brooklands farm primary school: our little book of...

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Brooklands Farm Primary School: Our Little Book of Mathematics

Teaching, Learning and Thinking Mathematically at Brooklands Farm

Becoming an effective mathematician at Brooklands Farm will link with aspects from our key policy of Teaching,

Learning and Thinking Policy.

Below are listed links with our Teaching, Learning and Thinking Policy (see complete policy for further detail)

Theory Direct links with Mathematics Teaching, Learning and Thinking

Piaget Developing conceptual understanding of mathematical concepts through effective use of models and images. Planning learning journeys which relate to real-life and scaffold understanding.

Vygotsky

Pupils value becoming a mathematician because they appreciate the social and cultural implications. Mathematical learning and understanding is developed through the use of Assessment for learning strategies.

Bruner

Pupils understand and learn mathematics through their learning being scaffolded through interactions with key models and images. Models and images (including ICT) can be effective in supporting conceptual understanding. Making connections within and between mathematical concepts will enable our learners to become effective mathematicians.

Loris Malaguzzi

Mathematical concepts become more embedded through being delivered in a cross curricular manner to ensure they are embedded. A child’s learning is well supported when parents and pupils work in partnership. In Mathematics we ensure that parents are aware of our school approach to calculation. We ensure the learning environment for mathematics supports pupil understanding. (will link with current learning and is likely to include models and images as well as worked examples and associated vocabulary) Also links with the appreciation of the power of mathematics in society • Appreciating mathematics as a longstanding part of worldwide human creativity • Creating and critiquing ‘mathematical models’ of situations • Appreciating uses/abuses of mathematics in social contexts • Using mathematics to gain power over problems in one’s own life

John Bowlby

Becoming resilient in mathematical learning is a key lifelong skill particularly when problem-solving and reasoning. We will provide learning opportunities which enable our pupils to overcome challenges and develop resilience through independent and co-operative learning.

Carol Dweck: Mindsets

We recognise and value learning efforts as well as correct answers and outcomes in mathematics. We recognise and value the process and skills that our pupils make use of in their mathematical learning. We enable our pupils to learn from their mathematical errors. (as well as the errors of others). This will help develop their own checking strategies.

Well Being Pupils need to be in their learning zone for all learning to be effective.

Blooms Questioning

Use Bloom’s taxonomy to include questions that require higher order mathematical thinking. It is appropriate to ask all learners open questions which are differentiated and require the explanation of mathematical reasoning and proof.

Black and Wiliam

Feedback marking in Mathematics supports pupils to be aware of next steps in their learning and understanding. Assessment for learning strategies are especially relevant to Mathematics teaching and learning including: learning journey, learning intentions and success criteria, mini plenaries, review of learning in partnership with pupils.

Brain research

There are mathematical skills which require regular practise (eg number bonds, times tables, calculation methods etc) We will adapt learning tasks in response to our learners in order to ensure pupils remain challenged.

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What is mathematics at Brooklands Farm Primary School?

The following research statements are incorporated into Mathematics learning and teaching at Brooklands Farm Primary

School as they relate to our school beliefs.

Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement

in mathematics

Mathematical reasoning and knowledge of arithmetic (as assessed in year 4) make independent contributions to children’s

achievement in mathematics in KS2 and 3.

While both are important, mathematical reasoning is more important than knowledge of arithmetic for achievement in KS2

and 3

Nunes et et al (2009)

The handling and manipulation of a resource does not guarantee the transference of conceptual understanding.

An inanimate resource, cannot in itself have any miraculous powers beyond the teachers and pupils who use it. Furthermore

there is no mathematics actually in a resource. The mathematics is brought to a resource by those who interact with it, or is

developed by them as they use it to support or develop their thinking.

(Delaney, K 2001)

At Brooklands Farm we believe we will enable our learners to become mathematicians and be prepared for their futures by

teaching our pupils to:

enjoy mathematics through an imaginative and stimulating mathematics curriculum

be curious about mathematics

talk about mathematics using a high level of mathematical vocabulary

understand mathematical concepts

be resourceful in using models and images to scaffold understanding

reason mathematically

communicate mathematically

apply their mathematical knowledge and understanding in a range of situations and contexts and make sense of

solutions

demonstrate high levels of fluency in written and mental mathematics

This will be in our daily mathematics learning and also in other subjects where we make use of mathematics.

3 We support our pupils to become mathematicians by adopting an approach which is based around the following:

Hands-on learning is important. We provide appropriate practical equipment for children to use and manipulate, to help them to explore how and why things work and to learn to visualise, describe and represent what is in front of them.

Seeing mathematics through models and images supports learning – help children to see how mathematics works and can be represented through physical objects, pictures or diagrams such as place-value cards, counting sticks, number lines and representations of fractional parts. We expect children to visualise and ‘see’ how something works from the use of models and images. Each classroom is equipped with a range of models and images to support mathematical understanding.

Talking mathematics clarifies and refines thinking – give children the vocabulary and language of mathematics; provide activities and time for them to use this language to discuss mathematics. Teach children the precision of language, for example, using: sum, difference, quarter of and quarter to, and how to express their reasoning using language such as if…then…, because, cannot be, never, sometimes, always. We expect children to explain and provide reasons by using, developing and refining the language they need.

All learners benefit from the above aspects and they are equally relevant to younger and older pupils as well as to higher and lower attainers.

Developing conceptual understanding with our learners

Conceptual understanding in mathematics are key ideas, notions and thoughts about how the world of maths works. This

helps pupils understand which ideas are key so that they can develop, test, connect, communicate and create ideas within

their mathematical thinking. This means pupils are better placed to use maths strategically in a range of situations including

cross curricular and open-ended learning.

It is crucial in our school that teachers understand how conceptual understanding has been gained. Firstly so that they can

check for gaps and, secondly, to identify misconceptions so that they can teach appropriate concepts developmentally which

will accelerate learning. The teaching and learning process is therefore brought together through using concrete materials,

visual images, talk and interaction as well as through real life contexts so that conceptual teaching and learning become

entwined.

Reference: The book by Deboys and Pitt called Lines of Development in Primary Mathematics is a key source for identifying

conceptual learning steps. Each year group in each school has a copy of this.

The learning and teaching of mathematics at Brooklands Farm School

At Brooklands Farm we expect to meet the needs of all of our pupils through ongoing Quality First Teaching both within

Mathematics lessons and in other subjects.

Through our teaching we incorporate an approach that we believe enables our pupils to develop a deeper conceptual

understanding.

Reference: Haylock, D. and Cockburn, A. (1989) Understanding Early Years Mathematics, London: Paul Chapman Publishing

Words

Action on

Objects

Symbols

Images

4 Our pupils will experience a blend of these elements to help them secure a deeper conceptual understanding.

Different pupils will benefit from different blends. For example some of our pupils will understand the symbolic values with

some experience of models whereas other pupils will benefit from additional experiences in order to deepen their

conceptual understanding.

The understanding and development of mathematical vocabulary is integral to maths learning. The key mathematical

vocabulary and terminology are in the Maths file on the Google drive.

Vocabulary linked to planning is listed in the Autumn term ladders on the Google drive.

