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.


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.


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.


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.