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.