Our pupils make use of mathematical vocabulary in their mathematical learning within maths lessons and when using

mathematics in other subjects

Teaching sequence for Mathematics

Our teaching sequence incorporates the following approach:

Collect …. Connect ….. Create and Communicate (Based on SOLO taxonomy)

Collect

At this stage pupils are taught the knowledge and conceptual understanding of discrete mathematical concepts before

reasoning about these concepts. This does include inverse operations being taught together to aid understanding.

Connect skills

At this stage pupils are connecting recent and previous learning in two or more mathematical concepts.

Connect skills and context

At this stage pupils are connecting and contextualising within and across mathematical concepts.

Create and communicate

At this stage pupils further develop depth in learning though routine and non-routine problems requiring them to select and

further apply their mathematical learning and understanding.

This approach could be represented as below

Deeper mathematical thinking

Create and communicate

Connect

Collect

5 We believe that our pupils will achieve deeper mathematical thinking if they

Have a secure conceptual understanding

Can talk about the concept

Can show the concept (using models and images)

Can explain the concept

At Brooklands Farm this approach will enable pupils to demonstrate understanding of:

Which mathematical ideas are fundamental and why they are important (connect)

Which ideas are useful in a particular context including problem-solving (connect, create and communicate)

How to reason their mathematical thinking and to challenge the thinking of others (create and communicate)

Transference of skills in routine and non-routine problems including cross-curricular learning (create and

communicate)

SEE THE PLANNING SECTION FOR FURTHER EXEMPLIFICATION

Mathematics teaching at Brooklands Farm

What does good maths teaching look like? The Ofsted subject specific guidance for Mathematics (March 2013) gives a useful indication.

Ofsted Maths subject specific Outstanding Ofsted Maths subject specific Good

Mathematics teaching is outstanding and, together with a rich and relevant mathematics curriculum, contributes to

outstanding learning and achievement. Exceptionally, achievement in mathematics may be good and rapidly

improving.

Pupils benefit from mathematics teaching that is at least good and some that is outstanding. This promotes very positive

attitudes to learning and ensures that pupils’ achievement in mathematics is at least good.

Pupils understand important concepts and make connections

within mathematics.

Pupils understand some important concepts and make some

connections within mathematics.

When investigating mathematically, pupils reason, generalise and make sense of solutions.

When investigating mathematically, most pupils are able to reason, generalise, and make sense of solutions.

Teaching is rooted in the development of all pupils’ conceptual understanding of important concepts and

progression within the lesson and over time.

Teaching develops pupils’ understanding of important concepts as well as their proficiency in techniques and recall

of knowledge, equipping pupils to work independently.

Teaching enables pupils to make connections between topics and see the ‘big picture’.

Teaching helps pupils to see that topics are connected and form a ‘big picture’.

Teachers nurture mathematical independence, allowing time for thinking and encouraging discussion.

Problem- solving, discussion and investigation are integral to pupils’ learning of mathematics.

Many opportunities are provided for problem-solving in various contexts, discussion and investigation, although these

are not always integral to learning.

Pupils think for themselves and are prepared to persevere when faced with challenges, showing a confidence that they

will succeed.

Many pupils show a developing ability to think for themselves, and are willing to try when faced with challenges.

Pupils embrace the value of learning from mistakes and false starts.

Pupils are willing to learn from mistakes and false starts

Barriers to learning and potential misconceptions are anticipated and overcome, with errors providing fruitful points

Barriers to learning and misconceptions are tackled well.

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Marking distinguishes well between simple errors and misunderstanding, and tailors insightful feedback accordingly

Marking identifies errors and misunderstanding and helps pupils to overcome difficulties.

From Ofsted Subject Specific Mathematics March 2013

Organisation of learning experiences in Mathematics at Brooklands Farm

In our mathematics teaching we use a wide range of teaching strategies including: whole class sessions, guided groups, independent work and one to one learning sessions.

Organisation This varies whether learning is

collect, connect, create and communicate

Providing focused opportunities to

Whole class sessions

ensure everyone sees, hears and discusses the mathematical methods, strategies,

processes and models, so they understand and are clear about further steps in their

learning and know what they are to do next

use questioning to prompt, probe and promote ideas and thinking, secure the

meaning of mathematical language and rehearse knowledge, skills and

understanding for all

provide structured support for the use and application of mathematics to practise

and extend learning

review progress during and following shared or independent activity, providing

further practical, consolidation or extension activity to personalise learning for

groups of pupils

Orchestrating learning through group work

develop the use of mathematical language to explain and reason

engage particular pupils in sustained mathematical dialogue or mental mathematics

use key models and images that support conceptual understanding and

mathematical thinking

develop a ‘can do’ and team work approach to problem solving and enquiry in a

wide range of contexts

review and refine the presentation, accuracy and efficiency of methods of

calculation

support pupils to overcome barriers to learning, sometimes using errors as fruitful

points for discussion

Independent work

Engage in child initiated enquiry, the teacher is likely to review and scaffold to

deepen learning and understanding

Explore a process in order to clarify how it works and when it can be applied

Use and apply mathematics that involves higher order skills including generalising,

testing and reasoning

Make decisions by choosing the mathematics needed to solve a problem and refine

methods and ways of recording

Carry out and sustain focussed mathematical enquiry and prepare feedback for

others

Practise key skills and methods to improve speed, confidence and accuracy

Take the initiative in solving problems in a wide range of contexts

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Individual support

Model their mathematical thinking and use precise mathematical vocabulary

Focus and develop methods to help the pupil to become more efficient

Support the pupil to take the next steps in learning through tailored modelling and

scaffolding

Involve the pupil in evaluating their own learning. This may include reviewing

feedback marking or targets.


They use a very wide range of teaching strategies to stimulate all pupils’ active participation in their learning, together with innovative and imaginative resources, including practical activities and, where appropriate, the outdoor environment.

They use an appropriate range of resources and teaching strategies, including practical activities and, where appropriate, the outdoor environment.


Mathematics curriculum at Brooklands Farm School

At Brooklands farm we will plan to ensure that all pupils access the National Curriculum 2014 and achieve its aims.

National Curriculum Aims 2014 How do we achieve these aims at Brooklands Farm School

Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately

Daily Mathematics learning Regular morning maths Daily mental mathematics Mental Mathematics tests Home learning Regular fluency and flexibility sessions

Reason mathematically by following a line

of enquiry, conjecturing relationships and

generalisations, and developing an

argument, justification or proof using

mathematical language

Planning opportunities for pupils to reason in every unit of learning. Planning based on the cycle of collect, connect, create and communicate Making effective use of the learning environment. We support our pupils to make links between mathematics and other subjects as well as with mathematics beyond the classroom as part of our learning taxonomy

Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions

Problem-solving and investigative approaches are an integral element of mathematics learning at Brooklands Farm. We enable our pupils to become effective problem solvers in readiness for their lifelong skills.

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We believe that, where possible, Mathematics and problem solving strategies need to be in real-life contexts and in other subjects

Our Mathematics Curriculum

At Brooklands Farm Primary School we deliver an inspiring, progressive and purposeful mathematics curriculum which

gives children the tools to reason mathematically and apply their knowledge and understanding to real life problems.


The imaginative, stimulating mathematics curriculum is skilfully designed to match the full range of pupils’ needs and interests and to ensure highly effective continuity and

progression in their learning and in the qualification pathways they follow, including into further study.

