Mathematicsin the National

Curriculum for Wales

Key Stage 2Key Stage 2

Aims Look at key definitions

Brief overview of Primary Numeracy Framework

Consider ‘Mathematics at Key Stage 2’

Develop understanding and awareness of how children learn and strategies to help support mathematical learning.

Focus in on key interventions

Discussion

What do you consider your own math capabilities to be?

How important do you consider numeracy to be outside of school?

Background

In 2001, an estimated 7 million adults had literacy, language and numeracy needs.

In 2003 research by DfES showed 5.2 million adults have literacy levels expected of an 11 year old. 15 million have numeracy skills expected of an 11 year old.

There are differences according to region, social and local variations.

Also a variation between primary and secondary schools. This is because too few secondary schools use other lessons to give pupils chance to develop their numeracy skills.

Definitions

Literacy unites the important skills of reading, writing, speaking/talking and listening.

Numeracy is a proficiency which involves ‘confidence and competence’ with numbers and measures. It requires understanding of the number system, a range of IT skills and the ability to solve number problems in a variety of contexts. It also demands practical understanding of the ways in which information is gathered, by counting and measuring, and how it is presented.

‘Being numerate helps us to function responsibly in everyday life and contribute effectively to society. It increases our opportunities within the world of work and establishes foundations which can be built upon through lifelong learning. Numeracy is not only a subset of mathematics; it is also a life skill which permeates and supports all areas of learning, allowing young people access to the wider curriculum

We are numerate if we have developed the confidence and competence in using number which will allow individuals to solve problems, analyse information and make informed decisions based on calculations.”

Curriculum for Excellence: Numeracy across Learning, Scottish Government, 2009

Being Numerate..

Competence in:

Basic number and number process

Estimation and rounding

Aspects of fractions, percentages and decimal fractions

Money

Time

Measure

Aspects of information handling

The national curriculum subjects have been revised and restructured.

The purpose of these changes is to identify the skills for each subject and the range of contexts, opportunities and activities through which these skills should be developed and applied.

The content has also been updated to ensure relevance to the twenty-first century and manageability for learners and teachers.

The revised national curriculum subjects will be implemented as follows

September 2008 Years 3, 4, 5 and Years 7 and 8

September 2009 Year 6, 9 and Year 10: Welsh second language and physical education

September 2010 Year 10: English, Welsh and Mathematics Year 11: Welsh second language and physical education

September 2011 Year 11: English, Welsh and Mathematics

To support the implementation of the curriculum, the document 'Making the most of learning – implementing the revised curriculum' provides guidance on focusing on the learner, planning learning and teaching and assessing learning.

National curriculum - Key Stages 2, 3 and 4

Primary Numeracy Framework

Key points:

Its aim is to support and increase all children’s access to excellent teaching, leading to exciting and successful learning.

All children should be appropriately supported to make the progress of which they are capable.

Children deserve:

to be set appropriate learning challenges To be taught well and given opportunity to learn in

ways that maximise their chances of success. To have adults working with them to tackle specific

barriers to progress they face.

Framework

There are seven numeracy strands:

Using and applying mathematics

Counting and understanding number

Knowing and using number facts

Calculating

Understanding shape

Measuring

Handling data

At Key Stage 2, learners build on the skills, knowledge and understanding they have already acquired during the Foundation Phase.

They continue to develop positive attitudes towards mathematics and extend their mathematical thinking by solving mathematical problems, communicating and reasoning mathematically using contexts from across the whole range of mathematics, across the curriculum and as applied to real-life problems.

They extend their use of the number system, moving from counting reliably to calculating fluently with all four number operations, including in the context of money, in order to solve numerical problems. They try to tackle a problem with a mental method before using any other approach and use written methods of calculation appropriate to their level of understanding.

They develop estimation strategies and apply these to check calculations, both written and by calculator. They explore a wide variety of shapes and their properties and, in the context of measures, use a range of units and practical equipment with increasing accuracy. They collect, represent and interpret data for a variety of purposes.

They select, discuss, explain and present their methods and reasoning using an increasing range of mathematical language, diagrams and charts.

