Here is part of a standard number line. I might call this a “unitised” number line, showing how many ones I have. One use of this number line might be to assist in the teaching of addition and subtraction of whole numbers. I could also use it to teach multiplication, say by two. For this … Continue reading More Thoughts (and Some Pictures) on Working With Fractions (and Other Numbers).
In what follows I aim to set down a broad overview of some of my current thinking about fractions. The ideas expressed here are just that: ideas and wonderings that are purely personal and not intended as judgements or pronouncements about other people's views or practice. I don't pretend to speak with any authority and … Continue reading Some Thoughts on Working with Fractions
I’ve recently been working to develop, among other things, my approach to introducing addition and subtraction of fractions with different denominators. In what follows, I shall outline my current thinking based on work I have done with two different secondary school classes and with a student teacher, Luke Ito, at certain points during the past … Continue reading Adding & Subtracting Fractions: A Learning Sequence
Recently I’ve come across some posts on Twitter that have led me off in unexpected directions. In short, they have served as prompts for me to ask and pursue answers to questions, processes that have given me both enjoyment and insight into some mathematical ideas and truths. I thought I would share one here. It … Continue reading A series of not unfortunate events: Peaches, pairs, primes and squares
I'm approaching the end of another session with another S1 class (the first year of secondary school in Scotland for pupils typically aged 11 or 12 on arrival after seven years of primary schooling). As the years go by I find I'm enjoying more and more working with these younger pupils - this particular group … Continue reading Interrogating Integers
This article is about some lessons that haven’t happened yet, inspired by a serendipitous realisation during a lesson that has. In a previous post, “No Teachers Are Really Young”, I described some other lessons on graphs of quadratic equations with the same class. That post provides some context for this one and I would recommend … Continue reading You’re Always Realising New Things: Graphs of Quadratic Functions (Part 2)
I recently began teaching my S1 class (12-year-olds) about volume. This is a topic most of them had met at primary school - they were keen to tell me they knew that Volume = length x breadth x height. In addition, since joining my class, they have learned to find the areas of rectangles and … Continue reading Cuboids: a context for learning