I’ve been reading Michael Pershan’s Teaching Maths With Examples this week. It’s really good. I recommend it. Quick, simple and easily digestible. Great stuff.
In the book, Michael describes using Venn Diagrams to give an overview of what, exactly, we mean when we talk about systems of equations. This really made me sit up, because I think students often don’t quite know what systems of equations ARE. They can procedurally solve them, but sometimes struggle to get a big picture of what they’re doing.
This resource aims to give the big picture, the WHY, before moving onto the HOW to solve.
So we do this by trial and error, then you swoop in and show students a more formal, better method for finding these answers.
We’re back learning from home this week, and it’s given me a bit of impetus to clean up some old resources and make some new ones. Everything here is quite short and simple, but hopefully it saves someone a bit of time.
I found when I was doing compound measures that my students needed extra practice on this. It was holding them back from answering speed questions correctly. So here is a quick lesson on converting time.
I delivered this digitally, sharing my screen over Google Classroom and using my iPad pencil to write my modelling over the example problem pairs. I added the PDF of the questions into the Google Classroom and gave them ten minutes to complete the questions either in their books or digitally on the PDF.
We then came back after these ten minutes to go through the answers. I then made sure they could not leave the lesson until they had handed in their work on Google Classroom. This a routine I go through pretty regularly and I find it works really well. It means I get a log of what they’ve done and there’s accountability as their work is checked then and there.
Really simple lesson. Really simple questions. However, I also added a little slide of 9 multiple choice questions. I like this format. It did require over 150 animations, though!
It was really nice to show this and go through the questions one-by-one discussing why I had chosen the wrong answers. I am not 100% happy with the question set, though. If you’ve got any good suggestions for questions, please tweet me @ticktockmaths.
A really simple starter. I made this because I did a Kahoot online with my year 10s and a large proportion of them got question 11 wrong. They knew how to do speed, but they instinctively didn’t really want to get a half as an answer. I made this as a starter for the following lesson to really hammer home the point.
Quite a productive week. It’s easy to make stuff when you don’t put yourself under pressure to make 1000 slide behemoths, but just simple, quick and easy resources that don’t reinvent the wheel.
I did the Sine Rule ages ago but never got around to doing cosine rule stuff. I think because the Mathspad activities are so good!
I didn’t go much into labelling the sides (which maybe I need to in future) or putting it all together. I think I’m going to do a resource called ‘Trigonometry : Putting it all together’ where several rules are used. Maybe with some exam questions and a bit of goal free stuff.
No posts for the next two weeks. I’m off on holiday.
I aplogise to the Hull City blog Amber Nectar, who I kind of nicked this post format off.
I’m really into ‘fill in the gaps’ activities recently. I love how they develop thinking forward and backwards. I love this worksheet on time calculations which I used recently. I went down really well and sparked great conversations. Love this kinda stuff. (Although for some reason TES won’t let me review the resource and give it 5 stars).
Talking of TES, I’ve updated my resources on Measuring Bearings, Calculating Bearings, Expanding Brackets and the Sine Rule and uploaded them on there. I’ve corrected mistakes, sorted out some formatting and freshened things up. I’m still unsure about all this. I don’t think my resources should be on their own website. I understand that we have far too many resource websites to check, but at the same time TES is pretty rubbish. It’s annoying to update a resource if I see an error and track changes, and it’s interface and search isn’t great. Plus there’s all this paid junk flooding the listings meaning that stuff never gets seen. The other thing is that I struggle to get feedback there. I don’t know if stuff is not getting downloaded because it’s rubbish or because people don’t see it. I’d love to have a platform with some quality control that I could submit resources to, but I realise that’s probably a pipedream considering how much such a thing would cost to run. Tweet at me if you want to discuss any of this because I think there’s potential in connecting things. I know it’s kinda pathetically attention seeking but I’ve been making resources for 10 years now and I feel a lot of it just gets lost in the mix. Which kinda puts me off doing it.
Talking about bearings… I did my measuring Bearings lessons the other day, and we’d lost a load of half protractors. So I used this template and printed them out on tracing paper. A game changer! It worked brilliantly. Just make sure you change the printer output setting to ‘transparent’ or whatever similar setting you are offered.
I’ve been thinking a lot about books recently. I’ve got some colleagues who are really on it with books and end up with classes that have awesome books. It’s something that I really want to work on next year (I’m sure I’ve said this before). I think it requires quite a lot of follow through and effort, though. Definitely something to think about.
I love this Tweet. Lots to think about in regards to the language that we use.
I have, again, tried to avoid inspection by using slightly annoying numbers. I would suggest that calculators are a must for this resource.
I also added the following page, which I really like.
