Lancashire Mathematics Newsletter...23 Lancashire Mathematics Newsletter Playing for Success @...

24 Lancashire Mathematics Newsletter

SOLUTION

Question Time On Monday the Pied Piper caught 1000 rats in a city. On Tuesday he caught 10% fewer rats than on Monday. On Wednesday he caught 20% more than on Tuesday. On Thursday he caught 30% fewer than on Wednesday. On Friday he rested. How many rats did he catch in total that week?

Gus is older than Flora. Alessandro is older than Zara but younger than Flora. Oliver is younger than Gus but older than Zara. Yvette is younger than Gus. Alessandro is older than Oliver. Flora is younger than Yvette. Which of these six friends is the youngest?

Lancashire Mathematics Newsletter Lancashire Mathematics Newsletter SUMMER TERM 2007

Full Mathematics Team List Senior Adviser Alison Hartley Primary Mathematics Consultants Shirley Bush (Senior Consultant) Sue Bailey Nicki Brough Lynsey Edwards Sue Farrar Cheryl Nelson Andrew Taylor Peter Toogood Secondary Mathematics Consultants Louise Hastewell Sue Taylor Jill Lane Maureen Magee

Team Contact Details

Phone: 01257 516102

Fax: 01257 516103 E-Mail: [email protected] Write to us at: LPDS Centre Southport Road CHORLEY

PR7 1NG

Website: www.lancsngfl.ac.uk/curriculum/math/

Helping children to achieve age-related expectations 3

Primary Framework - latest updates 4

Role of the Mathematics Subject Leader (Primary) 5 - 7

Learning and Teaching for bilingual children 8

Girls Allowed! 9

Wave 2 and Wave 3 Strategies 10

Progression in Data Handling & Interactive Displays 11 - 13

Webwatch 14

Clever Touch Software - Lynx 15

Early Years Foundation Stage 2

Espresso 15

ITP Reception to year 9 16 - 18

Progression Maps 19

ICT Pilot 19

Study Plus 20

Assessing pupils’ progress (APP) 20

Intervention on-line modules 21

GCSE Mathematics 22

Playing for Success 23

Puzzle Page 24

2007 L2007 L2007 LANCASHIREANCASHIREANCASHIRE M M MATHEMATICSATHEMATICSATHEMATICS C C CHALLENGEHALLENGEHALLENGE D D DISTRICTISTRICTISTRICT R R RESULTSESULTSESULTS SOSOSO FARFARFAR::: Tuesday 6 March 2007 1st Hutton CE Grammar All Hallows High School 2nd Balshaw’s CE High 3rd Lostock Hall Community High Tuesday 13 March 2007 1st Bacup & Rawtenstall Grammar School Bacup & Rawtenstall Grammar School 2nd Shuttleworth College 3rd Whitworth Community High School Thursday 22 March 2007 1st Holy Cross Catholic High - A Specialist Science & Sports College Bishop Rawstorne CE Language College 2nd St Michael’s CE High School 3rd Southlands High School - A Specialist Technology College Wednesday 28 March 2007 1st Ashton Community Science College Broughton Business & Enterprise College 2nd Our Lady’s Catholic High School, Preston 3rd Archbishop Temple CE High School & Technology College Congratulations to all of the above teams and all of the schools who have participated so far.


Early Years Foundation Stage The Early Years Foundation Stage (EYFS) is a comprehensive framework which sets the standards for learning, development and care of children from birth to 5. It builds on and will replace the existing statutory Curriculum Guidance for the Foundation Stage, the non-statutory Birth to Three Matters framework, and the regulatory frameworks in the National Standards for Under 8s Day Care and Childminding. All registered early years providers and schools will be required to use the EYFS from September 2008. Mathematical Development has been renamed Problem Solving, Reasoning and Numeracy. Children must be supported in developing their understanding of problem solving, reasoning and numeracy in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. They must be provided with opportunities to practise and extend their skills in these areas to gain confidence and competence in their use. Problem solving, Reasoning and Numeracy is made up of the following aspects: Numbers as Labels and for Counting - is about how children gradually know and use numbers and counting in play, and eventually recognise and use numbers reliably, to develop mathematical ideas and to solve problems. Calculating - is about how children develop an awareness of the relationship between numbers and amounts and know that numbers can be combined to be ‘added together’ and can be separated by ‘taking away’ and that two or more amounts can be compared. Shape, Space and Measures - is about how through talking about shapes and quantities, and developing appropriate vocabulary, children use their knowledge to develop ideas and to solve mathematical problems. Links are made to Key Stage 1 in the Practice Guidance for the Early Years Foundation Stage booklet. The Primary Framework for Mathematics and the EYFS have been developed alongside each other. The Primary Framework provides an overview of EYFS outcomes for school-age children and therefore contains some of the information that practitioners in schools need to work with children from birth to five. It matches the EYFS; however practitioners in schools need to access the full EYFS. Some children will not meet all the early learning goals in the EYFS, and Year 1 teachers need to know how to support and extend their learning to help them meet the early learning goals from the EYFS in Year 1 of primary school. The Primary Framework and the EYFS help nursery, Reception and KS1 teachers see how the six areas of the EYFS link to mathematics in KS1. Hard copies of The Early Years Foundation Stage: Statutory Framework and Guidance will be delivered into school, however, the document can be downloaded from the website below http://www.standards.dfes.gov.uk/primary/publications/foundation_stage/eyfs/ Further information can be obtained from http://www.standards.dfes.gov.uk/eyfs/


