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Numeracy Policy

Preamble

“Numeracy is different to the mathematics subject in that it is the application of the skills

learned in mathematics in a cross-curricular, real-world way, and not purely about the

skills themselves.” (Literacy and Numeracy framework consultation document 2012).

In September 2013 the non statutory ‘Skills Framework’ which currently covers

numeracy and literacy will be replaced with the statutory ‘Literacy and Numeracy

Framework’. This statutory document will make it the responsibility of all teachers to

develop, assess and report on the levels of numeracy of their pupils in their subject.

Aims of this policy

To enhance standards in Numeracy across the curriculum.

To enable students to transfer numeracy skills across subject areas.

To promote a consistency of approach.

To increase the awareness amongst all teachers where their subject can provide

opportunities for learners to enhance their numeracy skills.

To help pupils appreciate the importance of numeracy in their lives.

To ensure a consistency in assessment of numeracy in each subject area and to

report on the progress of all pupils in numeracy in each subject.

To synchronise the teaching of certain topics across the subject areas

Every subject makes a contribution to numeracy across the curriculum. Some subjects

have more opportunities than others to extend pupils’ experience through numeracy

than others.

Within Numeracy the new framework expects young people to become more

accomplished in:

Developing numerical reasoning

Using number skills

Using measuring skills

Using data skills

They will be accomplished when they have acquired the skills and been able to apply

them to complete realistic tasks appropriate for their stage of development.

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Policy

It is recognised that some departments are major users of numeracy whereas others

are minor users.

All departments will develop curriculum content to ensure that all learners have

opportunities to develop and refine their numeracy skills.

Schemes of work should include strategies to improve numeracy.

Teachers will integrate numeracy into their teaching.

Assessment at KS3 should be informed by the particular numeracy skills (as

described in the Numeracy Framework Matrix see Appendix 1).

It is the responsibility of all staff to address numeracy and to act as positive role

models.

Staff must actively intervene and support pupils who display a weakness in any

or all of the key areas of numeracy.

Staff must actively intervene and support pupils who display gift and talents in

any or all of the key areas of numeracy.

Process

SMT

Actively support and promote the drive for improved standards of numeracy for

all.

Help co-ordinate and sustain the policy.

Meet resource and training requirements.

Support the monitoring and evaluation of the policy on a whole school and

departmental level.

Recognise and adopt the policy in the School Development Plan.

Ensure that the interest and support of parents are engaged.

Departments

Provide realistic and appropriate tasks for their pupils’ stage of development to

develop pupils’ numeracy.

Clearly sign post where they provide numeracy opportunities in their scheme of

work.

Incorporate the training and resources provided, adapting and refining to suit

departmental need and character.

Develop and publish a departmental numeracy policy (including an action plan).

Assess and monitor pupils’ development in numeracy.

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Staff

Recognise the importance of numeracy in learning.

Follow the departmental policy.

Provide realistic and meaningful tasks for all pupils in their subject at an

appropriate level for their stage of development taking into account ALN, Basic

Skills and MAT pupils. (see Basic Skills/Numeracy Appendix 4)

Acknowledge the progression required in numeracy for their pupils (see appendix

1 ‘Numeracy framework Matrix’).

Work with the Mathematics Department in using common approaches to

numeracy and language where appropriate (see appendix 2 ‘Glossary of

Numeracy terms’).

Analyse and synthesise assessment data to support improvement.

Synchronise the timing of delivery of certain topics with other departments.

Numeracy co-ordinator

Review and promote policy and any further updates

Share information and ideas that will impact upon the delivery of numeracy

across the curriculum.

Support colleagues individually or departmentally.

Identify suitable training needs and resources.

Audit and advise on the provision of numeracy across the curriculum.

Promote numeracy strategy with parents.

Mathematics Department.

Teach the skills, where practicably possible before they are to be developed

by other subjects.

Provide guidance and strategies of support to other departments on standard

methods for use with pupils who have not established the skills required for

that level of numeracy.

Help develop common approaches and consistency of language used with

numeracy.

Provide guidance in the use of calculators (see appendix 3 ‘Calculator

Guidance’)

Make available any relevant assessment information regarding pupils’

numeracy ability.

Promote numeracy with parents.

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Procedures

The following table is a short summary of some of the topic areas where numeracy

across the curriculum can be found.

