This post continues from my previous thoughts about the Core Maths mock my students did recently. You can read the previous thinking here.

**7 Estimate vs Estimate**

Some of my students got a bit confused with what it means to estimate a mean and standard deviation from a table of results. I think that they well have been fine had this been in the year 11 course but some of them were getting muddled with the Fermi type of estimating and were doing all sorts of rounding and stating their assumptions. I think I can fix this by just telling them the difference and making sure I’ve explained why it’s only an estimation for the mean from the table.

__8 Working out ‘per year’__

When (Fermi) estimating something over a year, several students were working it out for one day and then ×7 ×4 ×12. This isn’t disastrous and the mark-scheme did allow for that but it is quite an underestimate for the number of days in a year. I’ll remind them to just ×365.

__9 Comparing Data__

This seems to go badly considering how ‘formulaic’ I think it is.

“State which average is higher. Tell me what that means. State which spread is higher. Tell what that means (use consistent or varied).”

I remember this going less well than I expected last year as well so I think I’ll need to incorporate more practise opportunities and probably more examples next year. I also need to do something to stop them comparing things like the Upper Quartile for no reason.

**10 PMCC**

This is something that went well. The students could almost always calculate PMCC on the calculators. Hurrah.

When comparing PMCCs, they were pretty good except for a couple of cases where the phrasing, “0.96 shows a there is a more positive correlation than the 0.84”. That doesn’t make sense but at least they have the right general idea.

__11 Convenience vs opportunity__

This is just a question that I could do with finding out the answer to (do you know? please tell me!)

When a question is expecting the answer “This is convenience sampling”, is calling it opportunistic sampling acceptable? I believe the two are interchangeable and opportunistic seems to be the phrasing used in psychology so I’d like it to be accepted really.

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There we go. Mixed results and generally in a similar place to where I was with the students last year. I’ve still got Normal Distribution and Confidence Intervals to go so I’m a little behind where I’d got to by this time last year. I think I’ll be alright but there are only 10 school weeks left until the exams are over!

We’re planning on giving them another mock, based on last year’s paper but with some questions related to this year’s preliminary material added in. If you’re not signed up for the AMSP’s Core Maths preliminary material webinar then you probably should. I was at it last time and it was really helpful.

My students took their mock exams in January and I’ve now got some time to write up some findings. Hopefully there may be something of use for you in here but it’s at least partly just to clarify my own thinking, plan some next steps and also have a reference for planning next year.

(There are quite a few points so this will be a two part blog post.)

**1 Percentages**

This gets flagged up by AQA as an area that students are not always very good at. I can certainly vouch for that as my students were thrown by the use of a percentage within a context. I am confident that all of my students would be able to 55% of 3.8 if that’s explicitly what they were asked to do but, given that that wasn’t the case, this didn’t always happen.

A number of students worked out how many bases could be made from one lorry-load and didn’t use all the ‘left-overs’. I’m not exactly sure how to teach this and I do wonder if it’s actually valid to assume that the left over bits can’t be combined (are the lorries all arriving at the same time? Can the spare concrete be kept appropriately overnight?)

**2 Sampling methods**

Responses to this varied massively. Some students got it but they were in the minority. For some reason, the idea that samples must be balanced has been badly misinterpreted to allow answers like:

“No, because then there won’t be the same amount of girls and boys included.”

“Yes. This means there will be an equal number of boys and girls in the sample.”

Both of these show worrying misconceptions about how stratified sampling works and it makes me think that my coverage of this needs to be more explicit. I need to create a resource that focuses specifically on the positives and negatives of each type of sampling.

I think this is a tricky question (and it caught me out first time I saw it). Some of my students did include caveats to explain what happens with duplicated numbers so I must have at least mentioned that well enough.

**3 Estimating capacity**

I think that estimating a capacity is very hard. Students’ estimates for this ranged from 0.3 litres to 35 litres although the vast majority were either 1 or 2 litres.

It’s fair to say that most of the students simply don’t know how a toilet works and have never had to think about it. It may be obvious to you that thinking about the size of the cistern gives you a good guide but I can promise you that students do not know that (and I think it is totally reasonable that they don’t – for example, can you explain how a fridge or a central heating boiler works?)

I’m not totally sure how to increase their experience of estimating capacity but if I have time, that would be well worth doing.

**4 Calculator usage**

Some students are finding the mean of a sample by adding all the numbers up and then dividing by n. Fair enough I suppose but, they then go on to type all the numbers in to the calculator function to find the standard deviation. Madness. I’ll have a word with them.

**5 Utter nonsense**

This mock made use of the food and drink cans question from a couple of years ago. (It a nuisance to mark!) The vast majority of students had a decent go at it and were able to get somewhere close to a reasonable method. I was struck by some of the complete and utter nonsense that was being done. For example, one student worked out the number of litres of soup that would be produced in a week and multiplied this by the area of one steel sheet. I have no idea what they were thinking (or how those units could be interpreted) but I assume this was a bit of an “I don’t know what I’m doing but I’ll try something” so, I think I should be grateful that they didn’t just leave it blank.

**6 Area units conversion**

As part of the same question, it was very clear that converting from cm² to m² is not well understood. This isn’t a massive surprise but I think I can do something to encourage students to make sure all their units match up before they start.

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That will do for now. More reflections to come soon.

Have you been experiencing similar issues with your students?

My students have a mock exam this week so we’ve spent some time revising. There were a few questions that came up that I wasn’t really expecting and I wondered if these are the sorts of things that come up in other core maths classes too. I’ve added my thoughts and/or answers as appropriate.

