Transcript Key Stage 3 National Strategy

Key Stage 3 National Strategy
Numeracy Across the
Curriculum
Key Stage 3 National Strategy
© Crown copyright 2001
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Points for discussion
Consider 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
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Key Stage 3 National Strategy
A definition of numeracy 1
By 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
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Key Stage 3 National Strategy
A definition of numeracy 2
By Year 9, pupils should:
• 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
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Key Stage 3 National Strategy
A definition of numeracy 3
By 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 1.5
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Numeracy in Ofsted inspections
In 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
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Key Stage 3 National Strategy
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 interdepartmental co-operation in this type of
activity
OHT 2.0
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Washing Up
Give a plausible explanation for the shape of this graph.
OHT 2.2
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Key Stage 3 National Strategy
Scales
OHT 2.3
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Objectives for session 3
• 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
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Key Stage 3 National Strategy
Objectives for session 4
• 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
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Key Stage 3 National Strategy
A definition of numeracy 1
By 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 4.1
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Key Stage 3 National Strategy
A definition of numeracy 2
By Year 9, pupils should:
• 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
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Key Stage 3 National Strategy
A definition of numeracy 3
By 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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Objectives for session 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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Some of the possible visualisations
OHT 5.4
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Objectives for session 6
• 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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Ageing fast
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
OHT 6.3
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Key Stage 3 National Strategy
Comparing calculators
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.
OHT 6.4
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Objectives for session 7
• 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
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Key Stage 3 National Strategy
The handling data cycle
OHT 7.1
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Common difficulties in handling
data 1 (i)
• Mean, median and mode are confused or used
inappropriately
For example, the mean is used when referring to the
average monthly rainfall in India
• Data are represented by inappropriate graphs or
charts
For example, a pie chart is used to represent the
distances of the different planets from the Sun
OHT 7.4 a
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Key Stage 3 National Strategy
Common difficulties in handling
data 1 (ii)
• Graphs and charts are incorrectly drawn or
labelled
For 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 inappropriately
For example, the vertical scale marked in thousands
on a population graph is misread: 350 000 is read as
350
OHT 7.4 b
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Key Stage 3 National Strategy
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 inferences
For 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
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Key Stage 3 National Strategy
Objectives for session 8
• 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
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Key Stage 3 National Strategy
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
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Key Stage 3 National Strategy
Possible contents of a wholeschool 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
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Key Stage 3 National Strategy
Possible contents of a wholeschool 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
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Key Stage 3 National Strategy
Objectives for session 9
• 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
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Key Stage 3 National Strategy