Ana was doing her school homework with me on Tuesday.

[conuly]

Simple, basic "add up the numbers and divide to get the average" stuff. (And let me just say that I cannot stand word problems that are just there to say they have a word problem. "Susie has 5427 books. What number is in the tens place?" For crying out loud, that's not a word problem! There's no need for a framing sentence, because nobody cares!)

But I digress. She did one problem that was 6, 14, and 10. After working it out she turned to me and said, excited and amazed, that you can take the 4 from 14 to make 10, and add it on to the 6 to make 10, and it will still work!!!

She was so enthusiastic about this idea that she spent a good five minutes breaking it down to me.

Evangeline is still doing double digit subtraction. Fun! In her extra math book she's working with money, which is slightly more fun, especially as her sister is doing decimals and she gets to be "just the same".

Comments

[mc776]

Ana is on the way towards great things.

(As for word problems, isn't the whole point just to throw in some distracting stuff to see if you could extract the math problem and discard the extraneous info? Or am I thinking about law school EDIT: where in real life the distraction could be the central concern of one or both parties that spells the difference between settling well and losing horribly on appeal depending on whether it is addressed in a timely manner?)

[conuly]

There's distracting and there's distracting. A properly written word problem with a distracting element would run something like:

Ana has five cats, three dogs, and seventeen goldfish. How many mammals does she have?

[janewilliams20]

Isn't working out the real principles behind things great? I'm glad to hear she gets such a kick out of it, I always did.

[conuly]

If she continues like this, she's bound to end up an engineer. Or cook.

[ncp.livejournal.com]

So my brother's downfall began when he explained, at the tender age of five, why 6 + 6 is the same as 5 +7. "You take one away from the seven to make six, and add that one to the five to make another six. And since six plus six is twelve, it's the same thing!". Then he spent the next eighteen years being forced into all sorts of academic accomplishments. After he got his PhD from Harvard, he spent five years as an underemployed hipster/"writer".

[eofs.livejournal.com]

But I digress. She did one problem that was 6, 14, and 10. After working it out she turned to me and said, excited and amazed, that you can take the 4 from 14 to make 10, and add it on to the 6 to make 10, and it will still work!!!

And there she has got to the core of how I do most of my mental maths. I have to be able to add/subtract times very quickly for my job, and I generally do it by meeting in the middle a bit like that.

Unfortunately I'm rubbish at explaining how I do it, because it's nothing I ever consciously learnt. I just sort of visualise the numbers and can see what belongs between them. I had a good go at explaining recently though, when someone at work just couldn't get her head round how to subtract times to work out the difference. She kept ending up with exactly the opposite of what she needed (ie if the answer was 32" she'd get 28"). She eventually came to the conclusion that her problem was she was trying to do it like it was maths. I wasn't quite sure how to respond to that...

I did once have a maths teacher who set us a challenge of doing addition using subtraction (or was it subtraction using addition) and I think this is the sort of thing he was trying to get us to head towards. I continue to be impressed by Ana's ability to see how maths works - she seems to understand it fairly instinctively. That could be quite an asset as she gets older. (Has she shown any inclination yet to head towards a particular area of study?)

[conuly]

Well, she wants to be either a chef who gives all her food away to the homeless OR an engineer who gives all her money away to the poor. She perseveres with math, but she doesn't love it, I don't think. Still, she doesn't loathe it either.