*How do I do XYZ on my calculator?*

My (internal) response is “How can you not know that!?!?”. Obviously, I show them again but I don’t really know how to make it stick. I have made some calculator drill resources (find them here) which is designed just to help with learning what buttons to press but I can’t help but think this is really down to the student to learn!

*What’s r again?*

This one again falls into the “how don’t you know that?” category but I’m beginning to wonder if there actually is a lot of new vocabulary and facts to learn. The very same students will then later ask me, “what’s the product moment correlation coefficient again?” even after I’ve told them that r is the correlation coefficient. This obviously suggests that it didn’t stick in their head the first time (and they haven’t revised independently). I’ll need to do something about planning for revision for the real exams.

*When you’re numbering the list of data for a random sample, do you number across or down?*

That’s quite a nice question and while to us, it’s probably obvious that it doesn’t matter, it’s good to reminded not to take these things for granted. I asked the student if they thought it would matter and they said “no” after thinking for a moment but I wonder if the fact that I asked that question implied that it didn’t.

*If I just wave my hand over the page and stab downwards, how is that not random?*

Quite hard to clearly argue this one but I went with the fact that you tend to stab near the middle of the grid (they annoying hadn’t though). I also pointed out that if you knew you’d stabbed near the top left, you’d probably avoid that again too much which isn’t random. I’m not sure how convinced they were.

*How do I know when to use frequency density and when to use cumulative freq?*

Well, cumulative frequency is for cumulative frequency diagrams. You’ll just have to learn that histograms are the one that use frequency density – nothing else does!

*What’s the correlation coefficient again?*

ARRRRRGH.

Next week is our year 12 mock exam week and I think it’s important the Core Maths has a slot in there. We’ve decided to use the Papers from 2018 with some questions swapped out if we haven’t covered the topic yet. We’ve also mixed the two papers together so that students are only sitting one paper at this time.

We are using some preliminary material (given out this week) which I will spend some time on in class but nowhere near as long as we will with the real one.

This approach to a mock is very similar to what we did last year so I’m hoping that I might be able to make some comparisons between the year groups too.

“Welcome back to term 3” is what’s written on the first slide in my power points for year 11 this term. This is the next slide:

We had an INSET day today and some of that time was given over to joint planning. I recommend this thoroughly as I find that I get much better lessons planned and a sense of sharing the workload that I always imagined happened in teaching. I spent some time with Elliot working out our approach for foundation tier year 11s this term and the overview of a ‘normal’ lesson is in the slide shown above.

We’re going to start with a clear routine of come in, get your Starter booklet out of the box and work on that in silence. These are Corbett Maths 5-a-day sheets that have been printed into booklets (which is easy to do as you can download a month at a time). We’ve gone for the Numeracy and Foundation options as I’ve found the Foundation Plus ones to be a bit challenging without some help and that is not my aim for the starter.

When looking for which topics to focus on, I found this TES resource which makes use of looking at which topics come up most often. I like the idea of telling students that the revision we’re doing now is linked to the most common topics and means that I’m not just choosing the ones I *think* it makes sense to revise. We decided to pick the top 9 topics to focus on this term but we’re skipping Questionnaires as it’s not in the course any more.

The main part of the lesson is going to try to use Variation Theory resources where possible as we’ve both found this to be useful for helping the class concentrate. The questions that form the intelligent practise are also seemingly straight forward but with some carefully considered twists thrown in. This is followed by some exam questions, usually taken from the Maths Genie GCSE revision resource page but we’ll go elsewhere if needed.

The section about rewards is just to prompt us into making sure that students that work hard get recognised for this. It’s a push in our faculty at the moment to be more consistent as currently, the teacher that has given out the most this year is at about 1800 while the one who’s given out least is at 150. We need to make this less variable!

We’re going to use this lesson format until the 9 topics have been covered with the intention being that that should be one lesson each (it’s *revision*, not completely new material!). Once we’re through that, the remainder of the term is those topics mixed up and with roughly 3 topics covered in questions per lesson. We want the students to be able to switch from one topic to another and recall their previous learning. Towards the end of the term, the lessons may well have all 9 topics with students switching fluidly from one to another (or so the dream goes…)

Two other things are:

- One lesson per fortnight is an exam questions lesson featuring other topics. We’ll use a “walking talking” approach here if that fits.
- We have one lesson that is in the afternoon. That lesson will have a slightly different structure:
- Starter
- Many questions – a sheet with a LOT of straight forward questions on with clear targets of how many need completing for a reward or 2.
- Bingo – Using the Maths Box bingo sheets (subscription needed) as we’ve both found that our students respond well to these.

I’ve been wanting to have a more structured approach to my year 11 revision for some time now and hopefully this is a good starting place. I’ll let you know how it goes!

Here’s a really nice Christmas themed activity from Matt, Katie and Zoe at Think Maths.

It takes the idea of the 12 days of Christmas and thinks about the true cost of Christmas with a price index based on buying all of those goods. Their (very comprehensive) set of notes and resources borrows from an idea of the PNC which really does its best to work out the cost of buying all the 12 gifts and has done for the past 36 years! You can see their work on this here.

In my class, I’ll use the Think Maths basic spreadsheet and get students to try and find the prices for each of the items. Then, we’ll use XPI (Christmas Price Index) as a way into the financial math we’re going to look at in January..

I think it’s going to be fun!

It’s worth checking out the other Think Maths Christmas resources too!

Snowflake or Snow-fake? – I’m doing this with my year 12 A level class

I still find the graphical aspects of Core Maths difficult to teach well – mainly because I can’t think of good uses for thing like histograms. I can’t say that I’ve cracked it but I think there’s some interest in the ages of prime ministers when they were appointed.

Here’s the data set: Prime Minister data for histograms

Here’s another resource (not mine) which I like.

If you have anything good for histograms, I’d like to hear from you please!