322. Accessing Quadratics

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!

Image Credit: No Fear adjustable quad skates/Amazon.co.uk

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

Patterns and sequences solutions (docx)

Patterns and sequences solutions (pdf)

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

320. Pre-A level skills boost

This is the time of year when Year 11 begin the last minute frantic revision, complete their exams in a haze of hay fever and late nights and then have a well deserved extended Summer Holiday. Over that long summer, they will mature into sensible young adults who are ready to make those critical decisions which will impact their future career choices.

Hang on … this isn’t some idealised political pamphlet describing the leaders of tomorrow!

In reality, Year 12 stroll into the first A-Level lesson like over-confident Year 11s in their own clothes. Except in Year 11 they knew more Maths. Odds are your fresh faced class haven’t looked at a Maths book in over ten weeks!

Despite what some students may think, we teachers aren’t evil. We know they need that long summer to just be themselves. What can we do to help out our future A-Level students and allow them to relax?

I’ve put together a booklet of Maths related activities for students to dip into over the holiday which will be given to them on their last lesson. I hope your students enjoy it!

Alevel prep for Y11 (editable docx)

Alevel prep for Y11 (pdf)

I printed these four pages as a colour A5 (A4 folded) booklet and also printed them as a poster set on A3.

 

 

319. Cunning codebreaker

Do you like a good codebreaker or crack the safe task? My first choice teacher for ideas is Alutwyche on TES Resources. Seriously, check out his amazing resources and follow him on Twitter (@andylutwyche).

Now the thing with ‘Crack the safe’ tasks is there will be a small group of students who everyone expects to win it. It doesn’t matter how long the code is, there can be an anti-climax when someone wins.

What if you could level the playing field or extend the challenge?

Introducing the ‘Lock out hasp’ – a common tool in the field of electrical safety. A very ingenious tool that you may want to look up. It allows you to add numerous locks to a puzzle – they could be differentiated solutions, they could be staged problems. The choice is yours!

Different

Different hasps have different numbers of holes, different locks have different numbers of digits: the hardware store is your oyster!

318. Election Stats

Very quick post!

Image Credit: Pinterest

If you are doing any form of data work, here is a great website to discuss bad graphs.

Skepchick Bad Election graphs

My GCSE class loved it. The image above was also a head-scratcher – how can you explain what is going on?

317. Pyramid Power

Just a quick post today – it’s such a busy time of year.

I’ve recently used Nrich resources on sequences with Year 7. These two activities encouraged good discussion and practical thinking.

Function machines

Pyramid Numbers

We used multilink to build pyramids which allowed students to develop their ideas. There were four different pyramids commonly built. The discussions the students had showed a real insight into their thinking.

After the lesson this photo of a golf ball stack appeared on my Twitter feed. This provided me with a starter for the following lesson – how many balls in the stack?

316. What should I revise?

Hands up all those who have challenged an underperforming teenager and got any of the following replies:

“I’ll do it with my tutor”

“Why aren’t we revising <unrealistic topic>?”

“It’s okay, I’ve got a tutor”

“It doesn’t matter what I do in class, I’ll do it with X”

“I don’t need to revise fractions (even though they can’t do them)”

“My tutor says this work is too easy for me”

“I don’t want to revise solving equations, I can’t do them”

“I’ve been doing cosine rule with my tutor (not even on the tier they are doing)”

“I’ve never done this (yes, you have but you talked through it every time we did it)”

“My mum says my tutor says I should be doing Higher”

“My tutor wants past papers”

Now don’t get me wrong, I know some amazing tutors – they know their maths, they are up to date with curriculum changes and they make a real difference. I also teach amazing kids who try their best all the time.

What really irritates me is the students who use tutors as an excuse for laziness and the tutors who teach complex topics but fail to reinforce the basics. So to combat this issue I’ve put together this PowerPoint – it got the message through to the students I was worried about in Year 11.

What should you revise (ppt)

What should you revise (pptx)