© Crown copyright 2001 Key Stage 3 National Strategy Numeracy Across the Curriculum.

© Crown copyright 2001

Key Stage 3 National Strategy


Numeracy Across the Curriculum



Objectives for session 1

• To consider the need to raise standards in numeracy

• To consider current images of mathematics and mathematicians

• To introduce the definition of numeracy

• To consider the need for improving numeracy skills across the curriculum

OHT 1.0



Views of mathematics

Mathematics is …

• an important subject

• nothing to do with real life

• a boys’ subject

• something you can either do or you can’t

• about learning rules

• about right and wrong answers

OHT 1.1



Points for discussionConsider the definition of numeracy (handout 1.2)

• Are there any areas of mathematics useful to your subject which you feel are not covered by the definition?

• Which aspects of the definition are most relevant to the work of your department?

• Identify the two most important aspects of numeracy you require for each of the Years 7, 8 and 9.

OHT 1.2



A definition of numeracy 1By Year 9, pupils should:

• have a sense of the size of a number and where it fits into the number system

• recall mathematical facts confidently

• calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculation strategies

• use proportional reasoning to simplify and solve problems

• use calculators and other ICT resources appropriately and efficiently to solve mathematical problems, and select from the display the number of figures appropriate to the context of a calculation

OHT 1.3




• use simple formulae and substitute numbers in the

• measure and estimate measurements, choosing suitable units, and reading numbers correctly from a range of meters, dials and scale

• calculate simple perimeters, areas and volumes, recognising the degree of accuracy that can be achieve

• understand and use measures of time and speed, and rates such as £ per hour or miles per litre

• draw plane figures to given specifications and appreciate the concept of scale in geometrical drawings and maps

OHT 1.4




• understand the difference between the mean, median and mode and the purpose for which each is used

• collect data, discrete and continuous, and draw, interpret and predict from graphs, diagrams, charts and tables

• have some understanding of the measurement of probability and risk

• explain methods and justify reasoning and conclusions, using correct mathematical terms

• judge the reasonableness of solutions and check them when necessary

• give results to a degree of accuracy appropriate to the context

OHT 1.5



Priorities for cross-curricular numeracy

• To improve accuracy, particularly in calculation, measurement and graphical work

• To improve interpretation and presentation of graphs, charts and diagrams

• To improve reasoning and problem solving

OHT 1.6



Numeracy in Ofsted inspectionsIn relation to numeracy, inspectors should establish:• whether there is clear understanding and consistent practice

among staff in the development of pupils’ mental skills, written methods of calculation and use of calculators

• if pupils can identify and use an efficient strategy for the calculations they need to do

• if pupils cope well with the mathematical demands made in different subjects, or are held back through lack of mathematical knowledge or poor basic skills in numeracy

• how well numeracy and, where appropriate, other mathematical skills are taught, developed or practised in other subjects

OHT 1.7



Objectives for session 2• To consider one school’s approach to

numeracy across the curriculum• To introduce activities to develop oral

communication skills• To discuss whether similar activities could be

used in other subjects when mathematical skills are required

• To explore possible areas for inter-departmental co-operation in this type of activity

OHT 2.0



Managing numeracy across the curriculum

• Which aspects of the work done in Ledbury on numeracy across the curriculum could be developed in our school?

• Are there any other activities that might help to raise standards of numeracy across our school?

• How can we maintain a focus on numeracy skills?

OHT 2.1



Washing Up

OHT 2.2

Give a plausible explanation for the shape of this graph.



Scales

OHT 2.3



Discussion points

Consider the activities modelled in this session.• Do you use (or might you use) similar

approaches to graphical interpretation or reading scales in your own subject?

• Could your own subject benefit from the group problem-solving approach?

• Are there are any examples you could offer the mathematics department, to benefit both subjects?

