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?
My annual Christmas maths quiz is here. I’ve made it early this year to give people plenty of time to find it. (Looking back, I’ve made some sort of this quiz for 6 years now!) This isn’t just a quiz, it’s a quiz with lots of links to maths.
I know some people like to teach up until the last second, but I’ve always liked to finish the term off on a nice little maths quiz. I think it’s OK for us sometimes to let our hair down a little. I say this. I’m bald.
The rounds this year include some repeats from last year. Like the Shakin’ Stevens video round.
I think it’s nice to kick off with a song. And I’m sorry but I find this video hilarious. It’s utterly cursed. I’m usually cackling all the way through.
Round two this year is inspired by Linkee. I love a quiz. I love Linkee.
The questions were really hard to write!
Round three is a cipher type thing.
Let them use a calculator. Go on. Be nice. It’s Christmas.
Round four is the Chris Moyles Quiz night round. These are always a good laugh.
Round five is sudoko. I found this worked well last year. So I kept it. Also I couldn’t think of a round to replace it.
That’s Christmaths!
Other thoughts
Just two more weeks to go of term. Then I’d have uploaded a resource every week of term one. That’s pretty good going if you ask me.
If you’ve used any of my resources this term and liked them, and have some spare cash about, please do me a favour. Please consider a gift to KidsOut. Their online shop is filled with gifts that you can purchase to send to children in refuges. Read all about them. I genuinely get a little teary each time I do. Here is a real challenge. Take a second to read their website and stay dry eyed.
I hope you are having a wonderful Christmastime. Teaching is stressful and difficult and I hope you get the rest and relaxation you deserve.
One thing I’ve noticed with pupils, is that literacy gets in the way of the mathematics more often then you would realise. There’s literacy issues with things like ‘range’ etc having very strict mathematical definitions, but we also use loads of different words for the same things.
Let’s take multiplication for instance. If we wanted to talk about 4 multiplied by 3, we might say : 4 times 3, 4 lots of 3, 4 groups of 3, four threes, etc. There’s loads and I think it can be quite a lot for a pupil to get their head around.
So I created 6 little starters that all use the same numbers but switch out the wording.
I think using them has been really helpful. There’s a few ambiguous ones in there, too. I love ambiguous cases, they provide great discussions.
Download these and have a look. I think they’re one of my best ideas.
This is a follow up to my factorising quadratics lesson. I taught this two weeks ago, but I was cleaning up the slides to be put online. I really think the exercise that goes along with it is nicely thinky. Some variation and slow build up of activity.
3 leads on to these problem solve-y questions Not a huge lot here, but I thought this lesson and my other quadratics lesson here sequenced well.
Other thoughts
I’ve been doing barvember. The pupils in my year 7 class have kinda hated it, which proves just how valuable and needed it was. These questions are so high quality, and it’s lovely to show how you can do some of these problems just with bars and basic four operations knowledge. I laminated some responses from the pupils, and they loved seeing their work up on the board. Great stuff.
This blog is going to break it’s usual format for the next few weeks. Next week I’ve got some starters for you, the week after … ChristMaths is going to be published early.
As always, thoughts and insights to @ticktockmaths on Twitter.
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.
I’ve packaged together some of the starters that I’ve been putting on Twitter challenging misconceptions I’ve seen in lessons. Stuff that I see a lot but doesn’t necessarily have a place in a SoW.
Stuff like the difference between a half and two
Or when we need to write trailing and leading zeroes.
I haven’t included the answers deliberately. These are meant for discussion. For instance, 12 here could be a currency.
I did the same with 1s.
I would do these with any class that have had algebra introduced. Even doing it with my 11 Higher class caught some misconceptions.
I would maybe only do this with lower years, though. I am trying to get at the idea that the digits stay in the same arrangement. I have found that I have two groups this year who find multiplying and dividing by 10, 100 and 1000 really difficult. On a recent assessment more than a few tried to do 2401/100 using the bus stop method.
I’ve reinforced it and reinforced it, but there are about 2 or 3 that still lack the skill and I’m running out of ways to address it. Any ideas to @ticktockmaths on twitter.
There’s also some that struggle with halving and doubling quickly. Again, really struggling to embed this.
This one tries to get at the unitary thing. It was interesting hearing student responses, especially as the answer depends so much on what x is. There’s a version with 3 if you want something more concrete.
The last one is identifying if the answer is a quarter (like half or two. I was kinda losing steam by this point.)
Also this page isn’t editable because of some stupid saving between computers bug 🙁
Right, that’s it for this half term.
I’ve managed to fill quite a lot of gaps.
Behind the scenes I’ve also got a lot of PowerPoints half started, ready to be finished up and polished up for uploading here. The goal of covering most things seems achievable, if still long way away.
No resource next week. It’s half term and I want a rest.
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.
