problem for parents seems to be that different schools use different methods, some even offering additional options for some (such as my niece) which others don't use (if they seem secure with another method). And they seem to change far too often, so if you have more than one child you might have to learn and then re-learn all of this. We have had support from previous primary school with maths evenings for parents near the start of the year at a couple of stages (something like entry to year 1 and again at Yr 3 and 5). Teachers actually worked through the methods that they would be teaching to pupils that year. But many parents were not able to attend and get the benefit of this, and the "takeaways" were not much use on their own, unfortunately.

As an aside, I find that some of the traditional methods of doing arithmetic are easier to replicate in your head, keeping track of only a few numbers at a time in working memory - especially addition, and multiplication of a longish number by a smaller one. Anything involving a grid of results to be added together later almost always blows working memory limits really quickly.
But yes, I can see that expanding brackets and other algebraic problems like that might make sense with a grid to ensure all terms are correctly calculated and none missed.

AdamV - the method you describe in not grid method; its Gelosia. No, proper grid method uses very little working memory and does not have the problem of 'carries' being in the way.

https://www.youtube.com/watch?v=3xDJDFmDrlg" onclick="window.open(this.href);return false; not a great video but shows you what a proper grid looks like