Category Archives: General

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.

333. Resource of the week

Just a quick resource for you today and apologies if you are already using this!

Plickers

Not some new ‘youth slang’, but an amazing online tool. Students have an individual card with each side labelled A, B, C or D. You ask a multiple choice or True/False question, they hold up their card with their answer at the top, you scan the class set of cards.

Image credit: Plickers.com

It really is that simple and here is what to do to get started:

  1. Create a free account at www.plickers.com
  2. Download the app to a portable device with a camera (phone, tablet etc)
  3. Print out the cards
  4. Allocate the cards to your class on the website
  5. Stick the cards in your students’ books
  6. Set a question
  7. Scan the cards

I have a tablet device that I use for school purposes as I keep my phone for personal use. The only problem I had was my android tablet doesn’t have a light source or as high quality camera as my phone, but we sorted that by having students move to a brighter part of the room for scanning. Instant feedback with no handheld devices!

Finally I have to say a huge thank you to Mr L, our trainee teacher, for introducing this to the Department.

332. Movement Maths

I’ve got to share a new YouTube channel with you. It was created by a former colleague who is not only an ace Maths teacher, but also a trained children’s fitness instructor. ‘Movement Maths: How to survive High School Maths’ is all about daily chunks of Maths with a fitness boost.

First – it addresses basic concepts that many students forget or stress over (initially it will be aimed at Foundation students)

Secondly – the videos are engaging and show that you can do Maths and exercise anywhere (my current favourite is the airport in video 13 – how did he find an empty sp?)

Thirdly – there are recaps and summaries built in

Finally – it was reviewed by students, who loved it!

Subscribe to the Channel, get fit and see what your students think

Update: 1st June 2019

It appears all the videos on this channel have been deleted.

331. Personalised student/parent feedback

How did I do in the test?

We get that question all the time. Is that a good result? Is it bad? Where did I come in the class? In general I never answer any of those questions, instead I have a little one to one chat as I’m handing out papers or in subsequent lessons.

But what if you’re not there to have that interaction?

I had that problem this summer. We were due to give our end of year test results back to students on the same day I was on a school trip. I couldn’t give the results out early and I didn’t want to make my class wait. If they were just given their test results or papers back, that would be a feedback opportunity missed. What to do?

I ‘wrote’ a letter to each student.

I use the word ‘wrote’ in the loosest sense. I mail merged their results and targets into Word, using my markbook spreadsheet as the data source. That addressed the facts element. The bigger picture for the class was the interesting part. If you search for ‘DESMOS’ box plot, you will find a sample box plot. If you replace the data with your test results, you will obtain a box plot of your results. I put my box plot into the master document and hit merge:

Each student recieved a personalised letter, in an envelope, in my absence. I could even give results to the students who were on the trip with me.

The letters were a big hit with my class. They liked that I had gone the extra mile for them, even though it took under 20 minutes. In the subsequent lesson we could get on with the test review without lots of questions about numbers and grades.

It got me thinking – could I use this idea in other ways?

I have refined the format (the initial letters served their purpose, but we’re basic) and have since used variations on this for other assessments and at Parents Evening. Parents Evening was particularly useful as I had all the target and assessment data, key exam dates, class summary box plots for the last two tests, suggested GCSE revision resources and a reminder of what the new GCSE grades mean. I didn’t have to keep refering to my mark book as all the relevant information was in front of me and the parents didn’t feel the need to make notes. I had very few questions about set changes as they instantly got a feel for where their child was within the class, but without any rankings. Several said that they wished all subjects would produce information sheets like this.

I could also give the personalised sheets to students whose parents couldn’t attend or email them home. It was a very useful tool for getting identical information to those families who are apart, but are equally supportive of their children. When the Head of Year asked for a brief summary of a student’s progress, as they were meeting with a parent on Parents Evening, it was already done.

Of course, the great thing is that I will only have to do a minor update for the next Parents Evening saving me even more time!

The next time you have to give out and/or discuss data with students or parents, try this. It really improve the experience.