Robert Low: Why is subtraction so hard?

Really interesting article and worth a read

Subtraction presents various problems to learners of mathematics, not least with the mechanics of hand calculating the result of subtracting one multi-digit number from another. But that’s not the kind of difficulty I’m interested in: I’m more interested here in the difficulties that arise when computations involving several additions and subtractions of integers are involved, or at the slightly more advanced level where algebraic computations involving several additions and subtractions are required. I’m going to take a look at what I think lies underneath the difficulty.

A little every day

Lack of updates. Sorry. Crunch time (plus exciting personal stuff). I will get on doing some things in a few weeks. PowerPoints to be done. More variation stuff to work on. More timed questions to set up.

In the meantime: These are GREAT.

I teach a lower attainment year 11 and they often struggle to revise. I like this idea of just doing one question every day to keep the mind fresh.

We’ve gone through some past month’s ones, too.

Great stuff.


SSDD Problems

I’ve been using Mr Barton’s SSDD Problems with my year 11 class. I think they’re really good. They do a really good job of making students pick out what they need to do.

Here’s a great one.

This is great because it makes pupils read the question. It was fantastic for revision because we got to discuss 4 topics in one lesson.

There are loads of great SSDD problems. I recommend Socks in a drawer, this nice circles one and this difficult formula one.

Some are less good, though. This one for instance:

I made this one. I’m not sure it’s a proper SSDD. It’s just 4 different questions based on the same image. Not sure it quite fits the SSDD criteria. I’m also not quite sure I can put my finger on exactly what the SSDD criteria is.

As ever, thoughts appreciated.

Maths in the real world – The Sun’s Brexit percentages

This piece of maths in The Sun was all over Twitter this week. It was retweeted and praised by MP Jacob Rees Mogg. The maths in it is wrong. Wrong, but interesting.

A lot of people tried to correct it on Twitter, but Twitter is not the place for explaining mathematical content.

The Sun has tried to calculate the cost of items – the tariff percentages. I’m not going to talk about things like tariff calculations being based on other things apart from the retail price, or the fact that some of these items are from tariff-free countries. I am merely going to talk about the common percentage misconception and why maths matters.

The easiest way to see the error The Sun have made is by looking at the calculation for butter.

This seems to make sense. 50% of £2 is £1, so take £1 off the price, and presto. Except, working backwards we can see that this doesn’t work.

If butter cost £1, and we applied a 50% tariff to it, the final cost would be £1.50. The maths doesn’t stand up when working in reverse.

How should we do it? 

I think the easiest way to think about this is to call the original price 100%. After the 50% tariff has been applied our new price (£2) represents 150%. To find 50% of this new amount, we actually have to divide £2 by 3, as \frac{150}{3} = 50 . We can then take away our 50%. 2 - \frac{2}{3}

The new price should be £1.33 (and a third).

Does this matter? 

Well, kind of. I don’t think anyone would have been less convinced by the new, accurate figures. I do, however, think that we need to be careful about promoting sloppy mathematical thinking in the public arena. At the very least, it is indeed an example of ‘real life’ maths.

Several people on Twitter have suggested it as a nice activity to do in lesson, to correct the figures. However, I would be careful about the surface of the problem distracting from what is intended to be learnt.

I think The Sun could do well to offer a correction, along with a page explaining the mathematics.

Ben Newmark: Why I killed my starters

So welcome to my lesson. Pens out. One to fifteen in your margins. Nothing new, it’s a review. Question one..

A thought: Maybe ‘fun’ starters were implemented partly as a behaviour tool. Might also explain the persistence of ‘high pace’ lessons with lots of superficial tasks. Keeps pupils busy, even if it doesn’t result in much learning.
I’ve found the Corbett Maths 5-a-day to be good starters, although Ben’s idea of 5 from the last lesson, 5 from the unit and 5 from anywhere makes sense.
Might start incorporating this into my lessons (when I get around to actually making them again).
Edit: I had a go at making something like this for the first lesson in my equivalent fractions unit. I’m not sure I’ve got the formatting right. It looks a little messy for me.
Download it here. I’ve done two duplicate pages and an answer pages. This allows you to print them off ‘two on a page’ which saves printing. I’ll continue to tinker.
Bad graphs

I collect misleading graphs. Here’s an excellent one I saw today.

What’s wrong with it? There’s more than the obvious.

How would you regraph it?

Here’s some other weird ones.

Although maybe it’s wrong to call these graphs