By Malcolm Watson (May 2023)
In order to understand how to extend our primary school pupils to reach ‘greater depth’ in mathematics, we first need to define what this is. In the end of KS2 SATS, a scaled score of 110+ indicates a child is working at ‘a higher standard’. This means they are able to answer more questions correctly relating to the curriculum but is this true ‘greater depth’ or just a broader understanding of the content?
At the end of KS1, children have to show evidence that they satisfy a variety of statements to be considered to be working at a greater depth, for example being able to tell the time to the nearest 5 minutes as opposed to the nearest 15 minutes. However, is this true greater depth or just more content?
In the National Curriculum, it states that children should be challenged with rich and sophisticated problems before being exposed to new content. Surely, solving these rich and sophisticated problems should therefore be the real indicator of greater depth?
Another thing I want to clear up before sharing my favourite resources for greater depth questions is the wording surrounding this. Anyone can be working at a greater depth within a single learning task, lesson, or area of Maths at a particular snapshot of time. However, no one is genuinely a ‘greater depth mathematician’ as this is a fixed label that indicates they understand and can do everything, which quite simply no one can.
The following resources are my favourite go-to places for finding rich and sophisticated tasks which go beyond basic reasoning and problem solving and in lessons I call these greater depth challenges:
NCETM assessment materials
The NCETM Primary Assessment Materials give a great indicator of the difference between a child mastering the curriculum (working at age related expectations) and one working at greater depth.
NRICH
The NRICH curriculum map is particularly useful.
Open Middle
The Open Middle website is based in America. The questions tend to follow the format of having empty boxes and using the digits 1-9 once only try to fill them. The lack of words makes them very accessible for KS1 as well as being highly challenging for all year groups.
YouCubed
YouCubed tasks, like NRICH, are great examples of low threshold, high ceiling tasks that can take children’s learning to a greater depth.
I See Maths
The I See Maths problem solving ‘extend’ questions have been developed by Gareth Metcalfe and come for a one off cost.
Writing our own
We can, of course, write our own greater depth questions which is super fun! It can, however, also be very time consuming and frustrating if none of the children then reach them in that lesson. My top tips for writing your own would be:
Use a real life but possibly unfamiliar context.
Use a range of other maths within the question that children have previously learnt about (fractions, the equality symbols, and time are good ones for this)
Go against the generalisation of the lesson, e.g. when comparing decimals ask children to draw diagrams to show how it is possible that 1/3 of Malcolm’s cake is bigger than 1/2 of Faye’s cake.
Tweak examples you’ve seen from the resources mentioned above and your own go-to places, thereby changing an element of an existing question rather than starting from scratch.
Good luck in your never-ending quest for greater depth.