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Fermi type Estimation Problems

A part of the Core Maths course I really like is the section dealing with estimation. Far too often, maths gets bogged down in unnecessary detail or leads students to think that getting an answer is all that matters, regardless of whether that answer makes sense! 

However, it’s not a topic I’ve ever taught before and it very much seems like the sort of thing that lots of varied practice would help with so I set about finding a list of questions. I could find some but not as many as I wanted so I set about collating a list and creating some more. Lots of people on twitter helped contribute ideas too so thanks for that.

Questions like these are included:

fermi questions clipping

It’s a little rough at the moment and I will do some fine tuning later on but, it’s a good starting point. At the time of writing, there are 61 questions and, if you have any more ideas, please let me know so I can add them!

Link to the full list of questions is here.


Some questions about Core Maths decisions

It’s the day before students start back for my school and, in the spirit of preparation, here are some questions I’ve been asked by @CoreMathsCat that relate to ‘setting up’ decisions. I’ll try to answer them here.

Why have you chosen AQA?

Primarily because I was a proof reader for a book called AQA Level 3 Certificate in Mathematical Studies by Hodder and Staughton which was tied to the AQA course.

I also like the fact that there are different options and although I’m starting with 2A (the stats option) this year, I’m excited about the possibility of running different classes as appropriate for different students with maybe those taking Geography and Psychology doing 2A while the Business students can take 2B (featuring critical path and cost benefit analysis).

Are you teaching the course over 1 or 2 years?

1 year.

A big driver here was wanting to make sure that the exam did not happen at the same time as the A level exams at the end of year 13. It has been a good ‘selling’ point and will also be something concrete to put on UCAS application forms.

How many hours per week have you been allocated?


I’m aware this is very tight and I will be making use of homework to help with this. If it is looking to be too short then I’ll talk to the 6th form team and see what we can do additional sessions. I will be upfront with the students and say that they’ll simply have to do additional work.

Are you accepting anyone with at least a 4?


The course is designed for anyone who got a 4 or higher so there’s no reason not to allow those students to take the course. It looks like we will also be having students who got grade 7s as well.

Have you written your own sow or using aqa/other ones?

My head of faculty has a friend who is teaching core maths already so she kindly let me have that as a starting point. I’ve adapted it a little as I really wanted to make sure the course starts with something new (Estimation). The scheme I’m going to start with is this but it’s obviously open to adaptation if needed.

SOW image 1

SOW image 2

Any more questions, please ask!


It would be good if people knew …

If you haven’t picked up on this yet, I’m starting to teach the Core Maths course (AQA) from September. Part of the course is estimation questions like “How much liquid would a small town consume in a month?” and this raises the question “Do people know a reasonable estimate for the population of a town?” (Do you?).

This sparked a thought along the lines of what things it might be helpful to prompt students into finding out just so they feel more confident about answering these questions. What is the population of the UK? How long would a car be? And so on.

Next, I realised that this isn’t really something that would only be useful to Core Maths students and I also thought that other people would come up with good ideas too, so I turned to Twitter. Unsurprisingly, there were plenty of good ideas and here’s my collated list. The ordering is somewhat arbitrary and you may well decide that some aren’t that important for your needs. That’s fine – use it as you wish. Perhaps these could also spark tutor time discussions!

Thank you to everyone who contributed ideas.

Population of the UK
Life expectancy in the UK
Average adult height
Average adult weight
Average UK temperature
How many countries are there?
Weight of an apple
Height of a house
Height of a door
How many people fit on a bus?
What temperature would be gloves and scarves weather?
Diameter of the Earth
How far away is the sun?
Population of a large town
Population of a small town
What temperature would be t-shirt and shorts weather?
Population of the world
Average hours of sleep per night
Weight of a melon
Average car length
Average car width
Width of the UK
Length of the UK
How many primary schools in the UK?
How many secondary schools are in the UK?
How many teenage pregnancies were there last year?
What proportion of the UK are over 65?
Volume of water in a bath
Water used per shower
Days in a year
How many people can a theatre hold?
How far away is the moon?
Average car petrol tank capacity
Average car miles per gallon
Average distance an electric car can go on a full charge.
Average family size
Weeks in a year
How many people are unemployed?
How many people fit on a train?
How much water does a flush use?

Ten pin bowling maths

I went ten pin bowling recently and thought of the following questions:

Fermi – type

How many times does a pin get knocked over in its life time? (This could affect how often they have to be replaced.)

How many pins might you get out of one tree?

How much money would a single alley make in a month?


Roughly what proportion of all balls bowled result in strikes?

If you have the bumpers up, how much does your score increase compared to if you didn’t?

How much do all the bowling balls in a bowling centre weigh in total?

After my first go, how many possible combinations of pins could be left standing?

What’s the maximum possible score?

Core Maths

In September I will be teaching a course that I’ve never taught before and is new to my school. It’s called Core Maths (or actually AQA Certificate Level 3 Mathematical Studies) it looks like a brilliant course and I’m really excited to be leading it.