OHT 2.4




• To discuss situations where the teaching of mathematics can be enhanced by using examples from other subjects

• To explore opportunities for collaborative planning and teaching of mathematical topics

OHT 3.0




• To consider the need to raise standards in numeracy

• To review the school’s existing practice in numeracy across the curriculum by:

• comparing existing practice with a video of work in another school

• checking the requirements of the National Curriculum

• discussing how best to sustain the work already started

OHT 4.0




• have a sense of the size of a number and where it fits into the number system

• recall mathematical facts confidently

• calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculation strategies

• use proportional reasoning to simplify and solve problems

• use calculators and other ICT resources appropriately and efficiently to solve mathematical problems, and select from the display the number of figures appropriate to the context of a calculation

OHT 4.1




• use simple formulae and substitute numbers in them

• measure and estimate measurements, choosing suitable units, and reading numbers correctly from a range of meters, dials and scales

• calculate simple perimeters, areas and volumes, recognising the degree of accuracy that can be achieved

• understand and use measures of time and speed, and rates such as £ per hour or miles per litre

• draw plane figures to given specifications and appreciate the concept of scale in geometrical drawings and maps

OHT 4.2



A definition of numeracy 3By Year 9, pupils should:• understand the difference between the mean, median and mode

and the purpose for which each is used

• collect data, discrete and continuous, and draw, interpret and predict from graphs, diagrams, charts and tables

• have some understanding of the measurement of probability and risk

• explain methods and justify reasoning and conclusions, using correct mathematical terms

• judge the reasonableness of solutions and check them when necessary

• give results to a degree of accuracy appropriate to the context

OHT 4.3



Discussion Points

• Discuss the definition of numeracy and compare it, where possible, with that used in our whole-school numeracy policy

• How should our policy be updated to incorporate any differences?

OHT 4.4



Our current numeracy policy

• How can we judge or measure our success in numeracy across the curriculum?

• How can we continue to involve all staff (for example, new staff/NQTs)?

• How can we incorporate any future changes in the curriculum into our numeracy programme?

• How can we make best use of ICT to improve numeracy?

• How successful have we been so far in informing and involving parents/governors in improving numeracy?

OHT 4.5




• To introduce teachers to the Framework for teaching mathematics: Years 7, 8 and 9

• To exemplify oral and mental work in mathematics

• To consider the approach to calculation

OHT 5.0



Contents of the Framework for teaching mathematics

• Guide to the Framework• Key objectives• Yearly teaching programmes• Supplement of examples: Years 7, 8 and 9• Vocabulary checklist

OHT 5.1



Strands of the yearly teaching programmes

• Using and applying mathematics to solve problems

• Numbers and the number system• Calculations• Algebra• Shape, space and measures• Handling data

OHT 5.2



Oral and mental work• Develop and explain mental calculation strategies, including

figuring out new facts from known facts

• Apply calculation skills in algebra, for example to substitute numbers in expressions or to solve simple equations

• Develop estimation skills

• Practise the interpretation of data

• Develop mental imagery of shapes, movements and constructions

• Rehearse the use of mathematical vocabulary and develop oral communication skills

• Develop the ability to generalise, reason and prove

OHT 5.3



Some of the possible visualisations

OHT 5.4



Skills of mental calculation

• Remember number facts and recall them without hesitation

• Use known facts to figure out new facts• Draw on a repertoire of mental strategies to work out

calculations, with some thinking time• Understand and use the relationships between

operations to work out answers and check results• Approximate calculations to judge whether or not an

answer is about the right size• Apply skills to solve numerical problems

OHT 5.5




• To review the use of calculators within departments

• To look at progression in calculator skills• To explore the features of different types of

calculators• To contribute to a school policy on calculator

use

OHT 6.0



Calculator skills that pupils need to develop• Selecting from the display the number of figures

appropriate to the context of a calculation

• Entering numbers and interpreting the display when the numbers represent money, metric measurements, units of time or fractions

• Knowing the order in which to use the keys for calculations involving more than one step

• Using facilities such as the memory, brackets, the square root, cube root, sign change and fraction keys, and the constant facility

• Judging whether an answer is reasonable

OHT 6.1



Calculator skills expected by the end of Year 6 (i)• Use a calculator to perform a one-step calculation

and interpret the result• Key in and interpret money and measurement

calculations• Extend to calculations with more than one step,

e.g. 18 x (137 + 258)• Recognise rounding errors, e.g. recognise

2.9999999 as 3• Recognise negative numbers and use the sign

change key if appropriate

OHT 6.2 a



Calculator skills expected by the end of Year 6 (ii)

• Find decimals equivalent to fractions

• Recognise recurring decimals, e.g. 0.33333333

• Start to use memory keys and perform more complex calculations, such as: (234 + 739) ÷ (145 – 89)

• Have a feel for the size of an answer and check it appropriately

OHT 6.2 b



Ageing fast

OHT 6.3

Juliet works out her age as 6 311 520 minutes.

Calculate how old she is (exactly!) in years, months and days.

Check your answer by reversing the calculation



Comparing calculators

OHT 6.4

For each key sequence, predict the outcome when you enter it on a basic calculator and a scientific calculator.

Now see if you were right.



Departmental policy on using calculators• Does our scheme of work make it clear when and where

pupils are likely to require calculators?• Are there times when we will expect pupils to do

calculations without resorting to a calculator?• Do we make it clear to pupils when and where we expect

them to use a calculator and when we expect them not to?• How do the calculator skills we expect pupils to use line

up with those in the Framework for teaching mathematics?• Are there opportunities in our scheme of work to teach or

reinforce identified calculator skills?• Is our departmental policy consistent with the school

policy?

OHT 6.5




• To become familiar with the approach to handling data in the Framework for teaching mathematics: Years 7, 8 and 9

• To explore possible opportunities for handling data across the curriculum

• To interpret graphs, charts and diagrams• To consider common difficulties in handling

data

OHT 7.0



The handling data cycle

OHT 7.1



Features of handling data in Key Stage 3

• Basing work on purposeful enquiry, using situations of interest and relevance to pupils and making appropriate links to other subjects

• Placing an emphasis on making inferences from data, drawing on a range of secondary sources to ensure that samples are sufficiently large

• Using ICT as a powerful source of data, and as a means of processing data and simulating situations

OHT 7.2



Handling data across the curriculum

• Are all the different stages of the handling data cycle applicable to your subject?

• Have pupils handled data in any lessons that you have taught recently?

• Which stages of the handling data cycle were pupils engaged in?

• Which stages of the handling data cycle could pupils have been engaged in?

• Which of the distinctive features of handling data were present in the lesson(s)?

OHT 7.3



Common difficulties in handling data 1 (i)

• Mean, median and mode are confused or used inappropriatelyFor example, the mean is used when referring to the average monthly rainfall in India

• Data are represented by inappropriate graphs or chartsFor example, a pie chart is used to represent the distances of the different planets from the Sun

OHT 7.4 a



Common difficulties in handling data 1 (ii)

• Graphs and charts are incorrectly drawn or labelledFor example, the bars in a bar chart representing the votes cast for candidates in a school election are joined together or are of different widths

• Graphs and charts are read incorrectly or interpreted inappropriatelyFor example, the vertical scale marked in thousands on a population graph is misread: 350 000 is read as 350

OHT 7.4 b



Common difficulties in handling data 2• Activities are aimless or contexts inappropriate

For example, vast quantities of data are collected without any consideration of the purpose of the enquiry

• Undue time is spent on mechanical skills and there is insufficient emphasis on interpreting data and making inferencesFor example, pupils are taught to draw pie charts or calculate a mean without understanding of when it is appropriate to use these or how to interpret them

OHT 7.5




• To agree a set of whole-school numeracy priorities

• To discuss the need for a whole-school numeracy policy and its possible content

• To agree a plan of action to sustain developments

OHT 8.0



Purposes of a whole-school numeracy policy

• To secure high standards in numeracy across the school

• To set out the school’s approach to the teaching of agreed numeracy skills

• To provide a basis against which progress can be judged

• To record methods, vocabulary and notation that have been agreed

• To assist the transfer of pupils’ knowledge, skills and understanding between subjects

• To indicate areas for collaboration between subjects and processes for facilitating such collaboration

OHT 8.1



Possible contents of a whole-school numeracy policy 1• Agreed approaches to calculation (including

calculations involving fractions, percentages, ratio)• School policy on calculator use• Agreed mathematical vocabulary and notation• Lists of units used for measurement• Agreed methods for drawing and labelling graphs,

charts and diagrams• Links with using and applying mathematics –

reasoning, communicating, investigating and problem solving

OHT 8.2



Possible contents of a whole-school numeracy policy 2

• Agreement on the order and timing for teaching topics with common content

• Agreement on any planned collaborative working/ shared activities

• Guidance for form tutors, where oral and mental work is included in tutorial sessions

• Advice from the mathematics department on common errors which arise

OHT 8.3




• To ensure that each department’s expectations for pupils’ mathematics are in line with those in the Framework for teaching mathematics: Years 7, 8 and 9

• To explore opportunities for continued joint working

OHT 9.0

© Crown copyright 2001 Key Stage 3 National Strategy Numeracy Across the Curriculum.

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Transcript of © Crown copyright 2001 Key Stage 3 National Strategy Numeracy Across the Curriculum.