Enigma Essence Toolkit

Essence of Mathematics learning and teaching with Enigma Maths Hub - School version.pdf

The content on this site highlights the essence of primary and secondary mathematics including relevant assessment material and supporting classroom resources.

This toolkit is designed to help schools capture the essence of maths learning across phases in maths education which will aid transition and progression across phases.

The essence of primary is taken from the DfE ready to progress criteria and guidance.

The essence of KS3 focuses on the core strands of the KS3 programme of study that do not have a significant overlap with KS4.

This toolkit can be useful for:


Contact us at enigmamathshub@denbigh.net and let us know how you have used the toolkit.

If you find any mistakes or have suggestions for improvement please contact us.

Essence map using RTP JYW5.pdf

This document above is part of a collaborative Work Group of Primary and Secondary schools from the Enigma Maths Hub region.

The focus of the Work Group is to support our schools to capture the ‘essence’ of maths learning across phases in education which will aid transition for pupils and students. The teaching, learning and assessment material contained in this site can be used to aid planning for Covid recovery.

With the publication of the DfE guidance which is being used to inform maths learning and teaching in core concepts we chose to use this as a starting point for our collaborative work.

Toolkit overview

The quizzes and resources in this toolkit can support:

long-term, medium-term and short-term planning.

At the long-term planning stage, this toolkit can be used to ensure that the most important elements that underpin the curriculum are covered at the right time, and to ensure that there is continuity and consistency for pupils as they progress from one year group to the next. At the medium-term planning stage, teachers can use the guidance to inform decisions on how much teaching time to set aside for the different parts of the curriculum. Teaching time can be weighted towards the ready-to-progress criteria in primary or the core strands in KS3.

The ready-to-progress tables in the DfE guidance at the start of each year group and the ‘Making connections’ features support medium-term planning by demonstrating how to make connections between mathematical ideas and develop understanding based on logical progression. At the short-term planning stage, the guidance can be used to inform teaching strategy, and the representations and ‘Language focus’ features can be used to make concepts more accessible to pupils.

Curriculum prioritisation in primary maths 2020/21

KS3 curriculum prioritisation documents.

pre-teaching and intervention

Pre-teaching - children who are less confident at maths and who may struggle with the concepts being taught, work in a small group with an adult immediately prior to the lesson, looking at the maths they are just about to cover.

This can enable pupils to feel much more confident as they are able to access the learning, which allows them to move along at the same pace as the rest of the class.


Maths interventions are often time-limited additional maths sessions to address gaps in learning. Maths interventions have the most impact when led by teachers. This can involve teachers leading the intervention or taking an active lead in supporting other adults to lead the intervention.

Student facing material to support pre-teaching and intervention

KS3 intervention.


Support conversations between teachers of adjacent year groups and phases, so that class teachers understand what pupils have been taught in previous years, how they have been taught it, and how effectively pupils have understood and remembered it.

Transition Work Groups

Year 4 to 5

KS2 to KS3

Middle to Upper

DfE Exams and Assessment Guidance

The DfE have cancelled the statutory Key Stage 1 and Key Stage 2 tests and key teacher assessments planned for summer 2021, including the Key Stage 2 tests in reading and mathematics.

The DfE suggest that schools should continue to use assessment during the summer term, using past test papers if you wish*. This will inform teaching, enable you to give information to parents on their child’s attainment in their annual report, and support transition to secondary school.

*Enigma Assessments are a perfect low workload high impact solution to assessing pupil understanding in core concepts and identifying gaps.

  • Pupils and learners won’t benefit from racing through subjects at pace.

  • This is about schools making intelligent choices, not simply cramming everything in.

  • What are the building blocks that will help them move on to their next stage?

Amanda Spielman's speech

A speech by Ofsted's Chief Inspector at the ASCL (Association of School and College Leaders) Annual Conference 2021.

Quizzes and Resources


Video introducing the DfE primary national curriculum guidance

This three-minute video introduces the new DfE primary national curriculum guidance, and explains how schools and teachers can use the ready-to-progress criteria to plan an effective maths curriculum.

Every strand in the RTP assessment contains:

  • links to exemplification resources from year 1 to year 6 including PowerPoints created for use in small groups or one to one to support review, practice, and consolidation.

  • MS form version of the assessment quizzes covering year 2 to 4 and year 4 to year 6 (ideal for transition)

  • PowerPoint containing pupil friendly versions of the example assessments from year 1 to year 6

PowerPoints containing pupil friendly versions of the example assessments by year group are available in the Primary section.

NPV1 Strand Example

Number and Place Value 1 - Content and Exemplification Resources

FS - ELG Verbally count beyond 20, recognising the pattern of the counting system.

1NPV–1 Count within 100, forwards and backwards, starting with any number.

3NPV–1 Know that 10 tens are equivalent to 1 hundred, and that 100 is 10 times the size of 10. Apply this to identify and work out how many 10s there are in other three-digit multiples of 10.

4NPV–1 Know that 10 hundred are equivalent to 1 thousand, and that 1,000 is 10 times the size of 100. Apply this to identify and work out how many 100s there are in other four-digit multiples of 100.

5NPV–1 Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1.

Know that 100 hundredths are equivalent to 1 one, and that 1 is 100 times the size of 0.01.

Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01.

6NPV–1 Understand the relationship between powers of 10 from 1 hundredth to 10 million, and use this to make a given number 10, 100, 1,000, 1 tenth, 1 hundredth or 1 thousandth times the size (multiply and divide by 10, 100 and 1,000).


Multiply and divide decimals by powers of 10


The KS3 section breaks each strand of the KS3 Programme of Study into a sequence of small steps. Each strand is linked to prior learning from year 5 and year 6 and GCSE content. Further exemplification is provided in the NCETM Secondary PD material. Each strand contains a Microsoft form with example assessment questions from the KS3 Mastery Assessment Material and Secondary Mastery PD material from the NCETM.

N1 Example

  • Understand and use place value for decimals and measures.

  • Understand place value in integers

  • Understand place value in the context of measure

  • Understand place value in decimals

  • Understand place value in decimals, including recognising exponent and fractional representations of the column headings in place value tables

N1 Quiz


N1. order decimals; use the symbols =, ≠, <, >, ≤, ≥

Prior Learning

5NPV–1 Know that 10 tenths are equivalent to 1 one, and that 1 is 10 times the size of 0.1. …

Know that 10 hundredths are equivalent to 1 tenth, and that 0.1 is 10 times the size of 0.01.

5NPV–2 Recognise the place value of each digit in numbers with up to 2 decimal places, and compose and decompose numbers with up to 2 decimal places using standard and non-standard partitioning.

6NPV–2 Recognise the place value of each digit in numbers up to 10 million, including decimal fractions, and compose and decompose numbers up to 10 million using standard and non- standard partitioning.

NCETM Secondary PD material 1.1.1

Core Representations in Primary and Secondary

The core representations in this document expose mathematical structure and help pupils to secure conceptual understanding. A coherent and consistent use of core representations can support transition ad enable pupils to make connections.

In secondary schools the use of core representations exposes the connections between number and algebra.

“symbolise manipulation leads to manipulating the symbols”

Pete Griffin, Assistant Director (Secondary), NCETM

Core Representations in Primary and Secondary for essesnce.pdf