Engaging Explanations

I was delighted to present a session at #MathsConfOnline from Complete Mathematics, August 22. The resources discussed in the session are all provided here with some relevant additional content.

‘When presenting content and ideas to students we need ‘engaging explanations that are just right for the students: neither too short nor too long; neither too complex nor too simple.’

Coe, R., Rauch, C.J., Kime, S., & Singleton, D. (2020). Great Teaching Toolkit: Evidence Review. Evidence Based Education.

Great Teaching toolkit: Evidence review – complete report, note the individual elements on page 6, including 4 Activating hard thinking.

Rosenshine’s Principles of Instruction – Research-Based Strategies That all Teachers Should Know.
(Further commentary and resources can be found in my post, Rosenshine’s Principles in the Mathematics Classroom).

White Rose Maths – Small Steps-Functions

White Rose Secondary Resources including Complete Secondary Small Steps


AQA – 90 maths problem solving questions

AQA’s 90 maths problem solving questions supports the problem solving requirement (AO3) of GCSE Mathematics. Very useful summary lists link questions to process skills and to content areas. Answers are provided for all the problems and very helpful full commentaries are given on 30 of the problems.


AQA GCSE Examination Questions

AQA GCSE Assessment Resources, AQA legacy GCSE question papers

AQA GCSE

There is also a good deal of evidence that the use of worked examples can
be helpful in introducing new ideas (Booth et al., 2017; Sweller et al., 2019).
Particularly effective are ‘completion problems’ where students are given
partial solutions and required to complete them
. These can help students to
focus on the examples but also manage the difficulty level while retaining
authentic tasks

For a collection of such problems, see Fill in the blanks…

Open Middle problems in GeoGebra

Distributive Property: Open Middle Theme


Building Blocks – Andy Lutwyche

Andy Lutwyche-Building Blocks

Spot the mistake resources including Erica’s Errors and Clumsy Clive from Andy Lutwyche
Show that… and What was the question? from Andy Lutwyche


PhET Interactive Simulations, University of Colorado Boulder, https://phet.colorado.edu

Use of Technology including PhET Simulations


Colour in Mathematics

Colour in Mathematics – the use of colour to add clarity


Here’s the diagram…what’s the question?


Colin Foster – including Mathematical Etudes


Transum Mathematics

Transum – Venn Paint Transum – Topic Index
Transum  Maths Map (Students)


AQA – Bridging the gap

AQA – Bridging the gap

This set of AQA resources was originally designed to support teaching and learning for the cohorts of students who studied the 2007 Key Stage 3 Programme of Study and were preparing for the then new Mathematics GCSE (8300). The resources are still very useful for students in KS3-KS4.
KS3-4 Bridging the gap.

This series of termly tests covers Years 7, 8 and 9 and can be used to check understanding as well as showing younger students what GCSE papers look and feel like. Extension tests are included and analysers are available for all tests.
AQA Key Stage 3 tests for Years 7, 8 and 9.


AQA Key stage 3 tests

AQA KS3 Tests