## Dumb Pride

There’s this photo doing the rounds.

I think I saw it ages ago but it’s resurfaced recently and I keep seeing it and it’s been annoying me. I have no idea who this lady is, nor do I understand why she is so proud of being unable to do basic maths, but it got me intrigued about the papers so I downloaded them.

There are 3 papers. 1 arithmetic (40 marks) and 2 reasoning (35 marks each). I know what you’re thinking, I thought it too, 25 percent of 110 is 27.5 and there are no half marks so it’s impossible to get 25 percent. I’ve assumed the lady in question has correctly rounded her percentage to the nearest percent and therefore got 28 marks.

I’ve looked at what marks are given for. You get 1 mark for being able to tell the time on an analogue clock. 2 marks for being able to read a bus timetable. 2 marks for being able to shade 3/4 of a shape that is split into equal parts that are a multiple of 4. 4 marks for ordering numbers. 7 marks for being able to add and subtract whole numbers, 15 marks for being able to multiply and divide by single digit numbers. That’s 31 marks. The means she didn’t even manage to get all those marks. There’s 7 more for dividing by 2 digit numbers another 8 for adding decimals (with tricky questions such as 0.2 + 0.05) which she must have got nothing for. 2 for finding percentages of amounts, another for finding a fraction of an amount and this not to mention the marks for multiplying and dividing decimals by powers of 10.

If I couldn’t answer those questions, I don’t think I’d be shouting about it.

## Angles or Angels?

When I marked my year 11 books the other day I noticed that quite a few had been working that morning on “Angels in triangles’. This peturbed me a little, surely by Year 11 they should know the difference and be able to spell each one.

To counteract this massive literacy issue I played a game of “Angles and Angels”. I spoke to them first about the difference, then about the spelling and then did a show me activity where I showed them various pictures and they had to show me on their whiteboards if it was an angle or an “Angel”. I was impressed that they even got the picture of Kurt Angle, although none of them recognised David Boreanas…..

The activity led to a discussing with a couple of them as to why it was important to discuss these things in maths lessons. Stemming from the inevitable question “why we learning about this? It’s maths not English.”

I explained my opinion that we may be learning maths, but that literacy is important in all subjects. As a maths teacher I educate these students and literacy has to be a big party of that, as I hope numeracy is a big party of those subjects that deal with numbers but aren’t maths. I also expressed the importance of maths specific vocabulary, such as ‘angles’ and how it’s not necessarily going to be covered in English.

It is these sorts of things that we need to be thinking about, literacy wise, to ensure our students are in the best position when they leave.

## A nice little triangle puzzle

Here is a nice little puzzle I saw from brilliant.org on Facebook.

Have you worked it out yet?

Here’s what I did:

First I drew a diagram (obviously).

And worked out the area of the triangle.

Then the area of each sector.

## Circles puzzle

Here’s a lovely puzzle I saw on Brilliant.org this week:

It’s a nice little workout. I did it entirely in my head and that is my challenge to you. Do it, go on. Do it now….

Scroll down for my answer….

Have you done it? You better have…..

I looked at this picture and my frat thought was that the blue and gold areas are congruent. Thus the entire picture has an area of 70. There are 4 overlaps, each has an area of 5, so the total area of 5 circles is 90. Leaving each circle having an area of 18.

This is a nice mental work out and I feel it could build proprtional reasoning skills in my students. I am hoping to try it on some next week.

Did you manage the puzzle? Did you do it a different way?

*This post was cross posted to better questions *here*.*

## Catchy MnemonicsĀ

I find most memory aids a little silly. Why learn a rhyme about horses when you can just learn the trig ratios? Why learn a rhyme about the duke of York when you can just remember the order the colours come in?

However, I find that music is a good way of remembering things. For some reason music is good for us to remember words. I can, for instance, remember the words to a great deal of 90s pop songs even though I didn’t like them and never chose to listen to them because I heard them out places and on TV so often that they got lodged in my brain forever.

This is something I have seen work well in learning maths facts. Year on year I hear pupils sing “mean is average, mean is average…” etc in lessons to remember the averages. And I also hear a great many variations on the circle song.

Last year when I was teaching kinematics one of the students said “Sir,play the SUVAT song.” I’d not heard of the SUVAT song and he found it on you tube and we listened to it. It’s simple and it’s catchy and it really helped him and his class remember those equations. So on Tuesday I played it to one of my mechanics classes. By the end of the leson I’d heard three people sing it and it has been stuck in my head all week.

*What do you think about mnemonics? Do they have a place? Have you any songs or rhymes that you use to remember things or that you encourage students to use? And do they help?*

## A lovely old problem

Recently Ed Southall shared this problem from 1976:

I’m not entirely sure if it is from an A level or and O level paper. It covers topics that currently sit on the A level, but I think calculus was on the O level at some point. *Edit: it’s O level* I saw the question and couldn’t help but have a try at it.

First, I drew the diagram – of course:

I have the coordinates of P, and hence N so I needed to work out the coordinates of Q. To do this I differentiated to get the gradient of a tangent and followed to get the gradient of a tangent at P.

Next I found the equation, and hence the X intercept.

And then, because I’m am idiot, I decided to work out the Y coordinate I already knew and had used!

The word in brackets is duh…..

Now I had all three point.

It was a simple division to find the tangent ratio of the angle.

The next 2 parts were trivial:

And then I misread the question and assumed I’d been asked to find the shaded region (actually part d).

Because I decided calculators were probably not widely available in 1976 I did it without one:

I thought it was quite a lot of complicated simplifying, but then I saw part c and the nice answer it gives:

Which makes the simplifying in part d simpler:

*I thought this was a lovely question and I found it enjoyable to do. It tests a number of skills together and although it is scaffolded it still requires a little bit of thinking. I hope to see some nice big questions like this on the new specification.*

*Edit: The front cover of the paper:*

## Old school Venn

Recently I saw this picture from Ed Southall (@solvemymaths) and thought it interesting:

It is an O level question on Venn Diagrams from 1988. I had a go at it.

The Venn itself was easy enough to fill in and the forming and solving part followed nicely.

As did the rest.

Having gotten used to A level statistics this was relatively straightforward, it manages to test use and knowledge of Venns but doesn’t go as far as probabilities.

I like Venn diagrams and I think questions like this are a good start point to build on, students who can do this will find A level Venns much easier. I assume that this style of question may be what we can expect from the new style GCSE, and even if it’s not its certainly something I intend to use with my classes.