Monthly Archives: February 2020

359. Proportional steps

Just a quick resource upload today.

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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.