The curriculum is broad, balanced and well informed by current initiatives in the subject. It is designed to match a range of pupils’ needs and interests, and ensure effective

continuity and progression in their learning in the subject and in the qualification pathways they follow, including into

further study.

Links with other subjects in the school are highly productive in strengthening pupils’ learning in mathematics.

Links with other subjects in the school strengthen pupils’ learning in mathematics.

Rigorous curriculum planning ensures that mathematics makes an outstanding contribution to pupils’ spiritual, moral,

social and cultural development.

Opportunities to promote pupils’ spiritual, moral, social and cultural development are planned and delivered systematically.


Elements of mathematics in our Mathematics Curriculum (Ref: National Curriculum 2014)

Number

Number and place value ~

Addition and subtraction ~

Multiplication and division ~

Fractions (Years 1, 2 and 3)

Fractions including decimals (Year 4)

Fractions including decimals and percentages (Year 5 and 6)

Ratio and Proportion (Year 6)

Algebra (Year 6)

Measurement

Geometry

Properties of shapes ~

Position and direction ~

Statistics (From Year 2)

Includes what has been previously known as data handling

~ indicates also a specific area of learning for the EYFS

9 As well as learning the content domain of the new National Curriculum we will also develop cognitive understanding with our

pupils. This will be achieved through our teaching taxonomy and it is crucial that all learners undertake learning tasks that

require an increasing demand whatever the ability.

While elements of mathematics appear distinct it is important that we consider the following:

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of

mathematical ideas and concepts.

Our pupils make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in

solving increasingly sophisticated problems.

Our pupils should also apply their mathematical knowledge to science and other subjects. (Ref: National Curriculum 2014)

Planning for effective mathematics learning

Long term

At Brooklands Farm this includes coverage of the National Curriculum 2014 as a minimum.

On the following pages are the National Curriculum Programmes of Study for each year group. This is the content domain of

the new National Curriculum.

Please note we have included the statutory elements but the non-statutory guidance is also useful and is found in the new

National Curriculum document.

10 National Curriculum 2014: Year 1

Number and place value � count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number � count, read and write numbers to 100 in numerals, count in different multiples including ones, twos, fives and tens � given a number, identify one more and one less � identify and represent numbers using concrete objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least � read and write numbers from 1 to 20 in digits and words.

Addition and subtraction � read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs � represent and use number bonds and related subtraction facts within 20 � add and subtract one-digit and two-digit numbers to 20 (9 + 9, 18 - 9), including zero � solve simple one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems.

Multiplication and division � solve simple one-step problems involving multiplication and division, calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Fraction

recognise, find and name a half as one of two equal parts of

an object, shape or quantity � recognise, find and name a quarter as one of four equal

Measurement � compare, describe and solve practical problems for measure and begin to record the following: � lengths and heights � mass/weight � capacity and volume � time (hours, minutes, seconds) � recognise and know the value of different denominations of coins and notes � sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening � recognise and use language relating to dates, including days of the week, weeks, months and years � tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

Properties of shape � recognise and name common 2-D and 3-D shapes, Including :2-D shapes e.g. rectangles, inc. squares, circles and triangles) � 3-D shapes (e.g. cuboids, cubes, pyramids and spheres).

Position and direction � describe position, directions and movements, including half, quarter and three-quarter turns.

11 Nationall Curriculum 2014: Year 2

Number and place value � count in steps of 2, 3, and 5 from 0, and count in tens from any number, forward or backward � recognise the place value of each digit in a two-digit number (tens, ones) � identify, represent and estimate numbers using different representations, including the number line � compare and order numbers from 0 up to 100; use <, > and = signs � read and write numbers to at least 100 in numerals and in words � use place value and number facts to solve problems.

Addition and subtraction � solve simple one-step problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures applying their increasing knowledge of mental and written methods � recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 � add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones, a two-digit number and tens, two two-digit numbers, adding three one-digit numbers � show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot � recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.

Multiplication and division � recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers � calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs � recognise and use the inverse relationship between multiplication and division in calculations � show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot � solve one-step problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Fraction � recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity � write simple fractions e.g. 1/2 of 6 = 3 and recognise the equivalence of two quarters and one half.

Statistics

interpret and construct simple

pictograms, tally charts, block diagrams and simple tables

ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity

ask and answer questions about totalling and comparing categorical data.

Measurement � choose and use appropriate standard units to estimate and measure length/height in any direction to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels � compare and order lengths, mass, volume/capacity and record the results using >, < and = � read relevant scales to the nearest numbered unit � recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value and match different combinations of coins to equal the same amounts of money; add and subtract money of the same unit, including giving change � solve simple problems in a practical context involving addition and subtraction of money � compare and sequence intervals of time � tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times.

Properties of shape � identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical line � identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces � identify 2-D shapes on the surface of 3-D shapes, for example a circle on a cylinder and a triangle on a pyramid � compare and sort common 2-D and 3-D shapes and everyday objects.

Position and direction � order and arrange combinations of mathematical objects in patterns � use mathematical vocabulary to describe position, direction and movement, including distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise), and movement in a straight line.


Number and place value .count from 0 in multiples of 4, 8, 50 and 100; finding 10 or 100 more or less � recognise the place value of each digit in a three-digit number (hundreds, tens, ones) � compare and order numbers up to 1000 � identify, represent and estimate numbers using different representations � read and write numbers to at least 1000 in numerals and in words � solve number problems and practical problems involving these ideas.

Statistics � interpret and present data using bar charts, pictograms and tables

solve one-step and two-step questions such as ‘How many more or fewer?’ using information in bar charts, pictograms & tables.

Addition and subtraction add and subtract numbers mentally, including: � a three-digit number and ones � a three-digit number and tens � a three-digit number and hundreds � add and subtract numbers with up to three digits, using the efficient written methods of columnar addition and subtraction � estimate the answer to a calculation and use inverse operations to check answers � solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Multiplication and division recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables � write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to efficient written methods � solve problems, including missing number problems, involving multiplication and division, including integer scaling problems and correspondence problems in which n objects are connected to m objects.

Fractions � count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 � recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators � recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators � recognise and show, using diagrams, equivalent fractions with small denominators � add and subtract fractions with the same denominator within one whole � compare and order unit fractions with the same denominator � solve problems that involve all of the above.

Measurement � measure, compare, add and subtract: lengths mass; volume/capacity � measure the perimeter of simple 2-D shapes � add and subtract amounts of money to give change, using both £ and p in practical contexts � tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24- hour clocks � estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; � know the number of seconds in a minute and the number of days in each month, year and leap year � compare durations of events, for example to calculate the time taken by particular events or tasks.

Properties of shape � draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations; and describe them with increasing accuracy � recognise angles as a property of shape and associate angles with turning � identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle � identify horizontal, vertical, perpendicular and parallel lines in relation to other lines.


