Category Archives: Shape, Space & Measures

314. Maths is a foreign language 

If I had £1 for every time I heard ‘I don’t get it!’, I could probably buy a new (modestly sized) car. That phrase is banned in my classroom. What does ‘get’ mean? What is ‘it’? Did you actually read the question?

And there we have it: reading the question.

Today’s little life skill strategy can work for all levels of literacy – because you don’t need any! I’ve taught a lot of students who just shut down when they see wordy questions and don’t look at the big picture – literally. There can be a really obvious diagram and they will skip the question. They just don’t try!

Now as you may be aware, I’m based in Wales in the UK. For those outside the UK, Wales is a principality within Great Britain. Although everyone speaks english, the traditional mother tongue is welsh – it’s particularly spoken in the North/West of the country. If you attend a welsh language school, you can do all your exams in welsh. A GCSE is called a TGAU.

But why am I telling you this?

Well, this means that the WJEC/CBAC exam board publishes their exam papers in welsh and english. Identical papers, different languages. I teach over the border in England, where only one or two students per year can speak welsh. This is where it gets interesting …

I went through a welsh language ‘Mathemateg’ paper and picked out the questions which involved diagrams – I also picked out the matching English questions so I was clear on the questions (not a native welsh speaker, just a learner). I gave my GCSE class the Welsh questions and told them to figure out what was going on. After the initial disbelief they had a really good go at the questions. Their comments included:

‘Well, it’s obvious it’s a tally chart’ 


‘Just fill in the table with the numbers from the pattern’


‘That’s got to be a special type of triangle’ (answer isn’t correct, but idea was)


‘Just use angles in a triangle to work it out’


I was impressed – they were constructively arguing about questions and covering diagrams in good maths. When we went over the questions they were telling me how easy it was, yet the week before they’d skipped questions like the angle problem in an assessment! I explained why I’d done it and told them they didn’t need to keep the worksheets as I’d made my point. I was stunned by the number of students who wanted to take them home to show their parents – they were proud of their problem solving – 16 year olds wanting to show off their Maths skills!

This idea can be used with any bilingual exam board or any language that you speak that the students don’t. It’s a good tool for getting over ‘question blindness ‘ and literacy confidence issues too.

These are the exam papers I used:

WJEC GCSE Maths 

CBAC TGAU Mathemateg

If you look at the web addresses there is one digit difference to differentiate between the languages, meaning if you go on the WJEC english language website you can find the welsh equivalent by swapping a 0 for a 5 in the second to last digit.

310. Menseki Meiro Area Maze

Menseki Meiro puzzle books crossed my Twitter feed a few months ago and I took the plunge.

Menseki

Image Credit: Amazon.co.uk

The problem is I couldn’t find an English language version. The Japanese originals were expensive so I bought the Spanish version. I don’t speak Spanish so asked my Spanish first language student who said it wasn’t Spanish – she suspected it was in Catalan!

But back to the Menseki puzzles …

They are ingenious puzzles where you simply use your knowledge of the area of a rectangle to solve the problem. Click on the image to see the cover problem. Puzzle 1 was so straightforward a nine year old could do it, puzzle 99 had Y13 Further Mathematicians befuddled. They make perfect starter or plenary activities for any age or ability.

Solutions are provided and if your copy is in a different language, like mine, you might just expand your mathematical vocabulary.

Whilst looking for a suitable image I also came across Alex Bellos discussing them on The Guardian website. Worth a look!

(By the way – the Menseki book also makes a good birthday present for that special geeky someone)

 

305. Get Carter

Seriously, you need to Get Carter ….

Get Carter 1971 Poster

Or rather head over to the amazing website by Mr Darren Carter: MrCarterMaths.com

I don’t know where to start – in a few clicks you have access to tiered questions on a multitude of topics with answers. Answer in an exercise book or on a mini whiteboard – it’s genius! Another click and the questions change.