Playing for Success @ Preston North End Football Club Playing for Success is a national initiative which provides out of school study support for pupils aged 9-14, using sport and its environment as a curriculum tool. The focus is to raise achievement in literacy, numeracy and ICT whilst also helping to develop self-esteem, motivation and independent learning. The centre at Preston North End uses the subject of football, the Deepdale Stadium and the National Football Museum within its sessions. The centre is based under the Alan Kelly Stand, in the Learning and Community Centre. PfS @ PNEFC is part of Lancashire School Effectiveness Service and is a DFeS initiative, in partnership with Lancashire County Council, the club and sponsors. The spring term has been a busy term at Playing for Success! Pupils have been improving their numeracy skills through personalised activities in the ICT suite and through numeracy activities around the stadium. PfS pupils have been working around the Deepdale pitch, in the stands and the changing rooms to develop their numeracy skills, using maths in real life and practical situations. Schools participating in Spring 2007: Primary Secondary Ashton Primary Moor Park Business and Enterprise School Brockholes Wood Community Primary Ashton Community Science College Deepdale Junior Tulketh Community Sports College Holme Slack Community Primary Holy Family Catholic Primary Ingol Community Primary Lea Community Primary St. Augustine’s Catholic Primary Daytime Sessions PfS also offers daytime sessions for schools, which are chargeable. This term, schools have been participating in our “Maths Around the Ground” Numeracy sessions.

For more information on Playing for Success in Lancashire, please contact:

Jane Icely, Centre Manager Preston North End Learning and Community Centre

PNEFC Sir Tom Finney Way

Deepdale PRESTON PR1 6RU

Tel: 01772 491410

Email: [email protected]


GCSE Mathematics In March 2006 the DfES asked QCA to develop two mathematics GCSE qualifications, each based on the key stage 4 programme of study. Functional mathematics will be incorporated into the first GCSE (hereafter GCSE Mathematics), which will count in performance tables and be a direct development from the current GCSE. GCSE Mathematics will be sufficient for progression to GCE. The second GCSE (hereafter GCSE Additional Mathematics) will include a greater focus on both reasoning and the application of higher-level skills within mathematics. Its assessment will focus on problem-solving and more open-ended questions. The assumptions that underpin the development are that: •The new two-tier GCSE Mathematics will be the ‘gatekeeper’ qualification; •GCSE Mathematics and GCSE Additional Mathematics will be free-standing and not linked as a double award; •GCSE Additional Mathematics will be aimed at higher achievers and more motivated students; •The programme of study will not be split across two single GCSEs; •GCSE Additional Mathematics will cover the whole range of GCSE grades; •GCSE Additional Mathematics will not be a requirement to progress to A level. Mathematics pathways In September 2006, awarding bodies began recruiting centres for the purpose of trialling and piloting aspects of the proposals for revised GCSE and GCE specifications and for Supplementary Mathematics Modules (SMMs, the new FSMUs) at levels 1, 2 and 3. GCSE Mathematics (including functional mathematics) and GCSE Additional Mathematics will be piloted beginning in Summer 2007 by 3 awarding bodies and by approximately 200 centres (with up to 15000 candidates); AS/A level qualifications will be piloted by 2 awarding bodies and by between 50 – 100 centres (up to 3000 candidates); FSMQs/SMMs (supplementary mathematics modules) will be piloted by one awarding body with approximately 200 centres. Additionally, one awarding body will be trialling a stand-alone Functional Mathematics assessment in February 2007. Information arising from piloting and the evaluation will be organised so that GCSE specifications will be available in centres in autumn 2009 and GCE specifications in the autumn of 2010. First teaching of the revised GCSE qualification will start in September 2010 and GCE in September 2011. Coursework In October 2006 QCA announced the withdrawal of coursework in GCSE mathematics for teaching from September 2007. For the next three years, data handling and using and applying mathematics will be assessed through development of new styles of questions in the already existing written papers; new specifications and specimen assessment materials will soon be available from Awarding Bodies. In the longer term the piloting of new GCSEs will support continued development of alternative forms of assessment.