Number and place value � count in multiples of 6, 7, 9, 25 and 1000 � find 1000 more or less than a given number � count backwards through zero to include negative numbers � recognise the place value of each digit in a four-digit number � order and compare numbers beyond 1000 � identify, represent and estimate numbers using different representations � round any number to the nearest 10, 100 or 1000 � solve number and practical problems that involve all of the above and with increasingly large positive numbers � read Roman numerals to 100 (I to C)

Addition and subtraction � add and subtract numbers with up to 4 digits using the efficient written methods of columnar addition and subtraction where appropriate � estimate and use inverse operations to check answers to a calculation � solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and Why? Statistics

interpret and present discrete and continuous data using bar charts& time graphs

solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Multiplication and division � recall multiplication and division facts for multiplication tables up to 12 × 12 � use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers � recognise and use factor pairs and commutatively in mental calculations � multiply two-digit and three-digit numbers by a one-digit number using formal written layout. solve problems involving multiplying and adding, including using the distributive law and harder multiplication problems such as which n objects are connected to m objects.

Fractions �recognise and show, using diagrams, families of common equivalent fractions � count up and down in hundredths; � solve problems involving harder fractions to calculate quantities, and fractions to divide quantities. � identify, name and write equivalent fractions of a given fraction. � add and subtract fractions with the same denominator. recognise and write decimal equivalents of any number of tenths or hundredths, recognise and write decimal equivalents to 1/4; 1/2; 3/4 � find the effect of dividing a one- or two-digit number by 10 and 100, round decimals with one decimal place to the nearest whole number, compare numbers with the same decimal places � solve simple measure and money problems involving, fractions and decimals to 2dp.

Measurement � Convert between different units of measure � measure and calculate the perimeter of a rectilinear figure � measure, compare, add and subtract: find the area of rectilinear shapes by counting squares

estimate, compare and calculate different measures, including money in pounds and pence

read, write and convert time between analogue and digital 12 and 24-hour clocks

solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Properties of shapes compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes � identify acute and obtuse angles and compare and order angles up to two right angles by size � identify lines of symmetry in 2-D shapes presented in different orientations � complete a simple symmetric figure with respect to a specific line of symmetry. describe positions on a 2-D grid as coordinates in the first quadrant � describe movements between positions as translations of a given unit to the left/right and up/down � plot specified points and draw sides to complete a given polygon.


Number and place value � read, write, order and com pare numbers to at least 1 000 0000 and determine the value of each digit � count forwards and backwards in steps of powers of 10 up to 1 000 000 �interpret negative numbers in context count forwards and backwards with positive and negative whole numbers through zero � round any umber up to 1 000 000 to the nearest 10, 100, 1000 and 10,000 � solve number problems and practical problems that involve all of the above � read Roman numerals to 1000 (m) and recognise years written in Roman numerals.

Addition and subtraction � add and subtract whole numbers with more than 4 digits, (columnar addition and subtraction) add and subtract numbers mentally with increasingly large numbers � use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy � solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Multiplication and division identify multiples and factors. � solve problems involving multiplication and division where larger numbers by decousing their factors. �use the vocabulary of prime numbers, prime factors and composite numbers � establish whether a number up to 100 is prime and recall prime numbers up to 19 � multiply numbers up to 4 digits by a one- or two-digit number including long multiplication , multiply and divide numbers mentally, divide numbers up to 4 digits by a one-digit number using short division and interpret remainders � multiply and divide whole numbers and decimals by 10, 100 and 1000 � recognise and use square and cube numbers. � solve problems involving addition, subtraction, multiplication and division and understand the meaning of the equals sign � solve problems involving multiplication and division, including scaling by simple fractions and simple rates.

Statistics � solve comparison, sum and difference problems using information presented in line graphs � complete, read and interpret information in tables ,including timetables

Fractions / Decimals / Percentages � compare and order fractions whose denominators are all multiples of the same number � recognise mixed numbers and improper fractions and convert from one form to the other � add and subtract fractions with the same denominator and related fractions; write mathematical statements >1 as a mixed number � multiply proper fractions and mixed numbers by whole numbers by materials and diagrams. read and write decimal numbers as fractions � recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents � round decimals with two decimal places

� read, write, order and compare numbers

with up to three decimal places � solve problems involving number up to three decimal places recognise the per cent symbol, write percentages as a fraction with denominator hundred, � solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25.

Measurement convert between different units of

metric measure understand and use equivalences

between metric units and common imperial units such as inches, pounds and pints

measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

estimate volume (e.g. using 1 cm3 blocks to build cubes and cuboids) and capacity (e.g. using water)

solve problems involving converting between units of time

use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.

Properties of shape angles at a point and one whole turn (total 360o)

angles at a point on a straight line and ½ a turn (total 180o)

other multiples of 90o use the properties of rectangles to deduce related facts and find missing lengths and angles

distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Position and direction identify, describe and represent the position

of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.


Number, place value and rounding � read, write, order and compare numbers up to 10 000 000 and determine the value of each digit � round any whole number to a required degree of accuracy � use negative numbers in context, and calculate intervals across zero � solve number problems and practical problems that involve all of the above.

Statistics interpret and construct pie charts and

line graphs and use these to solve problems

calculate and interpret the mean as an average.

Addition subtraction multiplication and division

� multiply multi-digit numbers up to 4 digits by a two-digit whole number using long multiplication � divide numbers up to 4 digits by a two-digit whole number using the efficient written method of long division, and interpret remainders � perform mental calculations, including with mixed operations and large numbers. � identify common factors, common multiples and prime numbers � use their knowledge of the order of operations to carry out calculations involving the four operations � solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why � solve problems involving addition, subtraction, multiplication and division � use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy.

Ratio and Proportion � solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

solve problems involving the calculation of percentages

solve problems involving similar shapes where the scale factor is known or can be found

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Algebra � express missing number problems algebraically � use simple formulae expressed in words � generate and describe linear number sequences � find pairs of numbers that satisfy number sentences involving two unknowns � enumerate all possibilities of combinations of two variables

Fraction / Decimal /Percentages � use common factors to simplify fractions; use common multiples to express fractions in the same denomination � compare and order fractions, including fractions >1 � associate a fraction with division to calculate decimal fraction equivalents � add and subtract fractions with different denominators and mixed numbers � multiply simple pairs of proper fractions and simplify � divide proper fractions by whole numbers � identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 � multiply one-digit numbers with up to two decimal places by whole numbers � use written division methods where the answer has up to two decimal places. � solve problems which require answers to be rounded solve problems involving the calculation of percentages of whole numbers or measures � recall and use equivalences between simple fractions, decimals and percentages

Measurement � solve problems involving the calculation and conversion of units of measure, using decimal notation to three decimal places where appropriate � use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation � convert between miles and kilometres � recognise that shapes with the same areas can have different perimeters and vice versa � calculate the area of parallelograms and triangles � recognise when it is necessary to use the formulae for area and volume of shapes � calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm3) and cubic metres (m3) and extending to other units

Properties of shape draw 2-D shapes using given dimensions

and angles recognise, describe & build simple 3-D

shapes inc. nets compare and classify geometric shapes

based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

illustrate and name parts of circle ,i.e. radius, diameter and circumference and Diameter= 2 x radius

recognise angles on a straight line, or are vertically opposite, and find missing angles.

Position and direction describe positions on the full coordinate

grid (all four quadrants) draw and translate simple shapes on the

coordinate plane, and reflect them in the axes.

16 Medium term planning

Our medium term planning involves the mapping out of the curriculum over the school year in order to achieve the long term

planning.

