The World Is Maths



Guest Post for the Learning Scientists

I was very excited to have written a post for the Learning Scientists last month, whose work is fabulous in spreading the word about effective (and ineffective) strategies throughout the teaching community.

I wrote for them about how I created a mathematics scheme of work trying to embed effective learning strategies from the outset.

You can read the post on their blog.

Algebra: you use the letter ‘x’ more than you ever have done in your whole life!

I started my first algebra unit with Year 7 on Monday.  It’s the essentials of algebraic manipulation: adding, subtracting, multiplying and dividing terms, including those with indices, as well as expanding and factorising single brackets, all pretty standard beginnings in algebra.  In the past I think my first lesson on algebra would consist of a brief introduction then some simple collecting like terms.  From what I’ve seen, that’s generally what comes up first in most schemes of work.  This time, though, I’ve tried to be more deliberate and more pedantic over the details.  Really, really pedantic, because it’s insecurity with the small details that causes so many mistakes for the rest of our students’ experience.  I’m starting out by assuming they have done no algebra.  Many of them have done a little but I’m not prepared to risk that all their different primary experiences were the same, or solid.  (This is a not a criticism of primary teachers, more that I want to take sole responsibility for something so important). Continue reading “Algebra: you use the letter ‘x’ more than you ever have done in your whole life!”


Truncation is new to the National Curriculum and the GCSE and there aren’t many resources out there (textbooks or worksheets).

I found a decent presentation by Rory Mathews, with some handy quick-fire questions on it.  It comes with a worksheet, but there is only a handful of truncation questions on the worksheet before it goes into rounding, so I’ve made a very simple worksheet with practice questions on truncating and writing the error interval for a truncated number.

After spending time on the basics, we’ve done this really nice activity by Peter Mattock which pretty much finished off the topic (apart from all the times we’ll revisit to stop them forgetting, of course!)

That’s it.  An appropriately short post I hope.

Adventures in Mastery 2: Writing a Scheme of Work

This is post 2 in a series.  In post 1 I discussed why we’re beginning a mastery scheme of work, some of my initial objections, and a brief description of “mastery” in its current incarnation.

In this post I will describe the process that produced my scheme of work, and share the working draft of the scheme itself. Continue reading “Adventures in Mastery 2: Writing a Scheme of Work”

Adventures in Mastery 1: Starting Our Journey

When you’ve been in education a while you see plenty of fads come and go and you become carefully cynical about the latest big pronouncement or the new product that’s going to “transform” your practice.  And so it was that I responded (in my mind) when everyone started to talk about mastery. Continue reading “Adventures in Mastery 1: Starting Our Journey”

Off We Go! (Desmos Activity)

My second Desmos activity is designed to reinforce understanding of the features of displacement-time graphs.  Students are asked to describe parts of graphs, interpret the gradient of the line, and write a mathematical story based on reading a displacement-time graph.

As always, all feedback is welcome.

(Photo by Martijn Van Dalen)

Picture Perfect Parabolas (Desmos Activity)

I’m intrigued by the Desmos Activity Builder and where it might be useful for my students.  One of the first activities I’ve made is based on the idea of fitting graphs to photos of naturally-occurring or man-made parabolas, which I first encountered in Adrian Oldknow’s book Teaching Mathematics Using ICT back in 2004.

In my activity, students are asked to fit some parabolas to photos of bridges and fountains.  And a banana.  They are also asked to explain their thought processes before they attempt the graphical transformations. Continue reading “Picture Perfect Parabolas (Desmos Activity)”

Conic Sections (Desmos)

EDITED:  Thanks to the wonderful folk at Desmos, who helped me solve my problem within minutes of tweeting it, I now have fully functional models.  The problem was making the black dotted distance lines only point to the relevant focus/directrix and not both.  Writing lines parametrically – that’s how to impose conditions on when they appear.

I’ve been trying to make some models to show the relationship between the curve, focus and directrix on conic sections, Continue reading “Conic Sections (Desmos)”

Continuous Random Variables (Desmos)

I dislike education acronyms, but I can make exceptions for mathematical ones.  One of my favourite topics in A-level Maths is full to bursting with them: DRVs, CRVs, PDF, CDF.  This is a visual representation of the CDF (cumulative distribution function) of a CRV (continuous random variable), which is the function for the area under the curve from x=-∞ to any other value, a, or more specifically, P(X<a).  Take note of the syntax for piecewise functions. Continue reading “Continuous Random Variables (Desmos)”

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