An attempt at some variation theory This one was hard. I spent ages rearranging questions and looking at what should be added. Specifically, I had a massive dilemma when it came to introducing fractions. I was trying to point out the ways in which simplifying fractions and simplifying ratio were similar, but I’m not sure that I haven’t just led students down the wrong path thinking they’re equivalent. For instance 5 : 6 is 5/11 and 6/11, not 5/6. Hmmmm. The variations I used for section A. An example where you can use a prime divisor The opposite way around. What happens to our answer. Order is important! Half one side. 8 : 5 becomes 4 : 5 One that’s already as simple as possible. Time for some questioning? How do you know you can’t simplify it? It’s not just reducing the numbers down. Here you have to multiply up. Deals with what simple is. I have changed this from the picture to make only one number vary from the previous question. Needs a non prime divisor. This isn’t really a variation, though. It has nothing really to do with the previous questions! Again, double one side Double both. Our answer does not double! Adding a third part of the ratio. Changes the answer significantly. Doubling two parts here. Our parts don’t double in our answer! If you amend this and it works better, please let me know.

A worksheet attempting to combine Craig Barton’s ideas on variation theory (only changing one part at a time) and Dani and Hunal’s ideas around making students make choices. I’ve tried to build up to that. Maybe by trying to combine both I miss the point of each. Would love criticisms and thoughts.

A few pie charts that represent funny ideas or jokes. The idea is that students get a feel for how pie charts work. I used it as a Y7 starter to generate discussion. The 'how often charts don't make sense' pie chart is particularly good for this. As always, please rate and comment with suggests and ideas. Thanks :)

GCSE algebra card sort. Really simple excel card sort. Cut out the tables, the equations and the graphs. Students have to match them together. As always, please comment and rate with suggestions for improvement.

Includes a worksheet that I think is really good (not blowing my own trumpet) and some random whiteboard questions, along with the usual stuff (example problem pair/questions/answers/learning check). Got some variation theory stuff in there, too. You should check out this resource by @edsouthall to use alongside this PowerPoint. It’s really good NOTE : I change my stuff every time I teach. I add new stuff and correct errors. But I don’t always have time to reupload them to TES. The latest version of the PowerPoint can always be found here.

An example problem pair A nice set of questions where students have to decide why two problems have been paired (a bit variation theory-esque) Lots of questions, including a big set of questions on moving between radius/diameter and circumference. Some whiteboard work A problem solving question I came up with A learning check NOTE : TES is annoying for keeping stuff up to date. I often change my powerPoints to add stuff and make them better, or simply to correct errors in maths and presentation. The latest version will always be found here.

Simple finding the hypotenuse worksheet, but I’ve made sure the triangles are rotated. There’s a few little tricks (1-3 are the same to emphasise rotation)

Inspiration from Mr Mattock (@mrmattock on twitter). Going from using diagrams to doing it without the diagram.

Just some practice questions on applying the Sine Rule

Trying to aim for a mastery/in depth lesson, rather than getting all the index laws done in one lesson. Huge credit to Jo Morgan (@mathsjem). Nicked a lot from her for this resource.

Tried to go through from simplifying right through to factorising to simplify. Lots of example/problem pairs Lots of work including some whiteboard work. A learning check. At least two lessons here. NOTE : I make lots of changes to my PowerPoints each time I reteach them, but reuploading them is a hassle. The latest version will always be here.

Loads of stuff here. Example problem pairs, exercises and other stuff. There’s also a ‘vary and twist’ worksheet here. Trying to use variation theory to draw out a bit of understanding. NOTE: My PowerPoints are updates often, but not always reuploaded to TES. The latest version of this PowerPoint can always be found here.

Worksheet and matching powerpoint covering -x^2 + bx + c in the form (x+a)^2 + b -a x^2 + bx + c in the form a(x+b)^2 + c Finding turning points Solving with completing the square 3 lessons worth of stuff

Worksheet. Interpreting/Representing data. A selection of misleading/confusing graphs culled from newspapers and online. Useful to talk about the difference between misleading and confusing/wrong.

Just the cosine rule. Finding the side Finding the angle Example problem pairs (see https://berwickmaths.com/ for an explanation of this) and some questions. Not much of putting it all together but a quick exercise in picking which rule to use. There is an exam question included, a hard one that involves using cosine and then basic trig to find an angle. I did this over two lessons. Finding the side was one lesson, finding the angle the next lesson

Lesson on measuring and constructing bearings. No calculations here, making that as a separate lesson. Covers compass points as well.

Quite an unweildy title. Some example problem pairs and quite a lot of discussion work. Maybe needs another ‘regular’ drill exercise, but there’s a million websites that will generate those for you

Just a quick little PowerPoint and worksheet. Finding percentage increase/decrease. There’s no multipliers here. I teach that as a separate lesson usually.

Designed to be used as a starter to get students to understand what a system of equations IS. Place in the Venn diagram pairs of coordinates that fit each section. Hopefully the pupils think it takes ages by trail and improvement. Then you say “Well, I have a method for solving these much more easily” You introduce the substitution or elimination method and they all look on, enraptured by the mathematical knowledge you’re imparting and the ‘short cut’ to doing these questions you’re showing them. No answers are provided as there is a infinite set of answers either side of the intersection.

Really simple little starter on something that I picked up on with my class : deciding when a result is two or when it is a half