If that wasn’t enough, you can print out individual worksheets at each level – differentiation without a headache.

I chose to print out the three tiers and award them points. Bronze = 1 point, Silver = 2 points, Gold = 3 points. I put together a cover sheet with instructions and the students instantly had control of their homework. All I asked for was 20 points of answers. The ones who need the practise can do lots of low scoring questions, the ones who need a challenge can do fewer questions at a harder level. My task is available to download below (full credit to Mr Carter given) – It prints nicely as an A5 booklet.

Tiered Proportion Homework Booklet

Once you’ve visited the site, follow him on Twitter @MrCarterMaths

298. The Mensuration Challenge

Here is a fun little activity, including task sheet, for recapping measuring distance, time and angles.

Image credit: freepik.com

It’s simply a set of mini-challenges designed to familiarise students with practical equipment and get them out of their seats. We had lots of fun measuring all sorts of things – width of a smile, length of a tongue, angle of a nose, time spent on one leg – the limit was their creativity!

Mensuration Challenges (pdf)

Mensuration Challenges (docx – editable)

293. Boxing Bounds

I thought this would make a nice little starter – address a few different topics, bit of problem solving, all over in 15 minutes. How wrong I was!

The Question: A company packs toys into boxes which measure 12cm by 8cm by 10cm (to the nearest centimetre). The boxes are packed into crates which measure 1m by 0.75m by 0.8m (to the nearest centimetre).
(a) Basic question – How many boxes fit into the crate?
(b) What is the maximum volume of a toy box?
(c) What is the minimum volume of the crate?
(d) Look at your answers to (b) and (c) – do they affect your answer to (a)?

It was a simple question about fitting toy boxes into a shipping crate. It extended to looking at upper and lower bounds, then recalculating given this extra information. Simple? No chance!

Problem One
Not changing to the same units

Problem Two
Working out the two volumes and dividing to find the number of toys. When challenged on this, it took a while to get through to the basics of how many toys actually fit – mangled toys and split up boxes don’t sell well.

Problem Three
Maximising the arrangement of boxes – remainders mean empty space

Problem Four
Using the information from Problem Three to find the total number of toys

Problem Five
Working out the dimensions and volume of the empty space in the box

Problem Six
Trying to convert centimetres cubed into metres cubed. I don’t even know why they wanted too!

Problem Seven/Eight
What’s an upper/lower bound?

Problem Nine
What do you mean that the original answer changes when the box size alters?

Problem Ten
All those who weren’t paying attention when you went over Problem Two and don’t ‘get’ why the answer isn’t 625!

289. The secret formula for success

You may remember this advert for Frosties cereal (US Frosted Flakes) from your childhood. If you do you’ve been around as long as me:

What was Tony’s secret formula? We never found out!

Enough reminiscing I hear you cry! How does this help anyone?

Well, in the new GCSE exam specifications the formulae sheets have gone. Specific formulae may be given in an individual question, but due to the lack of a working crystal ball we don’t know the frequency with which this will happen. To help with this I have typed up the Edexcel formulae into a PowerPoint. You can print it out and put it around the room, you could have a formula of the week, you could leave a slideshow running while students work, you could even print it small on card and make a pack of flashcards. Mine are laminated and hanging from a washing line, I’m going to move them around so that students have a varied view.

Whatever you do, increased familiarity improves retention – just think back to the posters you regularly saw as a child. I have made different versions for different situations – Edexcel vs no exam board, white background vs pale blue background, pdf vs pptx. Download whichever version you need:

Edexcel No Formulae Sheet blue (pptx)

Edexcel No Formulae sheet wihite (pptx)

Edexcel No Formulae Sheet blue (pdf)

Edexcel No Formulae Sheet white (pdf)

GCSE No Formulae Sheet blue (pptx)

GCSE No Formulae Sheet white (pptx)

GCSE No Formulae Sheet blue (pdf)

GCSE No Formulae Sheet white (pdf)