Dunmow St Mary’s Primary School

Dunmow St Mary’s Primary School

Policy for Mathematics

Policy for Mathematics

Contents

Part 1: Why do we teach mathematics?

Introduction (Ethos; Aims for Mathematics; Promoting Key Skills Through Maths) (includes Monitoring

of the Policy, Equal Opportunity, Cross-phase liaison )

Part 2: Teaching

Speedy Maths

Calculation Policy (see attached document)

Part 3: Assessment and Target Setting

- KPIs

- Acquiring mastery

See assessment and marking policy for more detailed explanations of marking and assessment in mathematics.

Part 1 Introduction

Why do we teach mathematics?

We teach maths...

...so that the children can manage themselves in later life; time, finance, getting the best deals at the shops...

....so that the children can effectively solve problems involving maths...

(contributions from Staff at Dunmow St Mary’s School 9th May 2012)

Ethos

We aim to provide a stimulating and challenging learning environment which gives every individual an opportunity to fulfil their

potential to the highest possible standard.

We expect that children will leave the school with confidence in their own ability, with the skills to extend and apply their

knowledge, and the belief that learning is enjoyable and rewarding.

We can best provide a supportive and stimulating environment for learning by working as a team and by providing every

opportunity for all staff to be involved in planning and policy making. An interesting and well planned curriculum is essential for

effective learning, as is a caring and well ordered environment.

In the interests of every child we endeavour to:

Match work to individual needs

Concentrate on educational processes as well as outcomes

Share responsibility for learning, planning and reviewing with the children

Encourage confidence and co-operative learning

Emphasize first hand experience

Teach basic skills in a consistent way

Emphasise the development of cross curricular skills

Teach respect for the abilities and views of others

Provide opportunities for success

Celebrate all kinds of achievement

Have high expectations of every child

Provide opportunities for exploration in depth.

Policy Development

Our policy was developed and discussed during a series of staff meetings in the Summer Term 2012. The maths coordinator also

employed a ‘Maths Team’ that was formed of governors, parents, teachers and Teaching Assistants. The INSET and maths team

focussed on Number and Using Applying strands of the Maths Curriculum. Development of the Maths Policy will continue and the

written policy will be modified and refined as our practices evolves.

Timetabling of Maths

All KS1 and KS2 pupils receive mathematics in a daily lesson lasting between 45 – 60 minutes. In certain instances, additional

provision is made for individuals or small groups (Maths Co-ordinator), or intervention (in small groups or on an individual basis).

Cross curricular links with computing may increase provision for maths or, on occasions take the place of the daily numeracy

session. All year groups also have an additional 10 minutes per day for Speedy Maths.

Generally, Years 1-4 are taught as a class, often with TA support. For the teaching of certain number concepts children may be

withdrawn for ‘Springboard’ type support groups.

At KS1 children receive their mathematics teaching as a whole class, differentiated (and supported by TAs) to suit groups or

individual children.

Children are set in ability groups in Years 5 and 6. In year 5, those who are working below age related expectations are taught in a

separate, smaller class by a specialist teacher whilst the other children stay in their own classes for maths. In year 6, these children

are taught in smaller groups by teaching assistants whilst the borderline children are taught separately by the specialist teacher.

Again, the rest of the children stay in their own classes. Groups are flexible and there is movement between groups.

Overview and aims

The national curriculum for mathematics aims to ensure that all pupils:

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.

reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an

argument, justification or proof using mathematical language.

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.

Programmes of study

EYFS Numbers

Shapes, space and measures

KS1 Number: Number and Place value

Number: Addition and subtraction

Number: Fractions

Multiplication and division.

Measurement

Geometry: Properties of shapes

Geometry: position and direction

Statistics

KS2 Number: Number and place value

Number: Addition and subtraction

Number: Multiplication and division.

Number – Fractions (including decimals and percentages)

Measurement

Geometry: Properties of shapes

Geometry: position and direction

Statistics

Ratio (Year 6)

Proportion (Year 6)

Algebra (Year 6)

Continuity and Progression

Year groups produce medium term (half term) topic plans. Teachers / year groups use the medium term plans for their weekly

plans. They take the appropriate objectives from the NC and supplement it with ideas from the White Rose documents to help

promote fluency, problem solving and reasoning. Al teachers are currently following the progression of units set out in the White

Rose.

Cross curricular links have been developed where possible, e.g. data handling often links with science or measures with DT.

