Applications of Pythagoras

Download the lesson here.

I find telling pupils the Pythagoras rules and then getting them to solve ‘problems’ isn’t enough. Often, the unstructured problem solving can be overwhelming for students.

Opinions vary. You might think that I’ve structured this waaay too much, and removed too much thinking from the students.

It would be interesting to hear people’s point of view on this.

Starts with a ‘do Pythagoras but with a little context’ and leads into a question that’s a little more unstructured.

Moves onto using Pythagoras to find the area of a triangle.

Maybe I’m over explaining things, but in the past I have not made enough things explicit and I’ve just assumed my students will work it out. I think I’d rather be more explicit.

Next, we pick from a complex diagram.

Now points. Which I don’t actually think is too complicated.

I’d love for people to feedback on this lesson. Is there too much spoon feeding going on here? How can I reduce the spoon feeding whilst also making skills explicit?

Ratio problems

Download the lesson here.

Just a load of interesting (ish) ratio problems to work though.

I used bar modelling. I am increasingly into bar modelling for KS3, although I’m still not massively convinced when it comes to negatives.

I call these ‘reverse’ ratio problems. I don’t know if that’s the correct terminology.

I have been watching a lot of Queer Eye recently.

I like bar modelling for questions like this.


Some questions adapted from Don Steward and White Rose Maths Hub’s Barvember 2017.

No posts for two weeks now. I’m on holiday. When I get back, Pythagoras and Trig!

Sharing in a ratio

Download the lesson here.

Something I’ve wanted to get around to completing for a while. I love ratio and I’ve got into doing a little bit of bar modelling. There’s some LOVELY questions in the White Rose Barvember stuff.

This lesson has an example problem pair and some mini-whiteboard work. When I taught this lesson, the mini-whiteboard stuff really, really worked on getting students on the same page and up to speed.

I put quite a lot of thought into this set of questions, too.

I think I’ve done a good job with question 2 in particular, there.

Also there’s some worded questions.

Question 5 might be my favorite question of all the questions I have ever written. There’s just something lovely and crunchy about it.

Obviously this lesson includes the plenary check as well and also a problem solving question.

Friday’s resource is the last one for a while. It’s the Easter break. If I’m writing maths on a beach in Laos, my wife will murder me. On a personal note, I’ve managed to have a blog ready every Monday, Wednesday and Friday this half term. Pat on the back for me, there. I hope to have the same schedule next term.

Updated resource : Solving linear inequalities

Download the lesson here.

Completely revamped lesson. Includes an example problem pair, lots of mini-whiteboard work, a regular activity (which is still kind of rubbish to be honest. I could do with thinking about these questions more) and a nice little codebreaker.

I prefer setting my code breakers out like this. I find if you do ‘collect a joke’ kids will just try and guess the joke. The answer here (au4a83 ) is how you type ‘password’ on a Taiwanese keyboard. From this very interesting article (not really maths related).

Also added some exam questions.


Download the word file here.

I’ve been reading Peter Mattock’s book Visible Maths. I’m only two chapters in but I’m really enjoying it. Visual representations is something I haven’t really learnt much about. I’ve dabbled in bar modelling, but I’m a stranger to things like Cuisenaire rods. So much so that I had to read up on how to spell them.

I particularly like this

I often do regrouping and addition as one lesson and maybe I need to be more explicit introducing regrouping as a skill in itself.

So I came up with this, using to generate the images. It didn’t take very long.

I’m quite pleased with this.

The Sine Rule

Download the PowerPoint here

Download the worksheet here

This took me about two weeks to complete! Don’t know why, it’s not that many slides. I drew lots of Geogebra diagrams. There’s a worksheet with 15 questions.

I made this for a class with really strong prior attainment. I think I could probably do with some questions where they have to pick the correct calculation. I have added 4 questions that can be done on whiteboards to kick off the lesson, though.

There’s also a chat on when to use the sine rule.

Obviously this animates so it doesn’t just display the answers!

And some more fun questions!

There’s a second lesson here, too. Using the sine rule. (although I could really do with some more questions here!)

And the ambiguous case

Measuring and constructing bearings

Get the PowerPoint here.

Get the worksheet as a Word file or PDF file.

Bearings is one of those difficult topics to teach, I think. Even though it’s reasonable easy.

I’ve done a lesson here concentrating on just measuring and constructing. No calculation at all. I’m going to put that in a separate lesson.

Which means you’re going to have to print out the example problem pair 🙁

Starts with a little discussion on if something could be a bearing or not.

Goes onto a worksheet on measuring.

I suppose I should have really presented an example with angles labeled and asked them to pick out the right bearing (like the exam question at the end of this PowerPoint) but I think I wanted to add that in next lesson.

Then some whiteboard work on the compass.

Then some construction questions.

My example problem pair here includes animations. I kind of hate it. I’ve really tried to move on from ‘clicking’. If you’ve downloaded my PowerPoint in the past you might have noticed that I’ve deleted a lot of stuff. I used to have animated multi-step solutions and examples. Indeed some of my older, non-updated PowerPoints still have that stuff. I really regret that now. I know it’s a crutch, and can be helpful in ‘scripting’ but I think kids need to see you WRITING and doing the calculation yourself (I use the pen tool in PowerPoint).

But there wasn’t a real way to get around using animations here, unless you have a visualizer. If you do, do that!

Updated/New resource : Linear inequality notation

Download the lesson here.

I’m not quite sure what I was thinking when I wrote these slides initially. They were a mess!

For a start, I bundled writing inequalities, number lines and solving all onto one PowerPoint! That’s waaaaaaay too much. It’s also a little ‘disrespectful’ to the topic of inequality notation. That skill is easily worth a lesson on it’s own! I clearly hadn’t sat down and thought clearly enough about the subtleties of the topic.

You can do loads of good spaced learning with inequalities. We can practice ideas of place value.


I’ve cleaned this slide up. Before it looked like this :

EEEEEEEK! This is NOT good slide design. Sir! Is number one 1.9 [] 5 ?

I’ve also added lots of whiteboard questions and a little bit of testing if an inequality is true. After all, inequalities are all about systems and logic tests, really.

I’ve also redrawn all my images of inequality number lines in GeoGebra because they looked gross before.


Some interesting answers to this!