Area and volume

Calculation techniques

Co-ordinates: 3D (CAD/CAM); Bearings

Estimation.

Formulae: triangle representation; use of words and symbols

Graphs: bar graphs; pie charts; pictograms; scatter graphs; histograms; line graphs; algebraic graphs.

Measuring: units; prefixes (e.g. pico, nano,etc) Units of compound measure

such as speed; Use of measuring equipment; Conversion of units.

Negative numbers

Proportions: fractions; percentages; decimals; ratio and scales.

Shape and space: nets; symmetry; tessellation; transformations.

Surveys and data capture.

Tables of data: constructing; reading; interpretation.

Trial and improvement

Standard Form, indices, terms such as square root, cube root and square etc.

Collect and record data and use averages: mean, mode, median and measures of spread, range.

Money Profit, loss, interest, savings

including compound interest.

Some of the more common topics are in bold.

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Appendix 1 The KS3 Numeracy Framework (January 2013 Final)

Numeracy KS3

Strands Elements Year 7 Learners are able to:

Year 8 Learners are able to:

Year 9 Learners are able to:

Developing numerical reasoning

Identify processes and connections

Transfer mathematical skills across the curriculum in a variety of contexts and everyday situations

Select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks

Prioritise and organise the relevant steps needed to complete the task or reach a solution

Choose an appropriate mental or written strategy and know when it is appropriate to use a calculator

Use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys

Identify, measure and obtain required information to complete the task

Select appropriate mathematics and techniques to use

Estimate and visualise size when measuring and use the correct units

Represent and communicate

Explain results and procedures precisely using appropriate mathematical language

Refine methods of recording calculations

Use appropriate notation, symbols and units of measurement, including compound measures

Select and construct appropriate charts, diagrams and graphs with suitable scales

Interpret graphs that describe real- life situations, including those used in the media, recognising that some graphs may be misleading

Review Select and apply appropriate checking strategies

Interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays are sensible

Verify and justify results or solutions, including discussion on risk and chance where relevant

Interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data

Draw conclusions from data and recognise that some conclusions may be misleading or uncertain

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Strands Elements Year 7 Learners are able to:

Year 8 Learners are able to:

Year 9 Learners are able to:

Using Number Skills Use number facts and relationships

Read and write numbers of any size and use the four operations and the connections between them e.g. apply division as the inverse of multiplication

Recognise and apply key mental facts and strategies

Use appropriate strategies for multiplication and division, including application of known facts

Use the terms square and square root

Recognise and apply key mental facts and strategies

Use known facts to derive others e.g. use 7 x 6 to derive 0.7 x 6

Use the terms cube, cube root and reciprocal

Use powers and understand the importance of powers of 10

Show awareness of the need for standard form and its representation on a calculator

Fractions, decimals, percentages and ratio

Use equivalence of fractions, decimals and percentages to compare proportions

Recognise that some fractions are recurring decimals e.g. 1/3 is 0.333

Calculate percentages of quantities by using non-calculator methods where appropriate

Use ratio and proportion including map scales

Use equivalence of fractions, decimals and percentages to select the most appropriate for a calculation

Simplify a calculation by using fractions in their simplest terms

Calculate a percentage, fraction or decimal of any quantity with a calculator where appropriate

Calculate the outcome of a given percentage increase or decrease

Use ratio and proportion to calculate quantities

Use equivalence of fractions, decimals and percentages to select the most appropriate for a calculation

Use and interpret different representations of fractions e.g. mixed numbers and improper fractions

Express one quantity as a percentage of another

Calculate a percentage increase or decrease

Use ratio and proportion to calculate quantities

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Strands Elements Year 7 Learners are able to:

Year 8 Learners are able to:

Year 9 Learners are able to:

Using Number Skills Calculate using mental and written methods

Use efficient written methods to add and subtract numbers with up to 2 decimal places

Multiply and divide 3 digit by 2 digit whole numbers; extending to multiplying and dividing decimals with one or two places by single-digit whole numbers

Multiply and divide whole numbers by 0.5, 0.2, 0.1

Use the order of operations

Use efficient written methods to add and subtract numbers with up to 2 dp

Use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.

