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)
Anne Porter Team News 2
Emma Radcliffe What Can I Do in Mathematics? 2
Andrew Taylor Renewed Framework for Mathematics 3
Peter Toogood Mental Mathematics Staff Meeting 3
Secondary Mathematics Consultants Effective Starters 4
Fractions Starter 5
Louise Hastewell Starter Activities - Level 5 6
Maths of the Month 8
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
One-to-One Tuition 16
Write to LPDS Centre Behaviour for Learning in the
us at… Southport Road Mathematics Classroom
CHORLEY Lancashire Maths Challenge 2009 18
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
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?
accompany the booklet
'Securing Level 3 and
Securing Level 4 in
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
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
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
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
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
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
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
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
deepen children’s knowledge.
To use mathematical vocabulary and interpret images, diagrams, text and
To use and apply acquired knowledge, skills and understanding through making
informed choices/decisions, predicting, hypothesising and proving.
• 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
• 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
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
• Any specific class issues
• Revisiting curricular areas to obtain
4 The Lancashire Mathematics Team
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
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
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.
Knowing and using Handling data
understanding Calculating Understanding shape Measuring
number facts Interpreting pie charts
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.
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
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
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
number.’ Give a reason why he
BEAM - Maths of the Month
Have you seen the free resources available from the BEAM website
The resources cover games and activities which are separated into
strands and age ranges.
Maths of the Month
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.
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
2. Can you finish
And these are Zeven. 3 12 9 6 15
Use squared paper to work out some
more Zodd numbers, and some more
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
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
Whole school planning Subject leader to complete a scrutiny of
short term plans.
Support teachers with the use of the
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
Children selected for intervention
programmes. Identification of underperforming
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
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
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
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
• 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/
• 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
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
the different schools
The teachers gained
who provided the
ideas of how they could
fun and meaningful
support children in the
games. The practical
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
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
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
• 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
At- Age Stand-
School Name titude equiva- ardised
Child Other survey lent scores
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
Preston St Matthew’s CE Primary School
45.8 4% 15.9% 14.5 18.7 21.4
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
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
“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
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
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
Date Venue First Second Third
Monday St Christopher's Clitheroe Royal - With Specialist
23rd March CE High School Grammar School Status In
All Hallows Balshaw's Church All Hallows
Thursday Mary's Catholic
Catholic High Of England High Catholic High
26th March Technology
School School School
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
Tarleton High Up Holland High Tarleton High
School: A School-Specialist School : A
Community Music, Maths Community Ormskirk School
Technology & Computing Technology
College College College
Longridge High Parklands
Thursday Albany Science School - A Maths High School
7th May College And Computing - A Specialist
College Language College
Broughton Our Lady's Ashton
Wednesday Temple CE High
Business & Catholic High Community
13th May & Technology
Enterprise College School Science College
Ripley St Thomas
Thursday Lancaster Royal Lancaster Girls' Church Of Lancaster Royal
14th May Grammar School Grammar England High Grammar 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
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
The Lancashire Mathematics Team 19
A church hymn book contains 700 hymns, numbered 1 to 700.
Each Sunday the people in the church sing four
The numbers of the hymns are displayed to
them in a frame by dropping in single-digit
boards like this:
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
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