Well, that was unexpected! I won’t go over the same things you’ve no doubt read many times already but I will say that I hope you and your loved ones are safe and well.

We are starting to find out about how GCSEs and A levels are going to be handled but I still have a number of unanswered questions about Core Maths qualifications.

In this post, I want to collate those questions and provide answers where/when I can find them. I will only use reliable sources (ie Ofqual, DfE, Exam boards) and will avoid speculation. If you have your own questions, please post them in the comments or tweet them to me. If you have links to answers to any of these, please let me know as well.

#### Are Core Maths exams going ahead?

No. From the Ofqual press release: (emphasis is mine).

This year’s summer exam series, including A levels, GCSEs

and other qualifications, and all primary assessments, have been cancelled as we fight to stop the spread of coronavirus.

#### Will Core Maths students get a grade?

That isn’t 100% clear but the answer seems to be “yes”. From the Ofqual press release: (emphasis is mine).

This means ensuring GCSE, A and

AS level students are awarded a gradewhich fairly reflects the work that they have put in.

I note that Core Maths is not, technically an AS level. It may well be phrased like this as a simplification.

There is a very wide range of different vocational and technical qualifications as well as other academic qualifications for which students were expecting to sit exams this summer. These are offered by a large number of awarding organisations, and have differing assessment approaches – in many cases students will already have completed modules or non-exam assessment which could provide

evidence to award a grade. We are encouraging these organisations to show the maximum possible flexibility and pragmatism to ensure students are not disadvantaged. Ofqual is working urgently with the sector to explore options and we will work with them to provide more details shortly.

This is the part that makes me think they will be given a grade.

#### Core Maths is taken in year 12 at my establishment. Will they get a grade?

That isn’t entirely clear but the answer seems to be “yes” based on the things above.

#### Will year 12 Core Maths student be able to take the exam next year?

Still not entirely clear but seems to be a “yes”.

In addition, if they do not feel their calculated grade reflects their performance, they will have the opportunity to sit an exam at the earliest reasonable opportunity, once schools are open again. Students will also have the option to sit their exams in summer 2021.

At the very least, I can’t see any reason why current year 12 students would not be able to take the qualification in the Summer 2021 series.

#### If there are additional opportunities to take the exam (early next academic year) will they use the same preliminary material?

There’s no information on this yet.

#### My students take Core Maths in year 12. Should they be continuing to try and study the course from home?

There’s no real way to answer that. You’ll have to be guided by your establishment.

Once again, if you have your own questions or answers I can add to this please let me know.

I’ll finish with a kind of Core Maths question. “How much more water is being used per day now that people are washing their hands properly?”

Today sees the release of the final episode of the podcast I’ve been recording with Colin for 7 years.

You can listen to it here

We’ve talked about a lot of maths over the years and had special guest co hosts that try to represent people from a broader demographic than Colin and I. It’s a good time to point out that Colin did the vast, vast bulk the co host finding work here and I’m grateful for that.

If you didn’t know I recorded a podcast, you might like to check out the back episodes.

We started the podcast to fill a gap in the maths podcasting world and there are now, fortunately, a number of other options available. Colin and I still like each other and haven’t ruled out working together in the future but it was time for this podcast to come to its end.

I have got loose plans for a new podcast with more of a focus on maths education. Given where we are in the world now, I don’t think it’ll happen any time soon but I’m sure I’ll mention it here when it does.

Thank you to all of the listeners and anyone who has contributed with suggestions for items to discuss. Thanks also to the (approximately) 40 special guest co hosts – it has been wonderful to be able to talk maths with such a great bunch of people.

Finally, thanks to Colin for all he’s done and for being willing to talk to me every month. If you weren’t aware, Colin writes books and they are actually good. Available in all good book stores, some less good book stores and probably your local library too.

*So, this has been episodes 1 to n of Wrong, but Useful. I’m @reflectivemaths, that’s Dave in real life. Cheerio!*

*(Now, how do we get into pretending this didn’t happen?)*

Here’s a slightly different approach to asking an estimation question and I’m using it with my year 11s going into year 12 next week.

It occurred to me that while getting an average/estimated result for something is certainly useful, there may well be times when knowing what reasonable boundaries are. There’s probably a loose link here to the idea of confidence intervals too.

Bonus points if you can work out what Len’s accent is!

If you’re anything like me, you’ll have a lot of people tell you that things are very weird at the moment. There’s no denying this at all and one of the aspects a number of teachers are trying to deal with is that of helping get students ready for the beginning of their courses in year 12. In this post I’ll outline what my school has done and then be more specific about the Core Maths tasks.