Use the order of operations including brackets

Use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places

Multiply and divide whole numbers and decimals

Use the order of operations including brackets and powers

Estimate and check Use a range of strategies to check calculations, including the use of inverse operations, equivalent calculations and the rules of divisibility

Use rounding to estimate answers

Present answers to a given number of decimal places

Use rounding to estimate answers to problems to a given number of significant figures

Present answers to a given number of significant figures

Make and justify estimates and approximations of calculations

Choose the appropriate degree of accuracy to present answers

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Strands Elements Year 7 Learners are able to:

Year 8 Learners are able to:

Year 9 Learners are able to:

Using Number Skills Manage money Use profit and loss in buying and selling calculations

Understand the advantages and disadvantages of using bank accounts, including bank cards

Make informed decisions relating to discounts and special offers

Carry out calculations relating to VAT, saving and borrowing

Appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing

Calculate using foreign money and exchange rates

Understand the risks involved in different ways of saving and investing

Describe why insurance is important and understand the impact of not being insured

Using measuring skills

Length, weight /mass, capacity

Find perimeters of shapes with straight sides

Read and interpret scales on a range of measuring instruments

Convert between units of the metric system and carry out calculations

Use the common units of measure, covert between related units of the metric system and carry out calculations

Use rough metric equivalents of imperial units in daily use

Find circumferences of circles

Make links between speed, distance and time

Time Measure and record time in hundredths of a second

Use time zones

Interpret fractions of a second appropriately

Use timetables and time zones to calculate travel time

Temperature Record temperatures in appropriate temperature scales

Convert temperatures between appropriate temperature scales

Convert temperatures between appropriate temperature scales

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Strands Elements Year 7 Learners are able to:

Year 8 Learners are able to:

Year 9 Learners are able to:

Using measuring skills

Area and volume Angle

Use formula for the area of rectangles and triangles

Measure and draw angles

Calculate areas of compound shapes (e.g. consisting of rectangles and triangles) and volumes of simple solids (e.g. cubes and cuboids)

Use compass bearings and grid references to specify locations

Find areas of circles

Apply understanding of bearings and scale to interpret maps and plans and to create plans and drawings to scale

Using data skills Collect and record data Present and analyse data Interpret results

Collect own data for a survey e.g. through designing a questionnaire

Construct frequency tables for sets of data, grouped where appropriate, in equal class intervals (groups given to learners)

Construct a wide range of graphs and diagrams to represent the data and reflect the importance of scale

Interpret diagrams and graphs (including pie charts)

Use mean, median, mode and range to compare two distributions (discrete data)

Plan how to collect data to test hypotheses

Construct a wide range of graphs and diagrams to represent discrete and continuous data

Construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate

Construct graphs to represent data including scatter diagrams to investigate correlation

Interpret diagram and graphs to compare sets of data

Use mean, median, mode and range to compare two distributions (continuous data)

Test hypotheses, making decisions about how best to record and analyse the information from large data sets

Construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, with the learner choosing an appropriate scale

Select and justify statistics most appropriate to the problem considering extreme values (outliers)

Examine results critically, select and justify choice of statistics recognising imitations of any assumptions and their effect on the conclusions drawn

Use appropriate mathematical instruments and methods to construct accurate drawings

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More able and talented Extension

Strands Elements Learners are able to:

Developing numerical reasoning

Identify processes and connections

Transfer mathematical skills across the curriculum in a variety of contexts and everyday situations

Select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks

Prioritise and organise the relevant steps needed to complete the task or reach a solution

Choose an appropriate mental or written strategy and know when it is appropriate to use a calculator

Use a scientific calculator to carry out calculations effectively and efficiently using the available range of function keys

Identify, measure and obtain required information to complete the task

Select appropriate mathematics and techniques to use

Estimate and visualise size when measuring and use the correct units

Represent and communicate

Explain results and procedures precisely using appropriate mathematical language

Refine methods of recording calculations

Use appropriate notation, symbols and units of measurement, including compound measures

Select and construct appropriate charts, diagrams and graphs with suitable scales

Interpret graphs that describe real- life situations, including those used in the media, recognising that some graphs may be misleading

Review Select and apply appropriate checking strategies

Interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays are sensible

Verify and justify results or solutions, including discussion on risk and chance where relevant

Interpret mathematical information; draw inferences from graphs, diagrams and data, including discussion on limitations of data

Draw conclusions from data and recognise that some conclusions may be misleading or uncertain