New CD-Rom “Helping children to achieve age-related expectations”

Ref: 00028-2007CDO-EN You will have recently received this cd-rom in school (distributed via the school bags by the Lancashire Mathematics Team). We are aware that schools receive a large amount of publications and information and so the aim of this article is to provide a quick overview of the CD-Rom and what the Lancashire Mathematics Team regard as the most useful aspects of this resource. Once you open up the CD-Rom you will find a range of resources and publications: many of these will be familiar to you. The aim of this CD-Rom has been to bring these resources together in one place for use mainly by Year 5 and Year 6 teachers (although some of the materials have whole-school implications). Resources/ publications contained on the CD-Rom are as follows: 1. “Learning about Learning” - a very interesting and useful document which would be an ideal focus for the whole teaching staff in terms of developing children’s positive attitudes towards their learning and their potential to achieve. There are clear links with work on Assessment for Learning and engaging children in their own learning. This document suggests approaches to discussions with children about their learning or ways of questioning in day-to-day teaching which develop a ‘can do’ attitude, self-belief and high expectations. As mathematics is a subject with regular challenge and requires children to take risks and be confident in their abilities the Mathematics Team recommends that this document is used to further develop practice in school. 2. The new tracking document from the renewed framework subject leaders’ DVD – as a maths team we have found this document to be useful and an improved version of this can be found on our website: www.lancsngfl.ac.uk/curriculum/math/ 3. Wave 3 materials: to support children with gaps in their learning – very useful for all teachers and teaching assistants, the materials on this disc can be put on your school network for all staff to access: if you haven’t already had your hard copy of these materials they are available from DfES publications on 0845 60 222 60. 4. SEAL materials - to develop positive attitudes towards learning and self-belief, essential in mathematics! This CD-Rom contains electronic copies of sections of the SEAL materials: because mathematics is a subject for which confidence and a positive attitude are essential the SEAL materials can make a significant difference to maths achievement. 5. Springboard and Booster materials – electronic copies of these materials which can be used as a teaching resource for whole class, focused group work or intervention group work. 6. Implications from 2006 SATs – this document details issues from last Year’s SATs papers which may reflect issues in your own school with regard to maths. 7. Maths Assessment materials for Y5 and Y6 – past SATs questions to aid assessment of children’s ability to use and apply: more examples of these at all levels can be found using the Testbase resource: available from www.testbase.co.uk 8. ICT resources: to access these you need to click on the icons that look like white rectangles with a web page in the middle: these take you to a whole range of ICT interactive resources which link to key mathematical skills. 9. Bilingual support guidance – linked with “Excellence and Enjoyment” these publications give support for schools with bilingual pupils to support their learning and create an appropriate school ethos. There is also a presentation in slide format which will guide you through the different materials and how these link together to help children to achieve age-related expectations. The CD-Rom contains materials useful to subject leaders in developing teaching and learning in mathematics across the school and also to Year 5 and 6 teachers for whom there are resources specifically aimed at their classes.


ICT Activity Notes Notes to support the use of ITPs and Excel spreadsheets, which are linked to Units, are now also available for Unit 3 for most year groups. These notes are also in the ‘Library’, under ‘ICT Resources’. Guidance notes for the ITPs are also available in the Library.

Pupil Tracker This is a PNS-developed excel based academic year pupil tracker. It is aimed at supporting schools to identify children who are at risk of underachievement. The spreadsheet is available to download and is accessible through a variety of routes. Try clicking on: Primary Framework Home – Library – Mathematics and the excel grid is at the bottom of the page.

Framework DVD A new updated version of the DVD will be sent into schools in the Summer term Interactive Planning Tool The Interactive Planning Tool is now being trialled in schools. Watch this space! Guidance Documents Six documents are now available under the Guidance Papers tab. These can downloaded or viewed online.

Primary Framework for Mathematics – Latest Updates • ‘Helping children in Years 5 and 6 to achieve age

related expectations’ - these materials recently sent into schools on CD are now available on the website – click on the front page of the mathematics area of the site.

• Under the Planning section, all the Blocks are now labelled A to E.

• The resource tabs have been renamed to aid navigation, and have more explicit titles.

• Pitch and Expectations – under Year 3 Resources, this contains the Assessment Questions recently shown on the 3+2 subject leader course and Mathematics Subject Leader meetings (Available in each Year Group section)


