Measurement Starter Question

Maths lessons

During measurement topic, ask the students, how can a shape be both bigger AND smaller than another. For example, I used this doing perimeter and area of a semi-circle. I drew two diagrams on the board with particular dimensions where one with the smaller perimeter had a larger area. It would work with many different ones though and could be used for example to show how the largest area for a ‘rectangle’ is when the sides are the same (ie. a square). On this last one, there was a good site I came across for exploring this – complete with video and an image I turned into a worksheet (Perimeter v Area). Also later discovered this resource looking at which shapes have the greatest area (with links to further resources!)

Introduction to Trigonometry

Maths lessons

With many thanks to Dan Pearcy I stumbled across his introduction to trigonometry lesson. I ran it with my year 9 advanced class and I thought it was great! Love the moment when I started writing out all the ratios and the comments around the room on cue started: “surely we aren’t going to write all these out”, “we are going to run out of room sir” etc! Good fun and a great way to get into the ratios without just plonking SOH CAH TOA on the board!!

(Just in case anything happens to Dan’s page, I’ve included the files below that students need to measure/fill out to build ratios)introduction-to-trig (1) and similar triangles

Book ‘review’: 7 Habits of Highly Effective People

General, Theory

Book by Stephen Covey

Here are a few key sections/quotes/thoughts that I gathered from a very brief flick through the book. I read the first few chapters more carefully, but was well overdue in returning it and so skimmed through the last sections…

Overall image sourced from p.53. A helpful overview and worth pointing out one of my favourites (also brought out strongly in last Emerging Leaders course):

“Seek first to understand, then to be understood”


Interesting insights from Covey’s own experience with son…p.16f – struggling in school, socially, athletically etc. They had desire to help him. Realised significance of how they saw him and treated him, i.e. Actions were communicating that they thought he wasn’t capable. Focused attention on their own motives and perception of him. See his uniqueness potential…they needed to affirm, enjoy and value him.

p.54 discussion on P (production of desired results) versus PC (production capability, asset that produces). Need a balance in maintaining/preserving both. Particularly, Covey later says (p.58) with regards to employees. “The PC principle is to always treat your employees exactly as you want them to treat your best customers.” Treat them as volunteers – indeed “they volunteer the best part – their hearts and minds”.

In ‘Habit 1’ discussion of proactivity, discusses value in being proactive, driven by well thought out values etc, rather than reactive, driven by feelings, circumstances etc (like the weather!) In responding to others influence/affect on you, Covey quotes Eleanor Roosevelt – “No one can hurt you without your consent”. Our consent hurts us more than what happens in the first place. Choose my response!


Table sourced from p.78 showing proactive versus reactive type responses.

IBM founder T.J. Watson quote on p.91:

“Success…is on the far side of failure”.

Ties in well with the growth mindset idea! Need to have a go, fail first, to reach success.


Maths/Math related stories

Resources, Theory

We know how much everybody loves a story. I was encouraged to pursue this through a number of talks/tweets/articles etc. I was also encouraged beginning this in 2016 with some attempts to incorporate stories into my maths class.

One of the best things I found was ‘crafting’ something that had happened in class into a story (eg. tale of someone who avoided something fearing they would get stuck, later worked it out etc, later revealing it was me!)

Aside from that though, here are some links to stories that I found I could weave into a maths lesson somehow: