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Lancashire Mathematics Newsletter Autumn Term 2009 Full Mathematics The Lancashire Mathematics Newsletters each follow a subject theme. The newsletter contains resources to support you in that area Team List of mathematics, including teaching ideas, staff meetings, staff INSET, starter activities, ideas for incorporating ICT and useful resources. Team Leader / Senior Adviser Current news and issues from the world of Alison Hartley mathematics teaching will still be incorporated. This term’s theme is: Primary Mathematics Consultants Lynsey Edwards (Senior Consultant) Sue Bailey “Lesson Starters“ Tracy Dimmock Sue Farrar Contents Anne Porter Team News 2 Emma Radcliffe What Can I Do in Mathematics? 2 Angeli Slack Andrew Taylor Renewed Framework for Mathematics 3 Peter Toogood Mental Mathematics Staff Meeting 3 Secondary Mathematics Consultants Effective Starters 4 Fractions Starter 5 Carole Ash Louise Hastewell Starter Activities - Level 5 6 Mary Ledwick Maths of the Month 8 Maureen Magee Helen Monaghan Subject Leader Autumn Planner 9 Children Who Attain Level 4 in English Team Contact Details 10 But Not Mathematics at Key Stage 2 Phone: 01257 516102 Maths is Special 12 Fax: 01257 516103 Numbers Count 14 E-Mail: mathematics@lancashire.gov.uk One-to-One Tuition 16 Write to LPDS Centre Behaviour for Learning in the 17 us at… Southport Road Mathematics Classroom CHORLEY Lancashire Maths Challenge 2009 18 PR7 1NG Puzzle Page 20 Website: www.lancsngfl.ac.uk/curriculum/math This newsletter will be available to download in the autumn term from our website. The Lancashire Mathematics Team Team News... Congratulations to Shirley Bush – our Senior Mathematics Consultant who has taken up a well-deserved post as a Regional Adviser for Mathematics with the Primary National Strategy. Her work for Lancashire has been invaluable in promoting and raising attainment in mathematics across the county. She will be sorely missed and we wish her every success in the future. Lancashire’s loss is the country’s gain! Also congratulations to Lynsey Edwards on her appointment to Senior Mathematics Consultant. Lynsey has been an extremely valued and influential member of the Lancashire Mathematics Team for seven years. She continually strives for mathematics to be taught well and to be enjoyed by all children. Her appointment will ensure the high standards of the mathematics team will be continued. However, it is with regret that we are saying goodbye to Tim Kirk who has been with the Mathematics Team for two years. He is returning to school at the end of his successful secondment. His work in schools and for the team has been of huge value and Tim would be welcomed back to the team at any time! What Can I Do in Mathematics? These resources accompany the booklet 'Securing Level 3 and Securing Level 4 in Mathematics'. They allow teachers and pupils to establish whether they are secure in key areas of learning related to level 3 or 4 in mathematics. They can be ordered for free or downloaded from Teachernet at www.teachernet.gov.uk. Level 3 DCSF-00434-2009 Level 4 DCSF-00133-2009 2 The Lancashire Mathematics Team Renewed Framework for Mathematics In late June this year, the government published the white paper entitled “Your child, your schools, our future – building a 21st century schools system”. Just prior to this being published, it was incorrectly reported that schools would no longer have to plan and teach from the National Strategy Renewed Frameworks for Mathematics and Literacy. The white paper actually states that successful schools have “taken on teaching frameworks developed by The National Strategies, including for the daily literacy and numeracy hours, and used them with enthusiasm… and we expect every school to continue with this practice.” Download the full report from www.dcsf.gov.uk/21stcenturyschoolssystem. Mental Mathematics Staff Meeting A staff meeting focusing on mental mathematics, which looks in particular at the starter session, is now available to download from the Lancashire Mathematics Team website. The CPD pack includes a PowerPoint presentation, presenter’s notes and appropriate handouts. This is the staff meeting delivered recently to mathematics subject leaders at their network meetings. The staff meeting (as well as previous staff meetings on shape and space; data handling and algebra) can be downloaded from www.lancsngfl.ac.uk/curriculum/math and then clicking on the School Based CPD tab on the left-hand side. The Lancashire Mathematics Team 3 Effective Starters The 6 Rs define what the role of the starter should be... To practise and consolidate existing skills, set in a context to involve children in Rehearse problem solving through the use and application of these skills. Recall To secure knowledge of facts, build up speed and accuracy. To draw on and revisit previous learning in order to assess, review and Refresh strengthen previously acquired knowledge and skills, or to return to work that children found difficult. To sharpen methods and procedures, extend and explain ideas to develop and Refine deepen children’s knowledge. To use mathematical vocabulary and interpret images, diagrams, text and Read symbols correctly. To use and apply acquired knowledge, skills and understanding through making Reason informed choices/decisions, predicting, hypothesising and proving. Starter sessions: • Occur in every lesson; • Should cover all aspects of mathematics; • Are objective led not activity led; • Are differentiated appropriately using targeted questions or separate starter sessions for different groups; • Should include counting and/or rapid recall every day as one part of the starter; • Do not have to link to the main part of the lesson; Guidance on the content – over the week address the following; • Curricular target area (twice per week) • Past target area • Assessing the prior learning of the upcoming unit • Any specific class issues • Revisiting curricular areas to obtain assessment information. 4 The Lancashire Mathematics Team Fractions Starter Objective: Identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents. Activity: Hold up a large sheet of paper. Establish that the children can see the whole of one side of the sheet of paper and you can see the whole of the other side of the sheet. Fold the sheet in half. Q: What fraction of the whole sheet of paper can you see now? Q: What fraction of the whole sheet of paper can I see now? Agree that the class and you can each see half of the sheet and ½ + ½ = 1. Unfold the sheet to confirm this, draw a line down the fold and refold. Fold the folded sheet and display a quarter. Ask the same two questions and by unfolding and refolding the sheet, confirm that ¼ + ¼ + ¼ + ¼ = 1 whole and establish that ¼ + ¼ = ½. Draw on fold lines, building up to the representation below. Continue to fold, generating eighths and sixteenths. Each time, pose the questions and agree the fraction and confirm the fraction statements. Unfold the sheet and invite the children to recall the fractional parts they have identified and used. Write these onto the sheet (see below). With the annotated sheet displayed, ask a series of questions involving these fractions, such as: Q: How many quarters are there in the whole sheet? Q: I am looking at one half of the sheet: how many eighths can I see? Q: How many eighths are there in a quarter of the sheet? Q: How many sixteenths are there in one half of the sheet? Q: I am looking at four sixteenths, how many eighths can I see? Q: If I shaded in three eighths and you shaded one half, which part would be bigger? Q: If we removed one sixteenth, what fraction would be left? Q: I see one quarter and one eighth, how many eighths is that altogether? Q: If I halve one quarter, what fraction would this give me? Q: If I halve one sixteenth, what fraction would I get? Q: Can you explain to me what happens to the denominator of the fraction as I keep halving? Q: What can you tell me about the relationship between halves, quarters, eighths and sixteenths? Q: Suppose I start with a sheet and divide it into three parts. I then divide these three parts into three parts, what fractions would I get this time? The Lancashire Mathematics Team The Lancashire Mathematics Team 12 5 6 We have put together some ideas for starter activities / questions for each of the seven strands within the mathematics curriculum, for each of the six Rs discussed earlier in the newsletter. This is just a sample of the resource. Levels 1 and 3 are also on our website under the Activities and Resources tab and the Mental and Oral Starters tab. Counting and Knowing and using Handling data understanding Calculating Understanding shape Measuring number facts Interpreting pie charts number Rehearse Write the largest whole number Use target boards to stimulate Gordon’s ITP – Percentage Feely bag – describe Play bingo on whiteboards When given whole sample size To practise and consolidate to make this statement true. questions such as: Fraction chains. properties of 2D and 3D where focus is to match variety and fraction or % of specific existing skills, usually mental 50 + < 73 Which 2 numbers multiplied shapes using Level 5 of objects/ measurements to an group, identify numerical size of calculation skills, set in a Number scales ITP will together give an answer True or false? vocabulary – class draw and imperial unit of measurement. group. context to involve children in provide an image to support nearest to 1? 10% = 1/10 so 20% must equal name shape based on Eg: Block of cheese - lb; e.g.: Sample size is 325, white problem solving through the this type of question. 1/20. description. Bottle of milk - pint. section is 30%. How many use and application of these Quick fire questions such as: Packet of butter - oz; chose white? skills; use of vocabulary and Write in the two missing digits. Distance from Lancaster to language of number, properties Decimal number line ITP – 0 × 0 = 3000 Sort shapes according to Preston - miles. of shapes or describing and give me a decimal fraction that What is thirty times forty times properties – use Carroll Height of the teacher – ft and reasoning. lies between 3.4 and 3.5 ten? diagrams, Venn diagrams. inches. Starter Activities - Level 5 Gordon’s ITP – Carroll shape Ordering fractions on a Six times a number is three Measuring Cylinder ITP number line/ counting stick. thousand. What is the number? convert quantities from l to ml Write two factors of twenty-four Use ITP Calculating angles - which add to make eleven. Example question: if we know the size of 2 of 3 angles on a This chart shows the amount of straight line/ in a triangle, what money spent in a toy shop in is the missing angle? three months. October November December 0 £10 000 £20 000 £30 000 Stephan says, ‘In November there was a 100% increase on the money spent in October’. Is he correct? Explain how you can tell from the chart. Recall Count on or back in steps of Number dials ITP –Using What’s my number? Reveal a shape – discussion Target board/ bingo – Recall Match samples of data to The Lancashire Mathematics Team To secure knowledge of facts, constant size. When using knowledge of table/division e.g.: I think of a number, around what it might be/ cannot relationships between units of suitable graphs or charts. usually number facts; build up integers, the start number facts and relating to multiples of square it and subtract 12. My possibly be based on measure – imperial to metric. speed and accuracy; recall should not be a multiple of the 0.1 and 0.01. answer is 52. What number did knowledge of properties at quickly names and properties step size. Relate to converting cm to m; cl I think of? Level 5. of shapes, units of measure or Use counting stick to to l I think of a number, divide it by types of charts and graphs to represent terms in a sequence. 