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Teaching MasteryModule 5

Supporting all students to succeed

Carys Hopkin

School Development LeadSecondary Maths


Clare Hill

Principle Development LeadSecondary Maths

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Dimensions of Depth

Understanding Students with Lower Prior Attainment

Understanding the LO's

Use the arrows in the top, right-hand corner to navigate through the trainingOr go straight to each of the chapters using the buttons below

Quiz & Evaluation

Planning Lessons for Success for All

This bar shows your progress through the training module

If you need to pause and come back to this training, use this page to navigate to the last chapter you were on. Please note that if you exit the session, you will not be able to see your previous answers

Dimensions of Depth

Conceptual Understanding

Mathematical Thinking

Language & Communication


Hover over each Dimension of Depth to remind yourself of their key principles.

Representing concepts using objects, pictures, words and symbols; making connections

Making conjectures, trying out specific examples, organising, comparing, looking for patterns and generalising

Explaining, justifying and discussing using accurate mathematical language

Dimensions of Depth


Conceptual Understanding

Mathematical Thinking

Language & Communication


Conceptual understanding: How will this task deepen understanding of perimeter?Mathematical Thinking: What 'bigger picture' thinking skills might the students use? For example, pattern spotting, testing, comparing, conjecturing. Language & Communication: What terms might students need to use? Write an example sentence.

Look at this Develop Learning task. (Click to enlarge)Where can you see the Dimensions of Depth within it?

*Some slides require answers to be submitted before moving onto the next task

Representing concepts using objects, pictures, words and symbols; making connections

Making conjectures, trying out specific examples, organising, comparing, looking for patterns and generalising

Explaining, justifying and discussing using accurate mathematical language

Dimensions of Depth

Click on each Dimension of Depth to see what we picked out from this task

Conceptual Understanding

Mathematical Thinking

Language & Communication


Understanding Students with Lower Prior Attainment

Chapter 1

This section focuses on the language of ability and attainment and what we mean when we describe students as low prior ability or attaining.The purpose of this is to establish a shared language as a team to ensure high expectations for all students.


Low Prior Attainment

Why is it important that we differentiate between attainment and ability?

Lower Prior Attainment

Click on the image to find out more.

Mastery is built with the success of all students in mind...

Attainment is not fixed


Think about your own experiences.Discuss or reflect upon a child that has come into year 7 well below expectation but then went on to succeed at GCSE.

The Mathematics Pipeline in England: Patterns, Interventions and Excellence. Noyes et al. University of Nottingham 2023

This diagram shows the movement of students from KS2 to GCSE through their attainment. Draw your attention to those students that move significantly up. The link to the paper is below.

Attainment is not fixed

The Mathematics Pipline in England: Patterns, Interventions and Excellence Noyes et al. University of Nottingham 2023

This diagram shows the movement of students from KS2 to GCSE through their attainment. Draw your attention to those students that move significantly down.


Prior attainment


Why is this important?


Prior attainment

In this study by Hodgen et al. 12 teaching strategies and approaches were identified that can be put in place to address pupils' low attainment.

Drag them into the order you think they were found to be most effective.

Click to learn more about this study



Computer-Aided Instruciton

Feedback to Pupils

Feedback to Teachers


Co-operative Learning


Tutoring by Adults

Peer Tutoring

Most Effective

Least Effective

Student- Centred Approach

Explicit & Direct Instruction


Prior attainment

Here is the order that the study found had the most impact on LPA students, compare them to your answers.

Click to learn more about this study

3. Manipulatives

8. Representations

2. Computer-Aided Instruciton

7. Feedback to Pupils

9. Feedback to Teachers

6. Heuristics

11. Co-operative Learning

10. Self-Instruction

4. Tutoring by Adults

5.Peer Tutoring

Most Effective

Least Effective

12. Student- Centred Approach

1. Explicit & Direct Instruction


Prior attainment

1. Explicit & Direct Instruction

During this training we will be exploring how we adapt lessons for the success of all students.This will include how you will plan to run lesson tasks.

  • What you will say
  • What you expect students to do

The study found that good explicit & direct instruction had the biggest impact on supporting LPA students.


Key Takeaways:

Chapter 1Review

Attainment is not fixed

  • Ability is often considered innate and therefore use of the word can imply that it is fixed.
  • Attainment can improve and thereore use of the word can lead to higher expectations for all students.
  • Students' attainment can improve or decrease over time.
  • High expectations for all students will also support students with higher prior attainment who are at risk of worsening outcomes.
  • There are a number of evidence based strategies that can support this.

Understanding Students with Lower Prior Attainment

In this chapter you focused on the importance of the language used to describe students.The trajectory for different students and strategies to support high expectations for all students were examined.

