Paper

I’m going to admit something: I often don’t enjoy teaching constructions. It’s fiddly. No matter how much you demonstrate whole-class, there’s no substitute for sitting with someone and showing them how to hold and move the compass.

One solution is experts. Getting competent students to pair up and help less competent ones.

Another solution is to use A3 paper.

Pupils are often unwilling to make mistakes in their books. OFSTED have been picking up on messy work, and there’s been a lot of focus of students showing that they are proud of their work, and presenting it as an exemplar document. I’m not so sure I’m a fan of this. Often working can be scrappy. There’s an argument to be made that this working can be done somewhere else and thrown away, leaving us with a beautifully presented bit of work. But this denies the reality that sometimes maths work isn’t a lovely linear process. I don’t know how I feel about the entire thing.

Anyway…Using A3 paper like this makes students way more confident in failing and trying again. It also allows them to ‘doodle’ (practice using a compass which is useful).

It can lead to much nicer results than trying to do anything in their books.

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The UK's cheapest mortgage?

HSBC launches Britain’s first fixed-rate mortgage below 1% [The Guardian]

The bank is offering customers the chance to lock in for two years at an interest rate of 0.99%, but they need a deposit of at least 35% and will pay a product fee of £1,499.

The question then is, is this cheaper that most people can currently get? How much cheaper.

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It seems like a lot! I’ve done a quick graph in DUDAMATH here comparing debt after 2 years between the new mortgage and a typical no-fee 1.89% mortgage. I’ve used x to represent the amount that you’re borrowing.

Stuff like this is good.

  1. It’s nice to demonstrate that the maths we do has real world applications. Solving equations links to mortgages.
  2. It’s nice to show all the different maths I’ve used here. Forming equations is useful when plotting graphs and comparing data. You can also see why I’ve plotted the graph. It gives a much nicer and easier to read handle on the financials when compared to the article.
  3. Teaching this in a lesson I could vary the interest rate using DUDAMATH. We could investigate at which point the 0.99% deal is better than a y% deal.

Balancing Equations vs Sign Change

 

I was showing a fellow teacher DUDAMATH on Friday. It was all going well until this teacher, who I respect greatly, recoiled in horror.

When you drag a term in an equation in DUDAMATH, and drop it on the other side, it changes the sign of the term. 4x becomes -4x.

‘Next you’ll be moving the decimal point!’ came the agonised voice of this fellow teacher. This fellow teacher also happens to be a member of our teaching and learning team. She knows her stuff.

This sparked a lively debated in the maths office. I’ve always been told to show students balancing equations. Another teacher pointed out that in his view balancing equations was essential, as it preserves the shows the fundamentals of the equals sign. This is something that is not explicit when using inverse operations.

Another teacher pointed out that when students who are taught inverse operations come across equations with unknowns on both sides, they struggle.

I’m undecided. I get that balancing is good, but I like maths because I enjoy using a variety of methods to get to the same answer.

Maybe students need a plurality of methods in order to learn. Maybe the best method depends on context. I ran a Twitter survey on this, but no one replied. I’m bad at Twitter.

Add your thoughts below the line.

The Progression Of Addition and Subtraction

I don’t know about you, but as a secondary school teacher I’ve not often thought about teaching some of the maths fundamentals. We assume students can already add, subtract, multiply and divide single digit numbers. Secondary teachers don’t pay enough credit to primary teachers, who have the critical job of embedding concepts like place value.

But sometimes students come in without these skills, and I’ve always found breaking them down really difficult.

This video is lovely It’s one of a series, talking about the progression of skills from first principles. I highly recommend all maths teachers watch them. I will certainly be trialling some of these ideas. I found the talk of five and tens grids particularly interesting.

DUDAMATH

I have found this. Makes patterns. Shows equations. Solves equations in an interactive way. Has some statistics stuff. Can’t believe I’ve never seen this before.

Setting up an equation and then showing how to rearrange it visually is powerful. Watch the hint videos under the ‘?’ on the right hand side of the page to get up to speed.

Good pun, too.

Play with it and get back to me.

Rio 2016 Maths

An attempt to follow in someone else’s footsteps.

rio2016 [pdf]

A PDF/worksheet thing about the Rio Olympics. Eight pages covering a range of maths content.

Kind of pointless as we won’t be at school whilst the Rio Olympics are on. I mainly did this for a little bit of practice making nice stuff.

If you use this, please feed back to me. Is it good? Does it work? Do some bits work more than others?

  1. All credit to @dooranran who I nicked the idea/style/everything off.

Design makes a difference

If you visit this website often (which, based on my stats, you almost definitely don’t) you might see that I switch the design around occasionally. I’m constantly fiddling with design and font use, trying to chase that holy grail : something that’s nicely designed. I’m the same for my worksheets and presentations. I’m constantly trying to make things in formats that look nice. I don’t think I’ve achieved it yet. I also think it’s really important. There’s something elegant to good design. An uncluttered clarity. A beautiful zen.

