MATHS
Department Handbook
2013-2014
Mathematics is not just numbers and arithmetic. Although we need
to become fluent in arithmetic to live our daily lives, there is so much
more to Maths. It is the study of structure and pattern. We use it to
explore, understand and simplify the world around us. Mathematics is
the study of connecting the unconnected.
Through studying Maths, we learn how to reason, how to solve
problems, how to ask ‘what if…’, how to explain why, how to create.
We learn how to think. In studying Mathematics we learn so much
more than just using numbers.
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Staff are also expected to familiarise themselves with the The Staff Handbook
and the details of their own personal contract of employment.
CONTENTS
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Our vision for our pupils
3
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Our vision for Maths at GFS
4
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Staff of the Maths department
5
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The Maths curriculum
6

Assessment in Maths
12

Department initiatives
17
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The public profile of the Maths department
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Appendices:
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List of staff contact details
19
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OUR VISION FOR OUR PUPILS
At GFS we believe that all pupils can achieve success if given outstanding
teaching and pastoral care.
The Greenwich Free School is a small, more personal school, where teachers get to know every pupil as an
individual, and are able to both challenge and nurture them. We demand a lot, setting high standards for
pupils and staff, with a “no excuses” approach to attitude, work and discipline. We also recognise the
importance of pupils’ wellbeing, building their characters and skills, and developing young people who will
truly flourish.
It is our aim for pupils that they will embody the values of Growth, Fellowship, and Scholarship while at
school and beyond. They will be well-rounded, confident, independent, and articulate young people with a
genuine love of learning and desire to succeed. They will hold high expectations of themselves and others
and will strive to have a positive impact as members of their communities. They will exemplify the GFS
learning habits and values as outlined in the ‘GFS brain’ below:
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OUR VISION FOR MATHS AT GFS
“If there is a God, he is a great mathematician” – Paul Dirac
Mathematics is not just numbers and arithmetic. Although we need to become fluent in arithmetic to live our
daily lives, there is so much more to Maths. It is the study of structure and pattern. We use it to explore,
understand and simplify the world around us. Mathematics is the study of connecting the unconnected.
In studying Maths, we learn how to reason, how to solve problems, how to ask ‘what if…’, how to explain why,
how to create. We learn how to think. In studying Mathematics we learn so much more than just using numbers.
There are three criteria for Maths teaching at GFS:

Create an environment in which all pupils enjoy Maths and feel they can do well in Maths.

Create ‘good mathematicians’ with a focus on independent problem solving skills.