Using number skills Use number facts and relationships

Use and interpret numbers in standard form within calculations

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Fractions, decimals, percentages and ratio

Use and understand the idea of reverse percentage to find an original quantity

Use multipliers as an efficient method when working with percentages e.g. multiply by 1.2 to increase the amount by 20%

Use and understand ratio and proportion in 2 dimensions

Calculate using mental and written methods

Estimate and check Recognise and define limitations on accuracy of measurements

Manage money Use and understand efficient methods of calculating compound interest

Understand and demonstrate the real-life process of foreign exchange

Understand and calculate income tax

Using measuring skills

Length, weight/mass, capacity

Understand and use a variety of compound measures

Time

Temperature

Area, volume Angle and position

Apply proportional change to 2 dimensional designs

Collect and record data Present and analyse data Interpret results

Understand slopes and gradients of graphs and relate to compound measures

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Appendix 2 Numeracy terms

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In everyday language we talk about our own weight in stones and pounds or kilograms. This is in fact our mass.

Most people get muddled on the difference between mass and weight in science. Weight is the force due to gravity on a mass.

Mass is just a measure of how much matter a body has. For this reason, your mass is the same on Earth or the Moon, or even in space. Your weight will be completely different!

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Appendix 3 Calculator Policy

Calculator Policy

Preamble

It is important that the school has a policy on the use of calculators. An over reliance on

the use of calculators often prevents fluency in computation and can affect confidence

in recalling basic number facts.

Each department that uses calculators will need to consider their use in their subjects

and may need to add to this Policy.

Policy

As a whole school, except under exceptional circumstances that would need to

be stated under this policy year 7 will be a non calculator year group.

The mathematics department will teach basic calculator use at the beginning of

year 8 and any department using calculators before this will need to take this into

account.

From year 8 and above the following should be considered when undertaking

calculations.

Pupils’ first resort should be mental methods

Do pupils have the technical skills required to use the basic facilities of a

calculator constructively and efficiently, the order in which to use the keys,

how to enter numbers as money, measures, fractions etc ?

Do pupils know how to interpret the calculator display in context (e.g 5.3 in

terms of money is £5.30) ?

The type of calculator: the order in which calculators work out calculations

can differ. Scientific calculators follow the rules of BIDMAS ( see below) but

most cheaper ones don’t. It is important that a pupil knows the type of

calculator that they are using as this may affect the order in which they use

the buttons.

Pupils should be encouraged to consider the appropriateness of their answer

that the calculator has given them and to consider the answer in the context

of the question. There should also be some check involved.

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Procedures

The mathematics department have appropriate calculators for sale, should pupils

wish to purchase them from school.

For examination papers where the use of calculators is allowed, candidates are

responsible for making sure that their calculator meets the awarding bodies’

regulations.

Calculators must:

Have removable lids, cases and covers so they can be free of printed

instructions and formulae during an examination.

Calculators must not:

Be designed or adapted to offer any of these facilities:

Language translator

Symbolic algebra manipulation

Symbolic differentiation or integration

Communication with other machines or internet

Have retrievable information stored in them including:

Databanks

Dictionaries

Mathematical formulas

Text

BIDMAS B - brackets are done first, I – indices, D – division, M – multiplication,

A – addition, S – subtraction.

Also used is BODMAS, where the O – orders (powers, square roots etc)

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Appendix 4 Basic Skills Numeracy Information

NUMERACY advice for Basic Skills pupils

Reference to other lessons where numeracy skills covered

• Teachers explain mathematical concepts when skills have not previously been covered

• Questions asked to assess pupils’ understanding of mathematical terms

• Mathematical terms explained and used consistently

• Pupils required to work out simple calculations mentally

• When appropriate to use calculators, guidance given and checks made of learners’ understanding

• Pupils encouraged to approximate to check answers

• Pupils permitted to use range of calculation methods

• Mini whiteboards and/ or number fans used for calculations so all pupils’ answer

• Resources are used to support the learning of mathematical concepts

• Pupils are asked to explain their methods and ways of working

• Strategies offered to help overcome difficulties

• Numeracy lesson starters used to prepare if significant maths is to be encountered in the lesson

• The use of measuring equipment is modelled

• There is a focus on suitable units of measure including conversion of units

• Support is provided to construct and interpret numbers in graphs, diagrams, charts and tables