Whilst I haven’t managed it, there’s a lot of people producing lovely stuff (often in very different ways), and I wanted to highlight a few of them, talk about what makes their work nice.

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The first person I want to talk about is TES user Dooranran. His stuff is lovely. He uses a lot of themes (particularly superheroes and football) . I’m wary of using a theme. Often I find as many pupils put off by the theme as are engaged by it, but every Dooranran activity I’ve used has been very successful. Especially this Euro 2016 maths activity. I’d say the reason behind this maybe to do with the efforts that Dooranran puts into combining his themes and his mathematical content. They often gel in a really nice way. The maths content of his work is often very challenging, too.

The other person I want to talk about is Don Steward. Again! I’m always talking about Don Steward. So I should. He’s ace! He’s also odd. He’s a fan of unicase, which means that all of work is lowercase. I’m sure this violates some schools’ literacy policy, but it does look nice. I’ve never noticed how capital letters are rubbish before. He’s also a big fan of white space. Have a look at the sheet below.

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It’s clean, it’s neat, it’s tidy. I think it can be tempting to cram too much on a sheet and overwhelm students. The other thing you notice about Don’s work is that he uses minimal instructions. I think this is a very underrated and important point of problem solving. Figuring out the problem is part of the problem. Look at this.

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I like this. The white space, the presentation. This isn’t a problem to be done quickly and moved on from. It’s a problem to be savoured and worked on.

I really need to work on my presentation. If you want to get involved in chat, what programs do you use? Are we too stuck to PowerPoint and Word when better tools could do a better job? I vaguely want to try InDesign but I feel it’s like taking a hammer to the problem. Am I being too picky? Is bad design perfectly OK. I’ve seen some horrendously designed presentations on TES with great reviews. I content ultimately king?

Some Board Game Reviews

As I’ve talked about before, I run a nurture group. We often use games to try to make maths learning a bit more fun. Here’s some reviews.

Orchard Toys Magic Cauldron
Amazon link

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This game is quite clever. You pick up a sum and try to work it out. When you think you have the answer, you rub the heat sensitive panel at the back and the answer magically appears!

You then get to add an ingredient to your cauldron.

The components are very nicely produced, and it’s got lovely artwork. It’s also the game that the children were most excited about playing. However, it quickly got boring because of the limited amount of sums involved. The sums also seem to be odd. There’s mostly two single digit addition and subtraction in there, but also two or three multiplications and a few three single digit addition sums.

In summary: Lovely, but limited shelf life. 3i+7/10

Pop! Addition and Subtraction
Amazon link

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Lots of one digit addition and subtraction sums in this box. A huge amount more than Magic Cauldron, which means they get less repetitive.

Students take a sum, solve it, and get to keep it if it’s correct. However if they get a ‘POP’ card, they have to put all of their earned cards back in the box.

Again, it’s produced really nicely, and the putting all your cards back is interesting from a nurture/learning to lose perspective. However it is possibly a bit too simple and thus its longevity is in question.

In summary : Good for short sessions. I wish they did a multiplication one. e^x  out of 10.

Your Number’s Up
Amazon link

Your Number’s Up! doesn’t really work as a game. It’s really ponderous and the components in my version are nasty. The cards in particular are horrible. I can’t quite explain how horrible they are. When your fingernail touches them it’s like nails on a blackboard.

There’s also way too many ‘?’ cards, which allow students to go without having to do a sum.

In summary: It’s too boring to make the maths practice invisible. \frac{1}{x^2}/10

Chalking, P Levels

I love chalk. It’s really useful.

For instance, I have a nurture group. They are currently practising their times tables, but can find it really boring. A fun way to practice, and something that’s a little different is writing out the times tables on the pavement in chalk.

That’s way more fun and they can make it look as pretty as they want.

If you’re trying to get students to memorise facts, often doing it in a variety of ways is key.

We have also played a game this week. The numbers from one to ten are written in a random order on the ground. A sum is read out and students must run to the correct number. Perfect if you’ve got a small nurture group as it also hits a key nurture target: learning how to lose and win without upsetting people.

Talking of nurture, I’ve found it really challenging this year to teach a student who came in with p levels.

I can’t find much about p levels on the net, so if anyone has got any resources please comment and link them here.

I’ve found this by Ben Cooper handy.  It’s an assessment for p levels. This is also useful. It’s a description of what students should be able to do at each level.

I’ve also tried to do some p level resources. Here’s my first try. It’s a worksheet talking about key words like left, right, most, all, some and altogether. I’ll be doing more of this kind of stuff.

I think there’s a lot of work to be done on trying to teach maths to SEN students. I would welcome any tips and good resources you’ve found. My approach has been around talking, games and trying to set up a classroom environment.