Computing is a further integral part of teaching the maths curriculum.

Homework

A mathematical task is included in the weekly homework, linked where necessary to the coming week’s concept(s). For example the

children in Year 2 might be asked to revise their two-times table, or in Year 6 to practise some simple percentages.

Links with Parents

Parents have the opportunity to discuss their children’s work formally during three parent meetings, one meeting in each of the

terms. Informally parents can speak to teachers during drop in sessions every Wednesday from 3:15 – 3.30 or by making an

appointment at any time.

Parents have been invited to a variety of Mathematics events, either in the evening (subtraction, multiplication); during mornings

(visiting classes and seeing mental/oral starters) and to sessions for understanding the progression of written strategies. These links

will be developed further.

Staff Development

The Head teacher and Mathematics Co-ordinator lead INSET for staff as needed. Teachers attend courses targeting specific areas of

Mathematics on a regular basis.

Resources

As a school we are well resourced with maths equipment to help support our CPA approach to mastery. We believe that all children,

no matter how old they are, should have access to resources which support them in their understanding of mathematical concepts.

Evaluation

The success of the mathematics policy will be assessed by

the enthusiasm and enjoyment children derive from applying knowledge and understanding of mathematical concepts

the progress they make in understanding and accuracy

the accuracy of predictions based on high expectations

Part 2: Teaching

Speedy Maths

Each year group in the school completes a short 10/15 minutes of speedy maths on a daily basis.

Main aims:

For children to develop their ability to solve mental calculations quickly.

To improve their speed and confidence in solving these.

To provide children with a range of efficient methods to help solve mental calculations quickly.

The table below shows the number facts/mental calculations that each year group covers during speedy maths.

Reception

Count reliably from 0-20

Using quantities and objects to add and subtract two single-digit numbers

1 more/1 less to 10.

Number recognition.

Year 1

Count to 100 forwards and backwards from any number.

Identify 1 more/1 less

Read and write numbers from 1-100 in words.

Represent and use number bonds and related subtraction facts within 20.

Count in multiples of twos, fives and tens.

Add and subtract one digit and two digit numbers to 20, including zero.

missing number problems such as 7= ? – 9

Doubles to 10 and related facts

Year 2

Multiplication and division facts for the 2. 5 and 10 times tables.

Counting in threes.

Add/subtract tens from any given two-digit number.

Addition and subtraction facts to 20 and 100

Add/subtract a two-digit number with a one-digit number.

Add/subtract two 2 digit numbers

Add 3 one digit numbers together.

Finding one half, one third, one quarter or 3 quarters of a number

< > =

Year 3

Find 10 or 100 more or less than a given number

Add and subtract numbers mentally, including: a three-digit number and ones; a three-digit number and tens; a three-digit

number and hundreds.

Read and write numbers up to 1000 in numerals and in words.

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

recognise the place value of each digit in a three-digit number (hundreds, tens, ones).

Add and subtract fractions with the same denominator within one whole

compare and order unit fractions, and fractions with the same denominators

Year 4

Count in multiples of 6, 7, 9. 25 and 1000

Find 1000 more or less than a given number

Round any number to the nearest 10, 100 or 1000.

Recall and use multiplication and division facts for multiplication tables up to 12 x 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 number

Recognise and use factor pairs and commutativity in mental calculations.

Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and ones)

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 ¼, ½, ¾

Convert between different units of measure eg hour to minute.

Round decimals with one decimal place to the nearest whole number.

Read Roman numerals to 100

Year 5

Read, write, order and compare numbers to at least 1000000 and determine the value of each digit.

Count forwards or backwards in steps of powers of 10 for any given number up to 1000000.

Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000

Read Roman numerals to 1000

Add and subtract numbers mentally with increasingly large numbers.

Multiply and divide numbers mentally drawing upon known facts

Multiply and divide whole numbers by 10, 100 and 1000.

Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

write percentages as a fraction with denominator 100, and as a decimal.

Recognise and use square numbers and cube numbers and the notation for squared (2) and cubed (3)

Add and subtract fractions with the same denominator and denominators that are multiples of the same number.

Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statement

Read and write decimal numbers as fraction

Year 6

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 long division, and interpret remainders as

whole number remainders, fractions, or by rounding, as appropriate for the context

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

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

multiply simple pairs of proper fractions,

divide proper fractions by whole numbers

identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving

answers up to three decimal places

multiply one-digit numbers with up to two decimal places by whole numbers

solve problems involving the calculation of percentages

use simple formulae

Use of vocabulary

The language of mathematics is a complex and varied one. It is expected that the children learn and use a full range of vocabulary to help them

understand the concepts that they are dealing with.