10, divide it by 10 again. My 20 questions – Yes/No represent data. Fizz Buzz – recall of square answer is 0.3. What number answers. Counting in steps of decimals numbers, prime numbers, did I think of? multiples of…, factors of… Refresh Use a counting stick and Bingo – square roots of perfect Would you rather have 17.5% Here is an equilateral triangle Play your cards right – using To draw on and revisit previous identify the 4th and 7th terms. squares to 12x12. of £200 or 30% of £120? inside a rectangle. 1 suit from a pack of cards. learning; to assess, review and Calculate missing terms. Encourage use of probability strengthen children’s previously Extend by including decimal Ratio and Proportion ITP when making higher/lower acquired knowledge and skills values in the sequence or step decision. Extend to more suits. relevant to later learning; return size. to aspects of mathematics with Spot the deliberate mistakes which the children have had – scale, key, accuracy of graph difficulty; draw out the key or chart against gathered data. points for learning. x 12° Calculate the value of angle x. Refine This sequence of numbers This three-digit number has 2 Tariq won one hundred pounds Calculating angles ITP - A tile is 0.2m long. What do you mean? To sharpen methods and goes up by 40 each time. and 7 as factors. in a maths competition. He Angles around a point – find One hundred tiles are placed Give the sample size, median procedures; explain strategies 40, 80, 120, 160, 200,… 294 gave two-fifths of his prize missing angle. end to end in a row. How long and mode of a set of data. With and solutions; extend ideas and This sequence continues. Write another three-digit money to charity. How much of is the row? talk partners, find the mean of develop and deepen the Will the number 2140 be in the number which has 2 and 7 as his prize money, in pounds, did Gordon’s ITP Area -Find area the data. children’s knowledge; reinforce sequence? Explain how you factors. he have left? of right angled triangle when How many seconds in 15 their understanding of key know. lengths of the 2 perpendicular minutes? Line graph ITP – tell your talk concepts; build on earlier sides are known. partner the story behind the learning so that strategies and A and B are two numbers on graph. The more outrageous techniques become more the number line below. the better, as long as the efficient and precise. interpretation of the graph is correct. The difference between A and B is 140. What are the values of A and B? Read p and q each stand for whole If I know 237 x 17 = 4029, how Set of balanced scales with Data handling ITP. Pupils To use mathematical numbers. can I calculate 238 x 18? 2.1kg marked as the total on pose and answer questions vocabulary and interpret one side. Opposite side has 2 relating to variety of graphical images, diagrams and symbols p + q = 1000 objects on it. The larger object representations – correctly; read number p is 150 greater than q. is twice as heavy as the smaller e.g.: How many people in the sentences and provide one. How much does each village are aged under 51? equivalents; describe and Calculate the numbers p and q. object weigh? Using the graph, can you tell if explain diagrams and features this is this a village in decline? involving scales, tables or How do you know? graphs; identify shapes from a list of their properties; read and interpret word problems or puzzles; create their own problems and lines of enquiry. Reason 5 is the third term in a Convince me that 1 is not a Always, sometimes or never Pose an ‘always, sometimes Here are two spinners. Compare 2 representations of To use and apply acquired sequence. The step size is not prime number; that square true? or never true’ statement to Jill's spinner Peter's spinner similar content but with different knowledge, skills and 1 or 2. What could the numbers have an odd number e.g.: (a+b)+c = a+(b+c) generate discussion. sample sizes. The Lancashire Mathematics Team understanding; make informed sequence be? Provide 2 or 3 of factors. e.g.: 5 65 e.g.: 2 pie charts; 1 pie chart choices and decisions, predict different solutions. Explain your Triangles have 2 acute angles. 6 4 7 4 and 1 pictogram; 2 line graphs and hypothesise; use deductive reasoning to your talk partner. Triangles have 2obtuse angles. 1 3 8 3 with different scales etc. Pose reasoning to eliminate or Triangles have 2 perpendicular 2 12 ‘Would you rather…’ conclude; provide examples In a school, the ratio of boys to sides. questions and allow Jill says, ‘I am more likely than that satisfy a condition always, girls is 4:5. How many children Pentagons have 2 pairs of explanations of reasoning. Peter to spin a 3.’ Give a sometimes or never and say might be in the school? parallel sides. reason why she is correct. why. Fixing points or Polygon ITP Peter says, ‘We are both to support proof/ images of equally likely to spin an even examples. number.’ Give a reason why he is correct. 7 BEAM - Maths of the Month Have you seen the free resources available from the BEAM website at www.beam.co.uk/mathsofthemonth.php? The resources cover games and activities which are separated into strands and age ranges. Maths of the Month Going dotty 1. Join the dots however you like. Can you make each one adapted for use in starter sessions, particularly These can easily bedifferent? those focusing on reasoning and refining skills. you need: Maths of the Month • squared paper 1. These are all odd numbers. 1 9 7 5 And these are all even. 2 8 6 10 How many odd numbers are there below 100? And how many even? 2. On Planet Zog, these are 1 5 4 8 7 2 Zodd numbers. 2. Can you finish these squares? And these are Zeven. 3 12 9 6 15 Use squared paper to work out some more Zodd numbers, and some more Zeven ones. 3. How many Zodd numbers are there below 100? And how many Zeven ones? 8 The Lancashire Mathematics Team 5–7 December 2004 9–11 February 2009 © BEAM Education © BEAM Education www.beam.co.uk www.beam.co.uk Subject Leader Autumn Planner These are suggestions for maths subject leader to use as a check list for their action planning Maths Subject Leader Autumn Planner Autumn Term 2009 Shaded areas are choice for Sept – mid Oct Oct – end Dec that term (not all in one term!) Auditing & action planning; Share revised action plan, to include Conduct Pupil interviews on setting priorities CPD and SL support programme, at identified area PDMs staff meeting. Ensure that children’s progress Analysis of data and work With headteacher, use school data such is tracked on a termly basis scrutiny; as RAISE Online, FFT and/or using formative and summative Curricular and numerical target Lancashire grids to inform discussion of assessment e.g. APP, teacher setting standards and setting of numerical assessments, QCA PDMs targets. Pupil Progress meetings Identify pupil underperformance Book sampling Agree procedures for monitoring Pupil interviews children’s progress across the term/year Scrutiny of work on identified Walkthrough e.g. agreed school tracker for school focus Focused support/monitoring monitoring termly progress SATs analysis Where targets have been set Curricular targets set Ensure all teachers have an effective discuss with teachers at PDM a learning environment which includes a review of year group curricular working wall and process success targets criteria to support children’s learning in Set whole school/year group mathematics. curricular targets for second half term as a result of analysis and audit. Whole school planning Subject leader to complete a scrutiny of short term plans. Support teachers with the use of the Renewed Framework. Children identified for SL supports headteacher in ensuring Implementation of intervention additional support resources and capacity to deliver groups. intervention programmes are in place. Organise training as needed. Review impact of additional support programmes. Children selected for intervention programmes. Identification of underperforming pupils Training for TAs responsible for delivering intervention programmes. Subject Leader support and Agree with headteacher specific CPD Subject leaders to attend Maths continued professional programme and focus of support for the subject leader support meeting development programme; year linked to mini audit. Monitoring of teaching and learning Agree monitoring programme with headteacher (pupil discussions, book scrutinies, pupil progress meetings, etc) in accordance with the action plan. SL to deliver relevant maths subject specific CPD The Lancashire Mathematics Team 9 Research Paper: Children Who Attain Level 4 in English Key factors affecting attainment in the number of pupils in a cohort who were mathematics identified as having special educational needs and the proportion of pupils in the cohort who The factors identified in this report that appear attained level 4 or above in English but not to affect the proportion of pupils who attain mathematics. The focus of the support for these level 4 in English but not mathematics by the children tended to be on improving English skills end of Key Stage 2 are identified below. and behaviour management rather than on mathematics. Uneven progress in mathematics through Key Stage 2 Level 5 attainment in mathematics Over half of the target-group pupils in the focus It was generally the case that where the schools attained the ‘benchmark’ level of 2b or proportion of pupils who attained level 4 in above in mathematics at the end of Key Stage 1, English but not in mathematics was significant, but did not go on to attain level 4 by the end of the proportion of pupils attaining level 5 in Key Stage 2. Progress for the target-group pupils mathematics was low. Put another way, schools (measured using average annual increases in that had a low percentage of pupils attaining point score) was markedly lower in Years 3 and level 5 in mathematics also tended to have a 4 than in upper Key Stage 2. In fact the progress relatively high proportion of pupils who attained the pupils made over Key stage 2 fell well below level 4 in English but not mathematics. the two levels expected, and while there was greatest progress made in Year 6, this was not Key areas of mathematics that pupils enough to compensate for the poor progress who attained level 4 in English but made over Years 3 and 4. not mathematics found particularly challenging when compared to pupils Differences in the attainment of girls and who attained level 4 boys Problem solving, communication and A high proportion of the target-group pupils reasoning in the focus schools were girls. In Lancashire we are currently running programmes on • Solving multi-step problems, particularly improving girls progress and attainment in those involving money and time. mathematics. • Reasoning about numbers, including the identification and use of the inverse The proportion of special educational operation to undo a process. needs (SEN) pupils in the cohort • Thinking through the steps in a question in a logical sequence and representing this Overall there was a positive correlation between to show their workings or to explain their 10 The Lancashire Mathematics Team but not Mathematics at Key Stage 2 method. calculations needed to answer a question using data read from a table, graph or chart Number and the number system • Labelling appropriately a scale on a graph or chart, or the groups in a Carroll diagram. • Completing a sequence involving three-digit numbers. Useful resources for schools • Recognising equivalence of fractions and decimals. Overcoming barriers in mathematics – • Recognising and finding simple fractions of helping children move from level 3 to shapes and numbers. level 4 • Solving problems involving multiples and (DCSF 00695-2007) factors of numbers. Overcoming barriers in mathematics – • Questions involving comparisons of two-digit helping children move from level 2 to and three-digit numbers and understanding level 3 relative values. (DCSF 00149-2008) Overcoming barriers in mathematics – Calculation helping children move from level 1 to level 2 • Multi-step problems involving multiplication (DCSF 00021-2009) and division of two-digit and three-digit numbers. These materials are designed to help teachers • Responding at speed to mental calculation ensure that children make expected progress. involving subtraction of two-digit numbers and calculations involving multiples of 10 in Lancashire Girls and Mathematics Programme all four operations. – access to this programme can be gained • Choosing and working out the calculations through the school’s SIP. needed to solve money problems including those involving change. Lancashire Mathematics Team website: • Calculating time differences. www.lancsngfl.ac.uk/curriculum/math. • Calculations involving decimals. The full report can be found at: Handling data and measures http://nationalstrategies.standards.dcsf.gov.uk/ node/166696. • Accurate reading of scales that had non- unit intervals when identifying values as a measure of quantity and when identifying values on a graph or chart. • Choosing and working out the appropriate The Lancashire Mathematics Team The Lancashire Mathematics Team 12 11 Maths is Special The ‘Maths Is Special’ event a variety of different foods, symmetry, and making seems to go from strength to your own pizza. Students from Pear Tree School led strength each year. This year the children through a Dave Godfrey song to end the Special School Network the event. All participating schools The Acorns, cluster chose the theme Bleasdale, Great Arley, Holly Grove, Kingsbury, of food for all the events and this turned out to be a Pear Tree, Pendle View, Red Marsh and The Loyne great success. The children received a framed certificate and all the children thoroughly enjoyed learning received individual certificates. about mathematics through a range of practical activities The event was further extended this year with the which involved problem inclusion coordinator for Pear Tree School inviting solving related to food. four of the school’s link primary schools to take part in a ‘Maths is Fun’ day. Ten children from The KS2 ‘Maths is Special’ event took place at Pear each school who would benefit from this practical Tree School and a special thank you goes to the experience, came to school for holding take part in similar the event and to mathematical activities. the different schools The teachers gained who provided the ideas of how they could fun and meaningful support children in the games. The practical mainstream setting. activities included data handling, length Building on the success which involved 'Maths is Special' at Pear Tree School of other years, seven making a monster, a schools took part in the KS3 ‘Maths is Special’ event number gingerbread man bingo game, investigating where the children had to work as a team to meet different shapes by making your own boat using 12 The Lancashire Mathematics Team certain challenges. The ‘Brunch Crunch’ had five rounds based on problem solving linked to the theme of food with elements of number, measures, ratio and proportion, memory and spatial awareness. The participants all enjoyed making and eating a trifle that they had made as one of the challenges. Many thanks to Michelle Westhead, Lee Toulson, Ian Richardson and Rachel 'Maths is Special' at Pear Tree School Kay for organising such varied and interesting activities. All participants were awarded certificates with Great Arley coming second and Broadfield winning the event. Both teams received medals and money to buy mathematics equipment for their schools. Congratulations also to Chorley Astley Park School, Broadfield Specialist School, Great Arley, Pendle Community High School , Sir Tom Finney Community, Tor View and West Lancashire Primary School Link Day at Pear Tree School Community High. Thank you to all the members of the team who organised such super activities as without this hard work the events wouldn’t be able to take place. A special thanks to Lee Toulson of Astley Park School and Carol Davies and Heather Hambilton of Pear Tree School for their hard work in organising and hosting the events. KS3 'Maths is Special' at Astley Park The Lancashire Mathematics Team 13 Numbers Count What is Numbers Count? Numbers Count is a new numeracy intervention that is at the heart of the Every Child Counts (ECC) initiative. It draws upon the recommendations of the Williams Review of Mathematical Teaching in the Early Years Setting and Primary Schools, upon lessons learned from existing intervention programmes and upon the findings from the ECC research phase (2007-08). Numbers Count was launched in September 2008 and will be built up and refined during the Numbers Count aims to enable Year 2 children ECC development phase (2008-10), by drawing who have the greatest difficulties with on impact data, feedback from a wide range of mathematics to make greater progress towards participants and stakeholders and the findings of expected levels of attainment so that they will an independent evaluation study commissioned catch up with their peers and achieve Level 2 or by the DCSF. Numbers Count Teacher Leaders where possible Level 2B or better by the end of and teachers will contribute actively to its KS1. development so that Numbers Count can provide increasingly effective support for young The 12 lowest attaining Year 2 children in a children who have difficulties with mathematics. school normally receive Numbers Count support during the course of a year. Each child is on the Professional Development for Numbers programme for approximately12 weeks, starting Count Teachers in September, January or April. Numbers Count aims to ensure the development of a numerate Numbers Count Teachers are trained through a child who is confident and who enjoys actively one-year professional development programme. learning mathematics. The professional development includes: A Numbers Count Teacher normally works on • 10 days of face to face events which a 0.6 timetable, teaching four children every are focused on delivering the Numbers morning or afternoon on a one to one basis and Count programme, early mathematical planning a personalised programme for each development and teaching and learning; child. S/he undertakes a specialised professional • At least 5 individual support visits from Emma development programme and liaises closely Radcliffe as Teacher Leader; with each child’s class teacher and parents or • Analysing and sharing video recordings of carers. S/he is trained and supported by a Local Numbers Count children with colleagues; Authority Teacher Leader, who in turn is trained • Participating in at least six Learning Partner and supported by a National Trainer. visits with other Numbers Count Teachers; • Attending additional network meetings as A Numbers Count Lesson takes place in a necessary; dedicated teaching area and lasts for 30 • An opportunity to apply to study for all minutes. It is lively and active and uses a wide or part of the MA Early Mathematical variety of resources. It focuses on number Interventions through distance learning with because research has shown that number Edge Hill University. development underpins children’s learning across all aspects of mathematics. Further Professional Development is available 14 The Lancashire Mathematics Team for teachers in their second year as a Numbers teachers working in Blackpool. Count Teacher. This includes: • 5 days of face-to-face events The Impact of Numbers Count Within • At least one individual support visit from a Lancashire - Spring Term 2009 Teacher Leader • Learning Partner Visits The table below shows the average score for Lancashire compared to the average scores Lancashire Schools Involved in Every nationally for Term 2. Child Counts 2008-2009 Lessons lost At- Age Stand- School Name titude equiva- ardised Lessons Child Other survey lent scores Taught abs reasons gains score gains The Blessed Sacrament Catholic Primary School, Preston (pts) (months) (pts) St Joseph’s Catholic Primary School, Preston National 40.7 5.6% 16.2% 10.3 14.8 16.9 Term 2 Preston St Matthew’s CE Primary School Lancs 45.8 4% 15.9% 14.5 18.7 21.4 Term 2 Seven Stars Primary School Accrington Hyndburn Park Primary School Attitude Survey Cherry Fold Community Primary School • Children’s confidence and attitudes towards Nelson Walverden Primary School mathematics are assessed through the use of the Numbers Count Attitude Survey when Walter Street Primary School children enter and exit the programme. Lord Street Primary School, Colne This includes children’s questions, teacher’s questions based on the participation in St. John’s Skelmersdale whole class and group work and parent’s questions. The Numbers Count Teacher at each of the • Additional gains around the children’s schools has been working towards gaining attitudes have also been reported by many their accreditation. They have had to provide schools. This related to an overall positive evidence that they have met the Standards and attitude across the curriculum, not just in Requirements of a Numbers Count teacher. In mathematics. order to achieve their accreditation they also have to have worked as a Numbers Count Maths Age Equivalent Gains During the Teacher for a year. Numbers Count Programme Schools Involved in Every Child Counts Children take a Sandwell Early Numeracy Test 2009-2010 when they enter and exit the programme. The test includes practical, pictorial, oral