Equations of parallel lines

Download the PowerPoint here.

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.

Adding and subtracting directed numbers

Download the PowerPoint here.

OK. So this is a big one.

Firstly, I have found teaching negatives difficult in the past. Teaching the rules is a bit useless. ‘Two negatives make a positive’ often leads students to doing things like -5 – 9 = 4 (or similar). I avoid the rules like the plague.

I guess pattern spotting helps.

Here I have used a Craig Barton idea. The idea is that you present each set of examples, asking students to predict the result. You then wait during the … (the gap of understanding) and ask them to predict the result of the next one. Hopefully they see through pattern spotting what the answer is.

I’ve got some questions to support this.

I have tried to write questions that help develop student’s strategies like grouping.

Notice at this point it’s still all addition.

Increasingly I have found, however, that multiple representations are helpful. I used to think that I didn’t want to complicate things in student’s minds, and that showing differing methods would confuse them.

I’m now of the opinion that switching between multiple representations is really, really useful. Students who can do this are much more successful and I’ve tried to be more explicit in adding in differing representations into my work.

This is an idea I took from the excellent Pondering Planning website.

Notice I’ve done this AFTER the questions. I think sometimes it’s helpful to get students being able to solve the problems first and then supporting understanding later.

Even more representations!

I like double sided counters for negatives. They fall apart when multiplying or dividing by a negative, but they’re a useful representation for supporting addition and subtraction.

Hopefully, having differing representations helps students do some worded questions. I think this is probably a nice time to break for a lesson.

When we come to the second lesson, we could start by trying some arithmogons. I like arithmogons. They feel ‘puzzly’. The numbers in the box is equal to the sum of the circles either side. They test a bit of fluency.

Time to move on to subtraction using a similar frame. Including more patterns, questions and representations.

These questions tend to come up a lot in SATs.

I even chucked in a crossnumber.

How about some negative arithmogons? You subtract along the direction of the arrow.

Maybe a little complex. I’ve written a sheet of them, though.

And of course, JMC questions often bring out a little understanding.

This is a pretty massive PowerPoint. 41 Slides. Probably 4 lessons. I don’t think I devoted enough time to doing negatives, before, though. This is pretty exhaustive.

Add a comment if you’ve got any suggestions for improvements.

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 Notation

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So … I can’t claim that I’ve done much original work here.

Most of this is stolen from Jo Morgan’s indices in depth presentation. Sorry Jo!

Normally I make a lot of stuff from scratch, but Jo’s work here is so good that I can’t really improve on it. If you get to see Jo do an ‘in depth’ presentation, go. The time and effort behind them is phenomenal.

PowerPoint contains a section on writing things in index and expanded form.

As well as some questions people might find a bit old fashioned. Also the first time I’ve put a ‘reveal all’ button on a page. Can’t believe I’ve not thought to do that before.

I like these little discussion slides. I think they’re fun.

Some UKMT questions, which I stole from this book. It’s a lovely little book.

I also added a little problem solvey bit where we talk about powers of two and binary.

Multiplying to come next (it’s basically copied and pasted from Jo again. Sorry Jo!)