361. Routes, Reindeer & Reasoning

Well, we are nearly at the end of a very crazy year. Congratulations on surviving it!

So, it’s been a while since the last blog post. Apologies for that. At the moment I am involved in Mixed Attainment teaching with Year 8. To finish off the term, I thought we deserved a bit of fun. We have a week of lessons left so I’m going for a mini project each lesson.

Lesson 1: Santa’s Route
I found this fab task on the Maths Drill website. There is a real chance for extension in this task, which is great for the mixed attainment classroom.

Lesson 2: Reindeer Ratios (Updated 13th Dec)
We have been following the White Rose Maths scheme for Year 8, which covers a lot of proportion and reasoning through ratio, multiplicative change and fractions. This task tries to cover some of these skills. The answers will be uploaded soon.

Lesson 3: Elf Box Packing Problem (Updated 14th Dec) Elf Box Packing Problem Solutions
This task involves using multiplicative change and fractional multiplication and division, with a dash of unit conversion. There is some work on shapes, but formulae are given where necessary. The first four pages print nicely into a folded A4 (A5) booklet. There is a help sheet for the box packing problem; this would be better printed on A4.

360. Preparing for online learning

A few tips for forward planning with Google Classroom in case of school closures, plus a few other hints and tips.

1. Check that all the correct students are on your Google Classroom class list – especially with leavers, joiners and set moves. Invite them by email if necessary. Same goes for other digital assessment platforms.

2. Check that the teachers of shared classes actually all have access to the classroom

3. Do not put everything on the Stream – it will get chaotic very quickly. Post all materials on the Classwork tab. It will automatically be put on the stream, but you will be able to categorise it.

This is an example of good practice. The classwork feed is set up with all the topics being taught, the shared teachers are identified and the tasks/resources are dated.

4. Check the functionality of your materials before you release a post to your class. If things don’t look right, convert it to a pdf. You can’t assume students have specific non-web based software. Also, you are looking to make it mobile phone friendly. The majority of kids have access to a smartphone, but you can’t assume computer access.

5. Make the most of embedding YouTube videos – copy the URL and paste it into the YouTube link when you create materials.

6. When creating assignments, think how students are going to assess – are you providing a markscheme? A link to a website with solutions or walk through? Is it a google form you can mark or auto-mark? A google doc or slide where you can actually mark each student’s work? An interactive website? Are they simply working in their regular book? In which case make sure they actually take it home.

7. Remember you can plan ahead by scheduling future tasks

8. If you want to use a digital textbook, but students don’t have access to it, you can ‘Snip’ the questions from the digital textbook and paste them into a Google Slides presentation or a document. This is probably slightly dodgy copyright wise, but if you can’t send every child home with a textbook during a school closure, it seems a reasonable stretch of copyright. You’d be using the physical books in your classroom if your school wasn’t closed.

9. It’s okay to model an answer on paper, take a photo/scan and upload it. There are many ways of doing this. Personally I use the Scribzee app as it doesn’t involve a computer and scanner.

10. Use it as an opportunity to share interesting maths with your class – the Parallel site, by Simon Singh is amazing. Also an ideal time to catch up with Numberphile videos and inspire future mathematicians.

11. I think Corbett Maths could be the main site for saving teacher sanity!

12. Exam classes are going to be tricky.
For GCSE classes sites like Mathsgenie are amazing. And don’t forget people like Access Maths, Piximaths and MsBsResources. Apologies to all the other awesome resource sites, not enough space to list them all.
For A-level Maths and Further Maths try Alevelmathsrevision and the AMSP (Further)

359. Proportional steps

Just a quick resource upload today.

Image credit: https://www.heyn.co.uk/

I’ve written a step by step resource on how to construct algebraic direct proportion relationships, including the answers.

Small steps in Direct Proportion (docx)

Small steps in Direct Proportion (PDF)

I used this with a Year 11 class who aren’t very confident with algebra. They were surprised by how straight forward the work was and were happy to now attempt problem solving with algebra.

358. A spatter of trig

The fabulous Mrs D (@mrsdenyer ) shared this forensics video, by crime scene analyst Matthew Steiner, on Twitter. At eight minutes in the presenter looks at blood spatter analysis. The use of basic trigonometry in a practical situation is a gift of a video for a starter in lesson.


My class were absolutely silent throughout and wanted to watch the whole video, however they may have just been trying to avoid work. I shared the video link with them via our digital classroom platform. We are now using blood spatter for 3D trigonometry examples rather then mobile phone masts. Gory, but effective!

357. It’s not square!

I do love a little challenge for A-level Further Maths students. They are often confident and very capable mathematicians, but occasionally overlook the small details. This challenge looks into which strategies students use when working with 3D vectors, lines and angles.

The most annoying thing? There is no single correct answer.

What is the investigation?

Students start with two points, create a line, construct two perpendicular lines and then join up the lines – did they create a square? How do you know? Justify it?

Download the instructions here: It’s not square (docx), It’s not square (PDF)

Skills required

  • Distance between two points
  • Equation of a line in three dimensions
  • Scalar (dot) product

Solution/Discussion point

  • Students need to use the same direction vector for both perpendicular lines too create a square
  • The two new corners need to be n the same direction away from the original line (not one above and one below)
  • It’s interesting to discuss what non-squares they made. Technology could be used to plot them in 3D.

356. Edexcel Shadow Paper

Wow, it’s been a while since my last post. Apologies for that. I’ve been busy with Key Stage 5 things. One of my projects has been creating a shadow paper for the Edexcel AS Maths exam. With so few past papers available and so many papers available online, I wanted an assessment that my students couldn’t find the mark scheme for.

I’ve taken the AS Pure 2018 paper and created a shadow paper, with markscheme. Same level of difficulty, different numbers. I publicised it on Twitter and shared it with over ninety educators in 48 hours. I was stunned by the popularity of this resource. To keep it secure, the lovely Graham Cummings from @mathsemporium has arranged for it to be uploaded onto the Edexcel Maths Emporium. Now I don’t have to directly email people the files.

You can access it with an Edexcel teacher login here. If you don’t have a login, there are instructions on the page on how to obtain one.

I hope this paper saves you some time. I intend to start work on more Pure shadow papers soon, as Pure maths carries the heavier weighting in the AS and A-level exams.

355. Toyota logic

My fabulous colleague, Mr G, has recently been to the local Toyota factory to find out about the Lean model.

The key principles involve efficiency of process. He told me about a school using the Lean model that had tape diagonally along the spines. Students put their folders back in order and the teacher can instantly see if a file is missing. Genius!

Now I happened to be about to cover my textbooks with sticky back plastic. I put duct tape around the spine before covering them. Each book has tape 1cm lower than the previous.

Now you are thinking – that looks nice, but it will never work.

I’ve got news for you – every time I use the textbooks with my class of 34 Year 9 students, they put the books back in order. On the first day I made a big deal of how tidy the books looked and challenged them to put them back tidy. And they did – every lesson!