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)

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.

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

• 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!

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.

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)