(no subject)

[tinyjo]

So, if we're going to buy expensive schemes to teach children maths, can the providers please make sure that the activities make sense and aren't, you know, wrong or anything.

Say the number: four thousand, seven hundred and eighty-three. Ask children in their groups to write this in figures. Write it on the board to check: 4783. What is the lowest number you can add so that all four digits change? Allow 3 or 4 minutes to try this, then take feedback. (1111 is the lowest number that can be added so that all four digits change, making 5894.) Will this always be the lowest number? Can you find a 4-digit number where all four digits can be changed by adding a lower number? Ask children to explore this, starting by finding different types of number (e.g. multiples of 10 or 100) where a lower number can be added. Ask them to write some general rules (e.g. if the number ends in 9, then the lowest number that can be added to make all four digits change is 1101.)

Just.... No, don't do that! I can't even think of an interpretation that might make that make sense.

Comments

but...

[jinty]

that question is expecting an answer where all the numerals increase, whereas you could easily get a new number where all the digits change without all increasing...

Re: but...

[phlebas.livejournal.com]

The bit at the end about numbers ending in 9 would suggest otherwise. I'd guess this is aimed at a level where your 'easily' doesn't apply.

Yes

[jinty]

it's a badly-phrased question is my point.

Re: but...

[tinyjo.livejournal.com]

I would expect our year 4s to figure out number bonds to the next thousand would do it - not all of them but about half our class.

Re: but...

[tinyjo.livejournal.com]

Yes, exactly. It's the fact that they categorically state an incorrect fact ("(1111 is the lowest number that can be added so that all four digits change, making 5894") which bugs me most - adding 217 makes a number where all the digits change!

[celestialweasel.livejournal.com]

This is trying to be about carrying I think e.g. If you have 9999 then you add 1 and all 4 digits change. So I think it makes sense but is awfully written. It reads more like some Martin Gardneresque mathematical puzzle than anything.

[tortipede.livejournal.com]

Yes, it's trying to be about carrying, but still... monumental fail. Someone say "217" to the author of that resource.

[raingirl26.livejournal.com]

Yes, of course it's 217. They probably meant to say what 'jinty' said that they want all the numerals to increase not just change.

One does need a command of one's language to do math.

[tea-and-cuddles.livejournal.com]

Alas, the last bit about numbers ending in '9', using the same language about all four digits changing, means they don't require all the numerals to increase.

[phlebas.livejournal.com]

It almost works - if the number ends in 9 and none of the other digits is a 9 then 1101 is indeed the lowest number you can add to change all four.
I'm not sure what they're talking about with the multiples of 10 and 100 though.

[tea-and-cuddles.livejournal.com]

It doesn't work.

For example, 8889 ends in 9, none of the other digits is a 9, and the lowest number you can add to change all four digits is 111, which is lower than 1101.

[phlebas.livejournal.com]

Indeed. But I presume the idea is that you start from the obvious mal-rule from 'what if it ends in a 9', come up with counterexamples, refine the rule accordingly and hope they end up with a better grasp of how it really works. It's a questionable approach to teaching maths (being a rough application of the scientific method) but not completely nonsensical.

[cleanskies.livejournal.com]

Is there a column in the Guardian you can send this in to? Or Bad Science? Please send it somewhere, because this is nonsense.

[tinyjo.livejournal.com]

There should be one in the TES, shouldn't there. Perhaps I'll start a blog for it. Or, as you say, send it to Ben G.

[truecatachresis.livejournal.com]

Contrary to other responders here, I suspect the question is asking for the smallest number added where all the digits change and remain different to each other.

Still, it's a really crap exercise that doesn't appear to be useful at teaching anything.

[tortipede.livejournal.com]

So when they say 1111, they actually mean 229? Well... probably not. Your valiant attempt to salvage some sense from this founders on the rock of its fundamental gibberishness. As does everybody else's, of course. If none of us can tell for sure what the bloody hell they're trying to get at, that does suggest at the very least that they've been a tad unclear...

[celestialweasel.livejournal.com]

I did wonder about this interpretation too, but as you say what would be the point?

[tortipede.livejournal.com]

Thinking this through more, and re-reading everybody's comments, I think what they're trying to do is to move children from a mathematical worldview that doesn't take account of carrying, where 1111 would be the only possible answer, to one that does — using, as phlebas said, a sort of vaguely scientific-ish experimentation approach. They're meant to start off with 1111 and arrive at 217, discovering the Joy of Carrying for themselves along the way — at least, that's how I read the business about 9 and 1101. But by implying that 1111 is the correct answer rather than a good starting point, they've neither said what they really meant nor meant what they said. Yesno?

[phlebas.livejournal.com]

I think you're right.

[celestialweasel.livejournal.com]

Hmm. I think you're right, but I seem to recall that in the happy days of new maths (circa 1970) carrying was taught through the medium of Deans (probably not spelt that way and can't be bothered to Google) blocks - along with bases and positional notation (or whatever you call it) - can you really separate the 3 concepts very much?

[tinyjo.livejournal.com]

Ah, that's interesting - it's so badly worded that I didn't realise what the teaching point might be! I was so blinded with rage at the categorical statement of wrong at the start :)

[bluedevi.livejournal.com]

It's surprisingly common, that. The Computing and ICT A-level papers are full of logical flaws. I have a student who's been programming for years and if he thinks about the problems logically, rather than in the sort of vague sloppy pseudocode idiom of the textbooks which does not exist except in the bubble of A-level computing, he gets them wrong.

But, I thought, surely the country is full of people who would delight in coming up with good puzzles for exam papers. I know a good few who would do brilliantly at that. But I imagine they're all programming for good money, not working at exam boards.

[tortipede.livejournal.com]

Speaking of computing, I think I have the solution. Scrap the scheme of work, make use of tinyjo's background in IT, and teach them 6502 Assembler. Once they've got used to ADC¹ they can be introduced to CLC² and BCS³, and voila! — problem solved :)

1 ADd with Carry
2 CLear Carry flag
3 Branch on Carry Set

[celestialweasel.livejournal.com]

And for the next trick, subtraction as 2s complement addition.
Does make multiplication tables easy.
"One one is one"