My school (Churchill Academy) has  a good track record of A level maths numbers and we have an excellent Key Stage 5 coordinator, Elliot. Along with the Head of Maths (Vic), they presented to our leadership team and also talked to various other faculty heads about the course and, as a result, we’re offering it to students from September this year.

The course is aimed at anyone who got a GCSE grade 4 or higher but doesn’t want to take A level maths for whatever reason. I would absolutely say that the A level maths course does a lot of things well but it is very heavily biased towards the pure maths elements whereas what a lot of students would find more useful are the applied and pragmatic aspects. That’s really where Core Maths steps in and, as AQA say:

It helps to develop students’ mathematical skills and thinking and supports courses such as A-level Psychology, Sciences and Geography as well as technical and vocational qualifications.

I think that under plays it somewhat! It certainly does do all those things but also covers:

  • Critical analysis of data
  • Financial maths (mortgages, APR, interest, loans)
  • Estimation skills
  • Correlation and regression

Anyway, to promote it, we had a stand about the course as part of our sixth form open evening and encouraged the other faculties to mention it where appropriate. As a result of this, we have got 50 students signed up to start the course with more on the reserve list. I can tell you from talking to other teachers that this is a huge number of students with most schools/colleges having under 20 in total.

I have the great privilege of being the person that is going to teach both classes. It is quite a lot to take on but my faculty is very supportive and I was a proofreader for a core maths text book (this one from Hodder and Staughton) so I feel like I have some insight.

There is a group of teachers on twitter that are very helpful regarding Core Maths and have been great about sharing ideas and resources (special mention to @p_glaister and @cvcltang). This blog post is intended to be the first of my Core Maths ones where I hope to give back to those that have helped so far.

Exciting times ahead!

Tutor time activity – Speed dating (ish)

Here’s an idea for tutor time.

Pair people up and get them to discuss a topic from the list for 2 minutes (or some other amount of time). Then, re-pair people and choose another topic. This should get people to talk to those they otherwise might not and also removes the barrier of “what shall we talk about?”.

These topics were thought of by members of my maths department. They are all intented to be fairly light-hearted but you could skip any you think might cause issues. If you have more, feel free to add them in the comments!

  1. Are cats or dogs better and why?
  2. What human invention would you show off to aliens?
  3. The best thing you did in the summer holidays
  4. Which historical character would you like to meet?
  5. If you could go anywhere in the world, where would you go?
  6. Favourite game
  7. Favourite chocolate/sweet
  8. Least favourite vegetable/s
  9. Which form of potato would you choose to eat for the rest of your life?
  10. Favourite thing you’ve read
  11. Is the Olympics overrated?
  12. Favourite time of the day
  13. Are snooker and darts sports?
  14. What do you want to do for a job?
  15. If I gave you £1000 what would you spend it on?
  16. If your friends were to compare you to an animal, which one would it be?
  17. What is your most treasured possession?
  18. Top 3 things you want to do in your life
  19. Favourite pizza topping/s


Currently reading: Cracking Mathematics by Colin Beveridge

TES review – 5 STAR resources

As a member of the TES maths panel, every so often I’ve given a set of resources to review. Here are some highlights from this batch!

Level 2/3 Perimeter Homework Question by Ayliean MacDonald @ayliean

Such a simple idea but really pushes students to think about what they’re doing. It’s important that we (and students) don’t assume that Grade 2 or 3 automatically means ‘easy’.

Level 3 CORE Maths Lessons Ch1-4 by tpayne89

I’m going to be teaching Core Maths (level 3) next year for the first time at my school. It’s a reasonably new/niche course and there isn’t much out there yet so a bank of investigations like this is great.

Quadratic Sequences 2 (Treasure Hunt) by David Morse @Maths4Everyone

I’m usually not a massive fan of treasure hunts  but this one is very well presented and  has an extra twist to make it worth using.

Algebra Assessment – Simplifying, expanding, factorising (100 marks, Grade 1-7) by askmrarya  @my2pennies

This is pretty straight forward and while it doesn’t break new ground, it is perfect for revision for my year 11. Loads of questions with variety and challenge.

Factorising 3 (Treasure Hunt) by David Morse @Maths4Everyone

Similar thinking as my previous treasure hunt comments above. This is really nicely presented, has good questions and an extra twist.

Maths Word Search with something extra (Names of Shapes) by David Morse @Maths4Everyone

I would never have expected myself to give a wordsearch 5 stars! This one is a bit different though as it doesn’t have the words to be searched for but the shapes instead. Given the trouble I’ve had recently trying to get my year 8 students to deal with shape properties, I’m going to put this one in the file for next year and use it as a way in to a discussion about how to describe/name/categorise the shapes.

In case you haven’t noticed, David Morse has made three of these resources so he’s obviously on a roll!

Why not take a look and see if you agree with my 5 star rating? I don’t give them out easily (I had 33 resources to review in this batch) so I think you’ll like them. You’ll obviously need a TES login to access them but it’s free, and frankly, if you’re reading this sort of blog you probably should have a login to the TES!