Derek starts the video by reading through the aims of the 2014 National Curriculum for Mathematics and focuses on one of them, ‘applying mathematics to a variety of routine or non-routine problems’. He gives an example of a primary school child showing how to reason in a mathematical way:

A 10 year old child declares to his teacher, ‘in a 99p shop, if you bought 99 things and paid for each of them with a pound then you would have enough change to buy another one!’

Derek demonstrates that by pushing the student further and asking questions such as, ‘what if it was a 98p shop?’ that teachers can encourage children to explore the generalizations around mathematical problems. Proposes that teachers will be able to identify genuine mathematical reasoning by end of Chapter 4. Derek then argues that genuine mathematics is much more than just doing calculations. He introduces Chapter 5, mathematical modelling and how that relates to problem solving. At 03:04 a diagram of the mathematical modelling process is shown, Derek mentions how this is explained in Chapter 5 before giving some detail on this. Each of the steps in the process are equally important according to Derek, all part of mathematical reasoning.