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.

313. Friendly Functions

Just a quick resource share today!

I’ve been doing functions with my GCSE class as part of the new curriculum and I’ve gone down the algebra route. I could have started with graph drawing like the parallel class did, but I know my class – drawing and accuracy are not their forte. We made brilliant progress with substituting into functions and even composite functions went smoothly. I wasn’t happy with the textbook resources on manipulating functions so I put together a step by step resource, including a basic skills recap:

Manipulating functions (docx)

Manipulating functions (pdf)

I also thought my class needed a little hand holding for inverse functions. There are many ways to do this, but the method I used was designed to allow the class to access the topic with teacher input verbally and on the board.

Inverse Functions worksheet (docx)

Inverse Functions worksheet (pdf)

Hope these help!

Oh and you can even use them as A-Level recap tools.

Updated (19:53): To fix typo on Inverse functions worksheets

312. Class Commentary

I don’t know about you, but going over higher level questions (eg A-Level) after a test can be a frustrating time. The students never seem to fully engage because they think they know it all – even though they do get things wrong! What if I could offer you a way to review the test and incorporate an understanding of exam board mark schemes?

Image credit: www.sri.com

Preparation

  • When you mark the test clearly indicate on the paper which questions students got fully correct.
  • Alternatively get your students to do this.

Set Up

  • List the question numbers on the board
  • Starting with the highest number (usually the hardest questions) students volunteer to answer the questions on the board by putting their name next to a question number. In this way the brightest students who got the tricky questions right can’t volunteer to do the easier questions, allowing other students a chance of success.
  • Long multi-part questions could have more than one student.
  • You can also allocate a calculation checker and algebra checker if you have spare students

Task

  • Bring up each student to go through a question on the board.
  • Whilst they do this you can do a commentary of where marks are allocated by the markscheme, alternative methods and misconceptions.

I did this activity with a Year 12 group whilst reviewing an A-Level paper and it was a such a better use of time. The students were more engaged and I could interact with the class on a much more productive level.

311. Sales starter

Here is a neat little starter photograph (click on the image to enlarge) – get the mini whiteboards at the ready!

Sale price starter

Possible questions

  • How much money could be saved with the different reductions?
  • What are the percentage discounts?
  • What is the price as a percentage of the original?
  • What is the exchange rate between pounds and euros (using the original prices)?
  • What would the sale prices be in Euros?

If you can’t read the data clearly, the prices are: £45, £30, £22.50, £13.50, 70 euros

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)

 

309. Christmaths news

Hello lovely people!

Unfortunately, due to work (i.e. being a full time teacher) I haven’t had time to upload my recent ideas or resources, however the usual service should resume after Christmas. Speaking of which – don’t forget to check out the Christmaths resources on the site:

Christmaths Cheer

 

308. Zombie stats

I’ve used word length analysis for years as a source of comparative statistics. The concept is easy – you take a children’s book and a grown up book and compare the word lengths of the first 20, 40, 80 words. After you collect the information in a table, you can use this data to compare averages and the range.

Image credit: www.comingsoon.net
But what texts to use? Well – you can’t beat a bit of Dr Seuss, but what grown up text could you use. I can highly recommend this extract from ‘Pride and Prejudice and Zombies’:

Pride and Prejudice and Zombies by Seth Grahame Smith

Not only will you be investigating mathematical concepts, but you might just be inspiring a student to pick up a book and read.
Update: If you use the first chapter (say thirty words) of ‘Pride & Prejudice & Zombies’ you get some interesting data. The range is wide, but the highest frequency word length is just two. It’s a great conversation piece – why does this happen? The language is a very precise parody of 19th prose with all the correct connectives and no contractions eg ‘it is’ not ‘it’s’.