Here is a range of vocabulary most commonly used. Monitoring will take into consideration the quality and range of vocabulary being used.

Please see attached document for our current calculation policy which is used alongside the White Rose.

Addition

The total of... The sum of.... Add Plus

Altogether ....more than.... Double How many more...?

Subtraction

Subtract Minus Take away ....less than....

Difference between How many less...? half

Multiplication

The product of... Multiply Times Double ...lots of.... ...groups of....

Division

Shared by... Divide Shared between groups of the quotient of .... half

Application / problem solving / thinking skills

What can you see...? What do you notice...?

Why...? What happens when...? What if...? What might happen if...? Imagine if... When might...? How does....?

What is the same/different? Give me another, and another… Prove it! How do you know?

Part 3: Assessment

Developing Mastery of Mathematical Concepts

School development in 2015-16 focused on how as a school we are developing our own assessment procedures in the wake of the

government’s decision to move away from ‘Levels’ and towards a system of targets which should be met by children in any specific

year group.

Within this system there are three stages in the development of each child within their year group’s expectations:

I am beginning to understand the year group targets

I am working at the expected standard

I have mastered the expected standard

Each half term, teachers use a range of evidence to place the children on a step within a band. There are Key Performance Indicators

for each band to help with this.

At the end of each term, years 2 and 6 complete past SAT papers and years 3, 4 and 5 use NFER tests to help inform summative

assessments.

Band 1

Number and Place Value

Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

Count and read numbers to 100 in numerals

Count and write numbers to 100 in numerals

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

Identify one more and one less of a given number

Addition and Subtraction

Represent and use number bonds within 20

Represent and use subtraction facts within 20

Fractions

Recognise, find and name a half as one of two equal parts of an object, shape or quantity

Measurement

Compare, describe and solve practical problems for lengths and heights e.g. long/short, longer/shorter, tall/short, double/half

Compare, describe and solve practical problems for mass/weight e.g. heavy/light, heavier than, lighter than

Compare, describe and solve practical problems for capacity and volume eg. full/empty, more than, less than, half, half full, quarter

Compare, describe and solve practical problems for time e.g. quicker, slower, earlier, later

Properties of Shape

Recognise and name common 2-D shapes e.g., rectangles (including squares), circles and triangles

Recognise and name common 3-D shapes e.g. cuboids (including cubes), pyramids and spheres

Band 2


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

Compare and order numbers from 0 up to 100; use <, > and = signs


Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving

numbers, quantities and measures

Solve problems with addition and subtraction applying his/her 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

Multiplication and Division

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

numbers

Solve problems involving multiplication and division, using concrete materials and mental methods

Solve problems involving multiplication and division using arrays, repeated addition and multiplication and division facts, including

problems in contexts

Fractions

Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity

Measurement

Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

Properties of Shape

Compare and sort common 2-D and 3-D shapes and everyday objects

Position and Direction

Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing

between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

Statistics

Ask and answer questions about totalling and comparing categorical data

Band 3


Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

Solve number problems and practical problems involving these ideas


Add and subtract numbers mentally, including a three-digit number and ones

Add and subtract numbers mentally, including a three-digit number and tens

Add and subtract numbers mentally, including a three-digit number and hundreds


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 he/she knows,

including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

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 show, using diagrams, equivalent fractions with small denominators

Measurement

Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

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

Properties of Shape

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

Statistics

Interpret and present data using bar charts, pictograms and tables

Band 4


Count in multiples of 6, 7, 9, 25 and 1000

Count backwards through zero to include negative numbers

Order and compare numbers beyond 1000

Round any number to the nearest 10, 100 or 1000


Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why


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

Fractions

Recognise and show, using diagrams, families of common equivalent fractions

Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by

ten

Round decimals with one decimal place to the nearest whole number

Solve simple measure and money problems involving fractions and decimals to two decimal places

Measurement

Convert between different units of measure <eg>kilometre to metre; hour to minute</eg>

Properties of Shape

Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

Identify lines of symmetry in 2-D shapes presented in different orientations


Plot specified points and draw sides to complete a given polygon

Statistics

Solve comparison, sum and difference problems using information presented in a line graph

Band 5


Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through

zero


Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and

subtraction)