Distinguishing between LPA and SEND students

Chapter 2

Not all LPA students are students with SEND and not all students with SEND are students with lower prior attainment.This chapter examines what this means for teaching.



Barriers to success

Look at the Develop Learning task below (click to enlarge).

Think of some ideas why students might be unsuccessful when attempting this task?

Write your ideas in the box below, these might include;

  • Learning of mathematics
  • Classroom norms
  • LPA needs
  • SEND

The students' behaviours

Classroom norms


The learning of mathematics

Specific Educational Needs

Difficulties in making links between topics


Language difficulties

Attention span

Language difficulties

How students enter the classroom


Seating plan

What happened at lunch

Challenge level


Fear of failure


Gaps in knowledge

Barriers to success

Look at the four categories listed below. We have also listed some barriers to successful learning in the pink lozenges but there are many more.Drag the pink lozenges into the category you believe they belong. Some of course may overlap.

Confidence and self-belief



Frequent absence from school

Anxiety or depression

Gaps in learning through teacher absence


Visual impairment

Barriers to success

Low Prior Attaining

Think about a HPA student that also has SEND needs.What do you do to support them?

A child may have not had schooling for the early part of their childhood and so may present as LPA but with the right interventions can catch up.

A student may be dyslexic but with the right support and resources can fully access the curriculum. Similarly, students with mental health problems or physical impairments may also fall behind without having had lower prior attainment.

Any of the elements in the SEND set or the LPA set could sit in the intersection. How we plan for these will go a long way to support students, whether they are LPA or SEND to access the task.

Overcoming barriers to success

Look at the Develop Learning task below (click to enlarge)

EEF SEND Recommendations

Click on each of the five strategies recommended by the EEF to support students with SEND

'...good teaching for pupils with SEND is good teaching for all.'


Using Technology



Flexible Grouping



Cognitive & Metacognitive Strategies


Explicit instruction



Key Takeaways:

Chapter 2 Review


SEND and LPA needs are often conflated but it is important to remember that not all SEND students are students with lower prior attainment and should be planned for according to their need.

Distinguishing between students with LPA and students with SEND

In this chapter you examined some of the many barriers that can exist for a student which prevent success.Many of these can be overcome through planning to allow appropriate entry points for students

Knowing the Learning Objectives

Chapter 3


The lesson slide decks always start with a unit overview slide containing the learning objectives for each lesson. In this chapter we will examine using the learning objectives to meet the needs of all students whilst maintaining high expectations for all.We will be looking at Year 7 Unit 11 Lesson 1.

Learning Objectives

Before you begin planning your lesson it is vital that the aims of the lesson are clear

What do you use Learning Objectives for?Look at the statements below, and sort them from most to least important to you.There are no right or wrong answers.

Finding the Learning Objectives

The Unit Overview is the first point of call for finding the Learning Objectives for each unit and lesson within it.Click on the buttons below to explore the Learning Objectives.

Exemplifying Knowledge Expectations

There are multiple places that exemplify what students should know.Two examples of this are the Start of Unit Quiz and the Exit Ticket.Click on eack of them to see how they can be used.

Learning Objectives


Click on the tasks to enlarge them.Answer the questions alongside them.

Learning Objectives: Lesson 1 - Describing Perimeter

  • Be able to work out perimeters of different shapes.
  • Understand perimeter as a measure of length expressed in appropriate units.
  • Experience connecting perimeter calculations to shapes using axioms of number and algebra.

Where can you see the Learning Objectives in each lesson task?

  • Talk Task
  • New Learning
  • Develop Learning
You may not see every objective in each task

Learning Objectives

Click on each lesson task to see where we found the learning objectives.

Planning with Learning Objectives in Mind


Look at this Talk Task, click on it to enlarge

You have students that might struggle to get started with this task. What will you say, or do to help them?eg. Giving sentence starters, giving additional examples, questioning prompts, or explaining in a different way

Planning with Learning Objectives in Mind

Look at this Talk Task, click on it to enlarge

1. What is a good answer to this Talk Task?Think about key terminology, full sentences, exemplifying and explaining why

2. You have students that might struggle to get started with this task. What will you say, or do to help them?eg. Giving sentence starters, giving additional examples, questioning prompts, or explaining in a different way

Here are the accompanying notes from the Notes and Guidance page in the slide deck.Read through and compare with your previous answers.

Planning with Learning Objectives in Mind

Here is an example of an adapted Talk Task.Click on each adaptation for more context.