Medium term planning (below) is linked to our taxonomy (collect, connect, create and communicate) for the new National

Curriculum and this will need adapting to the needs of the individual groups of pupils.

During the connect stage we will need to ensure that opportunities are incorporated for fluency and reasoning in order to

secure conceptual understanding.

In order to develop depth of understanding with our pupils, and to ensure that we will work towards the yearly standard, we

have identified some stepping stones towards the end of year standard and these will be useful for differentiating and

working towards the end of year standard.

The Content for the Transition points 1 and 2 are guidelines and minimum expectations for the majority of our pupils.

Use of Bloom’s taxonomy can be helpful to increase levels of cognitive demand and examples of Bloom’s taxonomy linked to

Maths is included in our medium term plans.

To meet all pupils’ needs there may be circumstances where learning will need to be tracked back to previous year groups.

Planning for mathematics will be based on our taxonomy (collect, connect, create and communicate) which will be evident

across units of learning as well as within some lessons. This taxonomy is also evident on our working walls and the way in

which we work with pupils in our classes.

Where the learning focus is not explicit on the medium term plan this allows us flexibility to further personalise learning.

17

Brooklands Farm Primary School Medium term planning Maths KS1

End of year standards are listed in Transition Point 3

Content for the Transition Points 1 and 2 are guidelines and minimum expectations. These transition

points may be different for different pupils.

MTPs include content and we will need to ensure that opportunities are incorporated for fluency, reasoning

and problem-solving.

This will be achieved through our learning and teaching taxonomy which includes the aspects of collect,

connect, create and communicate.

Yearly cycle is drafted across three repeat cycles each twelve weeks in duration. Therefore where terms are more

than twelve weeks long we will need to adjust the cycle

TIMINGS ARE FLEXIBLE AND ARE LISTED AS APPROXIMATE.

Year group

KS1

Learning

focus Weeks 1

and 2

Learning focus

Weeks 3 and 4

Learning focus

2-3 days

Learning focus

Week 5/6

Learning focus

Weeks 7 and 8

Learning focus

2-3 days

Learning focus

Week 9

Learning focus

Week 10

Week 11

Week 12 Assessment

Maths concept

Number and Place value

Addition and subtraction

Multiplication and Division

Fractions

Cycle

Collect Knowledge and Conceptual understanding of place value

Collect includes reasoning

Collect Knowledge and Conceptual understanding of addition and subtraction


Connect and review place value, addition and subtraction Eg add two numbers, what is the total rounded to the nearest 10 Eg Money

Create and communicate Connect previous learning to a context Eg Measures, Data,

Collect Knowledge and Conceptual understanding of multiplication and division


Connect and review addition, subtraction, multiplication and division Eg Money Measures Data

Collect Knowledge and Conceptual understanding of fractions, decimals and percentages


Connect, create and communicate with previous learning to a context Eg Measures Data

Narrow the gap

Some pupils may require additional targeted learning

Some pupils may require specific teaching of key learning linked to the context Eg skills of measuring, reading scales etc

Some pupils may require specific teaching of key learning linked to the context Eg £ and p, Interpreting bar chart

Some pupils may require specific teaching of key learning linked to the context


18

Brooklands Farm Primary School Medium term planning Maths KS2

End of year standards are listed in Transition Point 3

Content for the Transition Points 1 and 2 are guidelines and minimum expectations. These transition

points may be different for different pupils.

MTPs include content and we will need to ensure that opportunities are incorporated for fluency, reasoning

and problem-solving.

This will be achieved through our learning and teaching taxonomy which includes the aspects of collect,

connect, create and communicate.

Yearly cycle is drafted across three repeat cycles each twelve weeks in duration. Therefore where terms are more

than twelve weeks long we will need to adjust the cycle

TIMINGS ARE FLEXIBLE AND ARE LISTED AS APPROXIMATE.

Year group

KS2

Learning

focus Week 1

Learning focus

Weeks 2 and 3

Learning focus

2-3 days

Learning focus

Week 4/5

Learning focus

Weeks 6 and 7

Learning focus

2-3 days

Learning focus

Weeks 8 and 9

Learning focus

Week 10 Week 11

Week 12 Assessment

Maths concept

Number and Place value

Addition and subtraction

Multiplication and Division

Fractions, decimals and percentages

Cycle

Collect Knowledge and Conceptual understanding of place value


Collect Knowledge and Conceptual understanding of addition and subtraction


Connect and review place value, addition and subtraction Eg add two numbers, what is the total rounded to the nearest 10 Eg Money

Create and communicate Connect previous learning to a context Eg Measures, data, money

Collect Knowledge and Conceptual understanding of multiplication and division


Connect and review addition, subtraction, multiplication and division Eg Money Measures Data

Collect Knowledge and Conceptual understanding of fractions, decimals and percentages


Connect fractions, decimals and percentages as well as four operations Eg Number patterns involving fractions

Connect, create and communicate with previous learning to a context Eg Measures, money

Narrow the gap

Some pupils may require additional targeted learning


Some pupils may require specific teaching of key learning linked to the context Eg perimeter / area

Some pupils may require specific teaching of key learning linked to the context


19

Planning Process for writing short term plans from the medium term plans

Consider the objectives in the unit of the medium term plans and the relevant stage in the learning taxonomy.

This is the day to day planning.

I know what I am teaching but I am not sure where to get my ideas for teaching and assessing learning to match my

objectives (See Appendix 1 for short term planning resources)

Short term learning will be based on regular assessment within class as well as medium term planning

We aim to develop depth in understanding rather than acceleration through the curriculum. To do this we will incorporate

learning opportunities that increase and develop cognitive demand at all levels. It is important that all learners

experience higher level of cognitive demand in their learning.

The current short term planning grid is available on the Google drive along with guidance. This incorporates our learning

taxonomy and takes account of the collect, connect, communicate and create aspects of learning.

Maths learning at Brooklands Farm: Organisation

Fluency and flexibility sessions (taught in class groups)

In addition to daily core mathematics lessons we will also include regular sessions for our pupils to develop fluency and

flexibility. During these sessions we enable pupils to develop mathematical thinking and flexibility with their thinking as

well as improving speed. For additional guidance on these sessions please see Google Drive / Implementing the new NC in

Maths

Core Maths lessons

From Year 2 onwards core Maths lessons are organised as whole classes as well as ability groups of pupils. These are flexible

and regularly reviewed.

Learning ladders

Learning ladders link directly with learning journey walls and they are used by our learners to recognise their progress and to

know their next steps. This should include key models and images as well as vocabulary to scaffold understanding.

Use of the learning ladders enables pupils to make connections between learning and see the ‘big picture’ of their learning.

Learning ladders show the dialogue between teachers and pupils and they must show children’s responses to each of the

statements or ‘can Is …’

Our pupils ‘gold’ and ‘green’ their learning on the learning ladders. Highlight gold for got it! Highlight green for next steps

Making a maths learning ladder

Maths learning ladders link with the Maths medium term plan.

20 Use the transition point statements from the maths medium term plan and then consider the previous learning related to

that statement.

As we are developing our Mastery curriculum we also include talk and feedback opportunities as well as application and

development of the breadth in learning.

