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.

Why moving to teach abroad was the best thing I ever did

I was reading this article about teachers moving abroad. It’s a nice little read and I thought I’d add my little two cents, as this is something I’ve been thinking about recently.

In 2016 I was ready to quit teaching.

It’s easy to go through phases in teaching. Loving it, hating it, loving it again. I think a lot depends on your timetable and the structure of your day.

It had been an exhausting few years. Our school had been put into special measures a few years back and not really recovered. We were taken over by an outstanding school and went through 4 head teachers in 4 years as they scrabbled to find something that worked.

It was the behaviour that got to me eventually, though. The low level stuff that never stopped. We had a three strikes system. Three low level disruptions and you’d be removed from the lesson and put in isolation. Pupils were constantly being pulled out of my lessons. Disrupting the flow. Stopping me from actually teaching.

I blamed myself. Maybe my relationships with the children was poor. Until I did a walk around during a free period and found the number of kids being pulled out of lessons was in the double digits. Every period.

I don’t blame the school. It’s really hard to escalate these cases, and staff were trying really hard. The hours and time and commitment put into the kids at the school was miraculous. But behaviour never improved. What do you do if a kid is being removed from every lesson in a week? Exclude them? What if the behaviour continues? What if 20 kids are doing this?

I never really got upset when kids had an outburst. You can usually understand a child who punches a wall or throws a chair. But the constant cycle of low level, petty behaviours. Talking over me, throwing things. The lack of respect was what killed the joy for me.

I would go to mathsconf, or spend some time planning a great lesson, and never really get to deliver it. Then I would look into they eyes of the children who wanted to learn as we waited for SMT to remove a pupil again and just feel awful.

Then there was the UK EDUCATION STUFF.

Handing your books in to be checked. We all agreed that you couldn’t see progress in a book, but we did it anyway. We all agreed the ‘verbal feedback given’ stamp was rubbish. But it’s the done thing, you see. Eventually we got rid of the stamp, and a lot of the rules. Because the school acknowledged that it was a waste of time. But they still collected the books. To collect data. That was never used.

OFSTED came in one time and told us to be more consistent. So the school made sure that we all used the same learning objectives slide. Which was designed in the dark. Graphics stretched in the wrong ratio, a putrid green colour. Ghastly. I’m not sure that’s what OFSTED meant. I don’t think OFSTED know how their words are taken.

The worst thing was, everyone in the school wanted it to be better, and some of my colleagues where phenomenal people. Knowledgeable and committed and fantastic teachers. Dedicated, wonderful people. For some reason, it never quite came together. Which was horrible.

If all this feels like a rant, that’s because it is. I turned into a walking rant machine in my last few years in the UK!

I could have moved schools, obviously, but look on TES. It’s often the same schools in each area advertising constantly.

So I looked abroad.

It took a lot of attempts, but I ended up in a school in Thailand, and it’s been an absolutely wonderful year and a half.

I’m teaching better lessons than I ever have. I’m given the space to develop my practise and trusted. It’s made me love being a teacher again.

Our school is particularly great, to be fair. The department is fantastically organised. But the time makes the difference.

We run clubs and enrichment and we can do it because we’re not there typing up behaviour incidents 24/7.

I can take risks with my teaching. Card sorts work here! All pupils are respectful and kind and polite. I can work on a lesson and deliver it. My teaching has improved significantly because I’m not managing a room full of children, I’m teaching them. It’s great.

It’s no coincidence how much stuff has been added to this website in the last year and a half and how much better quality it is.

Recently I taught trigonometry to year 9 and it was joyous. We started with similar triangles. We went for understanding, not just repeating SOHCAHTOA, and it all worked because I had time to plan a good lesson and pupils who were receptive to what I was delivering.

Sometimes I have to pinch myself.

If you’re me in 2016, think about it. If you’re a bit beaten down, and feel like you could thrive if you just didn’t have to do so much rubbish that didn’t benefit the children, think about it. I would whole-heartedly recommend it.

Estimation

Download the PowerPoint here.

I created this after a discussion on Twitter.

Estimating is more complicated then I give it credit for. We have to decide the level of rounding that’s appropriate, based on the calculation being done. It’s not just as simple as rounding to 1 s.f.

I did some questions that are quite typical. Check the calculation by estimation.

Then I did some ones where we need to work it out.

And an emoji based exam question format I quite like

There’s nothing new here, nor anything really ground breaking. But it quite a bit more thorough than I have been in the past, which pleases me.

Rounding to significant figures

Download the PowerPoint here.

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

Download the PowerPoint here.

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

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

Download the PowerPoint here.

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

Download the PowerPoint here.

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.