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.

Addition Years 1-3                 Addition Years 4-6

Division Years 1-3                 Division Years 4-6

Multiplication Years 1-3        Multiplication Years 4-6

Subtraction Years 1-3          Subtraction Years 4-6 

Videos to support mathematical teaching and learning -NCETM website

(some links require you to register on the NCETM website, this is free)

Multiplication

KS1 - Multiple Representations of https://www.ncetm.org.uk/resources/40530

KS1 - The commutative law for multiplication

Lower KS2 - Grid multiplication as an interim step Upper

KS2 - Moving from grid to a column Algebra
 

Algebra https://www.ncetm.org.uk/resources/43649

KS1 - Look at ’missing numbers’

KS2 - Equations and substitution 

 

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

Division https://www.ncetm.org.uk/resources/43589

KS1 - Sharing and grouping

KS 2 - Place value counters for division 

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) 

Fractions https://www.ncetm.org.uk/resources/43609

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* 

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

Multiplicative reasoning https://www.ncetm.org.uk/resources/43669

KS2 - Bar model for multiplication