Mathematics at Key Stage 2

Pupils develop their mathematical skills, knowledge and understanding through learning about and using:

a)Numberb)Measures and moneyc)Shape, position and movement and d)Handling data

They should use a variety of ICT resources as tools whenever appropriate.

RangeKey Stage 2Key Stage 2

Programme of StudyProgramme of Study

Pupils should be given opportunities to:

1. Understand number and number notation

• count, read, write and order whole numbers

• understand place value in relation to the position of digits; multiply and divide numbers by 10 and 100

• identify negative numbers and decimals on a number line

• use negative numbers in the context of temperature, and decimals in the context of money and measures

Number

2. Calculate in a variety of ways

• use a variety of mental methods of computation; extend informal written methods to non-calculator methods

• round answers to calculations to an appropriate degree of accuracy

• use the relationships between the four operations, including inverses; recognise situations to which the different operations apply

• use fractions and percentages to estimate, describe and compare proportions of a

whole; calculate fractions and percentages of quantities

Number

3. Investigate patterns and relationships

• explore features of numbers, including number bonds, factors, multiples, even and odd numbers, primes, squares and square

roots, and sequences of whole numbers

• explore the inverse relationships of addition and subtraction, and of multiplication and division

• deepen their understanding of one-to-one

correspondence.

Number

Pupils should be given opportunities to:

1. Understand and use measures

• choose appropriate standard units of length, mass, volume and capacity, temperature, area and time

• understand the relationships between units, and convert one metric unit to another

• read times on analogue and digital clocks; use timetables and convert between the 12- and 24-hour clocks; calculate time differences

• know the rough metric equivalents of imperial units still in daily use

• interpret numbers on scales and read scales to an increasing degree of accuracy; understand and use scale in simple maps and drawings

• draw and measure angles

• find perimeters of simple shapes; find areas and volumes by counting and other practical methods

Measures and money

2. Understand and use money

know and use the conventional way to record money

• find approximate solutions to, and use the four operations to solve, problems involving money

• understand a calculator display in relation to

money, e.g. that a display of 21.4 (pounds)

means £21.40

• be aware of other currencies.

Pupils should be given opportunities to:

1. Understand and use the properties of shapes

• make 2-D and 3-D shapes and patterns with increasing accuracy

• understand the congruence of 2-D shapes

• name and classify 2-D shapes according to side and angle properties

• know and use the properties of 2-D (polygon) and common 3-D (polyhedron) shapes

2. Understand and use the properties of position and movement

• recognise reflective and rotational symmetries of 2-D shapes

• use positive co-ordinates to specify location

• identify properties of position and movement, and use these to classify shapes

• use right angles, fractions of a turn and degrees to measure rotation.

Shape, position and movement

Pupils should be given opportunities to:

1. Collect, represent and interpret data

• collect data for a variety of defined purposes, including those that arise from their own

questions, and from a variety of sources

• use and present data in a variety of ways including tables, pictograms, charts, bar charts, line graphs, diagrams, text and ICT

• calculate and use the mode, median, mean and range of a set of discrete data

2. Understand and use probability

• use everyday language for early ideas of probability

• know that the likelihood of an event lies between impossible and certain

Handling data

By the end of Key Stage 2, the performance

of the great majority of pupils should be within

the range of Levels 2 to 5.

Attainment

Pupils talk about their work using familiar mathematical language, and represent it using symbols and simple diagrams. They count sets of objects reliably, and use mental recall of number facts to 10 to add or subtract larger numbers. They order numbers up to 100. They choose the appropriate operation when solving addition or subtraction problems. They identify and use halves and quarters in practical situations. They recognise sequences of numbers. They use mental calculation strategies to solve number, money and measure problems. They use everyday non-standard and standard units to measure length and mass. They distinguish between straight and turning movements, recognise half-turns and quarter-turns and right angles in turns. They sort objects and classify them using more than one criterion. When they have gathered information, they record their results in simple lists, tables, diagrams and block graphs.

Level 2

Pupils organise their work, check results, and try different approaches. They talk about and explain their work.

