That shape/space/measures bit of the menu is looking awfully bare. Not as bare as the data/probability section, but still.
Simple PowerPoint here.
Little starter
Followed by some example problem pairs and some questions I am still loving fill in the gap resources. Interestingly, my group managed to do this without seeing the formula triagle/rearranging the formula. They just used thinking skills to work backwards.
Not sure that the reflect/expect/reflect bit of these questions works. I’ve tried to make sure they compare it to the first question each time, but I think it is better when it’s more of a ‘journey’ and you compare it to the previous question in each case.
Still A* for formatting. It looks good.
Then I’ve made a blooket for some checking, some exam questions and a plenary.
This worked well with my group but it maybe needs some mini whiteboard work.
A very simple resource, this. But there’s not much function notation stuff out there.
I find pupils’ responses to function notation interesting. Stuff they can do like 2x+3 = 5x – 6 becomes suddenly impossible when presented in the form f(x) = 2x + 3 , g(x) = 5x – 6, find f(x) = g(x). I’m not sure why.
Anyone found anything awesome on function notation?
Sometimes a resource benefits from you deleting stuff, not adding stuff.
I’ve got a much better understanding of what I want these resources to be, and how they’re helpful these days.
Case in point. This used to be a massive PowerPoint stuff with activities, just for the sake of doing activities. But there’s way better stuff on resourceaholic.com if you want nice worksheets.
I’ve cut right down on that. Now I know what I want. An example problem pair, some good questions and a base to build from. Other people have made interesting and fun substitutions tasks. I don’t need to put bad approximations of them in my slides. These are the bones of a lesson.
One thing I DO need is lots of feedback opportunities. Thus I’ve added in loads of mini whiteboard work.
These don’t move as quick as the gif 🙂 Clicking controls the speed.
And some questions whose progression makes sense
And that’s pretty much it. There’s some exam questions and a plenary, but I genuinely think that by deleting loads of stuff I’ve got much closer to the actual inquisition of the skill.
No solving here. Just concentrating on the core skill of factorising. I started with an example and then this
Giving them one bracket so we build up the skill. But wait.
*MISCONCEPTION TIME*
It doesn’t matter which way around the brackets go but on this exercise it kinda makes it look like it does
*MISCONCEPTION TIME*
Did this this cause an issue with my students? No. Because I pointed out this to them. Sometimes sharing your thought processes when planning is a really useful thing.
Then there’s a regular exercise, and then this
Yes. I’ve had someone make emojis of my own face to use in my lesson resources. This might be one of the most egotistical things any maths teacher has done. Which leads into…I’d rather do this as an extension rather than solving as I believe solving is this whole other thing. I’m going to do a PowerPoint wholly devoted to solving quadratics. I really do believe the skills are better split up this way.
Other thoughts
This only deals with quadratics where a=1. I’ve done a whole over PowerPoint on a>1 here.
Thinking about factorising quadratics in depth, you could easily do 2 lessons on factorising, 1/2 on non-monic quadratics and 1/2 on solving after you’ve factorised. And that’s without even talking much about graphs. My current year 11 scheme of work has ‘solving by factorising’ in one lesson. There is too much content in GCSE/IGCSE.
Quite a simple lesson here, but I’ve tried to fill it with some more thinky questions.
My teaching has become far too scripted into example problem pair – some questions – a plenary. I’m not building in enough opportunities for problem solving and struggle time.
Part of that is a scheme of work that forces pace. Part of that is my own routines, comfort zone and, quite frankly, a bit of tiredness. I massively admire those people on Twitter who keep putting out amazing task after amazing task. *cough* https://mathshko.com/ *cough*. Sometimes I question the usefulness of putting these PowerPoints online. Most people can write an example on the board, and the questions aren’t groundbreaking, just well thought out.
Anyway, I tried to add some stuff like filling in the gaps.
Some thoughts for the week
It’s important to think through your examples. I recently gave this example problem pair to year 11.
I was trying to teach them what happens when we have a non repeating digit in a recurring decimal to fractional problem. Anyone else see why this is a trash example problem pair?
This is one of those that’s not that interesting, but where I tried to be reasonable comprehensive.
There’s actually quite a few linear equations type questions that come up at GCSE, before you even get into the possibility of the unknown being on both sides. You could easily spend 2 lessons just looking at these.
I did spent one (scheme of work time pressures, something I can talk about for days), but I’m glad I did. In the past I might have mopped these up with exam questions, or been less explicit, or only expected the top students to answer these. However, all these questions are really approachable if you have the right scaffolding.
I’ve covered loads of different types of question. Here are some examples.
Modelling these explicitly with the group I had was absolutely the right choice.
I’ve added some exam questions (good old Dr Frost) as this is quite a GCSE focused lesson.
If I had to reflect on this lesson, I’d spread it out a lot more. I’m beginning to use diagrams a lot more effectively in my teaching, but I am on the beginning stages of that journey still. I’d like to have used more models and just really slowed down here.
More thoughts
One thing I’m trying to do this year is incorporating a lot more prior knowledge checks. I’ve done that here. I’m still finding them difficult, though. Sure, you can’t move on until every student is secure and has recapped the prerequisite knowledge, but I’ve also got to cover this in the time allocated on the SoW. What happens if a few students are just utterly clueless (I don’t mean that pejoratively)? What does a good lesson look like where 3 or 4 students just can’t even access the warm up? I’d love to hear people’s thoughts on this.
I maybe worry too much, but I was updating some old resources and looking though them. I’m certainly more happy with the look and general organisation of a lot of my newer resources. But they’re much less imaginative. The tasks are all becoming a bit samey. I write some questions, thinking about the maths involved. I try and make the questions interesting these days. But…I’m lacking a bit of sparkle somewhere. Some variation in the diet. I’ll have to think about that.
I can’t believe I haven’t made these slides before.
I have a group with lower prior attainment this year, so I wanted to really try and be explicit when teaching this.
In my example I went for both a number and a place value grid.
I’ve used the place value grid a lot more this year. It was useful to highlight the tens/hundreds column and talk about rounding to this column. I think I’ll stick with making the grid way more explicit when I teach rounding. It worked well.
There’s quite a bit of mini whiteboard work here, because I’ve found that this stuff is fairly easy, but sometimes students need a few cracks at it to make sure they’ve got it. I project a question for them to do on their mini whiteboards, then I explain it. I generally move on to the task only when the majority are displaying right answers. Then I can focus on the students who need a bit of extra support.
There’s a Blooket link, too. I am still into Blooket. I think it’s quite fun as a little plenary.
If you’ve got a suggestion or some feedback, get in touch on Twitter. Last week’s resource provided some really interesting discussions, especially about questions that require you to ‘add the brackets to make this sum true’.
I like the idea of the questions as extension when order of operations has been mastered. In the form you've suggested. A good opportunity to behave mathematically, conjecturing, specialising and generalising.
I use grid method to do this. I’m a big proponent of grid. Reading through Jo Morgan’s amazing Compendium of Mathematical methods, there’s loads of approaches. But I like to use grid for everything.
