You type in a number and it presents you with loads of facts about that number, breaking it down into it’s prime factors and some scales. It’s lovely. Try it yourself. Here’s the page for 2048.
Quick starter idea (after showing students this website):
56
Give me some facts about this number.
You could use this often, changing the number every time.
Quick investigation idea: What is the best number? Explain why. Give reasons.
Someone showed me this lately. It made me think about how much a tiny little twist can make a task massively more engaging.
Task One
5x + 3 = 13
7x + 11 = 25
4x + 8 = 32Find x.
Task Two
5x + 3 = 13
7x + 11 = 25
4x + 8 = 32In which equations does x=2?
Task one is boring. I want to do task two.
This thinking has come from Don Steward. My last blog was about his work, and it’s wonderful to dive into. There’s loads of stuff with simple twists like this and the way the work is presented is outstanding (There’s a lot to be said for this). Every maths teacher should check out Don’s blog.
I’ve been thinking about writing this post since the NUT strike ballot was announced.
I had been putting it off because I didn’t want to inject politics into this blog, but I thought the topic was important, and my feelings about the ballot are pretty strong. So here are my thoughts. (They’re mine, not my employers etc.)
I am a pretty hard line union person. I turn up to meetings, I go on the marches, and I remain fundamentally opposed to the direction of travel in current educational policy. But this week I voted for us not to strike. I did so for several reasons.
The first reason is simply question. Why now? The cynic in me believes that the NUT are striking simply because the doctors did, and the NUT want to mimic their success. This thinking is silly, for several reasons. Firstly, whilst the public were generally supportive of the doctors strike, they have recently been against teacher-led ones. This makes sense. The doctors were striking about a change to their terms and conditions about to be introduced. Teachers struck in retaliation on changes imposed. Striking again several years later for the same reason makes no sense at all.
Secondly, I think the original strikes achieved little. Teachers pay is currently deregulated. I seem to pay more for my pension every year. The only thing that was achieved is that a message was sent to Whitehall. Unfortunately that message was that the unions were easy to outmanoeuvre and utterly incompetent from a PR standpoint. There’s no getting around this, those strikes were an absolute failure.
The third reason is another question. Why at all? The official reason that the NUT give is ‘workload, pay and other conditions’ (emphasis mine) but this is vague. You’re never going to win over the public if you can’t nail down why you’re striking in the first place, and you’re certainly not going to win them over with long, tedious arguments that go from pensions to workload* to academy policy. If you want to win the public, and parents over you need to be talking about the effect things have on students. You need to be talking about one or two issues. Not a huge list of vague grievances.
Finally, the NUT seem lost. The things that really effect teachers rarely seem to be talked about, and if they’re thought about, that thought is badly communicated. Where is the discussion with members about OFSTED, about the principle of evidence based approaches? In fact, where is the dialogue with members at all? Sending members a voting form with an instruction on how to vote might just annoy some people.
It annoys me when my union ask me to vote on something and then tell me which way I should vote.
— James Theobald (@JamesTheo) May 30, 2016
Not only am I voting no, but I believe that others should, too.
Then maybe we can start remodelling the union into something that works better on a national scale**.
*As an aside, the focus on workload is absurd. I get that it’s a lot of work, but that’s never going to go over well with a public who work long hours. It’s also different from person to person and school to school. In some schools the workload is unreasonable, at my current school it’s very reasonable. In many ways, it also comes down to how individuals handle it, and are able to stand up for themselves. Teaching is a job which takes up as much time as you allow it.
** The NUT is very good at helping members in school and dealing with school issues. This is why I am still a member.
How have I not seen Don Steward’s blog before? Lovely stuff on there.
I’ve got to give a big shout out to DrFrostMaths.com.
I’ve only just discovered his website, and I think it’s something every maths teacher should have in their favourites.
It’s got brilliantly presented slides on nearly every topic, but what sets it apart is the amount of UKMT and JMC questions that he both adds to his slides and worksheets. These questions are brilliant for pushing students and getting them to think.
The man is a hero!
This the best blog I’ve read for ages. I love it and love the idea of swift key testing. So quick to work!
This is from OCR’s Foundation Sample Question Paper. Part a is ok. Look at part b.
If students thought Hannah’s Sweets was ‘unfair’ (it wasn’t), wait until they’re confronted with problems like this!
