Inspired by a recent More or Less article on coffee pod consumption, I thought I’d use it as a basis for some coffee-based revision questions. I’ve managed to get the following topics in:
- Critical analysis
- Estimation/Fact checking
- Correlation coefficient
- Normal distribution
- Confidence intervals
- Percentages
When I make resources from now on, I’m going to try to put together at least some sort of answers. This resource includes answers so you don’t even have to work them out yourself (although I’m sure you would have enjoyed doing that!)
I’m pretty pleased with the questions and it took a long while to find the information to put it together so I hope you find it useful.
Both versions below are the same with the ppt option for if you’d like to adapt it at all.
Recently, my students have been talking about Snapchat and their snap scores. Snap score is a unique metric in Snapchat that measures a user’s activity and popularity on the platform. It’s a numerical representation of someone’s engagement on the app and is displayed for them on their profile. The score is updated frequently and is it possible to see the Snap Scores of your friends. Snap Score is calculated based on the number of snaps sent and received, stories posted and other factors such as adding friends and using filters. The exact calculation method is unknown and deliberately kept secret by Snapchat, but it’s clear that the more a user interacts with the app, the higher their Snap Score will be.
In my class, the scores range from 8000 to over 1 million. I really wanted to make a resource based on this but, sadly, couldn’t find enough useful information. I can find a list of the users that have the highest Snap Scores but very little else of use.
With that, I turned to another major social media site for year 12s – Instagram. For this site, I was able to find the top users (by number of followers) and also some other interesting data. I’ve put it together into a revision page that covers:
- Critical analysis
- Correlation
- Regression
Here there are, complete with an answer page:
Hopefully it’ll be of use to you. If you can find out any more about Snap Scores, I’d be interested in hearing about it.
I know I’ve been a bit quiet on this blog recently. That’s mostly because I’ve been focussing my energy into the approximately-fortnightly newsletter I’ve been writing. If you want to check that out, please do click on this link and then confirm it in your email.
As part of our planning for year 11s’ futures, we hold a Sixth Form open evening and also have what we call Be a Sixth Former for a Day. On this day, year12 and 13 are not in school, year 11s don’t have normal lessons and years 7 to 10 have an alternative timetable. Year 11s pick A level sessions they’d like to trial and they can also choose Core Maths as a taster option. Now, typically, we don’t get many choosing Core Maths on that day as they are sensibly choosing to priortise finding out about the A level courses/options. I thought you might like to see what I did with the students.
Having thought about it quite a bit, I decided that the most ‘catchy’ bits of Core Maths are probably the estimation, critical analysis and financial aspects. I like statistics but this isn’t the place to be giving them a tast of Confidence Intervals.
With that in mind, I chose 8 short tasks and for each session I had, I asked them to pick the picture that appealed most. I said something like, “Which picture makes you think, ‘I wonder what that’s about?’?” Once they’d picked we played with the idea for as long as felt right and then, if there was time, picked another. The presentation is below for you to look at. It’s not incredibly thorough and does rely a little bit on teacher input to channel the conversation. Some of the topics have been discussed in my newsletter, which you should definitely subscribe to if you haven’t already.
In the open evening, we tried something a little different this time. Usually, there are talks in the hall from the Head of Sixth Form and Head Teacher and, other than that, people go around school and talk to the subject specialists. In the maths room, we have A level Maths, Further Maths and Core Maths all in the same place so that we can help people understand the different options.
In addition to that this year, we had more formal talks at alloted times for Core Maths and the EPQ so people could find out about it that way. I ran the Core Maths ones and this is what I did:
While people were waiting, I had the mortgage question displayed as I think it’s a particularly good hook at this point in time. I gave people a piece of A4 paper with A, B, C and D printed on in each quarter with the view that they could fold it up to show me an answer to my questions that are in the slides below.
It was very positive and there was a real buzz whenever I asked them to think about the multiple choice questions. Again, the slides aren’t very detailed so you’ll have to think about what to say for some of them. Having run the session, I would probably cut out one of the multiple choice questions and maybe also the Coach’s tweet as that didn’t fit in the middle of multiple choice questions.
Hopefully some of this will be useful to you and I’m sure you could adapt some of the these for normal lessons if that’s more use to you.
Just a quick post to flag up a fact I found while researching pumpkins. It might form the basis of some starter questions for your class on Monday.
The Guinness World Record for the heaviest pumpkin is 1226kg.
