99% invisible is a wonderful podcast about design, made in Oakland California. I don’t have much to do with the world of mathematics education anymore (at the moment?) but as I listened to this, I heard echoes of students’ questions about the relevance of learning unit conversion in the computer age. Well, NASA can give you $100millions of reasons! It’s really worth a listen.

I wrote Furbles a long time ago, in a darker age. Furbles though, have always been progressive. Although there a probably a few two-eyed Furbles that think the only proper shape is a square and the only proper color is red, the rest embrace diversity! Vive la difference. Happy Pride.

This looks like a really interesting game exploring graphs: http://sineridergame.com/

A little hit-and-miss, but all these links have some thought provoking ideas in them: 8 Cool Maths Video Resources.

This article about a fascinating piece of ‘academic research’ (that was published in a bonafide journal, somehow!) should be grist to the mill of any good Theory of Knowledge or A-Level Philosophy course.

## Task

Choose any 4 digit number except for 1111, 2222, 3333, 4444. *I’ll choose 1502*.

Rearrange the digits to give you the biggest and the smallest numbers you can. *5210 and 0125*.

Find the difference of these two numbers. *5210 – 0125 = 4995*.

Repeat for the new number you get (using zeros to supplement any missing digits if necessary; you must always have 4). *9954 – 4599 = 5335*.

Keep repeating until you have a good reason to stop.

## Example

*5210 – 0125 = 4995
5533 – 3355 = 2178
8712 – 1278 = 7434
7443-3447 = 3996
9963 – 3699 = 6264
6642 – 2466 = 4176
7641 – 1467 = 6174*.

I’m not going to repeat any more because 6174 => 7641 – 1467 which is the calculation I just did!

## Discussion

- So every number we’ve tested came to 6174. Do you think all numbers will come to 6174? Why? In maths we can’t say we’re sure about something unless we have a good reason, so unless you want to go through every number and check it, we can’t say that we know that every number sequence we choose will go to 6174! (This is how mathematics differs from science, we don’t just make hypotheses and wait until the next time they break, we find ways to be certain!)
- Would we have to check every different number to be certain or are there shortcuts we can take? (should we check both 1234 and 1243 separately?)
- My rules stipulated that you couldn’t choose all the same number: 1111 or 2222. What would happen if you did use those numbers?
- What about two digit numbers or three digit numbers?
- Could we frame the problem as (1000a + 100b + 10c + d) – (1000d + 100c + 10b + a)?
- What about five or six digit numbers (or more…)? You may need a computer to help!

## Thoughts

I just came across this interesting bit of mathematics via Twitter: http://plus.maths.org/content/os/issue38/features/nishiyama/index. It offers the opportunity for a beautiful open-ended task for secondary maths classes of all abilities. The initial task is easy and produces a startling result that feels like a trick; that hook can lead to discussion and further work about probability, permutations, algebra and programming.

Diane Ravitch describes the ills of the USA’s education system. There are echoes of the policies of both the last Labour government and the current Conservative government (yes, yes) in what she says. I worry that this is the UK’s future:

More or less, this is what I think, too.