I think the common cause of boredom among bright students in public school might be that the class performs drills on skills which the student in question has already mastered.
Are you already ambidextrous? On assignments that are simply repeating the same content, try doing the work with your off-hand. For repetitive lectures, try taking notes with your off-hand.
In some cases, it was performing drills at all whether I’d mastered it or not. 3rd grade is multiplication tables territory. That’s deadly boring even when you haven’t mastered it yet. And it’s one of the few times I really would advise just sucking it up and memorizing the danged thing.
Of course, it’s not so bad if you realize that there are only 15 ‘hard’ one-digit multiplication problems—those without either factor being 0, 1, 2, 5, or 9 (there are only 15 combinations of 3, 4, 6, 7, and 8, which require more than one simple step + one trivial step)
This is also a good time to introduce a variable x, when talking about the different shortcuts. Like, 9 x = 10 x—x. My daughter gets the idea of that at 7.
3rd grade is multiplication tables territory. That’s deadly boring even when you haven’t mastered it yet.
Not for me. I got into a competition with the other smarty pantses in the class to see who could get passed to 12x12 first. We all stayed after school one day in a round robin competition being quizzed by the teacher.
In some cases, it was performing drills at all whether I’d mastered it or not. 3rd grade is multiplication tables territory. That’s deadly boring even when you haven’t mastered it yet. And it’s one of the few times I really would advise just sucking it up and memorizing the danged thing.
I would advice to play some computer gain that trains multiplication. If you approach the problem in a gamified manner it’s not boring and you will likely learn it faster.
Splitting 13 7 into (10+3)7 is very much the kind of thinking as using the ‘easy’ multiplication problems like 9X. The idea was to focus on showing how addition and multiplication fit together.
But if there’s an ‘easy’ way to get 3*7, shorter than 7+7+7 and less brute-force than memorizing it, please do tell!
I think that 7+7+7 is short enough, with enough general arithmetic skills. Probably the best drill for that is keeping a running total at a external pace; that will take a long time to get boring if the total is something you care about.
If 7+7+7 requires paper and ‘carry the one’ twice, then the problem isn’t with multiplication, the problem is with addition. At the very least, everyone should be able to find the difference between two numbers when the difference is four digits or less, in their head, in the time it takes to receive change. People good at math should be able to add small amounts so that the change contains fewer coins.
That particular practical requirement doesn’t require being able to multiply 7 by 3.
There’s a large gap between ‘fast enough to be a decent substitute for a LUT’ and ‘needs paper’. There’s no doubt that one needs to be ABLE to add 7+7+7, but I don’t think that each repetition on the path to memorizing 3*7=21 needs to involve it.
I think the common cause of boredom among bright students in public school might be that the class performs drills on skills which the student in question has already mastered.
Are you already ambidextrous? On assignments that are simply repeating the same content, try doing the work with your off-hand. For repetitive lectures, try taking notes with your off-hand.
In some cases, it was performing drills at all whether I’d mastered it or not. 3rd grade is multiplication tables territory. That’s deadly boring even when you haven’t mastered it yet. And it’s one of the few times I really would advise just sucking it up and memorizing the danged thing.
Of course, it’s not so bad if you realize that there are only 15 ‘hard’ one-digit multiplication problems—those without either factor being 0, 1, 2, 5, or 9 (there are only 15 combinations of 3, 4, 6, 7, and 8, which require more than one simple step + one trivial step)
This is also a good time to introduce a variable x, when talking about the different shortcuts. Like, 9 x = 10 x—x. My daughter gets the idea of that at 7.
Not for me. I got into a competition with the other smarty pantses in the class to see who could get passed to 12x12 first. We all stayed after school one day in a round robin competition being quizzed by the teacher.
I would advice to play some computer gain that trains multiplication. If you approach the problem in a gamified manner it’s not boring and you will likely learn it faster.
I’d refine that- find/create a software toy that employs skinner-box methods to reward increasing skill at (withbout loss of generality) multiplying.
Rather than memorize how to multiply a small number of permutations of numbers, learn in the general case how to multiply small numbers quickly.
Few people who memorized the 12x12 grid and then moved on can quickly say that 13 times 7 is (70+21=91).
Caching the products of small factors will develop naturally as a result of training the general skill.
Splitting 13 7 into (10+3)7 is very much the kind of thinking as using the ‘easy’ multiplication problems like 9X. The idea was to focus on showing how addition and multiplication fit together.
But if there’s an ‘easy’ way to get 3*7, shorter than 7+7+7 and less brute-force than memorizing it, please do tell!
I think that 7+7+7 is short enough, with enough general arithmetic skills. Probably the best drill for that is keeping a running total at a external pace; that will take a long time to get boring if the total is something you care about.
If 7+7+7 requires paper and ‘carry the one’ twice, then the problem isn’t with multiplication, the problem is with addition. At the very least, everyone should be able to find the difference between two numbers when the difference is four digits or less, in their head, in the time it takes to receive change. People good at math should be able to add small amounts so that the change contains fewer coins.
That particular practical requirement doesn’t require being able to multiply 7 by 3.
There’s a large gap between ‘fast enough to be a decent substitute for a LUT’ and ‘needs paper’. There’s no doubt that one needs to be ABLE to add 7+7+7, but I don’t think that each repetition on the path to memorizing 3*7=21 needs to involve it.
Does it take longer to ad 7+7+7 than to say “Seven times three is twenty-one” and “three times seven is twenty-one”?
if you have to memorize 3x7 and 7x3 separately, you’re doing it wrong
Really? Which one is in the standard form? How long does it take to convert the other into standard form, as opposed to doing the multiplication?
He says he is willing to try this. Thanks!