If you’re told it had a width of 3.56m, can you work out the circumference?
Apparently, the actual circumference was 5.42m. What does this tell you about how close it was to a ‘circle’?
The previous record was 1190.49 kg. What percentage larger was this one?
Pumpkins are fruit. I’m not sure there’s a question here but it might start an argument!
While we’re at it, the record for travelling 100m while paddling a pumpkin, (yes, that’s right) is 2 minutes and 0.3 seconds.
That pumpkin only weigher 272.16kg although I’m not sure if that is before or after carving.
Perhaps you could play “Is paddling a pumpkin 100m faster or slower than…?”
And possible comparisons might be:
- Swimming
- Walking
- A snail
- A tortoise
- A candle burning 100m
- A jellyfish
- An elephant lumbering along casually
- A baby (human) crawling
- A student that desperately needed the loo despite it just being break time making their way back to class
Hopefully there’s something pumpkin themed in there that might be of use!
Newsletter
I’ve been busy working on a newsletter project. I’ve not mentioned it on here before but if getting fortnightly Core Maths themed newsletters (resource letters really) then you can subscribe here. Make sure you click on the follow up email you get.
As a flavour of what’s included, here’s a resource from issue 2:
and a sneak peek into tomorrow’s newsletter features some Hallowe’en themed resources, like a link to this infographic from the fairyLAND trust:
7 weeks into teaching
There are lots of positive things about Core Maths and one of my favourites is being able to look at challenging topics. I enjoy teaching PSHE and that was partly what inspired my sampling resource to focus on the NATSAL study into sexual attitudes. I find that students at this age are pleased to have a topic like this treated seriously and looking at it from a sampling/averages view point is new for them.
You can find my sampling resources here.
Over the half term, I’m hoping to finally get round to overhaulling my finance resources in line with the current tax brackets and how long I think should be spent on APR/AER. I’ll let you know when I do!
Well, it’s September and that time of year when we all try to remember what teaching is and how to talk loud enough that a whole room can hear you.
There aren’t any major changes at my school but we have managed to put on an extra class of Core Maths so that we now have 4 classes. We’re very pleased about this both in terms of the popularity of the course but also the support it’s getting from SLT in terms of timetabling it so more students can benefit.
So, what am I up to this year? Well, I have two main projects I want to work on this year:
Actually sorting out the vast bulk of the scheme of work
I’ve been teaching Core Maths quite a while now and while it has admittedly been interrupted by the pandemic, my resources arenj’t as up together as I’d like them to be. I am really lucky to another teacher working with me for her second round of Core Maths this year and she is really good at saying to me things along the lines of, “Dave, that’s a nice idea but what are we actually going to do with them in the lesson?”. I’m hoping/planning that by the end of this year we will have a pretty much sorted scheme of lessons ready to go. Naturally, they’ll need updating a bit each year but it’s absolutely a place I want to get to.
My Core Maths Newsletter
If you follow me on Twitter, you may have noticed me trying to get people to subscribe to my new newsletter. I’ve tried not to go on about it too much and I’m not (quite) arrogant enough to think that people are checking Twitter just to look for my posts. If you haven’t seen it, the subscription link is here. If you do want to subscribe, you have to then click on the link in your email to confirm it.
The first issue is out on Monday 5th September and I’d really call it a resourceletter but that’s not a word. Hopefully people will like it.
One more thing
I got a great game for my birthday and it has a nice crossover with the Core Maths topics of estimation and fact checking. It’s called Shot in the Dark and should be easy enough to find your own copy of from a games shop. I’m planning on using a selection of the question in class and most of the questions with my tutor group. Here’s one of the cards to give you a flavour:
As always, if you have any comments or thoughts, please do let me know.
In a recent post, I shared some general reflections on teaching Core Maths having been to a conference. I promised two more posts, one about estimation and this final one on critical analysis.
Intro
In my experience the two aspects of teaching core maths that I found the most difficult are the financial topics and getting my head around how to teach critical analysis. This session was led by Mark Dawes and provided another opportunity to reflect on my approaches to teaching core maths.
Why do I teach maths?
Mark started by asking us to think about what were the main reasons that we got into teaching maths. He mentioned that for a lot of people is the beauty behind the maths and some of those particular moments of understanding that come from having difficult concepts explained well. Certainly one of my favourite teaching points is in index notation when you get to the concept of a value to the power of zero. There’s something about that particular point that is an explicit transition from the concrete multiplying of a base together multiple times and pushing it to the “What if we think about this?” leading to an answer that jars slightly with your initial interpretation of the concept but also makes perfect sense.