There are examples of maths ladders in the Maths folder on the Google drive in the folder ‘Maths ladders’.

The Learning Environment

In Foundation Stage and throughout our school, the learning environment is used to stimulate our pupils’ curiosity and love

of learning within and across all areas of learning.

This includes a wide and diverse range of high-quality learning experiences and indoor and outdoor environments which

bring mathematics to life and support mathematical development.

Learning Walls

Learning journey walls provide learners with the ability to see where they have been on their journey, where they are and

where they are heading. At Brooklands Farm Primary School we believe that the knowledge of the whole journey enables the

learner to be more independent in setting the pace and next steps in their learning. Learning journey walls should be referred

to throughout all stages in the learning process.

Our Learning journey walls enable pupils to make connections between learning and see the ‘big picture’ of their learning.

What we expect to see: In Mathematics this might also include:

Overview

Where are we going?

What are we doing?

Examples of above.

Examples of problems that we are learning to solve Real-life links Questions from test papers Real outcomes eg if planning a school trip or event Links with collect, connect and create and communicate

Vocabulary

Linked to topic

Progressive

Developmental

See Appendix 1 for Maths vocabulary location on shared drive The development of mathematical language in terms of the concept as well as instructional vocabulary. Talk trios involving reasoning and explanations using mathematical language. (Eg speech bubbles and sentence starters)

Prior learning

Where did we last get to on this journey?

Examples of work

Examples of prior learning Samples of work demonstrating previous steps in learning Models and images used in previous learning

Clear links to main project/topic

Pictures of ignite

Examples of topic work to decorate

Links with purpose Real-life links Key models and images

Sequence of learning objectives Structure of learning steps through the week / unit Models and images used to scaffold understanding Worked examples

21

Differentiation

Learning ladders

Learning at different level / stages

Examples of shared and independent work under/alongside each objective.

Pupil work to exemplify the learning and progress in learning

Success Criteria

Pupil generated success criteria Promote conceptual understanding rather than procedures Visual prompts for the success criteria. In maths it is often possible to exemplify the success criteria through a worked example. Link to steps in learning. Eg LO: To Measure in cm SCr:

Put the 0cm on the ruler at the end of the line

Make sure the ruler is straight against the line

Look at the number on the ruler underneath where the line stops

Learning walls in practice

In order for learning walls to be an effective learning tool they need to include the following as a minimum

Prior learning

Statement of the ‘big picture’ of learning Eg By the end of this week (unit) we will be able to ….

Thinking prompts with questions

Key Vocabulary

An indication of whether learning relates to the collect, connect, create and communicate phase in learning

Children’s names

Current models and images that are being used to scaffold understanding

Examples of work including worked examples (preferably from the pupils)

Success criteria for the steps in learning

Steps on working wall matching steps on learning ladders

Here are some examples

of the above aspects.

22

Cross-curricular Mathematics

To enable our learners to make connections in their learning we plan to exploit mathematical links with other subjects within

our projects. Other subjects provide a rich source of stimulus and motivation for pupils to improve their mathematics

skills and learning is enhanced in both subjects.

We will teach shape and space as part of our whole school projects. This can be taught discretely throughout the project and

year group standards are included on the medium term plan documents.

In our taxonomy links are made at the connect as well as the communicate and create stages

Our children learn to apply their mathematics skills in meaningful, relevant contexts and we make links with other agencies and the wider community to provide a wide range of enhancement and enrichment activities to promote pupils’ learning and engagement with mathematics in the real world.

Maths topics that link well with other subjects: Data Handling

Children will use their skills of processing, representing and interpreting data as they:

consider the data needed to solve a problem represent data in appropriate ways (show us what you have found out) interpret secondary sources of data, such as tables, graphs and charts ( across number of areas eg fabrics that are

waterproof, distances cars travelled, natural/man-made materials etc) draw conclusions from statistics and graphs. (include charts etc)

23 Time

Timing activities in PE, Science, cooking etc

Reading timetables and clocks Measures

Measuring accurately in science, cooking etc

Using measuring instruments Calculations: Need to be able to calculate in order to find solutions

We believe that we will strengthen pupils’ learning in mathematics by enabling pupils to make links with other subjects.

Our project booklets detail the development of mathematics through other curriculum areas. See Google Drive in New

Curriculum Project Booklets Folder.

NOTE: Shape and space will be taught as an integral element of school projects. This will be reviewed in December


Teachers exploit links between mathematics and other

subjects, and with mathematics beyond the classroom.

Teachers have a clear understanding of the value of their

subject which they communicate effectively to pupils, often with enthusiasm.

Some links are made between mathematics and other subjects and with mathematics beyond the classroom.

Excellent links are forged with other agencies and the wider community to provide a wide range of enhancement and

enrichment activities to promote pupils’ learning and engagement with the subject.

Good links are forged with other agencies and the wider community to provide a range of enhancement and

enrichment activities to promote pupils’ learning and their engagement with the subject.


Mathematics Assessment

If we think of our children as growing plants (open grow believe)

Summative assessment of the plants is the process of simply measuring them. It might be interesting to compare and analyse

measurements but, in themselves, these do not affect the growth of the plants.

Formative assessment, on the other hand, is the equivalent of feeding and watering the plants appropriate to their needs –

directly affecting their growth.

In mathematics we use both formative and summative assessments.

24

Feedback marking in mathematics

Feedback is an integral element of our teaching and learning.

Our pupils receive feedback through self-assessment, peer assessment and teacher assessment.

Our planning is adapted in response to pupils’ needs.

In line with our Collect, connect, communicate and create learning approach feedback will vary.

Collect

● Teacher close the gap marking to inform teaching each lesson.

● Peer & Self-assessment of new concepts.

● Teacher VF- scaffolding, prompt, reminder in books and on ladders.

● Children’s own reminders on ladders & response to feedback in books.

Connect

● Joint dialogue between teacher and child during teacher marking.

● Peer & self-assessment of connect activities, using knowledge of key concepts to check methods.

● Teacher VF- scaffolding, prompt, reminder in books and on ladders.

● Children’s own reminders on ladders & response to feedback in books.

When giving feedback to our pupils the following table is useful in providing prompts for feedback relating to mathematics.

REMINDER PROMPTS To reinforce the learning objective.

1. Reiterating the learning objective Remember to… Please explain why this is correct/is the best method

2. Elaborating on the learning objective Please show me a different method you could use to solve this How would you describe this sequence/these numbers? Why does this work?

SCAFFOLDED PROMPTS To support and extend the child’s learning.

1. A calculation with missing parts + 53 = 127

2. A focused directive on a specific element We could check this by using the inverse… To make the method more efficient we could make these two steps into one. Have a go!

3. A question to delve more deeply If two more girls and one more boy joined the class, how would that change the graph?

If turning from North to East is 90, how many degrees is it if I turn from North to North-East? Would this still work with decimal numbers? Why/why not?

4. Open-ended questions How many different irregular quadrilaterals can you draw? How many other different ways can you write 1 metre?

25


Constant assessment of each pupil’s understanding through questioning, listening and observing enables fine tuning of teaching.

Teachers focus on pupils’ understanding when questioning, listening and observing.

Marking distinguishes well between simple errors and misunderstanding, and tailors insightful feedback accordingly

Marking identifies errors and misunderstanding and helps pupils to overcome difficulties.


