Julian's musings

Small angle approximations

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At a conference run by the BBO Maths Hub today, Jo Morgan mentioned that small angle approximations are a topic recently (re)introduced to the single maths A-level course, and many teachers may be unfamiliar with it.

During the day and on my journey home, I thought about this and some of the connections between it and other areas of the syllabus. So here are a few quick thoughts on ways we could think about them, making connections between this and other areas of the syllabus. I hope that this post offers some different perspectives on the topic.

Dividing fractions

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Why is it that

or as the rule that students are frequently taught: “turn the second fraction upside-down and multiply”?

I’ve been inspired to revisit this question after listening to Ed Southall talking on Mr Barton’s Maths Podcast, where he mentioned this question.

In this post I suggest a teaching sequence which might lead to an understanding of the rule above, as well as a procedural knowledge of how to perform the rule.

A curious Poisson distribution question

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Yvonne Scott posted the following question:

Stuart Price noted that the answer to the last part can be obtained as the answer to part (iii) divided by the answer to part (iv), by the definition of conditional probability.

But if we think about what’s going on a little further, we will be able to understand the structure of this problem more and see further connections.