Having said that, I wouldn’t really claim to be a huge fan of the pure aspects of maths. I can certainly see the beauty in much of it and would like many students to share that but it would be hard to argue that that is the way most students feel after they complete 11 years of education. A significant part of teaching for me is to help people get better at a vital tool that they can actually use in their day-to-day lives. I really do see Core Maths as being the epitome of this aspect of maths teaching with every topic either directly relevant to other subjects or just a pragmatic approach to things that will crop up in students’ lives. Even before teaching Core Maths I tried to incorporate aspects of newspapers where possible and the critical analysis part of this course leans so heavily into allowing students to unpick the information that they are told and all too often just to take as fact.
What is critical analysis?
It occurred to me that I hadn’t really considered what falls under the umbrella of critical analysis. Mark suggested three areas, three of which I would certainly have suggested and the fourth one that I haven’t considered quite so much:
- Criticising/improving graphical displays,
- Check through someone’s calculations,
- Verifiying a claim, based on the available information,
- Picking out the important aspects from an excess of information
The fourth point in particular reminds me of Dan Meyers talk in which he points out that textbooks for physics often give you exactly the numbers you need with no more no less. There is obviously a balance to be struck when students are learning but I do want to incorporate more of this aspect into my critical analysis teaching.
QUIBANS and What the Graph
It’s impossible to have a blog post featuring Mark and not mention QUIBANS. Part of the talk was Mark explaining what makes a suitable QUIBANS post and how he goes about taking a article and turning it into a teaching resource. I regularly make use of these in my lessons and if you haven’t heard of it yet you should definitely go and have a look.
We spent some time considering this graph and what it might show us:
If you want to see more about this one in particular, it is featured in Marks new website What the Graph which is another excellent addition to the critical analysis teaching repertoire.
Conclusion
This is still a difficult topic to teach, especially in the context of passing an examination. However, I think the general skills outlined above are absolutely our strongest line in justifying why maths is considered such an important tool that we insist on everybody learning it until at least 16. Maybe one day, Core Maths will become compulsory for anyone not taken A level maths.
In a recent post, I shared some general reflections on teaching Core Maths having been to a conference. I promised two more posts, one about critical analysis and this one on estimation.
Intro
This session was a mixture of Tom Rainbow and Rob Eastaway reminding us of and introducing us to some estimation questions and tools. Part of this involved grouped discussion about some estimation questions and Cat interviewing Rob about some of the estimation things he’s been asked to do on radio.
Powers of 10
Tom used this opportunity to give us an incredibly short length of time to go with some gut feeling responses to decide “Which of the following answers is most accurate?” It was a reminder of powers of 10 and also the frustration that you can feel when you’re not given enough time to work something out. One example was, “How much money does a single McDonalds take in a year?”
- £2 000
- £20 000
- £200 000
- £2 000 000
I’ve put these straight into my 6th form induction lessons and I’m thinking of extending the idea with once you know which power of 10 it is most likely to be can you narrow down what the starting digit might be?
What makes a good Fermi question?
Rob asked us to think about what makes a good Fermi estimation question and to some extent what makes a good puzzle. He suggested the following features that lend themselves towards a good question:
- Who cares? Is there an obvious reason why somebody might want to know the answer to this question or is it just inherently interesting from a curiosity point of view?
- Not easily “Googleable”. It’s hard to fight against that “what’s the point?” aspect if it’s something that can just be easily found by searching. There are plenty of great questions where we don’t/can’t know the answer.
- Certainly for puzzles (but perhaps less so Fermi estimation questions?) a sense of humour often helps people be interested. Rob has spoken many times about how getting people to laugh makes them more willing to get involved.
- What are the chances..? Rob said the lot of the questions he gets asked to answer on radio are based on how unlikely things are to have happened.
If you’re thinking of writing a Fermi question, it’s a good idea to make sure it ticks at least one of these off!
Chicago piano tuners vs How far will I walk in my lifetime?