Intervention on-line modules mathematics at Key Stage 3

There are nine individual online modules for Key Stage 3 mathematics intervention and all are standalone except MM8 and MM9 which should be viewed sequentially to gain the most from them. These can be found at www.standards.dfes.gov.uk/intervention/94.html Mathematics Module 1: Overview of the guidance and support available for mathematics teachers. This module sets the scene for the mathematics developments in intervention that you will be leading on. It summarises the structure and content of the mathematics programme and provides information on the use of the Progression Maps website. It explores an example of one specific Progression Map and suggests useful ways forward to sustain improvements in intervention. Mathematics Module 2: Tailoring teaching and exploring the three Waves approach. Here, we explore an approach to intervention built around targeted teaching and support at three levels or 'waves'. There are a number of scenarios and suggested approaches to help you interpret this in this module. The wave model starts with the premise that Wave 1 is all about quality teaching for all in all classes, while Wave 2 is concerned with additional, time limited tailored intervention support for individuals and groups. Wave 3 is about developing individualised (personalised) programmes of support, with increasing intensity, where appropriate Mathematics Module 3: Using assessment data to tailor teaching. The module considers the importance of using assessment to improve pupils' learning and achievement by: • considering the range of pupil performance data available to schools • improving the tracking of pupils during Key Stage 3 • using assessment data to inform teaching and support planning. The work is built around the use of school and pupil level data, comparing with national trends and considering the implications for targeted teaching. Mathematics Module 4: Tracking pupils' progress in mathematics. Here, we consider the purpose and principles of tracking pupils. The module examines approaches to tracking, using National Curriculum levels or GCSE grades and tracking through the teaching and learning. It also focuses, specifically, on strategies for ongoing assessment to track pupils' knowledge and understanding of algebra. Mathematics Module 5: Using errors and misconceptions. This module considers the identification and use of pupils' misconceptions in promoting learning and achievement by: • clarifying the differences between pupils' mistakes, misunderstandings and misconceptions • exploring teaching strategies to counter misconceptions - including the use of particular teaching resources. The module starts from the premise that pupils make mistakes for a variety of reasons. You will relate well to the problems associated with children getting their mathematics thinking wrong, for whatever reason. Some errors may be due to lapses in concentration, memory overload, or a failure to notice important features in a problem. Others however, are symptoms of more profound mathematical difficulties or misconceptions. Mathematics Module 6: Working effectively with a teaching assistant in mathematics support. Here, we consider the effective deployment and management of teaching assistants within the mathematics department. The aim is to help teachers to improve their management and use of teaching assistants, as a key resource, by considering examples of good practice. To support this, an audit document has been developed to help you to clarify your current situation and identify areas for further development. Mathematics Module 7: Resources to support planned intervention. This module aims to familiarise you with the full range of materials that are available from the Secondary National Strategy and to provide opportunities to access and explore them. Guidance is provided on how best to make use of the relevant materials with colleagues in the department. Mathematics Module 8: Using and applying mathematics - the approach (Part 1). This module considers the approaches to teaching and learning that are appropriate for using and applying mathematics. It also explores the overall structure of the Progression Maps in relation to this and leads into the next and final module in the series, MM9. Mathematics Module 9: Using and applying mathematics - supporting pupils (Part 2). Here, the module compliments MM8 and provides the opportunity to explore the Progression Maps for using and applying mathematics in detail.


These new resources are intended to support mathematics teachers in the assessment of mathematics at Key Stage 3. The resources include: • The APP Handbook, Assessing pupils’ progress in mathematics at Key Stage 3 • Focused assessment materials • Twelve assessment packages • Materials to help you implement APP in your department It is important to read the APP handbook first. The booklet Tracking for success in mathematics is also included. This is the mathematics subject leader version of the generic Tracking for success booklet (DfES 1454-2005FLR-EN). Resources can be downloaded from the standards website at http://www.standards.dfes.gov.uk/secondary/keystage3/subjects/maths/asses_maths/ Effective implementation of APP will take time but the benefits can be immense. APP has the potential to impact on: • teachers’ questioning skills; • the quality of talk about mathematics in lessons; • the depth of pupils’ understanding, including their ability to make links in mathematics; • teachers’ understanding of progression in mathematics; • teachers’ expertise in identifying and addressing misconceptions; • pupils’ awareness of their strengths and areas for improvement; • teachers’ feel for National Curriculum (NC) levels; • pupils’ standards in mathematics. Introducing and establishing good APP practice will provide powerful opportunities for your department to work collaboratively on planning, teaching, learning and assessment. These materials have been designed to help you use APP as a focus for continuing professional development.

Study Plus Due to the initial success of the two year Study Plus pilot 2006-2008, the materials will be available for schools to use in September 2007. Training will be available to teachers on using the Study Plus materials on June 13th 2007 at the Lancashire Red Rose Hub, there will also be inputs and advice from the Study Plus pilot teachers. If your school has opted to follow this course next year then please do not hesitate to contact the Lancashire Mathematics Team for more information on (01257) 516102 and keep a look out for our flier!!