Adaptations for Success

No student should lose out from the adaptions made

Learning Objectives can inform adaptations by:

  • Guiding the key concepts of the lesson
  • Ensuring you know the minimum that all students should know by the end of the lesson
  • Help you understand the purpose of each lesson task


Key Takeaways:

No-one should lose out when adaptations are made

The objectives for each lesson should be fulfilled, which will often require you to adapt slides maybe to move more slowly through the material, or by adding in alternative examples and explicit modelling.

Chapter 3 Review

Learning objectives

  • The objectives for each lesson can be found in the unit overview slide
  • The goals for each task can be found in the Notes and Guidance slide (Year 7)

The plenary and Start of Unit Quiz can also be used to exemplify skills students will need before starting the unit, and the skills all students will have acheived by the end of the lesson.

Knowing the Learning Objectives

In this chapter you have explored how examining the learning objectives can aid planning for success for all students without anyone losing out.

Planning for Success for All

Chapter 4

In this chapter you will plan and adapt a New Learning and Develop Learning slide to ensure success for all your learners


2. Write down two ways you would adapt this task for LPA studentsWill you use additional examples?What will you say?Do you need to plan for accessability?

1. What is the key learning from this slide?Think back to the Learning Objectives

New Learning


Look at this New Learning slide (click to enlarge),and answer the questions on the right.

New Learning

In Chapter 2 you saw the importance that Explicit & Direct Instruction had on the success of LPA studentsWatch the video below to see how this task could be modelled

New Learning

Here is an example of an adapted New Learning SlideClick on each adaptation for more context.

2. How will you introduce this slide?Will you talk through the first example?Do you need to add in an additional example?

Develop Learning

You have already explored this task using the Dimensions of Depth.Now we will look at how to adapt it.

1. What is one answer you want to see from your students in this task?

Complete these questions individually,then feedback as a team

Key Takeaways:

Chapter 4 Review

Planning for Success for All

In this chapter you have examined two lesson tasks and how they might be adapted to support success for all students, including students with LPA and SEND.


Your exposition and modelling are key strategies for supporting LPA students.

Use the Notes & Guidance slides to support your adaptations, especially when thinking about teacher exposition and prompting questions.


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Quiz and Evaluation

Chapter 5

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Evaluation & Quiz

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2. Cognitive & Metacognitive Strategies

  • support pupils to recall previously learned content, before they move on to new content?
  • help pupils to organise their thinking by ‘chunking’ the content into smaller steps?
  • ask metacognitive questions that support pupils to plan, monitor and evaluate their own learning?

This section states the intention of the New Learning from each lesson of the week

Having clear definitions on the board for key terms you will be revisiting throughout the lesson will help students remember themYou could also get the students to write this into their books, chant as a whole class, or print and stick this slide into their books


Mathematical Thinking

Students may start to make their own conjectures about how they form the shortest and longest perimeters. If they don't, ask them questions that may encourage this. Physical manipulatives will support students in trying this out.Ask students to try to justify why the shape with the longest perimeter will be formed from joining the shortest edges.

By using both straight and curved lines, the talk task emphasises perimeter as a linear measurement supporting students to understand perimeter as a measure of length.

Talk task

You may want to consider starting the task with a similar question that encompasses the same learning objectives.Here I want to draw the attention to the difference in lengths between a straight and curved boundary, before moving on to a more challenging example.

Building up gradually

Conceptual Understanding

Click here to link to the Unit 11 Area and Perimeter of 2D shapes overview video

Through this purposeful practice task of calculating perimeter, as students rearrange the rectangles to form different compound shapes they will discover that the perimeter changes. They may also recognise that althought the perimeter changes, the area remains the same.

Displaying key words on the board can help minimise the cognitive load for students who might struggle to recall prior tems easily.They can also help guide students to use the correct mathematical language during class discussions

Key Words

Adding prompts that come up on the slide can also help with cognitive load, and act as a reminder for students when attempting the next examples

Prompts on the slide

Maths Mastery is built with success in mind


Teachers have high expectations for every single learner, rooted in a belief that anyone can become an excellent mathematician. Teachers reinforce this attitude to build confidence and resilience. Helen Drury

1. Explicit Instruction

  • use clear and succinct language when explaining things to pupils, checking their understanding frequently?
  • use dual coding (i.e. diagrams, images or tables on a mini-whiteboard) to aid students’ understanding of new content?
  • model how to complete a task before expecting pupils to work independently?

Are there any words your students might struggle with?Explaining definitions before beginning a task can help make sure it runs smoothly.

Definitions & Key Terms

They form the basis for developing high-quality assessments for formative and summative purposes.

Learning Objectives

They set student expectations, guide their learning processes, and help them focus their study time.

Clear learning objectives enable teachers and departments to create consistent learning environments, aligning the aims for each lesson.

