Greater depth maths: change the rules

    Published: 23 November 2018

    One of the most frequently asked questions the HfL maths team gets asked in schools relate to where teachers can get their hands on more ‘greater depth’ materials. The vast majority of the schools we work in regularly have moved away from the ‘three boxes’ approach to differentiation, whereby every lesson different groups are working on completely separate skills or tasks. However, some teachers report they are still spending a long time searching the internet for the elusive ‘greater depth’ materials - the needle in the haystack. In this blog, I will share one strategy which teachers in any year group, teaching any domain, can apply to add extra depth and challenge to age-related questions.

    Many blogs seek to define the elusive term ‘greater depth’. This includes our 2017 blog by Rachel Rayner ‘Greater depth at KS1 is elementary my dear teacher’ which unpicks how pupils working towards greater depth can demonstrate confidence when tackling increasing demands in reasoning, deduction and complexity. Existing users of the ESSENTIALmaths plans will know that we provide some activities to allow pupils to explore ideas at greater depth, however many schools are seeking more regular opportunities to add additional challenge to the age-related destination questions.

    A parameter can be described as a boundary or limit which defines the scope of a process or activity. Whilst opening up questions can be a great way of providing challenge, this approach aims to do the opposite by using parameters to add greater complexity by closing down the question and challenges. Pupils are challenged by having to frame their response whilst juggling additional conditions to meet. This blog focuses on how teachers adding parameters can increase the complexity of an age-related question and thus provide greater challenge for pupils by adding depth.

    Year 1 puzzle

    The age-related question at the top of this year 1 example comes from the ESSENTIALmaths sequence 1LS13 which appears at the end of the autumn term. This was a tricky one as the context of the parameters had to stay within the remit of autumn year 1 pupils. It could have been very tempting to accelerate pupils onto larger two or even three-digit numbers. Instead of using ‘digit sum of 5’ I chose to use ‘digits that add up to 5’ to ensure that pupils could access the question.

    Year 4 example

    This year 4 example focuses on the application of calculating with fractions within ESSENTIALmaths sequence 4LS20. These open-ended calculations with more than one possibility provides the opportunity for pupils to go beyond simply adding and subtracting fractions with the same denominator which should have been secured within year 3.

    Year 5 example

    Finally, this upper key stage 2 example is taken from ESSENTIALmaths sequence 5LS6. Each example here requires pupils to consider two or more conditions with the digit cards. Writing these problems requires deeper thought about the concepts being covered, and one way of extending pupils’ thinking is to ask them to write tasks with the same (or greater) level of complexity as those provided. 

    Given the time pressures, teachers often comment that they do not have the time to write these questions. However, when I have shared examples like this with teachers who have then referred back to them to support them, they have found it has saved time overall and they have become more confident at including extra challenge both at the planning stage and within lessons. I’d urge you to step away from the search engine and give adding parameters a try!


    Related courses

    Moving from acceleration towards depth as challenge in Key Stage 1 - 28th January 2019

    Moving from acceleration towards depth as challenge in Lower Key Stage 2 - 29th January 2019

    Moving from acceleration towards depth as challenge in Upper Key Stage 2 - 30th January 2019

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