Look out for the flier in schools

THE ROLE OF THE MATHEMATICS SUBJECT LEADER (PRIMARY) Continuing with our section on Subject Leader development

Ideas for a Mathematics Subject Leader’s File

Please remember that these are suggestions and your S.L. file will probably be slightly different from another file. The information it contains will build up over time until it forms an ongoing record which shows the picture of mathematics within your school. A suggestion is to keep a separate ‘Monitoring’ file’ that can easily be used as you complete your monitoring of standards 1. POLICY

• Mathematics subject leader’s job description • Mathematics policy • Long term plan / curriculum overview

2. SCHOOL IMPROVEMENT

• Audit of Mathematics • Annual review of priorities / SDP / Action plan • Mathematics development plan • Mathematics year planner

3. MONITORING AND EVALUATION

• Monitoring and Evaluation Policy • Cycle of subject monitoring and evaluation • PLANNING – Evaluation of planning • WORK SAMPLING – Evaluation of children’s work • CLASSROOM OBSERVATION – Individual evaluation forms • INTERVENTION PROGRAMMES – Springboard / Wave 2 + Wave 3 Identification of and monitoring of progress made • CONDITIONS FOR LEARNING (Environmental Walkthrough) • PUPIL INTERVIEWS • PUPIL AND PARENT QUESTIONNAIRES

4. STANDARDS

• Test results & analysis • Level descriptors / OFSTED standards • Whole school targets • Improvement targets • Tracking

5. RESOURCES • Audit of resources (including human resources) • Resource list / location • Budget allocation / Record of expenditure • Relevant ICT resources

6. STAFF DEVELOPMENT

• Professional development activities • Evaluation of professional development activities • Diary of Advice / Support / Release time

Subject Leader Meetings - Summer Term 2007

Thursday 14 June 2007 9.30 - 11.45 am Holiday Inn, Lancaster Thursday 14 June 2007 1.30 - 3.45 pm Holiday Inn, Lancaster

Monday 18 June 2007 9.30 - 11.45 am The Preston Hotel (formerly Novotel) Monday 18 June 2007 1.30 - 3.45 pm The Preston Hotel (formerly Novotel)

Tuesday 19 June 2007 9.30 - 11.45 am Clayton Park Conference Centre Tuesday 19 June 2007 1.30 - 3.45 pm Clayton Park Conference Centre

Wednesday 20 June 2007 9.30 - 11.45 am Lancashire College, Chorley Wednesday 20 June 2007 1.30 - 3.45 pm Lancashire College, Chorley


Key theme 2: How good is the quality of teaching and learning?

Comments

The quality of the teaching Is agreed medium and short-term planning in place across the school? Is the school using the NLS and NNS medium-term plans and units of work? Are the planning mechanisms appropriate? Are structured lessons in place for teaching literacy and mathematics? Do the lessons exemplify the main features of effective teaching in both subjects?

Subject knowledge Is subject knowledge in literacy and mathematics secure and sufficient to teach the age-related objectives in the Frameworks?

Key theme 1: Raising Standards and Accelerating Progress

Comments

What are learners’ achievement and standards in their work? What data is collected, how and by whom? What assessments are currently in place in the school? How are they analysed, moderated and used? Is the data about standards shared with all staff?

What is the evidence of progress relative to starting points; target setting and pupil tracking? What systems are in place for setting numerical and/or curricular targets? How do they inform teaching and learning? How are they monitored and evaluated Are there school systems for tracking pupils’ progress – across a key stage, a year group? If so what does the tracking look like? How is the tracking data used?

Additional support/intervention programmes

Are intervention programmes in place, working and monitored What is the evidence of progress relative to starting points?

Primary School Mathematics Initial Audit

The information taken from the audit below, helps to inform the School Improvement Plan and Subject Leaders Action Plan

THE ROLE OF THE MATHEMATICS SUBJECT LEADER (PRIMARY) CONITNUED………...


Secondary National Strategy - Progression Maps To complement existing resources and support better focused responses to pupils who are failing to make expected progress, new mathematics progression maps are now available and can be found on-line at www.standards.dfes.gov.uk/progressionmaps What are they? The progression maps comprise a set of objectives in a sequence of ten steps in each strand of mathematics. They describe the progression in each strand. The objectives are drawn from the Framework for teaching mathematics teaching objectives. The progression maps: • Span the range from approximately below level 3 to GCSE grade C • Help teachers to identify appropriate curricular targets • Link with ‘Tracking for success’ and support assessment for learning through the use of probing questions • Help teachers where pupils are having difficulties How do I use them? First Refer to your planning and identify the main teaching objective for the lesson or sequence of lessons for the pupil or group of pupils. Locate the section of the maps for this objective. Find which step it is on or near to and look at the Examples of what pupils should know and be able to do. This will help you to confirm that the work is at the right level. Next The maps will help you to decide whether the pupils have understood the mathematics by providing you with some Probing questions to ask them. Finally If you have a pupil or group who clearly have not understood then the What to do if pupils find this a barrier will give you some suggestions of how the understanding may be built up. Sometimes this will be to look at the previous steps but more often there are teaching ideas and materials provided for that particular objective

