Calculation - guidance on pencil & paper methods
Pencil and paper procedures - Key Stages 1 - 3
LA Recommendations
written by the Leicestershire Numeracy Team
This policy contains the key pencil and paper procedures that we recommend be taught within a school across Key Stages 1 to 3. It has been written to ensure consistency and progression throughout the school. It is vital that this document is considered, discussed and agreed upon by the whole staff before implementation. As well as the paper version given out and discussed at the coordinator conference each section is available here for you to download to make the policy your own. This will allow you to adapt, amend or adjust the policy for your school or development group. Discussing this type of policy across a development group, as well as in individual schools, is a positive way of ensuring continuity and progression across all schools.
Although the focus of the policy is on pencil and paper procedures it is important to recognise that the ability to calculate mentally lies at the heart of the Numeracy Strategy. The mental methods in the Framework for teaching mathematics should be taught systematically from Reception onwards and pupils should be given regular opportunities to develop the necessary skills. However mental calculation is not at the exclusion of written recording and should be seen as complementary to and not as separate from it. In every written method there is an element of mental processing. Sharing written methods with the teacher encourages children to think about the mental strategies that underpin them and to develop new ideas. Therefore written recording both helps children to clarify their thinking and supports and extends the development of more fluent and sophisticated mental strategies.
Children should be encouraged to see mathematics as both a written and spoken language. Teachers should support and guide children through the following important stages:
- developing the use of pictures and a mixture of words and symbols to represent numerical activities;
- using standard symbols and conventions;
- use of jottings to aid a mental strategy;
- use of pencil and paper procedures;
- use of a calculator.
This policy concentrates on the introduction of standard symbols, the use of the empty number line to aid mental calculation and on the introduction of other pencil and paper procedures. It is important that children do not abandon jottings and mental methods once other pencil and paper procedures are introduced. Therefore children will always be encouraged to look at a calculation/problem and then decide which is the best method to choose - pictures, mental calculation with or without jottings, structured recording or a calculator. The long-term aim is for children to be able to select an efficient method of their choice (whether this be mental, written or in upper Key Stage 2 using a calculator) that is appropriate for a given task. They will do this by always asking themselves:
'Can I do this in my head?'
'Can I do this in my head using drawings or jottings?'
'Do I need to use a pencil and paper procedure?'
'Do I need a calculator?
- Background and front cover
- Key questions to consider for each operation (primary)
- Key questions to consider for each operation (secondary)
- Addition Y 1, 2, 3
- Addition Y 4, 5, 6
- Addition Y 7, 8, 9
- Subtraction Y 1, 2, 3
- Subtraction Y 4, 5, 6
- Subtraction Y 7, 8, 9
- Multiplication Y 1, 2, 3
- Multiplication Y 4, 5, 6
- Multiplication Y 7, 8, 9
- Division Y 1, 2, 3
- Division Y 4, 5, 6
- Division Y 7, 8, 9
Supporting documents
NEW September 2005: Updating division - a paper discussing the progression in division . This highlights some of the key knowledge and understanding children need to meet the age-related expectations set out in the Framework. It explores the idea of division using partitioning realted to multiples of the divisor.
- Division (objectives that support chunking/division)
- Multiplication (language and images)
- Questions from the 'Supplement of Examples' that imply division as grouping & sharing
- Questions from the 'Supplement of Examples' that imply subtraction as 'difference & take away'
- Extra guidance for recording in mathematics for years R to 3. This document offers more detailed guidance to support the LEA Recommendations for pencil and paper merthods. It is a WORD document to allow you to adapt it for your needs. (all tables/images are 'grouped' so if you wish to make changes you will need to 'ungroup')
- Homework Help sheets. These documents are intended to accompany specific problem solving/calculation homeworks. They are written as a step by step guide to inform parents about the particular method of calculation suitable for the homework. They are all WORD documents so can be adjusted to match your specific calculation policy. They are all written as A4 but could be reduced to A5 and/or laminated for repeated use. All use word problems to help illustrate the calculation procedure. No ages or levels are indicated on the sheets to allow them to be used whenever appropriate.
- Using arrays with grid multiplication. Here are 5 examples that can be photocopied/enlarged for classroom use together with a Powerpoint presentation to use on a monitor, with a group, or projected for class discussion.
- 14x2 array sequence, 14x5 array sequence,14x8 array sequence, 24x8 array sequence, 42x14 array sequence, Powerpoint versions (zipped)
- Using empty number lines in addition and subtraction - early developments
- Choosing calculation strategies - some ideas for encouraging children to select the most approriate strategies for different calculations
- Mathematics outside - -ideas for reception and foundation
- Early recording - ideas for reception
- Powerpoint presentations for maths coordinators to use in staff development. These include 'Introducing the Leicestershire Pencil & Paper Procedures', 'Using Number Lines and Beadstrings' (this is a big file) and detailed presentations on 'Subtraction, Multiplication and Division'.
Each Powerpoint presentation comes in a zipped file and has notes in the 'view notes' format of the Powerpoint presentation. Most have a Word version of the same notes. These provide presenter notes for each slide of the presentation.
Powerpoint notes for Pencil & Paper Procedures, Using Number Lines, Subtraction, Multiplication and Division.
(NB At present you will need POWERPOINT on your computer to run these presentations after you have unzipped them. You will obviously need to be in presentation mode for the 'animations' to work. We are intending to add versions complete with a viewer for those who have not got Powerpoint).
- Using models and images to support mathematics teaching and learning in Years 1 to 3
Reference/Code/Order number(s): DfES 0508/2003.
This is an interactive CD ROM with accompanying models and images charts. It includes video clips showing different models and images for teaching mathematics in Years 1 to 3. It also contains examples of Unit Plans for Years 1 to 3; Support Sessions for helping children needing support in coping with the mathematics in the Unit Plans; and Interactive Teaching Programs. Accompanying the CD are six Models and Images charts addressing key areas of mathematics in the Years 1 to 3 curriculum. The clips can be selected and controlled to allow for reflection and discussion. Each clip highlights how models and images are being used.
Page Last Updated: 21 December 2009