They use and interpret mathematical symbols and diagrams. They find particular examples that satisfy a general statement. They use place value in numbers up to 1000 to make approximations.

They use decimal notation in recording money, and recognise negative numbers in the context of temperature.

They develop further mental strategies for adding and subtracting numbers with at least two digits. They use mental recall of the 2, 3, 4, 5 and 10 multiplication tables in solving whole-number problems involving multiplication and division, including those giving rise to remainders.

They use standard units of length, capacity, mass and time. They classify shapes in various ways.

They extract and interpret information presented in simple tables and lists, and construct and interpret bar charts and pictograms.

Level 3

Pupils develop their own strategies for solving problems, and present information and results systematically. They search for a solution by trying out ideas of their own. They use their understanding of place value to multiply and divide whole numbers by 10 and 100. They use a variety of mental and written methods for computation, including recall of multiplication facts up to 10 x 10.

They add and subtract decimals to two places. They check their results are reasonable by considering the context or the size of the numbers. They use simple fractions and percentages to describe approximate parts of a whole. They recognise and describe number patterns and relationships and use simple formulae expressed in words. They use their knowledge of shape to make 3-D mathematical models, draw common 2-D shapes in different orientations on grids, and reflect simple shapes in a mirror line.

They choose and use suitable units and instruments, reading, with appropriate accuracy, numbers on a range of measuring instruments. They find perimeters of shapes, areas by counting squares, and volumes by counting cubes. They use and interpret co-ordinates in the first quadrant. They collect discrete data, group data where appropriate, and use the mode and median as characteristics of a set of data. They draw and interpret frequency diagrams and construct and interpret simple line graphs. They understand and use simple vocabulary associated with probability.

Level 4

Pupils identify and obtain information to solve problems, and check whether their results are sensible in the context of the problem. They describe situations mathematically using symbols, words and diagrams and draw their own conclusions, explaining their reasoning. They make general statements of their own, based on available evidence. They use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers. They check their solutions by applying inverse operations or estimating using approximations. They calculate fractional or percentage parts of quantities and measurements. They construct and use simple formulae involving one or two operations. They use co-ordinates in all four quadrants. They measure and draw angles to the nearest degree. They recognise, identify and describe all the symmetries of 2-D shapes. They convert one metric unit to another and know the rough metric equivalents of imperial units in daily use. They make sensible estimates of a range of everyday measures. They find areas of rectangles and triangles and volumes of cuboids. They read scales on maps, plans and graphs. They use the mean of discrete data and compare two simple distributions. They interpret graphs, diagrams and pie charts. They use the probability scale from 0 to 1, and appreciate that different outcomes may result from repeating an experiment.

Level 5

• Out-of-class support groups often focus on literacy learning, but the acquisition of numeracy skills is also important.

• The Primary National Strategy Wave 3 mathematics materials offer valuable support for small group work, as do a number of published schemes.

• When considering interventions, the following points may be useful:• Research shows that planned interventions can make a substantial impact on

children's difficulties with calculation, improving their understanding and raising performance. You can make a big difference in a relatively short amount of time.

• Short but regular interventions, involving individualised work, can result in a child being able to benefit much more effectively from the whole-class teaching that they receive.

• It's important to find out what specific strengths and weaknesses an individual child has and to investigate particular misconceptions and incorrect strategies. A good way of establishing this is to observe and take notes (or ask a TA to do this) during oral/mental starters in the classroom. Interventions should then be targeted towards particular difficulties.

• Whichever materials you decide to use, they should be sufficiently flexible for the teacher to be able to adapt them.

• Remember to use plenty of practical activities and concrete examples before moving on to abstract operations.

Strategies to help pupils with numeracy difficulties

Key Programmes

Catch up Numeracy

Number Partners

Every Child Counts

The second two programmes offer students the chance to enhance their numeracy skills by playing specially developed number games with responsible adults.

Catch Up has developed two educational interventions to support struggling learners: Catch Up Literacy and Catch Up Numeracy (both in English and Welsh).

Both interventions are targeted to the needs of individual learners, both are grounded in rigorous academic research, and both have been shown to lead to gains of more than twice the period of intervention.