Secondary National Strategy

ICT Pilot: Improving learning in Mathematics This is a national project in which the main focus will be exploiting the power and potential of ICT to enhance learning in mathematics classrooms, particularly on the use of ICT for intervention and underperforming groups of pupils at various stages. There is a parallel pilot for improving learning in English. The North West will be represented by Cheshire and Warrington Local Authorities with mathematics consultants working with a small number of schools to research and trial materials and activities. It is expected that each school will identify two teachers to participate in the project so that they can work collaboratively and share ideas and findings. The project will work with groups of teachers to identify and fully develop the key features of effective ICT use for whole class teaching and group work. The aim is to build up a compendium of ‘best case models’ and consider strategies for training and supporting mathematics teachers more generally to make use of the findings. It is anticipated that the project will continue into the next school year but details for 2007/8 have yet to be finalised. It is expected that the final outcomes from the project (possibly summer 2008) will be published on the web and consultancy support will be put in place to support schools in developing the use of ICT for: • efficient and effective teaching of mathematics, where the use of ICT helps particularly with

intervention • innovative teaching using a range of ICT tools


Year 7 - Recognise and use multiples and primes less than 100

Sieve of Eratosthenes Using the multiples facility, highlight multiples of 2, 3, 4, 5, 6, 7, 8, 9 and 10 to leave only prime numbers visible. Show this is true by tiling two copies of the ITP (see Spring 2007 newsletter for how to do this) and displaying the prime numbers on the blank grid by clicking on the primes button.

Year 8 - Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic form. Use letter symbols to represent unknown numbers or variables

L Totals Mask an L shape by following the instructions from the Y6 activity notes. Look at this L-shape drawn on a 9 by 9 number grid. The total of the numbers inside the L-shape is 1+10+19+20 = 50. This is called the L-Total (T). The number at the bottom of the L-shape is called the L-number (N).

Translate the L-shape to different positions by following the instructions from the Y6 activity notes. Investigate relationships between the L-total (T) and the L-numbers (N). Use grids of different sizes and investigate relationships between the L-total (T), the L-numbers (N) and the grid size (G). Try other transformations and combinations of transformations using the rotate function. Investigate relationships between the L-total (T), the L-numbers (N), the grid size (G) and the transformations. Year 9 - Construct and solve linear equations with integer coefficients, using an appropriate method. Use logical argument to establish the truth of a statement Problem: Alan and Betty work in a bakery. Alan has every ninth evening off and Betty has every sixth evening off. Alan is off tonight and Betty is off tomorrow night. What is the next date when will they both be off together? Hint: Assume Alan is off on day 1 and Betty is off on day 2. Alan’s sequence of days off is 1, 10, 19, 28, 37… nth term = 9n – 8 Betty’s sequence of days off is 2, 8, 14, 20, 26… pth term = 6p – 4 If they are off together then 9n – 8 = 6p – 4. Is this possible? Use the number grid to support your argument. Find all of the ITPs through the Lancashire site – www.lancsngfl.ac.uk/curriculum/math under Interactive Teaching Programmes in the ‘ICT in Mathematics’ section on the Primary Site and ‘Mathematics and ICT (ICTAC)’ section on the Secondary Site.


Key theme 3: Improving the conditions for learning

Comments

Learning environment/resources Are additional adults deployed to raise achievement, standards and the personal development of learners and accelerate progress? Does the learning environment support learning and teaching in numeracy?

Promoting positive behaviour Are there agreed expectations about how children and adults behave? Are achievements for behaviour and learning recognised and celebrated?

Key theme 4: Developing the school as a professional learning community

Comments

Leadership and management How effective are leaders and managers in setting a clear direction leading to improvements and high quality education? Has everyone in the school got a single vision? Are both SMT and teachers aware of their individual needs? How are strengths and weaknesses identified and what strategies are put into place to provide support? How effective is governor involvement in raising standards? (Contact with subject leaders, informed of new strategies undertaken by school, regular updates?)

Developing a learning culture Does the school involve parents/carers in their children’s education? (Parental training ie written calculations, SATs info etc) (Are they informed about their child’s targets and how they can assist them? Do they receive a regular termly newsletter regarding curricular areas covered during that term in each class?) (Parents evenings, open evenings, concerts and assemblies etc?)

CPD focus Is there an agreed CPD action plan which forms part of the school maths action plan? Do the subject leaders have a good idea of the needs of the whole school and where they want their subject to move to ?

Issues and Actions:


Excellence and Enjoyment: learning and teaching for bilingual children in the primary years

Talk in maths Many of the resources found within the Excellence and Enjoyment units for bilingual children identify the difficulties that many EAL children suffer from in mathematics. Key issues are often: • A lack of understanding in written problems • Use of higher order maths vocabulary • Difficulty in communicating reasoning • Accurately using the correct mathematical vocabulary • Understanding the instructions within a maths test e.g. draw a line between……two

different ways…. • Accessing the mental maths test Many of you reading this would agree that it is not only bilingual children who encounter these problems. Do we, as teachers, model language enough? Do we give children time to rehearse language? Did you know that the average teacher v child talk time is 90% to 10%? We need to provide children with the opportunities to talk about mathematics and some ideas might be to: • Talk about calculation • Use model verbs in problem solving • Use language of comparison in shape and space • Formulate questions and interpret findings in data handling • Use logical connectives to explain strategies and reasoning • Provide opportunities to make links between what we use in literacy to model language