### Whole school approach

I’m really pleased with the way my school has handled the transition work. We already had our applications in for 6th form so, students have been put into classes on SIMS based on their options. We have been able to include external candidates as guest students so they are not missing out. The classes appear on the relevant teachers’ timetable in a new “lesson 6” slot. (We have 5 lessons a day and are *not* moving to 6, this is just a temporary thing.)

Each subject is responsible for setting appropriate work to help them bridge the gap between year 11, especially finishing early, and the start of year 12.

**Core maths**

There are 5 weeks in this term so I’m setting five chunks of work with the help of the KS5 coordinator, Elliot. We are looking to strike a balance between introducing some new aspects and brushing up on some of the most important fundamentals.

We are using Google Classrooms so all of the tasks are set and handed in on there with all of the students being in one single class for the sake of this.

**Introduction**

I recorded a short audio for them to listen to. I can’t upload it here but if you want to hear it, get in touch and I’ll see if I can send it to you. (It’s only 1 minute long and basically says “Welcome. Tell me why you chose Core Maths.”)

**Week 1 – Estimation**

*Task 1* – Mental arithmetic warm up. Complete the 30 seconds challenge (like these ones here) and type the answers into a google forms quiz.

*Task 2* – Read the extracts of Rob Eastaway’s book *Maths on the Back of an Envelope*. Then leave a comment giving an example of when estimating might be useful.

*Task 3* – “What is the total value of all the boxed Easter Eggs sold in England this year?” Answer this and submit a picture of their working. I told them not to just google the answer but it was ok to google something like “What’s the population of England?” I’m marking this and giving them (very positive) feedback.

*Task 4* – Optional extra. Looking ahead to next week. Percentages revision.

**Week 2 – Percentages practice**

Look at these two examples of percentages being used in the news (here and here).

“Their report ‘Parenting Generation Game,’ says 81 percent of under-18s in the UK regularly play online games, but only 58 percent of parents have tried it for themselves.”

- Does that 81% value fit with what you’d expect?
- Give an example of why writing ‘online games’ is not very clear

Forty-nine percent of male parents agreed that gaming was a valid form of quality time with their child, while only 39 percent of female parents felt the same way.

- In your view, is 49% much different to 39% in this context?

From the jobs article:

The overall results show they are three times more likely to want to be a YouTuber (29%) than an Astronaut (11%)

- Is it acceptable to say that 29% is “three times more” than 11% ?

After this, I’ll put some percentage revision questions (these ones) into a google quiz for them to answer.

**Week 3 – Critical analysis with QUIBANS**

Two fairly short tasks based heavily on Mark Dawes‘ QUIBANS blog posts:

I’ll probably simplify these a little and give my students a bit more structure as I’m not there to talk them through.

**Week 4 – Budgeting**

Some questions taken from this article about ‘money maths’.

I’d like to put a simple budgeting task in here. It’ll be something like getting them to think about what monthly expenditures they’ll probably have to think about when they’re adults, then trying to figure out the general price of some of them. Finally, how much does that come to in a year.

**Week 5 – The Power of Data**

Search for a news website and tell me the name of the first type of graph you see. (Data representations are used all the time.)

Watch Hans Rosling’s amazing video 200 years in 4 minutes.

- What have you learnt about the world that you didn’t know before? (Not a Core Maths Question as such but still.)
- Describe one way in which having the graphs makes it better than a table of values.

Then, two options to do with histograms (I haven’t found these resources yet):

- A simple intro to histograms for those that haven’t done them before,
- A more advanced question for students that have seen them before.

These aren’t set in stone, especially the later ones so if you have any good ideas, I’d like to hear them.

I hope these plans are of use to you and if there are any you particularly like, let me know!

Nice and simple fact-checking task this one. You can see in the image that Royal Mail claim to deliver 16 billion items every year. Does that sound believable?

Here are some prompts if needed:

- Is this just household post or business too?
- Letters
**and**parcels? - Are they counting ones delivered abroad?
- How many letters does a school send in a year?
- How many Christmas cards does your house get?
- Are the ones to Santa ‘delivered’?

- Extension -how much money would they take in postage?

It’s that time of year again when AQA Core Maths teachers get hold of the preliminary material on which some of the exam questions (roughly 25% in recent years) will be based. There is the following warning on the front:

This Preliminary Material is to be seen by teachers and candidatesonly, for use during preparation for the examination on Wednesday 13 May 2020. Itcannotbe used by anyone else for any other purpose, other than as stated in the instructions issued, until after the examination date has passed.

It mustnotbe provided to third parties.

It’s a pretty strong warning but, last year, I phoned AQA and asked about this. They were very helpful and after the conversation, sent me this clarifying email:

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.

*******************************************

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.

*******************************************

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.