We were given some time to compare and contrast the classic Chicago piano tuners question with How far will I walk in my lifetime? I’ve always avoided the piano tuners question even if adapted to a local city as I think it has some issues. Here are some of the things my group thought:
| Pros | Cons | |
| Piano tuners | A good example of how you can get a surprisingly close answer with very little information. | Somewhat skewed by a students’ background and requires them to have some idea of how often a piano might get tuned (which seems fairly middle class). |
| How far will I walk? | This has a fairly easy starting point as students are usually aware of they suggested 10,000 steps a day. Leads nicely into a discussion as to whether people follow guidelines. | Suffers a bit from the “Who cares?” aspect. |
As mentioned, I don’t usually do the piano tuners question but I am now considering it to see how it goes.
I suggested a tweak to the how far I walk question and have just created another variant:
I’m getting fairly old now and I’m not a fan of buying shoes. [Adopt a suitably whiny voice] How many more am I likely to have to endure buying?
I love buying shoes. How many can I justify buying as ‘necessary’ over the rest of my life?
I think this minor tweak to the question introduces an element of humour and seemed to be popular.
The power of ish
Rob has spoken to lots of students/teenagers/parents in lots of different scenarios and finds that a useful way to encourage people to have a guess is by getting them to put ish on the end of their guesses. It is pretty liberating to have guesses and just put ish on the end. It really does get you out of feeling bad about being ‘wrong’!
How many episodes of Coronation Street have their been?
We were given some time to answer this question. I don’t think we get to see people’s attempts at these often enough so you might like to see my answer here:
Turns out that I had underestimated as it’s been going longer than I thought (that’s the arrow point to the 40) and it used to be on 6 times a week! I’ve covered myself by putting the ish on the end though.
While I think this might be a struggle for teenagers (do any of them watch soap operas?), a nice added bonus to this particular question is that you can see celebrities having a go at it in the following clip:
I think there is probably something valuable in this but I’m not sure how to incorporate more of it into lessons at the moment.
Conclusion
Fermi estimation is still one of my favourite aspects of core maths and it’s my go to topic for engaging students when trying to get them to apply for the course. It was good to be reminded of some of the basic tools such as powers of 10 and also get to have the concept of ish to put into my lessons.
Another great session!
Recently, I had the pleasure of attending the first face to face Core Maths Conference for quite some time. It was in Birmingham, in a nice location and it was really delightful to actually meet a lot of people I only know because I’ve seen them in a Zoom window. As one of the 10 AMSP Core Maths Advocates (a role that is being developed as we speak) I did play a small part in delivering one session and you can read about that briefly here.
This site was originally called “The Reflective Maths Teacher” blog but that was too many characters for a twitter handle so it got shortened. However, the main point was that I do like to think about my teaching and resources and this conference really did give me a lot to think about and reflect on. I’ve decided it would be best to split it into multiple parts following the main themes of the sessions: Overview, Estimation and Critical Analysis. In this overview post, I’ll reflect on some big picture aspects of Core Maths. Bear in mind that I teach the AQA 2A course when you’re reading this.
How different Core Maths is to other maths teaching
It’s very hard to put my finger on it but there’s something different about the approach to teaching Core Maths and the reception it gets from students. Maybe it’s to do with absolute lack of “When am I ever going to use this?” or the feeling that there’s less of an emphasise on “Follow these methods and get to the correct answer” (even though there definitely is some of that). At no other point in my teaching career have I had so many opportunities to think, “That would make a great Core Maths topic” or “I could use that in class” because although we know that maths is relevant at all stages, it never seems to quite fit into a GCSE or KS3 class quite so well. I don’t think that in my teacher training, I would have ever really thought that I’d be browsing news websites for the starting points for maths lessons but that is a regular occurence now.
The support from AMSP and the Core Math community
I know there are a lot of supportive teacher groups out there and I feel that the Core Maths one has the advantage of being a more select group than just “all maths teachers”. I also think that the nature of the Core Maths course and the fact that it’s often only delivered by one or two people in a school means they are more inclined to find ways of reaching out. Twitter has been great for me to find Core Maths teachers and they are often incredibly helpful. The AMSP events and resources are excellent and I’m constantly astonished that they are effectively free. I don’t want to name members of the community (mostly for fear of missing some out) but Cat and Tom are exceptional in being helpful, encouraging and inspirational. Thanks!
My resources and the thanks I got
On a related note, it was truly lovely and humbling to hear so many people thank me for the resources I’ve shared. There was more than one occasion where I was referred to as “a life saver” and whilst I can hardly claim Craig Barton, Jo Morgan or Colin Hegarty status, it was nice to be met with, “Oh, you’re Dave Gale”. I know this section is egotistical but if you meet someone who’s made something you’ve used, please do thank them!
