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Maths Newsletter - Autumn 2009 _For Web_

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Maths Newsletter - Autumn 2009 _For Web_ Powered By Docstoc
					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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