Baseline assessments in Autumn 1 KH to send to JP

At Brooklands Farm we ensure that we plan for children’s next steps with astute and accurate assessment. We baseline

children immediately in September to identify and quickly close any gaps.

See Making Feedback count policy / Little Book of Assessment for further detail

Assessment of maths learning is about depth of learning rather than coverage of content.

Assessment in the Foundation stage is ongoing as part of daily provision. Assessment procedures are in line with the EYFS.

See Foundation stage manager for further details.

Throughout our school assessment in mathematics is used to narrow the gaps in learning as well as to give an attainment

judgement at assessment points during the year. (See above outline of mathematics assessments)

Our planning is adapted following assessments to meet pupils’ needs.

What do I use to guide my assessments?

We use expectations outlined in our mathematics curriculum to guide our assessments.

From the expectations we make a judgement alongside our teacher knowledge.

Our Prove it learning is used in a formative manner to inform assessments and future learning.

We use mapping attainment grids from OTrack to track pupil progress. These grids enable us to see the progress and

attainment of our children in line with yearly expectations. See Making Feedback Count policy / Little Book of

assessment for further guidance on effective analysis of this data.

EXAMPLE PROMPTS To offer a choice of ideas as possible improvements.

1 Alternative methods Circle the method you think is correct or choose your own… Which of these is correct? Why?

2. Alternative reasons/explanations Circle the explanation/description of the graph you think is correct or write your own… Which of these reasons is correct? Why?

26 Entry levels on the mapping attainment grids are informed by both Prove its and six weekly assessment points in order to

reflect the child’s true ability. We also use Alfie Cloud progress tests at each transition point.

You may also find the Rising Stars resource, which is available in school, useful.

Testbase and Alfie Cloud questions can be useful to assess pupil learning and understanding and progress. See Maths Team

for login details.

For next steps and self-assessment the child friendly ladders in all pupils’ books are integral to learning and these link with

our new National Curriculum medium term plans. (Examples of ladders on the Google Drive)

Calculation

We have developed our Brooklands Farm School approach to calculation which is on the Google drive. (See Appendix 1)

The calculation policy is also publically available to our learning community through our school website.

Our approach incorporates our beliefs about how we enable our pupils to become confident and competent mathematicians

who are equipped for their future lives.


Pupils show high levels of fluency in performing written and

mental calculations and mathematical techniques.

Pupils are generally fluent in performing written and mental

calculations and mathematical techniques.


Approach to calculation

When faced with a calculation we encourage our pupils to consider the following:

Can I do this calculation in my head?

Do I need to make some jottings?

Do I need a written method?

Mental Mathematics: Developing fluency and flexibility

It is essential that our pupils become more confident and competent in mental mathematics as this underpins their

mathematical learning.

From September 2015 we will have regular ‘Fluency and Flexibility’ mental maths sessions with our classes.

There may also be mental maths at the start of core mathematics lessons.

Being proficient in mental mathematics is also a life skill and one that we see as an essential component in developing

lifelong learners.

In Appendix 1 there is a list of resources to teach the development of mental mathematics. These resources are useful but

please be aware that the year groups link with the Primary Framework curriculum and not the National Curriculum 2014.

27

It is essential that our pupils become fluent and flexible in number bonds and times tables as these underpin mathematical

learning.

Here is the progression in number bonds and times tables in line with National Curriculum 2014

Number Bonds

Counting in multiples

(from Number and Place Value) Times Tables

FS

Year 1

Represent and use number bonds

and related subtraction facts within

20

count in multiples of twos, fives and tens

Year 2

Recall and use addition and

subtraction facts to 20 fluently, and

derive and use related facts up to

100

count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward

recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

Year 3

count from 0 in multiples of 4, 8, 50 and 100

recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

Year 4

count in multiples of 6, 7, 9, 25 and 1 000

recall multiplication and division facts for multiplication tables up to 12 × 12

Year 5

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

Year 6

28

Progression in Mental and Written Calculation

Expectations in mental and written calculations for the four operations

Mental Calculation: Addition and subtraction Written Calculation: Addition and Subtraction

FS

Year 1 Add and subtract one-digit and two-digit numbers

to 20, including zero

read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs (appears also in Mental Calculation

Year 2 add and subtract numbers using concrete objects, pictorial representations, and mentally, including: * a two-digit number and ones * a two-digit number and tens * two two-digit numbers adding three one-digit numbers

Year 3 add and subtract numbers mentally, including: * a three-digit number and ones * a three-digit number and tens * a three-digit number and hundreds

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction

Year 4 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

Year 5 add and subtract numbers mentally with increasingly large numbers

add and subtract whole numbers with more than

4 digits, including using formal written methods

(columnar addition and subtraction)

Year 6 perform mental calculations, including with mixed operations and large numbers

Pupils practise addition and subtraction for larger

numbers, using the formal written methods of

columnar addition and subtraction.

Mental Calculation: Multiplication and Division Written Calculation: Multiplication and Division

FS

Year 1

Year 2

show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

Year 3

write and calculate mathematical statements for

multiplication and division using the multiplication

tables that they know, including for two-digit

numbers times one-digit numbers, using mental

and progressing to formal written methods

(appears also in Written Methods)

write and calculate mathematical statements for

multiplication and division using the multiplication

tables that they know, including for two-digit

numbers times one-digit numbers, using mental

and progressing to formal written methods

(appears also in Mental Methods)

Year 4 use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying

multiply two-digit and three-digit numbers by a one-digit number using formal written layout

29

together three numbers recognise and use factor pairs and commutativity

in mental calculations (appears also in Properties

of Numbers)

Year 5

multiply and divide numbers mentally drawing

upon known facts

multiply and divide whole numbers and those

involving decimals by 10, 100 and 1000

multiply numbers up to 4 digits by a one- or two-

digit number using a formal written method,

including long multiplication for two-digit

numbers

divide numbers up to 4 digits by a one-digit

number using the formal written method of short

division and interpret remainders appropriately

for the context

Year 6

perform mental calculations, including with mixed operations and large numbers associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) (copied from Fractions)

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

divide numbers up to 4-digits by a two-digit whole number using the formal written method of short division where appropriate for the context divide numbers up to 4 digits by a two-digit whole

number using the formal written method of long

division, and interpret remainders as whole

number remainders, fractions, or by rounding, as

appropriate for the context

Written approach to calculation

Please see our school approach to calculation in order to maintain a consistent approach to the learning and teaching of

calculation through our school.

Our approach is based on developing conceptual understanding of the four operations and includes the use of models and

images to scaffold understanding.

A summary of our school approach to calculation is in the table below. For further detail (including models and images to be

used to scaffold understanding) refer to the complete policy on Google drive.

