## Words and numbers

I think this resource is quite good.

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.

## Solving by factorising

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.

## 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.

## Substitution with positive integers

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.

And some questions whose progression makes sense

Sometimes, less is more.

No solving here. Just concentrating on the core skill of factorising. I started with an example and then this

*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

## 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.

## Thinkers!

Final resource of this half term.

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.)

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.

Richard

## Addition and Subtraction of Decimals

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.

## Solving Linear Equations with Fractions

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.

Until next week.

Richard

## Rounding to decimal places

Another rounding lesson.

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.

Until next Friday

Richard

## Rounding to 10, 100 and 1000

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.

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’.

## The Order of Operations

Get the PowerPoint here

Everyone hates the term BIDMAS, right?

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.

Happy Friday

Rich