To engage pupils and expose them to the beauty and relevance of Maths.
The growth mind-set is fundamental to mathematical development; all pupils at GFS should feel as though they can
do well at Maths. We want all pupils at GFS to believe they can achieve great things if they demonstrate
perseverance, resilience and flow. Only through removing the anxiety that surrounds Maths can pupils enjoy it.
Scholarship means making our pupils good mathematicians. We would like pupils to be independent and curious
problem solvers with a desire in pupils to learn mathematics for its own sake. That said, underpinning this is the
rigour required to be a successful Mathematician. Whilst pupils at GFS will learn about the beauty and depth of
Mathematics, all planning and assessment is anchored by the GCSE curriculum; we do not lose sight of the fact that
for our pupils to be successful, they must perform well in their exams at KS4 and KS5.
Perhaps one of the most important skills as a Mathematician is making links. How can we connect different areas of
Maths together? How can we connect Maths with other subjects across the school? How can connect Maths with
the world around us? It is the teachers’ responsibility to demonstrate the value, beauty and relevance of
mathematics to all pupils.
Maths is best learnt through fellowship; learning from and with others. Maths lessons at GFS are focused on
collaboration not competition, with pupils working together to achieve a common goal. Through mixed ability
teaching and the use of rich mathematical tasks, pupils will have the opportunity to share knowledge and learn from
each other.
Finally, Maths lessons at GFS should not just about ‘doing Maths’; they should also aim to teach pupils the social
implications of Mathematics, and how it informs decisions in the world around us.
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STAFF OF THE MATHS DEPARTMENT
“Alone we can do so little; together we can do so much.”
– Helen Keller
Being part of a new school provides us with a rare opportunity to build a community of avid learners from its
foundations. We are building individual departments but also the GFS family. This is a great responsibility, which
comes with both extreme rewards and extreme challenges. Teachers at GFS are expected to go the extra mile. As is
outlined in the staff handbook, GFS teacher are expected to consistently maintain a high standard of quality
teaching, reporting, and pastoral care. This includes providing high quality enrichments and extended learning
opportunities. Impact on pupil outcomes is at the core of what we do and as the school grows we want to be a
model of good practice in education. We acknowledge that we are learners as well as teachers, eager to be at the
forefront of teaching innovation and to develop ourselves as well-rounded individuals capable of supporting our
pupils at the highest level. We have high expectations of ourselves and, just as we encourage our pupils to be
ambassadors for the school, we too strive to represent GFS positively in the wider community.
The culture among teachers at GFS is one of supportive collaboration. Teachers are encouraged to engage in crosscurricular planning to ensure that departments are not isolated entities but part of a larger network contributing to
the design of a purposeful curriculum across the school. At GFS our colleagues’ professional development is as
important as our own. Our classrooms are always open and peer observations are embedded in our culture as a way
of learning from one another. We offer each other regular, informal, formative feedback and the staffroom is a place
for sharing and working through new ideas in a supportive environment. Celebrating moments of success is of huge
importance to us and we strive to highlight the joyful moments in each day. GFS is a wonderful place to work where
staff members are friends as well as colleagues.
Within this, teachers of the Maths department will be expected to work together to develop the very best learning
experience for pupils at GFS. We can only do this by having the very highest expectations of pupils and ourselves,
striving for excellence in all pupils at all times. In addition, we must always support each other, whether that is
through creating resources together, sharing teaching practices and ideas, maintaining a positive and professional
attitude, or just listening to and helping each other.
Regarding the creation and sharing of resources, you will be expected to work with others (both within and outside
the Maths department) to contribute to the Maths scheme of work and the Maths website gfsmaths.com. You
should never be happy to ‘play it safe’, and should always seek to create interesting lessons that will engage pupils.
You should always aim to find ‘new’ Maths, or ways of teaching Maths, that excite you, and subsequently share this
excitement with the pupils. The only ‘limits’ to your creativity are the promotion of the GFS values, developing
problem-solving skills and exposing pupils to the beauty and applications of mathematics. The quality of our teaching
is the most important factor in ensuring our pupils receive the very best Maths education.
You will also be expected to be a reflective and modern practitioner; you are encouraged to maintain a blog
reflecting on the success of your teaching and showcasing the exciting Maths that is happening in your classroom.
You should aim to use a range of media to evidence and enhance the learning that is taking place, and seek to
employ the latest technological advances where you consider they might improve learning. These accounts should
be shared with each other, the pupils and the parents to promote transparency, foster improved learning, and to
help create a cutting edge Maths department.
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THE MATHS CURRICULUM
“Education is not preparation for life; education is life itself.”
- John Dewey
The aims of the KS3 Maths curriculum are to:

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Create an environment in which all pupils enjoy Maths and feel they can do well in Maths.
Create ‘good mathematicians’ with a focus on independent problem solving skills.
To engage pupils and expose them to the beauty and relevance of Maths.
All teaching should be undertaken with these criteria in mind. These criteria are evident in the current Maths KS3
schemes of work as shown in the diagrams below. As outlined in the section ‘Staff of the Maths Department’, this
scheme of work is not fixed and will be developed by the department as a whole.
Here is the content element of the KS3 curriculum at GFS. Teachers must encourage pupils to make links between
various topics within Maths. The GCSE criteria form the basis of the work covered in order to prepare pupils for
assessment at KS4.
Year 7 - Number
You can view the popplet here: http://popplet.com/app/index.php#/1103100
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Year 8 - Algebra
You can view the popplet here: http://popplet.com/app/index.php#/1321180.
Year 9 - Geometry
The latest version can be found here: http://popplet.com/app/index.php#/1103105
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Yrs 7-9 - Probability and statistics
Pupils will complete a range of probability and statistics projects, one per term, throughout the three years of KS3
alongside the main threads of number, algebra and geometry.
The investigations are outlined here: http://popplet.com/app/index.php#/1321063. I have not included an image of
the popplet as it is large; here is a small part of it, for the first probability project in Year 7:
Many of the statistics projects have the further advantage of meeting the SMSC requirement of the Maths
department; here is one such unit, studied in the Summer Term of Year 7:
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Maths Mastery
Maths Mastery is a fundamental part of the Maths Curriculum. In year 2 of GFS, there are currently 14 hours of
Mastery a fortnight across years 7 and 8, 8 hours being ‘small group’ mastery and 6 hours being 1-to-1 mastery.
Pupils are selected for Mastery generally according to their KS2 data and performance in the baseline test, with
pupils working at levels 1 to 3 being selected. This is subject to change during the year according to suitability as
determined by the Mastery teachers.
Activities in these sessions are designed to improve the basic number skills of those involved, alongside developing
their ‘using and applying’ maths skills. Pupils learn these skills through a mixture of play, investigation and
consolidation exercises.
Here are the levels by which pupils are assessed, with red matching levels 1 and 2 of the National curriculum, orange
level 3 and green level 4 (taken from the APP grids).
Each pupils’ progress towards each of these targets is recorded in a central datasheet and monitored termly.
Teacher’s should also record a diary of pupil progress following each session.
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The planning process
Here is a sample lesson plan:
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What to consider when planning a unit of work:
Here is an outline of the planning process:
1 What am I teaching this year/term? See SOW above.
2 What should I teach within each unit? The underlying objectives are given by the GCSE criteria on the SOW. For
more detail refer to the GCSE specification. Descriptions by grade are given in the grade descriptor documents
http://www.gfsmaths.com/teachers.html. Note: some units may not be linked GCSE criteria, such as logic, or
‘strange algebras’. See assessment below for more information.
3 How should I teach it? Research suitable methods and activities from: http://www.gfsmaths.com/index.html and
http://www.gfsmaths.com/the-book.html, teacher resources in http://www.gfsmaths.com/teachers.html (eg ATM,
Tanton, ...), plus any other books or online materials (e.g. nRICH).
4 Plan units of work through regular planning meetings, put in popplet and link to gfsmaths teachers area. All unit of
work plans must contain reference back to the GCSE criteria they are aimed to meet.
5 Make assessments to meet these criteria, saved in tests and assessments area in gfsmaths.com, with assessment
based on GCSE criteria if suitable.
What to consider when planning a lesson
There are various considerations when planning a lesson:

Content: Lesson content should be based on the schemes of work given above. Teachers should aim to meet
the dual objectives of improving problem-solving skills in line with the Bloom’s triangle, whilst aiming to
cover content topics as set out in the GCSE grade descriptors; lesson plans should contain explicit reference
to the GCSE criteria being met if applicable, though these must not be shared with pupils.

Activities: Should preferably be low-threshold, high-ceiling to allow effective differentiation to take place,
with explicit planning for support if required. They should generally (but not always) be ‘rich’ mathematical
tasks of an investigative nature, designed to meet the curriculum content while improving problem-solving
skills

Differentiation: All lessons should be fully differentiated, extending and supporting pupils where necessary.
This may be done through choice of activity (see above) but this does not mean that differentiation should
not be planned in detail. Teachers must anticipate where support and challenge may be required, and
intervene when necessary.

EAL/SEN: Full consideration of SEN and EAL needs of pupils must be considered in line with SEN department
policies. It is a policy of the maths department to maintain weekly contact in advance of lessons with LSAs
regarding the objectives and expectations for pupils with SEN. Similarly, all needs of EAL pupils must be
planned for, preferably with google translate where necessary (and certainly for assessed work).

