Trigonometry

Download the PowerPoint here.

This is basically a lot of ideas knicked from Resourceaholic. Sorry @mathsjem! Quite happy with this, though. I have used this with my year 9 class this year and I think I’ve taught trig better than I ever have before.

Starts with sine. Talking about similar triangles.

Not using the calculator yet. I want them to appreciate that these are ratios, not just buttons on a calculator!

Then it moves onto two example problem pairs. I introduced the button on the calculator at this point.

Then some questions.

I went through the same process for cosine. I really spent a lot of time talking about just sine and just cosine this year. I think it really helped understanding.

Then, picking between (Don’t worry. The highlights animate in).

Then I introduced tan in the same way.

Some more practice on just tan, very much like the sin practice.

Then a mix of everything.

That was 2.5 lessons. And we didn’t even talk about finding the angle.

Trying to take the time and teach it right first time.

I think there’s possibly more to add here. I think I could have written something about answers or questions when you’re given a ratio like cosx.

Obviously there’s no problem solving AT ALL here.

There’s no mention of SOHCAHTOA. Good.

I think I’m going to write a separate trigonometry problems PowerPoint.

Rounding to significant figures

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I didn’t want to have an example problem pair for this. Instead I went with more of a pattern spotting thing.

I think this is quite nice (it all animates in so isn’t displayed at once).

Then some fluency questions.

Then another PIXEL PUZZLE. I like these, and my ratio one is my most downloaded TES lesson.

There’s also a little venn diagram task. Mathsvenns.com by Craig Barton has got some nice ones of these.

Also all the usual gubbins. A learning check etc.

I guess I could have added some ‘real life’ stuff to this, but I didn’t want to. The football stadium holds 25,675. Round this to one significant figure etc. I find those kind of questions a bit drab.

I did, however, add this:

It provoked some discussion.

Adding fractions and mixed numbers

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So, I’ve been unhappy with my adding fractions lessons for a while. They were always ‘good enough’ but not actually good. This year, I decided that good enough wasn’t good enough. I needed to finally attack them. Flesh them out, make them interesting, build in opportunity for students to really test their skills.

As I’ve gone through a lot of my older slides, I’ve removed a lot of ‘narration’. That’s true of these slides, too. Out with the clicking through written talk and animated examples, in with example problem pairs.

I thought about what I really wanted students to do. I wanted them to calculate properly, not take shortcuts. Hence :

I wanted them to get a sense of what fractions where. Not just mindless calculate, but think and interrogate their answers. Hence:

I added a little thinky thing about diagrams.

I would have added more, but I think that’s best done with something likes mathsbot.com and not with PowerPoint.

I wanted more puzzly and interesting ways to get students practicing those core skills.

I hope now you’re starting to get a sense of how big this one is!

I also wanted some good old fashioned SLOP.

I actually had these questions in the slide before. But I have tidied them up significantly. They look a lot nicer now!

What about a question where we simply have to identify WHEN we should add fractions.

I just thought of this format this week and I’m already in love with it.

I wanted to add a little mini-investigation, also.

I HAVEN’T EVEN GOT TO MIXED NUMBERS YET.

Let’s do some practice with them.

How about some practice but in a different format to change things up a bit?

What about continued fractions? Those are interesting. Maybe have a chat about those.

We could even play a game!

After I uploaded this screenshot, I noticed the bad wording at the top and edited it.

I don’t think I’ve put together a more comprehensive lesson.

There maybe too much here, but you can always skip the bits you don’t wanna do. I don’t think you could say there’s too little.

Probably won’t have another lesson for a while. It’s half term and then I don’t quite know what to make a start on next (rounding?)

Equations of perpendicular lines

Download the PowerPoint here (thanks to MrBriggs on Twitter for pointing out that I forgot to add this link in!)

This lesson went well, actually.

Work out the gradients and try and notice something.

Then there’s a little bit on making sure we can properly identify when something is a negative reciprocal.

Obviously, an example problem pair.

Then some nice questions.

Quite pleased with this one. Enjoy.

via GIPHY

Next lesson : I’m going to re-do my fractions slides and add a load of stuff in.

Equations of parallel lines

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I quite like this one.