To date, approximately 180,000 learners in England and Wales have benefited from Catch Up support.

The Catch Up interventions have both been identified by the DCSF as evidence-based Wave 3 interventions (interventions that have been shown to provide effective one-to-one support for struggling learners).

The Catch up Programme

1) Structured one-to-one intervention for learners who struggle with numeracy, based on Ann Dowker’s ten components of numeracy

2) Targeted to the identified needs of the individual, and maximises the effective use of resources (including ‘Overcoming Barriers’) and approaches already available in classrooms

3) Grounded in rigorous academic research, and shown to be effective in schools across 37 local authorities

4) Available as part of an accredited comprehensive, integrated and award winning training and resource package that supports both management and delivery of the intervention

Catch Up Numeracy: Four key messages:

Number Partners – Case Study

Tower Hamlets Education Business Partnership

Been sending employees from local businesses into schools to help children with numeracy for over 10 years.

Over 500 volunteers visit over 40 schools.

“The Children start to see a use for the numeracy they do in terms of a job or university and it helps bring maths to life. They see what doing well at maths can bring them and it gives them a reason to work hard” (Catherine Mayers, 2010)

According to Tessa Wray, KC Cares Business Manager, “In the school year 2009-10, 78% of 11 year olds who received additional one-to-one tuition in maths achieved a level 4.” Compared to 49% without.

Number Partners

Launched 2001 – now in 60 regions. Enhances the numeracy skills of 7-16 year olds Mainly in Primary schools but also in

secondary schools. Volunteers from business and the community

play specially designed numeracy games with young people to give them a confidence boost.

As well as numeracy support, it also supports the development of interpersonal skills for targeted pupils.

It develops young people’s confidence, motivation and gives a positive insight into the business world.

The Games

12 ‘number challenge’ games for 6 to 11 year olds.

Each game is based on a specific number of skills, such as addition and subtraction, a times table or, for more competent children, a range of calculations.

Main aim is to reinforce the national literacy strategy and focus on mental maths.

Every Child Counts

Part of the Every Child A Chance Trust, formed in 2007.

Aim was to improve mathematical skills of the poorest performing six and seven year olds. (lowest achieving 5%)

Modelled on success of Every Child A Reader, it provides skilled, specialist one-to-one or small group ‘Numbers Count’ teaching for lowest achieving children in Year 2.

Taught for half an hour every day for around twelve weeks.

Schools involved should be about 2000 now, impacting 30,000 children.

Numbers Count

Two week diagnostic assessment period, eight weeks personalised teaching and two weeks of activities to ready the child to continue to make progress in class.

Lessons are interactive, fun and tailored to the individual needs of the child.

Emphasis on using models and images that support the child’s thinking, on developing language skills and on repeated practice so knowledge is fluent.

Structure of the lessons are simple: practice with familiar to build confidence; practice in counting; new learning including applying this to the ‘real world’; and finally a recap on what has been learnt.

What it involves

Number recognition using vocabulary of number

Counting forward and back

Counting in ones, twos and threes

Ordering, sequencing and comparing by size

Number bonds, additions and subtractions

Begin to recognise patterns and relationships in number

Money including use of real coins

Problem solving in everyday contexts.

Examples

Conclusions

The Maths Curriculum

Widely agreed that a child who is having significant difficulties at an early stage (i.e during KS1) is likely to under-achieve in maths throughout school life and beyond.

To help address this the Primary National Strategy made provision for the lowest performing children to receive personalised, individual teaching.

Research has shown that effective interventions early on can make a massive difference. Interventions should be seen as part of a bigger picture.

Further Reading

Davies, R (2006) Numeracy in Wales – Latest Research (January 2006) WAG:Cardiff

http://www.guardian.co.uk/news/datablog/2010/dec/07/world-education-rankings-maths-science-reading

http://www.counton.org/resources/numeracy/pdfs/plan_gd.pdf

http://www.niched.org/docs/the%20primary%20framework.pdf

Every Child a Chance Trust (2009), Every Child Counts: The Results of the first year 2008/09

Wag (2005) Words Talk – Numbers Count Crown Copyright