Assessment: A mixture of formative and summative assessment methods should inform teaching, enabling
every pupil to progress. Strategies to be used include exit tickets to ensure objectives have been met. See
next section for more detail on monitoring pupil progress. A formal assessment of pupil understanding
should be taken once (or more) per unit of work.

Learning habits: All lessons should contain reference to the GFS learning habits being used in that lesson.
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ASSESSMENT IN MATHS
“Learning is not attained by chance; it must be sought for with ardour
and attended to with diligence." – Abigail Adams
Giving feedback to pupils: Bloom’s Taxonomy
At GFS, an emphasis on individual pupil progress is at the core of our vision for assessment. As a result, we
have developed our an assessment model based on the revised Bloom’s taxonomy:
Assessment model based on Bloom’s taxonomy:
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Bloom’s in Maths
Each department has used the Bloom’s Taxonomy to develop their own assessment triangles. Here is the general
assessment ‘triangle’ for Maths:
These are generic criteria, designed for formative assessment, based on general aims given in the previous section.
They are designed as a means to foster discussion and guide pupils on how to conduct a mathematical investigation
and improve their problem solving skills; they intentionally do not contain any reference to curriculum content. This
is because we would like all pupils to develop problem-solving skills, but it does not mean we do not value the
acquisition of content (see next section).
Most if not all maths lessons at GFS should aim to allow pupils the opportunity to solve problems, thus becoming
‘better mathematicians’, and as such any these criteria form the basis for this process. This assessment triangle
forms the basis of feedback to pupils; teachers must use the language of the above assessment criteria when
giving any verbal and written feedback.
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Here is an example of the criteria adapted specifically for an algebra assessment:
Investigations and other assessed work should contain reference to these objectives, made explicit for that particular
piece of work. They should be shared with pupils before an activity in order to share learning intentions, and
afterwards as a means of discussing what went well and what could be improved. Following all assessment, pupils
are encouraged to self-assess using the language of these criteria.
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How often should teachers assess pupils’ work?
As a teacher you will assess pupils’ understanding continuously, using a variety of methods in the usual way. In
addition to this, here are guidelines for how often, and in how much depth, work is to be assessed in Maths:
Weekly DIRT
As part of this continuous assessment, teachers in Maths are required to set a short exit activity at a convenient
point each week - it could be a small set of questions, or a hinge question, or a written task where they explain
something; whatever suits best. The only requirement is that it should be carefully selected to find out if they have
learnt the basic objectives for that week.
This should be reviewed by the teacher to assess whether the basic objectives have been met. Feedback could be as
simple as a tick or cross, or preferably it should contain a few words about which objectives require improvement.
Most importantly, the assessment should then be used formatively. The subsequent lesson should contain
Dedicated Improvement and Reflection Time (DIRT), where pupils work on differentiated activities, based on the
requirements for improvement identified in the exit activity. [While this is happening, all pupils who achieved all the
objectives should be given something more challenging to develop their skills further.]
Following completion of DIRT, pupils should put the exit activity and subsequent work in their folders. Pupil data for
these activities need not to be recorded (although teachers should make notes on directing pupils towards the
correct DIRT activity as part of their planning).
Unit assessment
In addition to this, teachers must fully assess one piece of work for each unit in line with Bloom’s Taxonomy. This
will be approximately once every 3 weeks. Full written feedback must be given in line with Bloom’s taxonomy, with
detailed information of what went well, and instructions on how it could be improved. Then teachers should devote
a whole lesson for DIRT, including self-assessment, and ensure pupils have achieved the basic objectives. Pupils will
save unit assessments in their folders. Teachers should then record a Bloom’s level for each unit to assist half-termly
summative assessment of progress.
GCSE assessment
Underlying the Bloom’s assessment model, the department/school uses a shadow assessment structure firmly
rooted in the GCSE content specification and assessment criteria. This is not to be shared with pupils or parents; this
is strongly against the values of the school, and the maths department, to provide pupils with absolute levels. It is to
be used as a means of summative assessment, for measuring pupil progress and to identify intervention when
necessary. It also provides a structure for planning to ensure pupils are prepared for future study.
Teachers must assess one major piece of work per half term according to the GCSE assessment criteria set out in
the SOW and grade description documents http://www.gfsmaths.com/teachers.html (although they can assess more
pieces in this way if they wish).
The GCSE Maths assessment objectives are split into three areas: AO1 - content, AO2 – application of methods and
AO3 – problem solving. For each assessment at GFS, we record two grades: one for content and application of
methods (AO1/AO2) and a separate ‘AO3’ grade for communication, problem solving, investigative skills and proof,
which we feel is crucial in capturing what we are trying to achieve at GFS. Progress based on these assessments is
reported through the GFS reporting system (see record keeping below).
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Record keeping
The recording and reporting of data, target setting and other assessment practices within the Maths department
must be in line with the school assessment policy given in the staff handbook.
The basic requirements for the assessment of pupils in the Maths department are as follows:

A pupil book for taking notes to be kept in the pupil folder. This does not need to be marked, but teachers
should ensure pupils are using this appropriately.

A maths folder to keep all assessed work.

A pupil portfolio containing best work across all subjects in years 8 and 9, as part of the mini-bacc; one or
more pieces of ‘best’ work per half term from maths should be copied and put into this folder.
Here is a timeline of annual events for recording and reporting data:
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DEPARTMENT INITIATIVES
"People of excellence go the extra mile to do what's right."
– Joel Osteen
The Maths department is currently running a number of initiatives to help meet the needs of all pupils:
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Maths mastery for lower attaining pupils to consolidate basic maths skills.
Really hard maths club where pupils come and work on difficult mathematical problems.
Preparation for, and entry into, the UKMT Junior Maths Challenge and the UKMT Team Challenge.
Participation in the National Cipher Challenge.
Maths wrangles, to develop (mathematical) communication skills. These have run at a tutor-group level so
far.
Problem of the fortnight to provide opportunities for challenge for all pupils.
Maths4Parents evenings to inform parents about the teaching and assessment practices within the Maths
department, and within GFS as a whole.
Participation in NSPCC Number Day to raise money for charity and raise awareness of numeracy across the
curriculum.
The delivery of Maths and… units of work. This year we have delivered a unit of work with the …Philosophy
department on ‘What is intelligence?’ incorporating an assembly on the work of Alan Turing. We have also
delivered a unit of work in connection with the …History department on the ‘History of Maths’. We also hold
a project with the …English department called ‘Writingmaths’ which awarded a prize for the best creative
writing about Maths.
Incorporation of Computing into Maths lessons, through programming in Python and use of Excel. This is to
be developed further through the use of Raspberry Pi’s.
Creativity in Maths through the quilting club and maths embroidery, with the help of Ms Jones!
Innovative rewards scheme such as the Mathemagic scheme.
Development of a cutting edge scheme of work through the gfsmaths.com website and blog, and the
creation of GFSMaths – The Book to augment the Scheme of Work.
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THE PUBLIC PROFILE OF THE MATHS DEPARTMENT
"I alone cannot change the world, but I can cast a stone across the
waters to create many ripples." – Mother Teresa
AT GFS we believe in celebrating successes and sharing best practice. As part of this commitment, each department
has created a public website using Weebly to showcase pupil learning and achievement. This enables pupils to
review and evaluate their learning and to share their work with their parents. It also provides the opportunity for us
to engage the wider teaching community by sharing our ideas.
The Maths department website can be found at www.gfsmaths.com. It contains a page of information for parents
and prospective parents, with information on how pupils at GFS learn Maths, what Maths they will be learning, and
when: http://www.gfsmaths.com/parents.html
For up-to-date reflections and information from the maths department, follow @greenwich_FS on twitter.
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APPENDIX 1: LIST OF STAFF CONTACT DETAILS
“No man is an island, entire of itself; every man is a piece of the
continent.”– John Donne
Danny Brown, Head of Maths: dbrown@greenwichfreeschool.co.uk
Michael Bennett, Teacher of Maths: mbennett@greenwichfreeschool.co.uk
Megan Hibbert, Teacher of Maths: mhibbert@greenwichfreeschool.co.uk
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