Differences between Core Maths courses
A bit of a gripe. I do love Core Maths. I really like the philosophy and principles behind the courses. I do not like the pretty massive variations between the major exam boards approach to it. It’s probably true to say that each variant has its merits but the confusion this causes isn’t justified. I think some degree of choice is a good thing but currently it’s too much and makes resourcing and promoting the broader course difficult. The wildly different amounts of time allocated from school to school doesn’t help either.
How good Core Maths is for teachers (like me)
Over my career, I’ve been a Head of Year, Advanced Skills Teacher, Senior Leader of Education and, obviously, a maths teacher. After about 16 years, I was beginning to wonder if I would stay in teaching much longer. I was finding A level teaching to be pretty good but very narrow and I (still) think that GCSE teaching has some major flaws in what it’s trying to achieve. It is definitely the case that starting to get involved in Core Maths (I proof read a textbook) and then teaching it truly revitalised my interest in teaching. Learning some new things like finance and estimation while reframing statistics to be more about the doing and interpreting (as it should be) rather than the “How can we make this as much like pure maths as possible?” approach that A level seems to take was, and is, revitalising. I’ve been teaching Core Maths quite a few years and the fact that it can be constantly refreshed with new contexts and news stories means that I really don’t see myself getting bored of it any time soon.
Imposter syndrome
The finance material is hard and overwhelming. I’ve literally never thought about APR before.
How do you teach estimation skills when there isn’t even a right answer anyway?
What does it mean to criticise an argument in maths? Does that mean they expect actual sentences?
Preliminary material? It’s paragraphs of writing – what am I supposed to do with that?
If you’ve taught Core Maths (or are about to) then you’ve probably had some of these thoughts. The feeling of being out of your depth as a qualified maths teacher when teaching a maths course is not something that we’re used to. It might be true for some aspects of A level and Further Maths but it’s not generally the case for years 7 to 11.
It’s pretty scary.
Finance took me a long time to get comfortable with. You might not be there yet, but Income Tax and National Insurance are just examples of applied percentages. APR and AER are basically algebraic fractions and they’re not a major part of the course. Google stuff you don’t know and ask on Twitter or this blog.
Estimation is fun. Embrace the not knowing the answer aspect. Students are fine with it most of the time and understand that we can’t be sure of the ‘correct’ answer. Even with that, they still see the relevance and importance of estimations skills.
Critical analysis is, in my view, one of the most useful aspects of maths. If you’re a mathematician, you naturally have this skill. If you’ve received an email about sports day and thought, “They don’t seem to have considered this,” then you definitely have this skill. Just find a terribly drawn graph and openly mock it in front of your class. That’s a start. Make up some fake statistics and see if you can get them to believe it (the “You swallow 8 spiders in your sleep” one is a great example of how people just believe things blindly). Yes, sentences are important. Good communication is important. Being a human calculator is not the point of being a mathematician. Communicating your findings and results coherently with your target audience in mind is a valuable skill.
The preliminary material is still a bit scary. This is the best time to lean on the support I mentioned above. Get in touch with an AMSP rep and they’ll point you towards some discussion groups.
You will be fine at teaching this and there’s a good chance it will be the highlight of your teaching week.
I’d love to hear your thoughts. Check back soon for my reflections on Estimation and Critical Analysis.
As part of the AMSP’s Core Maths Summer Conference, I’m presenting a small slot on the financial aspects of the course. This blog post is just to support that session but may well be useful for others too.
The expensive brownie
£10 for Pensioners
£1 000 000
Would one million pounds be enough money for someone to retire at the age of 50?
Car vs Moped
Get students to compare the cost of buying and running a car versus a moped.
APR and AER
A reminder that these are not big parts of the course.
There are several Core maths videos I’ve made in this playlist here.
Buying a House
Using Rightmove, Compare the Market and a Mortgage calculator website, what sort of job might you need to afford the house you want?
National Insurance and Tax
Could be an interesting year as the tax bands are the same as last year for Income Tax but the National Insurance bands are different and also change part way through the year!
An older blog post about this.
This Income Tax video will still work.
This National Insurance video has the right concepts but the numbers will change.
What interesting questions could be asked in the exam (or class) based on this?
Hopefully that’s enough ideas to inspire you. Feel free to follow this blog to stay updated and I’d welcome any comments.
reflectivemaths's Blog 