Progression in Calculations

Progression in calculations at West Jesmond Primary School

This series of documents have been created to support our school in the implementation of the new National Curriculum for Mathematics (2013). A separate document for each operation (addition, subtraction, multiplication and division) addresses how each is ideally taught year by year.

The key to successful implementation of a school calculation policy is consistent use of representations (models and images that support conceptual understanding of the mathematics) and this policy promotes a range of relevant representations, across the primary years. Mathematical understanding is developed through use of representations that are first of all concrete (e.g. Dienes apparatus, Numicon,), and then pictorial (e.g. array, place value counters) to then facilitate abstract working (e.g. Columnar addition, long multiplication). This policy displays a logical and appropriate progression of representations and written strategies that develop children's conceptual understanding and procedural fluency. If at any point a pupil is struggling with a procedure, they should revert to concrete and/or pictorial resources and representations to solidify their conceptual understanding.

Videos to support mathematical teaching and learning -NCETM website
(some links require you to register on the NCETM website, this is free)
Algebra
https://www.ncetm.org.uk/resources/43649
KS1 - Look at ’missing numbers’
KS2 - Equations and substitution
Division
https://www.ncetm.org.uk/resources/43589
KS1 - Sharing and grouping
KS2 - Place value counters for division
Fractions
KS1 - Adding fractions and mixed numbers
KS2 - Using an array to add fractions
KS2 - Bar model dividing by fractions KS3 - Fraction wall to add fractions*
Multiplicative Reasoning
KS2 - Bar model for multiplication
 
 
 

Multiplication
KS1 - Multiplication representations of https://www.ncetm.org.uk/resources/40530
KS1 - The Commutative law for multiplication
Lower KS2 - Grid multiplication as an interim Upper
KS2 - Moving from grid to a column algebra
Number Facts
https://www.ncetm.org.uk/resources/40533
KS1 - Number bonds to ten KS1 - Consolidation and practice (Addition and Subtraction)
KS1 - Reinforcing Table Facts
KS1 - Rapid recall of multiplication facts multiplication facts
Number and Place value
https://www.ncetm.org.uk/resources/40534
KS1 - Counting in steps of one and ten
KS1 - Partitioning in different ways
KS1 - Addition and Subtraction
KS1 - Using resources to develop fluency and understanding
KS2 - Partitioning (subtraction)
Subtraction
https://www.ncetm.org.uk/resources/40532
Lower KS2 – Partitioning
Lower KS2 - Discussing Subtraction Strategies
Lower KS2 - Developing Column Subtraction Upper
KS2 - Column Subtraction Multi