Category Archives: General

342. Revision jotters

With the exams looming large, I thought I’d share how my class have been revising. To give you some context roughly a third of the class are doing Foundation GCSE, aiming for at least a Grade 4. The rest are doing Higher and aiming for a Grade 5 or better. We have three, one hour, lessons a week. I’m rotating between doing an exam paper, a whole class revision activity (eg a revision clock) and tiered revision.

I know if I tell the students to revise independently the results are going to be mixed. Some will be brilliant, some will be more laid back. To resolve this I pick a topic (or two) from each tier that I know they need to improve on from or that they have requested. It’s helpful if there is a theme to the work. I’ve recently done things like y=mx+c (F) with plotting inequalities (H).

Now the genius part: PixiMaths revision jotters

How to run the session

Photocopy a big stack of revision jotters. If you are doing black and white copying, use the b&w version. We requested the b&w version and, because PixiMaths is awesome, it is now on the website.

Clearly put on the board which topic each tier is revising

Eg Foundation: exact trig values, Higher: trig graphs

Give students 5-10 minutes to fill their revision jotters with everything they know. Have textbooks or maths dictionaries available to fill in the gaps. You may find that Higher students want to do the Foundation topic too – no problem, just make sure they have two jotters. Due to the complexity of the Higher topic, they will need more time to make initial notes.

My students are allowed headphones in revision sessions. At this point it’s headphones in for Higher and out for Foundation.

Do a skills recap on the board (exact trig values), with maybe an exam question too. Students can ask questions on the topic and add to their jotter. Then have a worksheet for students to do eg Corbett Maths or KeshMaths GCSE exam questions booklets. They can refer to their revision jotter or scan the Corbett Maths QR code for extra help.

Swap over. Headphones in for Foundation and out for Higher.

Repeat the process for Higher, with drawing trigonometric graphs. Issue an appropriate worksheet.

Once you’re done, make a judgement call. Are there students who could push it further? Maybe transform a trig graph or problem solve? Go for it. Foundation are busy, Higher are busy, spend some time stretching your most able. Every mark counts.

A huge thank you to PixiMaths for the revision jotters (and everything else).

Examples of students’ work

Shared with permission of students. You can see that they have personalised them to meet their needs and some are a work in progress. Also, the b&w jotter photocopies so nicely.

341. Dragon Bridge

Here is a little starter picture for you:

This is the ‘Pont y Ddraig’ at the marina in Rhyl, in North Wales. What mathematical questions could be inspired by this?

‘Pont y Ddraig’ means Dragon Bridge. Find out more about the bridge here

339. Broken rotation

This is a quick post following a discussion in the office today. The prompt was a colleague asking “How do you teach rotation to a child with two broken arms?”

The last ‘child’ I taught with two broken arms was a sixth former and it involved profuse photocopying of notes.

But back to the problem. You could cut out shapes and rotate them on a gridded whiteboard. The student could get a feel for what was going on and be part of the whiteboard Q& A session. For the main classwork, photocopy the worksheet or textbook and increase it to A3. Make a second colour copy and cut out the shapes in the questions. The student can then move these into the correct places to answer the questions. The work could then be photographed, emailled to the teacher or printed out.

Of course I do mean use a phone to take a picture, because it’ll take more than two broken arms to stop a teenager using their mobile phone.

(BTW I’m not making light of the student’s problem. It’s important we think around these issues to ensure all students can access the curriculum)

337. Surreal symmetry

I stumbled across this splendid website and Instagram feed through an article in ‘The Guardian’ newspaper:
Accidentally Wes Anderson
The site owner has collected together images of buildings that look like they could be in a Wes Anderson film.

Image Credit: #accidentallywesanderson

The result is a stunning collection of images of symmetrical architecture from around the world. The photos could be used as a starting point for a discussion on symmetry, shape or the mathematics of the world around us.

336. Geometry Snacks

If you are looking for a very last minute gift for that special Mathematician in your life, or you have Christmas money to spend, may I recommend “Geometry Snacks” by Ed Southall (@solvemymaths) and Vincent Pantaloni (@panlepan)?

It is a nearly pocket sized book of geometry puzzles whose construct of simple, elegant problems can decieve the unwary into thinking the solutions are easy. This is a book for those who embrace mathematical rigour, rather than repetitious guesswork.

In fact, forget buying it for someone else – get one just for yourself!

Geometry Snacks is published by Tarquin (ISBN: 9 781911 093701)

335. The power of colour

As Mathematicians we appreciate the importance of getting the basics right and building a firm foundation. With this in mind I’ve been an absolute harridan with my Y8 students regarding presentation and technique for solving equations. If they can nail good algebraic presentation now, their future studies will be be much easier.

When we started there were students doing everything in their head, not always correctly. Some insisted on working backwards, which is great for basic cases but not for unknowns on both sides. Most frustratingly some students were breaking up the logic by putting extra working out between steps and losing track of what they were doing.

For example:

2x – 10 = 5x + 8

5x – 2x = 3x

3x – 10 = 8

So we had a really good discussion about logical presentation. We decided to write down what we were doing in the margin, try and keep the = sign lined up in the working and put any extra working out on the right.

This worked really well for most of the class, but I had a small group of students who just lost track of what they were doing and why. They knew things had to balance, but struggled to cope with equations with an unknown on both sides.

While I was talking things over with them using a mini whiteboard, I noticed they had a profusion of coloured pens and highlighters. Bring on the colour!

By highlighting the key point of each line of algebra and matching it with the balancing step they started to build the structure of good solutions. It was slow work to start with, but a couple of lessons later and these same struggling students are now hitting the extension work every time. And most of them no longer feel the need to highlight key information.

334. Frustrating worksheets

Now, I’m straying from my usual positivity today because I’m frustrated by a worksheet. It was set for the eldest in Primary School as non-calculator classwork to be finished at home for homework. Topic is straightforward enough: Percentage Problem solving.

First gripe: I don’t think the teacher had time to check whether the later questions were suitable to be non-calculator. There were divisions my KS4 students would baulk at. Fair enough, we’re all human, we’ve probably all misjudged an activity like that.

Main gripe: this was a paid for resource. The Primary school will be paying a yearly subscription for these worksheets and I think they are being written by someone who actually doesn’t understand percentages. Someone is being paid for writing poorly worded questions.

But it gets better (or worse depending on your viewpoint). The last question is just … Well, let’s just say I’m not a fan. I was so annoyed I picked up pencil and paper and did it myself.

The set up asks you what percentage a tree must grow by each year, if it needs to reach a certain height by a certain year. Any decent student should know that percentage is proportional and thus it will grow in proportion to its existing height each year. That’s a compound percentage problem.

I remind you this is a 10 year old without a calculator doing this work. They calculated the required growth, divided by years and multiplied by 100. The result was a recurring decimal!

I assumed compound growth and worked out the answer as 20%.

I think the person writing the question added on 20% each year, then put their final answer in the question. That is a rubbish understanding of what a child would have to do to solve the problem.

As a teacher, I am fuming that schools’ valuable depleting budgets are being wasted on dross like this. I’d like to say this is the first worksheet from this online provider with questionable mathematical knowledge, but it isn’t. A teacher has trusted that the resource they printed out was accurate and useable and will now have to go back over this in class.

Of course critics will say that the teacher should have thoroughly checked every question, but this is the real world. If there was time to do that then there wouldn’t be companies making money from charging for resources.