It starts with a little whole class activity saying if two lines are parallel or not. If you click ‘check’ it’ll show you the graph. Nice!

Then students have to do some solo work on this, matching up equations with the same gradient. This is a nice little chance to interleave some rearranging formulas work and some fractional work.

I thought about these questions reasonable hard. The activity format is stolen from mathspad.co.uk. If you’re not subscribed, you need to be. It’s one of the best value for money sites out there.

Then we’re onto the typical example/problem pair.

And some nice little questions with a bit of variation theory. I deliberately wrote less questions that I maybe would normally, and focused on the quality of the questions and making sure that there was a good amount of stuff to talk about in regards to the answers.

Then onto some more difficult problems…

Overall, I was pleased with this lesson. I really felt that these questions and slides gave me a good structure to teach this content.

The only issue is that it’s a little too atomised. There isn’t quite enough here on picking out when to use these skills. Maybe that’s for the teacher to draw attention to.

As always : Hmmmmmm.

Highest Common Factor / Lowest Common Multiple

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Just an update, really. Someone contacted me about my HCF and LCM lessons being linked wrongly on here, and I realised that they were a bit crap, so I tidied them up.

I removed a lot of ‘narration’ (I initially put these in to help teachers who just wanted to pick up and go, but it made the lessons too click-y, I always skipped them) and put in example problem pairs. I also added a whole lot of questions. For instance:

I noticed that these type of questions come up a lot in exams so I thought I should add them into my lessons.

There’s also a whole lot of worded questions now.

There’s three lessons in one here, really. HCF, LCM and HCF mixed, worded questions.

Think this is a lot closer to being comprehensive.

Fractional Indices

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This is my first post of the term.

I guess I’ve started a week late. The reason is quite simple, I think I’ve got a bit of resource writer’s block!

This PowerPoint is fine.

It’s got an example problem pair.

A discussion (which I’ve found a useful bit in my lessons. I guess some people might call them a hinge question) and some questions.

But I’m not sure how I feel about the questions at all. They’re a bit… bleugh. I guess they increase in difficulty level, and some of the questions link back, but it all seems a little bit boring. There doesn’t seem to be anything here to get your teeth into.

In fact, I nearly didn’t share this resource at all. It lacks … seasoning. I’ve tried to reflect on this and improve it a little, but I’m drawing a bit of a blank. Eeek. I couldn’t even find any JMO type questions.

I did add a little codebreaker, but I feel that I’m exhausting that format.

If you’ve got any thoughts, give me a shout on Twitter (@ticktockmaths) or below.

Calculating bearings

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Bearings is a topic that I’ve taught really badly in the past. It’s due to a number of factors (teaching measuring, use of worksheets) but mainly I think due to a lack of thinking on my part about the different processes and skills contained within bearings work.

I often lumped all of bearings together, maybe throwing a few calculation questions around as they’re not seen too much at GCSE. This was clearly a mistake.

In my measuring and constructing bearings lesson I tried to really atomise the concepts involved in bearings as much I could and sequence the lesson in a much more thoughtful way.

I’ve tried to do the same here with my calculating bearings lesson. It mainly covers question types like the following.

But I tried to think about what challenges pupils could have. Pupils could have different angles given. They could have questions that require them to remember that a bearing is a three-figure value. There could be more than one bearing. My attempt to look at these question types is below.

Looking at these, there’s a few things I like and a few things I don’t.

I’ve managed to build in a bit of variation so that students have to think about the angle they’re trying to find. Maybe there could have been some more straightforward questions to build confidence first, though. I also tink it’s a little crowded and messy from a visual standpoint, but I found it very hard to make it look any nicer whilst still being readable.

I took a lot of inspiration from this excellent solvemymaths sheet.

I also added some worded questions.

And this

I love the question ‘what can you work out?’ when it comes to angles. It really does make such a huge difference in how student approach their work.

Index Laws : Division

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Completing index law week here.

I added some whiteboard questions/rapid fire questions as I felt I didn’t have enough build up.

As in the last few PowerPoints I spent time thinking about the questions I ask and the skills required.


An SSDD type question. I need to add more of these to my teaching.

PS: No update on Monday, it’s a public holiday here in Thailand. See you on Wednesday.