345. Practical percentage skills

It’s perfectly obvious that fluency in the use of multiplication tables directly impacts students ability to divide. This grows into confidence with algebra and reverse operations. Students are able to see the links between the concepts. Our understanding of the importance of such skills is part of the success of programmes such as TTRockstars and Numeracy Ninjas.

Why is it then that so many textbooks, websites and resource banks keep the manipulation of percentages as separate skills sets? Percentage increase / Percentage change / Reverse percentages. We know that when concepts overlap, fluency increases when these links are pursued. So that’s what I set out to do.

I have a bright Year 8 class and started working on percentages with them. It didn’t take much to have them confident using equivalent decimal multipliers to find percentages of amounts. Using a multiplier for increase/decrease was a walk in the park. Then finding percentage change came up. Over the years I’ve seen a lot of students get very confused with half remembered methods:

“Which do I take away?”

“What number do I divide by?”

“Is this calculation the right way around?”

I tend to teach new value divided by old value and interpret the answer. It got me thinking – why am I teaching them this? They can increase by a percentage using a multiplier, why can’t they rearrange their working to find the actual percentage? Same goes for reversing a percentage.

After a good discussion, I used this worksheet to recap and develop their skills:

Warning: “Original Amount” section, question (d) is a tricky one.

As with all new approaches, it’s always good to see if it worked. I set the following task from Don Steward’s website:

MEDIAN percent problems

I have GCSE students who wouldn’t know where to start on those questions, yet my Year 8 with their ‘have a go’ attitude were absolutely awesome. I’m definitely using this method again!

If you teach in the UK and haven’t used the excellent Access Maths site, why not?

Seriously, you are missing out!

I’ve used and recommended to colleagues lots of the Access Maths resources. This is the latest worksheet I’ve downloaded (click on the image to link to the 9-1 GCSE resource page):

Image credit: www.accessmaths.co.uk

I used these pentagonal problems (I believe they are know in pedagogical circles as ‘Fox Diagrams’ – but you try Googling that term and not getting a page of pictures of foxes) with my GCSE class as a two part homework. The first homework was to do the outside skills – if they felt confident they could skip questions, if they needed help they should come and see me. I stressed that they would need to use these techniques to part two and it was their responsibility to make sure they were ready. Part two of the homework was to complete the middle ‘exam’ question in their books in their books, showing the full method.

I actually enjoyed marking this homework as it gave me an insight into how they visualised problems – there were at least four different ways to complete this task. Unusually I made any low achieving student come back and redo their homework in an informal detention. By spending a few minutes reflecting on the skills they’d already practised (or should have practised), every student jumped from 0 or 10% to 100% correct. I did little more than point out where their technique had started to fail them. These students left the extra maths session with big smiles and a sense of achievement.

Inspired by the talented @AccessMaths (you really should follow them on Twitter) I’ve done my own triangular resource on expanding, factorising and solving quadratic equations.

Down the pdf here: Staged Quadratics problems

321. Patterns and sequences

Now what have a pair of roller skates got to do with number sequences? If you can guess before the reason, I’ll be surprised – it’ll mean there is more than one person as random as me!

As you may have guessed from my earlier post 317. Pyramid Power I’m currently doing an Algebra unit on Number Sequences. I’ve changed the way I’ve taught this topic this year to incorporate a ‘Big Picture’ view as opposed to one lesson on drawing the next picture, the next on finding the Term to Term rule and finishing with a lesson on finding the Nth term. The beauty of mathematics lies in the connections we make, not the disparate skills.

After the investigative approach of the Pyramid Numbers lesson, we did some text book work on generating number sequences (eg Start with 5, add 3) expanding to look at the physical patterns each time, so the previous rule would have looked like N groups of 3 dots plus 2 dots. As with any class (mixed ability or not) there were varying levels of progression in these lessons. To pull everyone forward I wrote structured worksheets and allowed the students to choose which they did. I described them using the following comparisons with the roller disco at our local Sports Centre:

• Sheet 1 – beginner on roller skates, need a bit of hand holding (I’ll own up to demonstrating our local instructor’s technique for teaching beginners in front of the class)
• Sheet 2 – okay on skates, just a word of encouragement every now and then
• Sheet 3 – speedskating, no fear of the next challenge
• Extension – all the skills! Some tasty questions from a tough textbook exercise

After a student completes a sheet they just move to the next – there are no duplicate questions. I printed them A5 to stick neatly in their books but you might prefer A4. Solutions are provided.

Patterns and sequences A4 one per page

Patterns and sequences A4 two per page

BTW I can tell you from personal experience that landing on your rear whilst speed skating really does hurt!

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 (docx – editable)

267. A little factorising TLC

Here’s a quick resource for you:

This worksheet metaphorically holds students’ hands as they work through factorising quadratics where the co-efficient of x squared is greater than zero. My students liked this sheet as it gave them a starting point, it stopped them putting their hand up for every question and it would be useful for future revision.

263. Percentages Tick or Trash

To quote a famous DIY company from the UK, this post ‘Does exactly what it says on the tin’!

Image credit: www.ronseal.co.uk

Here is a tick or trash worksheet on percentages, including a couple of tricky ones:

Percentages Tick or Trash inc solution

I usually tick these worksheets until I find a mistake. I then tell the student to have a rethink. Obviously the correct answer is the other option, but the working out will need to be corrected. I also do not tell them how many of the remaining questions are actually correct – they then recheck these before I mark it again.

The only difference with this worksheet is that students have space for working out – no more guessing! The extension task asks students to try and figure out where the wrong (misconception) answers come from – that can be quite tricky and tests their understanding.

241. Histogram Hysteria

Are you fed up of explaining the difference between a histogram and a bar graph/chart?

Cheer up! Help is at hand…

I teach a class of bright students with very little self-belief in their abilities and total fear of leaving their comfort zone. Instead of telling them what to do and set page X of textbook Y, I let them tell me what was going on and let them take small steps. After all, you wouldn’t take a beginner climber up the North face of the Eiger, would you?

Let us begin: