CLASSROOM PRACTICE
Good use of concrete, pictorial and abstract (CPA) representations are provided and pupils are encouraged to connect and see relations between these different representations.
The CPA approach is based on Jerome Bruner’s stages of representation.
Using technical and precise language. Asking lots of questions to check for understanding.
Concrete Pictorial Abstract
CPA - An article by Leong Yew Hoong, Ho Weng Kin, Cheng Lu Pien.
White Rose CPD Video
CPD Video and resources from White Rose Maths Hub about using concrete apparatus.
Mr Barton Podcast
A podcast by Mr Craig Barton and Bernie Westacott about using manipulatives to support mathematics.
Representation at KS3
NCETM guidance for some of the most useful representations for Key Stage 3 mathematics.
Improving Learning in Mathematics
Standards Unit by Malcolm Swam, University of Nottingham.
NCETM Bar Modelling
An overview from NCETM of use of the Bar Model for visualisations.
Addition and Subtraction Bar Model
Powerpoint shows developed from a workgroup in Kent and Medway. Designed to be used as a self study guide.
Multiplication and Division Bar Model
Powerpoint shows developed from a workgroup in Kent and Medway. Designed to be used as a self study guide.
Fractions Bar Modelling
Powerpoint shows developed from a workgroup in Kent and Medway. Designed to be used as a self study guide.
Bar Model Padlet
A collection of resources by Dawn Denyer about using the Bar Model.
NCETM Video Short
A video 'Moment' from NCETM on answering in full sentences.
Singapore Maths
Links from their website on problem solving.
Thinking Blocks
Thinking Blocks - Interactive tutorials for use with the Bar model.
Numicon
Youtube video about using Numicon.
Cuisenaire
Cuisenaire website.
Mathsbot
A great website with interactive demonstrations and manipulatves.
Nrich Directed Number
A nice page from Nrich about adding and subtracting postive and negative numbers. Includes some nice use of double sides counters.
Representations at KS3
A page from NCETM looking at representations at KS3.
NCETM Manipulatives in Secondary
Don’t abandon counters just because it’s secondary school - an article from NCETM.
Manipulatives in the Primary Classroom
NRICH Report by Jenni Back on the use of manipulatives in the classroom.