and written During the academic year of 2009/10, 24 new tasks and questions. It is administrated by the Numbers Count Teachers will be trained by the Numbers Count Teacher on entry and a trained Teacher Leader. The teachers will work across Link Teacher on exit. The results have improved the Lancashire consortium with seventeen significantly comparing Term 1 and Term 2. The teachers working in Lancashire, four teachers LA has achieved age equivalent gains that are working in Blackburn with Darwen and three above the national average. The Lancashire Mathematics Team 15 One to One Tuition - Real Personalisation! This is a huge new strategy nationally, spearheaded by Sue Hackman on behalf of pupils in Key Stages 2 and 3 and, in National Challenge schools, in KS4 in English and mathematics. The introduction to the guidance for Local Authorities states:- “Ensuring that the right support is in place for all children, regardless of class or social background is important in closing the attainment gap. For those who can afford it, individual tuition has always been the preferred method of additional support for pupils not achieving their potential. children and who are unable to afford extra one to one tuition. All schools will have a percentage of While our current catch-up arrangements are their students in this category and so all schools will effective for many, we know that they are not be involved in this project in one way or another. working for all pupils. Some need a level of support The funding is ring-fenced. which is beyond our control to deliver in the context of whole class or small groups. Without an As teachers of mathematics, you will potentially individualised approach it will be very hard for this be involved in two ways. Firstly in liaising with the group to make the progress needed to achieve their tutor on the child’s identified needs [using APP full potential. assessment tools] before and after the ten hour long sessions and secondly, as a potential tutor. The pilots Even in the personalised classroom, we know that identified the difficulties in recruiting tutors and Sue some pupils would benefit, at key moments, from an Hackman has therefore insisted on a high rate of intensive burst of individual tuition, which the class pay for tutors. It is recommended at £25 per hour. teacher can guide and reinforce, but simply does not The LA is mandated to provide support and training have the time to deliver.” for tutors and to assist schools in every possible way with discharging their responsibilities in this initiative. Lancashire has funding for over 6000 places in There will be extra consultants in primary and these key stages from September 2009, rising secondary maths and English to support the project incrementally next year. The roll out has already in schools. started in KS2. Tutors have to be qualified teachers and tuition can take place in or out the school day in A project co-ordinator has been appointed to deal various venues. By the time you read this the LA will with front line support. If you have any queries at already have decided on a funding formula to meet all please email Hilary King at one-to-one-tuition@ the needs of the target cohort and the roll out will lancashire.gov.uk or telephone 01257 516120. have started in earnest. Alternatively you may access the materials available The target cohort will comprise students who are at present on http://www.teachernet.gov.uk/ disadvantaged and vulnerable e.g. looked after teachingandlearning/schoolstandards/mgppilot/. 16 The Lancashire Mathematics Team Behaviour for Learning - Support for NQTs These prompts were developed as part of 7. Choice/consequence the course for NQTs in mathematics Before a consequence is imposed, pupils should be given an explicit choice to comply or to 1. Non-verbal signals reduce intrusion into accept the consequence; for example, ‘Peter the lesson I need you to move seats now or you will be Often a look is as effective as verbally given a detention. Your choice’ reprimanding a pupil. But remember this strategy may not work as well with children on 8. Assertive direction the autistic spectrum. Pupils need clear instructions and are more likely to comply if delivered assertively. I need you to 2. Focus on pupils making choices be quiet whilst I’m speaking…thank you.’ The They are more likely to cooperate if they feel use of ‘Thank you’ following the instructions some control over outcomes. If we present allows the teacher to model politeness while two choices that are both acceptable to us conveying the expectation that pupils will then they are less likely to make a different and comply. The tone of voice should make it clear unacceptable choice. ‘I need you to move seats that this is an instruction not a request. you can move to either here or there’ 9. Broken record 3. Direction and delay A first response to overt non-compliance could Sometimes called ‘take up time’. Pupils may be be to repeat the assertive statement in a calm influenced by peer pressure not to comply with neutral way possible two or three times. instructions. There are times when giving a pupil thinking time and moving away from them 10. Label the behaviour not the pupil helps pupils to comply and not lose face. When directly challenging inappropriate behaviour, pupil’s self esteem is vulnerable. 4. Rules to provide distance Express your disapproval of the behaviour not Correcting pupils with direct reference to rules the pupil. Use ‘ I find it very difficult to carry on shifts possible resentment away from teachers. when you are interrupting me, listen quietly, ‘What’s the school rule about mobile phones?’ thanks’ rather than ‘ you need to learn some manners and stop being so rude. Just shut up!’ 5. Partial agreement (‘you’ messages can be confrontational). Pupils who try to justify their non-compliance are trying to express their own needs and acknowledgement of these needs allows a connection that can simulate compliance. 6. Tactical ignoring of secondary behaviour If the pupil follows teacher instructions but does so with an ‘attitude’ for example tutting or sighing, this secondary behaviour can be ignored. The initial objective has been achieved and responding to the secondary behaviours is likely to be confrontational and distract from the flow of the lesson. The Lancashire Mathematics Team 17 Lancashire Mathematics Challenge 2009 The Year 7 Lancashire Mathematics Soon June 18th was upon us and it was time for the County Final. Our nine district winners Challenge this year was based arrived at Woodlands with their parents, around the Jules Verne book, teachers and some headteachers. ‘Around The World in Eighty Days’. The theme stayed with Phil Fogg only this The questions for the district finals time he was on holiday with his companion Nancy. The atmosphere in the Oak Room was and the County finals were once buzzing as our young mathematicians worked again set by Maureen Magee and as teams to solve the context based challenges. The final result was very close but this year the proved a good test of pupils’ team Mathematics Challenge champions were the work and skill. four young ladies from Lancaster Girls Grammar School. Well done! The district finals saw Phil Fogg off on a gap year prior to going to university. He worked in various countries and teams had to assist him with key tasks and work out how much money he had earned on his travels. Second Prize: Leyland St. Mary's Catholic Technology College Once again the Maths Challenge was only made possible through the sponsorship of Lancashire County Developments and the First Prize: Lancaster Girls' Grammar School hard work of the Lancashire Mathematics Team of consultants. Not forgetting our very Once again the host schools for the district able administrative officer Alison Kenyon finals did an excellent job and aside from the fire who developed the resources and made sure alarm going off at one venue all went without everything ran smoothly at each venue. a hitch. Some schools decided to involve their PTA in providing refreshments which proved extremely successful. Business Award: Broughton Business and Enterprise College We look forward to visiting the winning schools Third Prize: Clitheroe Royal Grammar School for next years district rounds and meeting your young Year 7 mathematicians. 18 The Lancashire Mathematics Team Winners 2009 Date Venue First Second Third Bowland High The Hollins Monday St Christopher's Clitheroe Royal - With Specialist Technology 23rd March CE High School Grammar School Status In College Performing Arts Leyland St All Hallows Balshaw's Church All Hallows Thursday Mary's Catholic Catholic High Of England High Catholic High 26th March Technology School School School College Bacup And Bacup & Fearns Tuesday 28th All Saints Catholic Rawtenstall Rawtenstall Community April Language College Grammar School Grammar School Sports College Lytham St Anne's Carr Hill High Cardinal Allen Carr Hill High Wednesday Technology And School and Sixth Catholic High School & 6th 29th April Performing Arts Form Centre School Form Centre College Tarleton High Up Holland High Tarleton High School: A School-Specialist School : A Tuesday Community Music, Maths Community Ormskirk School 5th May Technology & Computing Technology College College College Longridge High Parklands Bishop Rawstorne Thursday Albany Science School - A Maths High School CE Language 7th May College And Computing - A Specialist College College Language College Archbishop Broughton Our Lady's Ashton Wednesday Temple CE High Business & Catholic High Community 13th May & Technology Enterprise College School Science College College Ripley St Thomas Thursday Lancaster Royal Lancaster Girls' Church Of Lancaster Royal 14th May Grammar School Grammar England High Grammar School School Ss John Fisher West Craven And Thomas Wednesday Colne Primet High Pendle Vale High Technology More Roman 20th May School College College Catholic High School Leyland St The Final - Lancaster Girls' Mary's Catholic Clitheroe Royal Thursday Woodlands Grammar Technology Grammar School 18th June Conference College Centre, Chorley Business Question - Broughton Business & Enterprise College The Lancashire Mathematics Team 19 Puzzle Page Holy Numbers A church hymn book contains 700 hymns, numbered 1 to 700. Each Sunday the people in the church sing four different hymns. The numbers of the hymns are displayed to them in a frame by dropping in single-digit boards like this: 2 The board for 6 may be turned upside down to serve as a 9. What is the minimum number of small boards that is needed to show any possible combination of four hymn numbers? How many of each number must there be? Taken from www.nrich.maths.org.uk. Solution to previous puzzle He picks one piece of fruit from the box labelled Oranges and Lemons. If it is a lemon, then that box should actually say Lemons. The box labelled Oranges can’t contain just oranges, and must really be the mixed one. This leaves the box labelled Lemons to contain oranges. The Lancashire Mathematics Team

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