I do the bat and the ball problem with low effort, and the exponential growth one with no effort, but I find the machines one a bit confusing.
For the bat and the ball, I do something similar to the margins example. I visualise an amount (represented by a length on the number line), I visualise a dollar higher than that amount on that number line, and then move them around so that they’re not overlapping, then see that the sum is $1.10. Then I realise there’s two identical bits that are added to the $1, which means they’re 10⁄2 each.
(Btw, the bit about them adding a hint and there still being people who wrote 10 cents made me laugh out loud, that’s hilarious.)
I’m not sure how to visualise machines taking 5 mins to make 5 things. Do they all do a different bit of the job? Can they all work on one widget simultaneously, speeding that one up? I guess you’re expected to assume they each work on one widget. Okay, I guess that kind makes sense, and is intuitive if that’s true.
I do the bat and the ball problem with low effort, and the exponential growth one with no effort, but I find the machines one a bit confusing.
For the bat and the ball, I do something similar to the margins example. I visualise an amount (represented by a length on the number line), I visualise a dollar higher than that amount on that number line, and then move them around so that they’re not overlapping, then see that the sum is $1.10. Then I realise there’s two identical bits that are added to the $1, which means they’re 10⁄2 each.
(Btw, the bit about them adding a hint and there still being people who wrote 10 cents made me laugh out loud, that’s hilarious.)
I’m not sure how to visualise machines taking 5 mins to make 5 things. Do they all do a different bit of the job? Can they all work on one widget simultaneously, speeding that one up? I guess you’re expected to assume they each work on one widget. Okay, I guess that kind makes sense, and is intuitive if that’s true.
To confirm: the machines are all doing the same thing is the idea. So you could rephrase it as 5∗(1machinetake5minutesper).