Operation

Key Stage 1

Mental and written

approach

Key Stage 2

Written approach

Key Stage 2

Mental Calculation approach

Addition Number lines Partition

Column method includes

‘carrying’

Number lines for jottings

Partitioning

Subtraction Number lines: Counting

backwards

Number lines: Counting

forwards (finding the

difference)

Column method

Decomposition (exchanging

/ repartitioning)

Number lines for jottings

30

Multiplication Arrays

Repeated addition

Number lines

Grid leading to long and

short multiplication

Jottings / partitioning

Division Arrays

Grouping and sharing

Number lines

Short division

Long division: (can be an

efficient form of chunking)

Jottings

Chunking

Becoming mathematicians: Developing the application of Mathematical Skills and Concepts

Problem solving and investigative approaches are central to mathematical learning for our pupils and in order to achieve the

aims of the new National Curriculum (Fluency, reasoning and problem-solving) link with our school taxonomy for Maths


Pupils develop a broad range of skills in using and applying mathematics. They show exceptional independence and take

the initiative in solving problems in a wide range of contexts, including the new or unusual.

Pupils develop a range of skills in using and applying mathematics. They are able to work independently, and

sometimes take the initiative in solving problems in various contexts.

Problem-solving and investigative approaches are central to learning for all pupils.

All pupils have opportunities to solve problems and investigate, although the extent to which these are integral to

their learning may vary.


Raising standards in Mathematics

Tracking

We hold six weekly meetings with teachers to review progress and attainment data of our pupils and to consider the

implications from our most recent data. These are known as Pupil progress meetings.

Through these meetings we identify pupils who may be making slow progress, pupils whose attainment has remained the

same and pupils who are not ‘on track’ for their end of year standard.

Where the data indicates that individual or groups of pupils are not making the expected progress or are not achieving the

expected attainment then we consider:

Can the need be met through day to day quality first teaching?

If the identified need or barrier to learning requires a specific intervention then this is put in place by the class teacher with

clear (measurable) entry and exit data. This will be recorded on the Narrow the Gap plan.

Common obstacles to progress for some slow

moving pupils Actions to consider

Struggle to explain their thinking and methods? Have difficulty in remembering and using mathematical vocabulary?

Activities and approaches to help engage pupils in mathematical thinking. To use mathematical vocabulary and language to express

31

Lack flexibility with number, for example they struggle to identify related facts from those they know? Tend to rely on one method when calculating and solving problems? Struggle with problems, particularly those that involve two or more steps? Lack self-help strategies?

Were weak at mental calculation – they had few mental calculation skills and were reluctant to use them. Had difficulty in keeping intermediate information in their heads. Had a preference for using formal written methods which they considered better than mental methods, but made mistakes. Lacked images and models such as number lines to help with visualising mathematics. Experienced a low level of challenge and tended to work within their comfort zone.

Developed a low appetite for risk taking

their explanations and thinking with other pupils and their teacher in all mathematics lessons. Confidence and greater flexibility with number and calculation through shared discussion about links and how alternative methods work. To explore and focus on how and why different methods work rather than just on the answer, e.g. devising questions for a fixed answer, exploring when statements are true and false, matching linked facts. Time and support in developing independent learning and self-help strategies e.g. comparing approaches when stuck, referring to displays.

A greater focus on the use of mental calculation strategies. To develop a range of mental calculation strategies through guided teaching to help them choose efficient methods. Support in deciding when a mental or written method is more appropriate and why. To see, use and evaluate different approaches to solving a problem. To use images and models to help with visualising mathematics, e.g. using number lines and hands-on resources more flexibly. A greater level of challenge, including experience of working in a range of different groups. Support and encouragement to take risks so that they are less anxious about always getting the right answer.

Ref: Making Good Progress Materials

Common obstacles to progress which may affect

progression in some higher attaining pupils

Actions to consider

Had a range of mental calculation skills but had difficulty selecting the most efficient method. Were better at adding and multiplying mentally than subtracting and dividing. Were not aware of the importance of reading a calculation and deciding whether to do it mentally or use a formal written method.

Practice on how to ‘read’ calculations and decide on the most efficient approach. Paired and small group work to explore and evaluate different methods and approaches. Further guidance on the use and value of visual images to aid

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Had difficulty with understanding place value of decimals and relating fractions to their decimal representations. Were familiar with visual images such as number lines but did not appreciate the value of them to aid mental calculation. Had difficulty seeing the relationships and connections in mathematics. Did not understand division

calculation. Time to explore relationships and connections in mathematics, e.g. between fractions, decimals and percentages. To address their weakness with division e.g. through strengthening links between subtraction and division and helping them see the relationship between multiplication and division.

Ref: Making Good Progress Materials

We are also aware that as well as mathematical barriers to learning some pupils would benefit from additional support to

enable them to become more numerate. The table below lists some characteristics of numerate pupils.

This list might be useful in supporting some pupils to develop their numeracy skills

Characteristics of numerate children

Is confident and enjoys mathematics

Has a sense of the size of a number and where it fits into the number system

Calculates accurately and efficiently

Makes sense of number problems, choosing and exploring strategies for solving them

Uses what s/he knows by heart to figure out answers mentally

Talks about mathematics using appropriate language and vocabulary

Has strong mental images of mathematics

Makes connections across mathematics and beyond

Is an active learner and is willing to ‘have a go’

Reflects on his/her learning

Ref: Every Child Counts

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Maths and Parents

For Parents’ evening the child’s learning ladder in their ‘Grow it’ books can be useful to show parents the next steps they can

support their child in with their mathematical learning.

The Brooklands Farm approach to calculation is also useful to share with parents so that they know more about their child’s

learning and can understand the way their child is learning mathematics.

Key documents for our parents are available on our website in the Mathematics section and also in areas for individual year

groups.

Appendix 1: All Mathematics resources are stored on the Google Drive

Activity Banks

In the folder called ‘Implementing the new National Curriculum in Maths’ These are useful activity banks based on yearly standards and expectations

Exemplification of the yearly

standards

In the folder called ‘Implementing the new National Curriculum in Maths’

Mathematics vocabulary

Pathway: Maths / Maths vocabulary / bottom icon / vocab in maths areas and year Teacher glossary for mathematical terms: Pathway: Maths / Mathematical teacher glossary

Calculation approach at Brooklands

Farm

In the folder called ‘Implementing the new National Curriculum in Maths’

Mental Maths

Progression in mental maths Maths / Mental Maths Progression The progression is useful but note that the year groups link with Primary Framework so you may need to look to the next year group. Mental Maths tests

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Maths / Mental Maths test / Choose the correct year group and read the guidance

Challenge and Problem-solving

NRICH: http://nrich.maths.org/help The five maths content stages correspond to US Key Stages. Stage 1: Uses mathematics you would normally meet before the age of 8 Stage 2: uses mathematics you would normally meet before the age of 11 Challenge level on NRICH: Indicated by 1, 2 or 3 stars 1 star: Problems that require some initial investigation and planning 2 stars: Problems that extend pupils beyond normal curriculum demands and which challenge students working at the next stage 3 stars: Very challenging problems Testbase: www.testbase.co.uk Username: 719178_43 Password: 3ACFC This is a collection of past test papers. From the search you can find questions which are challenging in terms of level and/or application. There is also a Using and Applying Mathematics area from the initial menu. Text books – For guided group work – see Abacus books in each year group

This document has been informed by the following:

Brooklands Farm Learning and Teaching policy

Other Brooklands Farm School policies: Maths, Literacy, Science

Research including: Haylock and Cockburn

Ofsted Mathematics subject specific guidance

National requirements: New National Curriculum 2014

Primary Framework for Mathematics

http://nrich.maths.org/help

brooklands farm primary school: our little book of...

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