If you want to check that your students are ready for the New Learning question, you may want to add some additional examples that build up gradually to it.This is a good time to look at the prio knowledge students need from the Start of Unit QuizThese wouldn't necessarily be on the slide all at once, they could be animated to show up one by one, or you may prefer to draw them on a whiteboard to save planning time creating them in powerpoint

Building Up Gradually

Language & Communication

In the Notes and Guidance slide for this Develop Learning we suggest that you offer students different prompt questions to encourage their thinking:“Compare the number of edges on the inside/outside of your shapes.” “Compare the number of long/short rectangle sides on the outside of your shape” “Can you form two different shapes with the same perimeter?'Encourage students to answer these questions in full sentences.

Having prompts for students can ensure that they are boing pointed in the right direction, that they are noticing the important parts of this task.

What are YOU going to say?

They are showed alongside the tasks that accompany each lesson.The lesson objectives can be found in each task, although every task may not encompass every one. By completing the lesson students will have been exposed to all the objectives.

This section goes through the objectives for each lesson

When planning your lessons, the Exit Ticket can provide key information about the learning objectives.By the end of the lesson students should have the neccessary skills and understanding to complete these questions.

Exit Ticket

Coordinating mathematical success: the mathematics subject report

The Ofsted subject review report of June 2023 evaluated the common strengths and weaknesses of mathematics in the schools inspected and considers the challenges that mathematics education faces. In paragraph 69 they found that

i.e. the practice of using prior attainment data informs decisions about curriculum choices for year 11 from year 9 data.


5. Using Technology

  • utilise technology as part of the delivery of interventions?
  • support pupils to use technology to record their learning, i.e. through speech-to-text software?

The New Learning slide is an opportunity to explicitly model calculating a perimeter so that students are able to work out the perimeter of different shapes.In this task they will also experience being aware of the sides of the square and triangle that are not a part of the perimeter of this compound shape.For some students, modelling the calculation using the distributive property of arithmetic would also be appropriate allowing students to experience connecting perimeter calculations to shapes using the axioms of number and algebra.

New Learning

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These are only our recommened discussion points, but there may be other areas where you might wish to pause and come together to discuss.

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These set out the overarching objectives for the whole week of lessons

3. Scaffolding

  • use scaffolds (visual, verbal, and written) that support pupils to access the learning?
  • use scaffolding in a way that reduces pupils’ reliance on adult support, lessening scaffolds over time?
  • provide scaffolds in a non-stigmatising way (i.e. providing them for a small group or pair, rather than only for 1 pupil)?

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Having key words written on the slide can help minimise cognitive load, but also prompt student discussion in the right direction.

Key Words

Think about breaking the question down into smaller chunks.You may want to scaffold the question to make it more accessible.

Adapting the Question

Students continue to demonstrate their undersanding of what they are able to do within this task and what they have understood about perimeter.This lovely task gives students an opportunity to develop their language in reasoning as they explain why Xavier is correct.


Ability is not fixed

Althought the term 'ability grouping' is frequently applied in the United Kingdom, in their report on The Achievement Gap, Hodgen et al say: 'We avoid this terminology, which suggests a perception of ‘ability’ as fixed. We refer instead to ‘attainment grouping’.'

achievement gap: The impact of between-class attainment grouping on pupil attainment and educational equity over time https://bera-journals.onlinelibrary.wiley.com/doi/10.1002/berj.3838

The National Curriculum Inclusion Statement states that teachers should set high expectations for every pupil, whatever their prior attainment.

High Expectations

See section 4:https://www.gov.uk/government/publications/national-curriculum-in-england-framework-for-key-stages-1-to-4/the-national-curriculum-in-england-framework-for-key-stages-1-to-4

4. Flexible Grouping

  • work with several different pupils, forming temporary groups when several pupils have the same current difficulty?
  • promote peer tutoring, facilitating pupils learning from one another?

The start of unit quiz can identify some key prior knowledge that students will need when accessing this unit. If you think students might need additional support with some of the aspects of this unit, ask your Mastery Lead to refer to the PL4 training module on Interventions.

Start of Unit Quiz

In this Low Threshold, High Ceiling purposeful practice, all students can practise calculating the perimeter of different compound shapes and some students can continue to practise and experience the axioms within their calculations.This task also lends itself to Mathematical Thinking as some students start to conjecture as to how they may make the longest and shortest perimeters.

Develop Learning

Planning your own questioning prompts will ensure that you are working with the Learning Objectives in mind.You will be able to guide students to the desired outcome of the task.You may want to include prompts that scaffold, such as 'What do you already know about the side lengths of squares?' and ones that challenge, 'Can you find multiple calculationsto work out the perimeter? '

Questioning Prompts