## Probability words

I know, it’s strange that I’ve left this one until last. I did the silly thing of assuming that since I taught a high ability year 7 group, that they’d be ace at this, but they weren’t, which I caught during a quiz during a plenary.

I’d made the classic mistake of assuming prior knowledge.

As an addendum, I hate stuff like ‘the chance of it being Sunday tomorrow’ because I feel like that’s not really a probability statement.

## Adding and subtracting algebraic fractions

Two lessons (at least).

Includes quite simple ones…

Has a task that worked really well with my class. Write the missing step. Cognitive load and that.

Plus some questions.

Goes onto more complicated examples and exercises.

As an aside, I posted a picture from this resource on Twitter and it got (at the time of reading) close to 200 likes and I ended up picking up about 50 new followers.

Which I don’t quite get. Normally my stuff gets 0-20 likes despite being pretty similar. I don’t understand social media at all.

## Sample space diagrams

Obviously includes the ‘horse race’ game. I did it a bit differently this year. I gave out dice to everyone and a sheet to everyone. I then collated all the results so we could see exactly how many had 7 as their ‘winner’. It worked really well. Especially with a bit of ‘acting’ to sell the idea that the result was interesting and surprising.

## Experimental Probability

Wrote some questions including some moving between relative frequency and frequency.

Discussion. Also a task I’m not sure if I like.

I’ve included this at the end. I have run this task a few times and been dissatisfied every time.

In my head, I imagine students trying to make the die loaded by weighting it, rolling it lots of times to test the relative frequency to see if they have got close, then refining the weight inside their cube. There’s a few reasons I think it’s never gone as well as I would have wished.

1. It’s quite fiddly to make the net, put a weight in it, fold it up, take out the weight and fold it up again.
2. It’s harder than it looks!
3. What MATHEMATICALLY are students thinking about when they’re doing this task? Are they just adjusting weights. I don’t really know if the focus of the task is the MATHEMATICS.

I’ve left it in here (at the end), though, because it’s the first task I ever thought up (in my PGCSE year) and one day I want to run it and make it work.

One day.

PS: These are a game changer in terms of noise! Every school should have a set.

## Single event probability

I am aware I’m kind of uploading a rag-tag bunch of random resources at the moment.

I’m making lessons for what I’m teaching and uploading the ones I feel are polished enough to be shared.

Started this one with a bit of a brainwave. I’m always astounded by pupil’s lack of knowledge about simple facts I feel they SHOULD KNOW. Like weeks in a year, cards in a deck etc. But this makes no sense. How can I be ALWAYS surprised? Surely by now I’ve internalised it that this is just something a lot of kids don’t know! So rather than get grumpy, I added a little bit of a check at the beginning of this lesson.

Something I’ve been working on for a while. Making this explicit.

Rest of the lesson is pretty standard. Although pretty.

## Updated resource: Percentage change

I’ve changed this one quite a bit. I would love to hear other people’s take on this. I fear I’m made some kind of pedagogical mistake here in the sequencing of what I’m doing.

I quite like this, though.

## One number as a percentage of another

I’m teaching percentages at the moment and as I do so, I’m updating my slides. I’ll mention what I’ve updated here.

This PowerPoint I’ve split up from ‘percentage change’ and made them two separate lessons.

I’ve added example problem pairs. Instead of trying to do everything at once. I had a real think and there’s 3 skills here.

1. One step – > Simply multiplying or dividing once to get /100
2. Two step -> First finding the factor of 100 and then multiplying or dividing to get /100
3. Having to divide and convert the decimal

I’ve split them up into the four different skills. I also added some whiteboard work so pupils could practice 1 and 2 step, as there wasn’t quite enough fluency bits on these.

I also added some questions like 60/50. It occurs to me that I don’t ask enough of these type of questions, so students don’t become used to seeing things like 125% and often then can’t express these.

Comment appreciated.

## Division of algebraic fractions

I know this is usually covered in multiplying as one lesson, but I think there’s room to slow down.

Example problem pair

A card sort! (kinda). The idea here is that you don’t need to cut the cards out, just project them and ask the kids to copy them down in the right order. Suppose you could print and use a card sort.

Card sorts were in fashion for a bit. So were Tarsias. Then they went out of fashion. I love a Mathsloop.

They are difficult in terms of behaviour and making sure that all children are engaged. I’m really lucky in my current school that the pupils are awesome. Give them a task and they’ll try their best.

I still think there’s value in getting kids to talk to each other about the mathematics. Varied diet and all that.

There’s also another task and an applied problem and a learning check.

## Rearranging formulas and equations

This is a big one! It’s at a minimum 3 lessons, probably 4.

Starts numerically

Next is something I have added after listening to the Mr Barton podcast with Naveen Rizvi. I realised I didn’t spend enough time talking about what the subject means!

Some example problem pairs come next, and two activities. One on making sure that you can put the steps in the right order, one a simple grid of questions (although thought about and grouped properly). There’s also some mini-whiteboard work.

I should have added more questions on using just a single step, I think. Maybe I’ve moved too quickly. This is on my to-think-about list for the next time that update this resources. Of course, comments on this post or to @ticktockmaths on twitter are highly welcome.

Some stuff on using this with scientific formulae.

Moves on to using factorising including an activity and a ‘write the missing line of working’ activity.

Finally, multiplying across, regrouping, and then factorising.

This section is a tad underdeveloped (it does have a learning check, though), but the PowerPoint was getting quite long.