Another pair of kids' logic problems

[Cudzoziemiec]

It used to be a cliche that Norway's score in Eurovision was always... a round number.

[drossall]

I have never been able to master the tricks of shuffling the sides of an equation without actually knowing what numbers the letters represented.

I was taught to think of it as a see-saw or balance. If it's balanced now then, as long as I do the same to both sides, it will stay so. Hence, I can double everything (all the weights), or take the same amount off both sides, or whatever, without upsetting things. I don't need to know how much the bags I take off both sides weigh, only that they weigh the same as each other.

[Wowbagger]

I know that both sides of an equation, by their very nature, are the same, but I invariably get very muddled when I don't have concrete numbers to deal with. I would never have known where to start with the wording of the original question.

[clarion]

I love playing with equations.  One of the best fun things in maths, to my mind.

[red marley]

I like rearranging equations as much as I do fettling my bike (which is this: none much). Both are a means to an end. Problem questions that take people to that end are the ones that I find most interesting.

[mrcharly-YHT]

the weird thing about kids and maths is how some find arithmetic puzzles intuitive but can't cope with transferring that onto paper.

At 6, my not-academic son could answer questions like: It takes 50 bricks to make a one square metre wall. How many bricks are needed for a wall 6 meters long and two meters high?
At 15, he absolutely struggled with even simple GCSE math. Very very painful long sessions of tutoring him and he managed a bare C.

He's 23 now and has an intuitive grasp of ratios, fractions, equations and the real world problems that can be tackled (fish is supplied in whole kilograms. Servings are in x hundred grams. Chef wastage is x percentage of servings. 48 hour shelf life and y dishes sold per day, what is the most efficient quantity of fish to buy?). It's quite impressive.

But present him with abstract symbols and he goes blank.

[Kim]

I remember answering some of my grandad's puzzles by doing numerical integration in my head, when I was under 10 with barely a concept of algebra.

Brains are odd.  They can solve the equations to make a hand arrive at the exact point where a ball is going to be at some point in the future, but struggle at basic arithmetic.  I can't help wondering if some people are able to tap into that hardware acceleration somehow.

I was never a very good mathematician, but have always had a strong intuition about physics, and can often 'just see' what's going on (which provides a useful starting point for approaching and checking calculations) in a system - I got through a lot of maths by thinking of it in physics metaphors.  The problem comes where there is no intuitive metaphor and I end up calculating blindly.  Especially now I'm 15 years out of practice.