I love Eurovision. I love it because you often see something different or weird or silly. It’s mad and that makes it great.
But recently Eurovision have tamed these impulses. They’ve started to make it less silly and, quite frankly, more boring.
They’ve done this with judges votes. There was a time when telephone voting was all that mattered. And that led to things like the UK giving this glorious entry by Lithuania 10 points in 2006. It also led to Lordi winning in the same year. Lordi!
This year’s winner was Sweden. It was an OK song. But it was very safe for Eurovision.
But DID Sweden win? Did the judges make a difference? Luckily, there’s a way to find out. Eurovision publishes it’s full results. I simply took out the judges voting and ranked all of the countries by phone voting. (San Marino appear to have to have not done telephone voting, so I’ve excluded their results. This means that their judges decided to give Electric Velvet 3 points. Madness)
According to my calculations, Italy won. By a lot. Here’s the final standings:
| Italy | 349 |
| Russia | 282 |
| Sweden | 272 |
| Belgium | 190 |
| Estonia | 144 |
| Australia | 124 |
| Israel | 102 |
| Albania | 93 |
| Serbia | 86 |
| Latvia | 83 |
| Armenia | 77 |
| Romania | 69 |
| Georgia | 51 |
| Azerbaijan | 48 |
| Poland | 47 |
| Noray | 37 |
| Montenegro | 34 |
| Lithuania | 32 |
| Slovenia | 27 |
| Spain | 26 |
| Greece | 24 |
| Hungary | 17 |
| Cyprus | 8 |
| Germany | 5 |
| UK | 4 |
| France | 3 |
| Austria | 0 |
I’m glad in the real results Germany did better than our AWFUL entry. Sad to see no points for Austria.
I think Judges votes were brought in to get rid of ‘political’ voting (ie countries near each other and having similar cultures liking the same type of song). If that’s the case, it’s failed spectacularly. Russia have LESS points with telephone voting than with judges and telephone voting. All it does it hurt acts like Italy, Eurovision outsiders.
Let’s also talk for a second about another outsider. The learning disabled act Pertti Kurikan Nimipäivät, who played punk rock. Not Eurovision’s usual thing. They didn’t make it through the semi final.
But here’s the thing, they should have made it through to the final. They lost exclusively on judges votes. Televoting actually favored them significantly. If it was just based on the voice of the people we’d have seen Pertti Kurikan Nimipäivät in the final. And it’s a shame we didn’t. Because since Conchita Eurovision stands for something. Maybe it always has, but it’s more obvious now. It’s about inclusiveness. About similarities not differences, and I think to exclude this band because of the type of music they play was rubbish.
I don’t normally ask people to share stuff. This is a maths website aimed at providing resources to other maths teachers, but please share this. Hopefully if enough people see this, the system might change.
Peace out. My spreadsheet here-> ESC-2015-grand_final-full_results
I’ve been thinking a lot recently about problem solving.
The new maths GCSE introduces a lot of it, and some of the sample questions I have seen include almost Fermi-like questions.
I’ve always liked problem solving, I particularly like the Dan Meyer stuff, but I’ve not written much about it. So here is an example of a problem solving lesson I’ve created.
Problem Solving Lesson : Phone Contracts.
Equipment required:
Graph paper
A3 paper
Prior Knowledge Desirable:
Linear graphs
I simply showed students this slide.
We talked about it for a while. I have obviously had to massively simplify the problem. I was upfront with students about this. We talked about contracts and a little about data, texts and things like WhatsApp meaning that they didn’t really need minutes. This time was important. These questions about the validity of the task I think helped draw out thinking and were useful in getting students into the task. It’s important not to shoot students down when they ask them.
We then talked a little about how the task seemed simple. But it’s deceptive.
The real question comes in how we present our answers. Students started to ask questions. How long does the average person spend on the phone? Do different users have different needs? This last question unlocks the potential of the task.
Which phone is best for which person? How many minutes do you have to be on the phone for before buying the initially more expensive phone is the better option? How can I show this information clearly?
Students came up with a variety of responses. Not everyone used graphs. Some went around and surveyed other pupils to find out how long they sent on the phone. I liked that idea.
Not all answers/conclusions were of high quality, you can see a selection of student work below, but I’m OK with that.
I will look at these and give feedback next lesson. Hopefully they will gain confidence in this sort of task.