and apply it in our maths lessons The CD-Rom that is part of the Excellence and Enjoyment learning and teaching for bilingual children in the primary years contains a video sequence of a maths lesson where the teacher uses speaking and listening skills to develop language. It also contains sections on Raising standards in mathematics – achieving children’s targets, Criteria for effective planning for mathematics, Prompts for lesson observation (EAL focus) – Daily mathematics lesson, Whole school curricular target for mathematics – multiplication / measurement of length, Guided talk for mathematics: language of chance or likelihood and many interesting and helpful materials. You can get hold of all of these by Phoning: 0845 60 222 60 Faxing: 0845 60 333 60 E-mail: [email protected] and asking for The Excellence and Enjoyment: learning and teaching for bilingual children in the primary years Ref: 2135 – 2006DCL - EN


Year 4 - Recognise and extend number sequences formed by counting from any number in steps of constant size

Year 5 - Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking ‘What if…?’

Year 6 - Find examples that match a general statement. For example, explain and make general statements like ‘If you add three consecutive numbers, the sum is three times the middle number’

Click on the down arrow under the columns icon and select the number of columns to 6. Count on in 4s from 0 and shade the numbers you land on. What do the children notice? Ask questions such as: - If you went on, would 44 be in the sequence? - Would 52 be in the sequence? - What happens if you start at 2? Is the pattern the same? - What happens if the grid has 5 columns?

Ensure the square in the bottom left hand corner is set to yellow. Click on the arrow at the bottom of the first and last columns. Ask children to total the first and last cells in each row and write them down at the sides. What do they notice about the pattern? Can they explain why this pattern is occurring? (Because each number is ten more than the one before, so each number is 20 more than the last.) This activity can be extended by changing the number of columns.

11 31 51 71

Mask the grid as outlined in the Y2 activity. Then click on three consecutive cells to take off the mask. Children can use the arrows on the mask move tool to reposition the three numbers and investigate the statement. This is an ideal activity to introduce children to the concept of ‘mean’ average.


Take an ITP ……. Number Grid

Each issue we look at an ITP and suggest activities which link to objectives from Reception to Year 6. Year R - Recognise numerals 1 to 9, then 0 and 10, then beyond 10

Year 1 - Compare two familiar numbers, say which is more or less, and give a number which lies between them

Year 2 - Position whole numbers on a number line and 100 square

Year 3 - Derive quickly all pairs of multiples of 5 with a total of 100 (e.g. 35 + 65)

Click on a number on the grid, the number will be highlighted in yellow. Ask the children to either match the number to a number on their number fan, hold up the correct number of fingers, or say the number. Give the children a number and ask a child to come and click on it.

Use the number grid to support children with developing their knowledge of understanding numbers that lie between. Give children two numbers and ask them to identify a number that lies in between. Check responses by clicking on the numbers. To change the highlighting colour, click on the colour icon and select.

Click on the mask icon. Click on the outside border of the mask grid. Then click on the centre of the mask moving grid. This will mask the whole grid. Give the children a number and ask them to click on the grid where the number should be. For lower ability children, ensure that some of the other numbers are uncovered to support them.

Ask the children to find how many different ways they can make 100 with multiples of 5. Children can be supported by the ability to work out the number of squares in each colour. These could be printed out and used to form a display.


Article produced by Gillian Hodgson from St John’s Catholic Primary School, Poulton-le-Fylde

Girls Allowed! Maths Group

A particular group of girls at our school, having been tracked since Reception, is not making the expected progress, despite having the mathematical knowledge and ability. Having reached Year 6, and still protesting they knew nothing, the Girls Allowed! Maths group was set up – to allow them to succeed in mathematics. The group (9 girls) works together on a Thursday morning after play, when another teacher works with the Maths Challenge! group (level 4As and 5s – 9 boys, 3 girls) and the teaching assistant works with the Maths Practice! group (level 3Bs, 4Cs and 4Bs – 8 boys). The following report was written by the Girls Allowed! pupils. There is a skipping club for Year 6 boys and girls every day at morning playtime. We practise routines, Double Dutch skipping and different steps and moves. We also aim to beat our previous week’s total number of skips done in 5 minutes. On a Thursday, the day our Girls Allowed! group meets, the music we skip to is by Girls Aloud. Our favourite tracks for skipping are Something Kinda Oooooh, Jump and I Think We’re Alone Now. Our teacher prefers the original Tiffany version, though! This gets us in the mood for our Girls Allowed! maths group, which is straight after play. Our teacher chose us for this group because when she said the word “MATHS” all our faces went blank and confused!!!!! We were also chosen for this because we didn’t know what to do in our maths work, or we thought we didn’t know what to do. Our main problem seemed to be as soon as we heard any word to do with maths, some of us immediately switched off. We sometimes have trouble remembering mathematical facts, knowledge and vocabulary. We all like this group because it helps us in class and we get some equipment to use in the group and in class. On the first day of Girls Allowed!, we received a pocket jotter (notebook) to make notes during maths lessons in class and in the group. As well as the note pad we were given a maths set to help us with our work, stickers, pens, pencils and rubbers. We were told that this group is practising maths for our SATS at school in May. Furthermore to help us to be confident maths we made a chant –

“WE LOVE MATHS, MATHS IS GREAT! WE LOVE MATHS, MATHS IS GREAT!”