Add and subtract numbers mentally with increasingly large numbers

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why


Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Fractions

Compare and order fractions whose denominators are all multiples of the same number

Read and write decimal numbers as fractions e.g. 0.71 = 71/100

Read, write, order and compare numbers with up to three decimal places

Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a

denominator of a multiple of 10 or 25

Measurement

Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and

millimetre; gram and kilogram; litre and millilitre)

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

Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and

square metres (m²) and estimate the area of irregular shapes

Properties of Shape

Draw given angles, and measure them in degrees (°)

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

Statistics

Solve comparison, sum and difference problems using information presented in a line graph

Band 6


Round any whole number to a required degree of accuracy

Use negative numbers in context, and calculate intervals across zero


Solve multi-step problems in contexts, deciding which operations and methods to use and why.

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.


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 number using the formal written method of short division where appropriate,

interpreting remainders according to the context

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Fractions

Solve problems which require answers to be rounded to specified degrees of accuracy

Use written division methods in cases where the answer has up to two decimal places

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Measurement

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 to up to three decimal places

Properties of Shape

Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals,

and regular polygons


Draw and translate simple shapes on the coordinate plane, and reflect them in the axis

Statistics

Interpret and construct pie charts and line graphs and use these to solve problems

Calculate and interpret the mean as an average

Ratio and Proportion

Solve problems involving the calculation of percentages e.g. of measures, and such as 15% of 360 e.g. and the use of percentages for

comparison

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Algebra

Use simple formulae

Acquiring Mastery

Mastery of the year group targets has four broad definitions (as defined in the NCETM ‘Teaching for Mastery’ documents, 2015):

1. A mastery approach: a set of principles and beliefs, including a belief that all children are capable of understanding and

doing mathematics given sufficient time

2. A mastery curriculum: where all children need access to the concepts and ideas of mathematics and the rich connections

between them

3. Teaching for mastery: where all children work on the same topic, whilst at the same time addressing the need for all pupls

to master the curriculum and for some to gain greater depth of proficiency and understanding. Challenge is provided by

going deeper. Teaching ensures and learning is sufficiently embedded over time. Long term gaps in learning are prevented

through speedy teacher intervention. Lessons engage children reasoning and the development of mathematical thinking.

4. Achieving mastery of particular topics: where mathematics involves knowing ‘why’ as well as ‘that’ and ‘how’

Through focusing on the Mastery documentation, INSET in March 2016 supported teachers to understand the following key aspects

of defining a Mastery approach in their lessons.

A pupil really understands a mathematical concept if he or she can:

describe it in their own words

represent it in different ways

explain it to someone else

make up his or her own example

see connections between concepts (and non-connections)

recognise it in new situations

make use of it in new ways

Acquiring mastery

Developing mastery with greater depth is characterised by pupils’ ability to:

solve problems of greater complexity (i.e. where the approach is not immediately obvious)

independently explore and investigate mathematical contexts and structures, communicate results clearly and

systematically explain and generalise mathematics

Through analysis of the exemplification of maths contexts at ‘mastery’ and ‘mastery at greater depth’ levels, the teachers agreed that

ways to present mathematical problems to children, and the vocabulary (printed in bold underlined italic) to be used by teacher and

pupil alike, might include:

tasks where children are required to prove or explain

tasks where children might investigate a concept (e.g. ‘No multiple of 7 will ever appear in this sequence).

Develop connections and relationships between concepts (e.g. what do you notice that is the same or different in these

numbers: 334, 34, 304)

Make a clear emphasis on ‘What do you notice?’

Create their own conjectures (what could happen if I rearrange the number square in rows of 5, what numbers could not

be in the following sequence: 10, 12, 14...)

Encourage children to think and talk creatively, through exposure to ‘unusual statements’ e.g. Ben says he can tell the

time just by using the hour hand. Do you think he is right?)

A focus on mathematical explanation by referring to examples (‘connections’ and ‘non-connections’

Tasks which are open-ended (Express how many ways... , make up possible sequences which are like this one...)

Supporting less able children to acquire mastery of year group expectations

The NCETM documents refer to advice that children who struggle mathematically are supported by teachers: “Long term gaps in

learning are prevented through speedy teacher intervention”.

Differentiation is provided through the support of the less able, with fluency taught through essential practice and consolidation

tasks, teaching conceptual understanding through multiple representations and dealing with misconceptions immediately.

“I can recognise

coins 1p and 2p.”

Dunmow St Mary’s Primary School

Documents

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