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’ve added a load of whiteboard work with this one. I really think mini whiteboards are the best place to deal with this kind of stuff.
Again, I’m trying to use more things like number grids in my examples.
This defiantly needs another little activity, but I haven’t quite worked out what that should be. Tweet me @ticktockmaths if you have some suggestions.
I used to wait until these where comprehensive before posting them but I think it’s better to publish something barebones and build on it throughout the years.
Maybe I’ll look at putting some SATs questions in there at some point.
Some notes
The other week I published an Order of Operations ppt, and I forgot that Jo Morgan has done an AMAZING topics in depth video on it here. Great stuff. I need to make sure I’m rechecking a lot of these before I make my lessons. I love these things. The exam boards/the DofE should provide these videos for every topic. They’re incredible.
I was reminded about them because I’ve started a new job, in a new country. It’s scary stuff, but I now have a bit of a commute. I’ve been listening to the Mr Barton Maths podcast on the way to and from work. These podcasts are so good. I’m loving finding room for them again.
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.
Lots of reasons, but the left to right nature of multiplication and division (and addition and subtraction) must be the most important reason.
This week’s lesson is nothing too fancy. An example problem pair, which is way harder than the exercise.
I’ve been mulling this for a while but I just haven’t found a nicer way of doing this. Making the EPP too easy results in students not being able to do the harder questions, and splitting it up into multiple EPPs is just tedious. Maybe I should make the exercise harder, but keeping it simple at the beginning builds confidence nicely.
We move onto examples with a fraction.
These are important, because there’s an implied bracket in there. Students should not have to infer things. We should demonstrate things to them explicitly.
Then there’s an exercise on putting brackets in to make something true, which I always like doing.
As an addendum, I want to publish a resource every single Friday this academic year. We’ll see how that goes.
I was going through my old PowerPoint slides looking at my column addition and subtraction stuff. Which was fine, I guess. But I’ve abandoned using slides for a lot of that stuff and set up examples using mathsbot’s place value counters. They’re awesome. (Although I’d like to be able to save an example for later use). I then use loads of randomly generated questions. Usually I’m a fan of writing my own questions, but randomly generated addition and subtractions, especially if you put them in a crossnumber are where it’s at.
What I like talking about, though is efficient calculations. I’ve extracted them and made them into their own lesson here. I really believe in talking about this stuff. My year 7s will sit for ages and work out a calculation left to right without even thinking about number bonds.
We’re sometimes so tied to hitting examable objectives that we forget this stuff can be really powerful. My ideal year 7 scheme of work would move away from these skills and move onto covering things a bit more nebulous like ‘Tricks’ or ‘Diagrams’ (drawing bar models etc) so by the time we’re in year 8, we are all efficient and able calculators. I’d also add loads of binary and bases stuff. I don’t really care that it’s not in the GCSE. Stuff can be valuable without being a examined skill in the GCSE.
Probably the last resource I will do on vectors, because I’m not sure how much more value I have to add on this topic. I think a lot of it just comes down to practice.
There’s only 4 slides here. A little exercise about identifying when vectors are parallel, which I haven’t done enough of before
Then there’s an example (but no ‘your turn’ as the differences between questions are simply too extreme to make the comparison worth it) and some exam questions that I took off exam wizard.
It’s a bit lightweight, but I found isolating the skill pretty tricky.
If you do this in an awesome way, please tweet me @ticktockmaths.
Ok, so I found a bit of time today and put this together.
It’s very basic, but covers finding ‘routes’ using vector geometry. It also covers midpoints.
There’s not enough practise here, but that was deliberate. I would set them key skill K652/K653 on Dr Frost Maths to reinforce this skill. Those randomly generated questions are much better for loads of practise than my slides will be.
There’s no parallel line chat, nor co linear chat in this PowerPoint. I’m saving both those skills for the next PowerPoints I make. I’m trying to split the skills up as much as possible.
As always, comments and suggestions and stuff to @ticktockmaths on Twitter.
There’s two nice tasks here, and some presentation that I’m proud of.
For instance, I tried to build up the difficulty here pretty gradually. There’s also room for discussion on the magnitude of vertical and horizontal lines.
Moving to the skill we really want
I thought this was a clever way to combine two things I like. Code breaking exercises like this one and also questions where we do two different calculations, but get the same answer.
It all comes with example problem pairs and a nice plenary.
I probably won’t upload a PowerPoint for more than a week as
I have half term starting Thursday
The next resource on my list is vector geometry and I think that’s going to a massive amount of work. I’ll have to think how I can break it down into nice chunks. Otherwise the PowerPoint will be 700 slides long.