We think our Girls Allowed! maths group has improved our confidence and made us all realise that maths is fun! Furthermore we are offered extra help, and more helpful information, about our working subject in maths. We also help each other with work and are able to complete our work. And we are very grateful to our teacher for choosing us in this great maths group. It has changed us from hating maths to loving and enjoying it! And, most importantly, we are getting better at doing our maths work!


A leaflet has been produced to help schools meet the needs of Wave 2 and Wave 3 children in Literacy and Numeracy. Here are some of the pages from the leaflet but the full leaflet will be posted on the Lancashire Mathematics Team website. Contact Lynne Bold (Primary Literacy Consultant), Eleanor Hick (Inclusion/SEN Adviser) or Sue Bailey (Primary Mathematics Consultant) for further information.


Have you got a Clever Touch Interactive Whiteboard? If so the presentation software that comes free with this board is called Lynx. Lancashire have bought the county-wide licence for this software so any school can use it as it will operate on any Interactive Whiteboard. The latest, improved version will soon be available to you. Lynx is multi-faceted software that has been created for use with any interactive whiteboard. Here are some of the features that Lynx offers you: • A selection of prepared lesson plans you can download from the Lynx website. The Lynx website also offers

updates to your software. • Curriculum specific clip art and information resources for a wide range of subjects and key stages. • Annotation toolkit including pen, paintbrush, highlighting and area fill tools. • Screen Capture allows you to prepare and build lessons easily and also allows annotations and lessons to be saved

for later discussions. • Internet access with a single button. • Easy to use virtual keyboard and calculator. • Links with any Windows application so frequently used programs and resources are available quickly and easily from

the Lynx handset. • A variety of subject specific screen backdrops are available to enhance lessons including lined, graph, isometric,

squared, hexagonal and music manuscript paper. • Interactive and simple high definition maps are also provided – ready to use for lesson preparation. • Electronic coloured and plain Venn diagrams are also found in Lynx. • A variety of interactive facilities are also provided within Lynx, these include clocks, number squares and calendar. • Arrange, transform, fill and group objects. • Modify and customise shapes to your requirements. • Use the curtain, spotlight and magnify facility. • Use the keyboard to write, align, rotate and transform text. The Lancashire ICT team will be contacting schools shortly with details of how to download this free software.

Espresso

If your school still subscribes to “espresso” have you thought of using the maths content to develop pupils’ learning? OFSTED have recently commented on the lack of evidence of pupils using ICT independently to develop their understanding of mathematics. You can search Espresso by key stages for mathematical content. Within the foundation stage there are activities on numbers, shape and counting rhymes.

KS1 content includes learning about number, shape and space and time, whilst searching KS2 finds activities covering number, interpreting data and real life problems. There is even an activity related to “Ready, Steady, Cook”. Many of the topics begin with a video clip and have related independent activities; perfect for the ICT suite or your bank of laptops. (or even the computers in your classroom.)


BGfL Birmingham Grid for Learning has an area which contains some excellent interactive resources for Foundation through to Keystage 4. Click on http://www.bgfl.org/bgfl/index.cfm?s=1&m=220&p=136,index then select the relevant activity. For example, the activity above is called ‘The Difference Between Two Times’, and tackles word problems involving timetables by using a number line.

Count Us In A lovely site from ABC in Australia (their answer to the BBC!). The site contains a range of colourful and interactive games and activities to help children understand basic number concepts.

http://www.abc.net.au/countusin/default.htm Try Game 1 and see what happens if you try to move too many sheep from one paddock to the other!


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Smarties pictogram where 1 unit represents one smartie.

Questions about the graph

Curricular targets displayed Venn diagram

Horizontally presented bar chart

KS2

Progression in Data Handling Interactive Displays

Block graph NB vertical axis labelled in ones. The pictures are attached with blue tack.

Laminated table which can be altered regularly and the children can change the block graph to represent the data

KS1


Axis graduated in twos

Moveable columns which can be changed to represent the data in the table

Laminated table on which different data can be collated

Pictograms where each picture represents 10

Variety of scales for the vertical axis. Children can choose the most appropriate scale for the data.

Moveable pie chart

from Peel Park Primary School Accrington

Curricular Targets Moveable columns with ribbons

Carroll diagram criterion

Venn diagram on laminated card which is easily changed

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