Hopefully questions 9 and 10 provoke a good discussion. I love a bit of direct instruction, but I also love a bit of debate and discussion. I think there’s a little misconception that direct instruction is just dull lecturing. As with anything, it’s about the mix and variety.
I’m still thinking of a good way to share these. In the summer term, when I have more free time, I’m going to a proper evaluation of what I have that is good enough to show people, and how I can present stuff so that it’s useful and findable. There isn’t any current reason for this stuff to all be consigned to this site, I think it would be better to bring disparate resources together.
I love it when a student goes away and voluntarily does extra work because the task is so fun. This week I did a bit of Artful Maths’ Impossible Objects. Wonderful lesson and I got some great results. More than that, I got some really, really enthused students.
I’ve been using my iPad a lot recently. I really like it, but it’s made me think about my board work. I have a few colleagues who make beautiful board notes using colour and shape. I’ve never got there and I really would like to. I really would love to invest my time in this in the future. See the Tweet from Ed Southall at the bottom of this post. It’s gorgeous.
We’ve been using Times Tables Rockstars a bit for our younger learners and it’s really nice. But it also made me think that the issue is not our lack of resources, but the abundance of them. It’s rather like Netflix. All of this content and I spend ages scrolling the menu deciding what I want to watch. It’s why I think Resourceaholic is so good. It’s just good stuff, well curated. I was saddened to see Jo is having a tough time at the moment. If you haven’t already, you should buy her book, It’s fascinating and a really good exploration of different methods. I think it’s really worth knowing these, and there’s great discussions to be had with classes as to which methods are better and why. She also has a buy me coffee page.
I was talking to my tutor group about social media the other day. We were talking about the Pavlov’s Dog ping of pleasure if you get a like or something. I’m real susceptible to this. I posted my perimeter lesson, and it got a ton of likes, but my last One Step Equation lessons got not likes or retweets. Got no idea why.
I couldn’t think of 5 things, but I wanted to get into the habit of blogging more regularly.
Another attempt to take lessons that were a bit rubbish and update them, with a focus on good questions.
I’ve taken what I think is quite a brave choice to use decimals extensively throughout. There is a reason for that, and that is thinking about the skill that I want students to understand. The skill here is rearranging to solve. Using ‘nice’ numbers can lead students to solving by inspection. Great! They get the answer, but they often are not using the very skill I’m trying to teach.
Hopefully by using more ‘difficult’ numbers (with the aid of a calculator), students will do the thing that I want them to do.
I tried to cover every possible type of question, but if I’ve missed one, let me know. I haven’t bothered with worded questions at all. I think maybe that’s a separate thing altogether, but it could go here.
I think I haven’t spent enough time doing this before and I’ve tired to be really in depth. As always, feedback is welcome.
One of the best MathsConf sessions I’ve been to, and one that I come back to again and again is Jo Morgan’s Indices in Depth (Watch a recorded version here). It really stuck with me because of something she said.
I’m paraphrasing, but Jo said that she used to cover all of the index laws in one lesson, but she now realises how that wasn’t good.
When I watched that presentation, I was also covering index laws in one lesson. By doing that we rob ourselves of the opportunity to develop mathematical thinking. We rob ourselves of doing interesting questions or delving into specifics and really covering things in the detail and sophistication that we should.
Anyway, I normally cover perimeter in one lesson. Add up the sides!
But it in trying to make some better slides I realised how much you can do with it. Change of units! Being explicit about what the different marks on the lines mean?
So this is an attempt to address all of that.
There’s example problem pairs and exercises for:
Regular perimeter, including the notation
Finding a side, given the perimeter
Finding missing sides and compound shapes
Measuring the perimeter (by plotting coordinates and using a ruler to measure the perimeter)
Using different units
Some algebraic stuff.
also a lovely discussion picture
You could probably easily do 3 lessons on this. Using perimeter to build mathematical thinking, rather than just teaching the content. The content is a conduit.
One of the best ways to do this is I’ve seen is Mr Draper’s lessons here. I’d highly recommend you checking that out. Especially these questions, which I think are gorgeous.
So that’s a good 5 lessons you could probably do with perimeter, not including the old area/perimeter investigation when you try and keep one constant and change the other.
One lesson I’d been using. Think of all the lost opportunity.
Sometimes you look back at your old work and feel it was written by another person. I went to teach completing the square this week and I couldn’t understand my own resource. It was all over the place. I’d clearly thought about activity first and the learning journey second. It was all messed up. I introduced ax^2 + bx + c waaaay to quickly.
Well now it’s a lot better (in my opinion).
There’s an example problem pair with a simple example and two exercises on doing the simple stuff before we go anywhere near anything harder.
THEN we move on to doing harder ones, and finally turning points.
There’s also a matching worksheet with all the questions on.