Category Archives: Algebra

313. Friendly Functions

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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

305. Get Carter

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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

302. Log Proof Puzzle

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If you can guess where today’s blog image came from you obviously consume too much damn fine cherry pie and fresh coffee!

log lady

Image credit: Pinterest

You may have guessed that the topic of this post is logs. If you are introducing the rules for adding and subtracting logs or revising them, I have just the resource for you. It’s a basic proof of both rules with a twist. The instructions are in the wrong order and you must rearrange them into the right order.

Easy!

Are you sure?

For those of you who have a student or two who rush everything and don’t read the instructions there is a sting in the tail. One of the lines of proof is a tiny bit wrong. The methodical student will find it, the one who races through may end up changing more than one line – hence breaking the rules.

Have fun!

Proving log rules for addition and subtraction

Answer: It’s the ‘Log Lady’ from the cult classic ‘Twin Peaks’!

300. Name that Number

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Simple little starter for you today. Minimum preparation, personalised challenge.

Equipment

  • Paper or whiteboards

Instructions

  • Hand out mini whiteboards or use paper.
  • Write the alphabet on the board.
  • Assign each letter a value. You can go for the standard 1 to 26 or choose a mixture of big/small numbers – maybe a negative number or two.
  • Get each student to write down their name and associated numbers.
  • Write a target number eg 100 on your board.
  • Each student must use the numbers of their name to make the target. If they can’t, they must get as close as they can.
  • If they make that target either find another way or change the target number.
  • Alternatively once they’ve finished they could use their classmate’s name – did they use the same method?

Variations

  • You can make this as easy or difficult as you want by changing the target or the alphabet numbers.
  • Throw in some fractions or decimals – go all the way and thrown in algebraic indices or standard form. You are the best person to judge your students’ level of challenge..
  • You could allow surnames, you could insist all numbers are used.
  • Put three alphabet variations on the board for mixed ability teaching.
  • If you are teaching a class not in the English language (eg Welsh, Greek, Russian), where the alphabet is different, this still works just assign each letter/character a number in the same way.
  • The possibilities are huge – have fun!

Note: this isn’t numerology, it’s proper Maths!

297. Crabby Functions

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I take no credit for this ‘aide-memoire’ – it comes from a most delightful and hardworking student. To quote a colleague “She is the poster-child for the benefits hard work”.

Let’s call this student Natasha (not even close to her real name). Natasha had been struggling to work out the difference between graph/function transformations, in particular f(x+a) and f(x)+a. Which way did the graph move? How could you tell? Then she had a brain wave:
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She drew little Y shapes on the brackets:
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One of the brackets now looks like a little crab:
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And we all know crabs move sideways – so it most be a horizontal translation!
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Simple!

Logical!

Genius!

Thank you Natasha!

289. The secret formula for success

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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)

288. Seriously, when am I going to use this?

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Oh, that question … heard often from the mouths of those who will not go on to study Maths at a higher level! But when it’s more able students who can’t see the necessity of fundamental principles … Well, that’s a bit worrying.

M’colleague, Mr D, has nailed the answer to this question. When I say ‘nailed’ I obviously mean ‘stuck’ and he has literally* stuck the answer on the wall.
*Note: Mathematician using correct definition of literally.

Here you go:

image

If you zoom in on this student work, on A2 Differentiation, you can see that he has annotated all the skills used and when you first meet them in the curriculum:

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Such a simple idea to tie together seemingly unrelated parts of the Maths curriculum. It also reinforces the need to keep all basic skills sharp.

I’d say it was genius, but then I’d never hear the end of it!