Our Vision for Mathematics
We will prepare students to become confident, numerate individuals who are able to deal with all aspects of Mathematics in their next steps after their time at Castle Newnham School.
There is a large focus on developing the fluency of number which will help the pupils to solve problems related to new concepts taught. This ensures that the children have a deeper understanding of number which they are able to interrelate into other aspects of Maths.
Curriculum Intent
Mathematics is the basics of science and science is life and so our aim is to ensure that we make our pupils highly numerate with a knowledge of mathematical patterns which will help them to understand and operate in the modern world. They should be able to apply knowledge of maths to everyday events as well as abstract concepts.
This will be accomplished through our commitment to excellent teaching, a welldesigned curriculum, with an interesting variety of lessons to motivate and inspire all students.
We have high expectations of all students and we work with them to ensure that they develop their skills in numeracy, analysis, reasoning and problem solving.
Curriculum Implementation
At Castle Newnham we teach maths using the Maths Mastery Programme.
The ‘mastery approach’ to teaching maths is the underlying principle of Mathematics Mastery. Instead of learning mathematical procedures by rote, we want pupils to build a deep conceptual understanding of concepts which will enable them to apply their learning in different situations. The programme uses the Concrete Pictorial Abstract (CPA) approach with three main dimensions of depth; conceptual understanding, language and communication and mathematical thinking.
Children have a range of opportunities to investigate, problem solve and make connections with a variety of mathematical topics. Through the use of daily KIRFs (Key Instant Recall Facts) in Primary, children develop fluency and automaticity and they build on their knowledge and understanding taught in the main maths lesson.
Times tables
Children are also expected to learn key maths facts like times tables and addition facts by heart to free up working memory and give them the mental space to focus on new concepts. We do this by teaching and practising number bonds and times tables in every Maths lesson during the primary phase. We use Numbots and Times Tables Rock Stars to support the children’s learning and we encourage parents to support them with this at home also. To download a copy of the Time Tables Rock Stars parents handbook, please click here.
By the end of Year 4, the children are expected to know all of their times tables up to x12 and the corresponding division facts in any order and rapidly. The Year 4 children will all take part in the National Times Tables Check.
Year Group Content
Maths is taught through adultled learning which supports a mastery approach to number: for example, in the autumn term  a depth of understanding of what the number ‘3’ means. This is consolidated through high quality provision during childinitiated learning: for example, representing amounts in a range of ways using manipulatives and developing an understanding of pattern through outdoor learning.
Number
Children will:  Have a deep understanding of numbers to 10, including the composition of each number; Subitise (recognise quantities without counting) up to 5; Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
Numerical Patterns
Children will:  Verbally count beyond 20, recognising the pattern of the counting system;  Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;  Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.
Although the expected outcomes are focussed on number and numerical patterns, our Castle Newnham Reception mathematics curriculum forms the foundation of mathematical learning across areas below including measure, shape and space, date and time and number.
Pupils will be taught the following topics:
1.1 Place Value (Within 10)

1 more

1 less

Fewer, more, same

Less than, greater than, equal to

Comparing numbers

Ordering numbers
1.2 Addition and subtraction (Within 10)

Partwhole model

Fact families

Number bonds within 10

Number bonds to 10

Addition introduction

Subtraction introduction
1.3 Geometry (Shape)

Recognise and name 3D shapes

Recognise and name 2D shapes

Patterns with 2D and 3D shapes
1.4 Place Value (Within 20)

Number 11 to 20

Tens and ones

Comparing objects and numbers

Ordering objects and numbers
1.5 Addition and subtraction (Within 20)

Add by making 10

Subtraction  not crossing 10

Find and make number bonds
1.6 Place Value (WIthin 50)

Numbers to 50

Comparing objects and numbers

Ordering objects and numbers

Counting in 2s and 5s
1.7 Length and height

Comparing lengths

Comparing heights

Measuring length

Introducing the ruler
1.8 Mass and volume

Measuring mass

Comparing mass

Introducing capacity and volume
1.9 Multiplication and division

Counting in 10s

Making equal groups

Making arrays
1.10 Fractions

The whole

A half

A quarter
1.11 Geometry (Position and Direction)

Describing turns

Describing position
1.12 Measurement (Money)

Recognising coins

Recognising notes

Counting coins
1.13 Measurement (Time)

Time to the hour

Time to the half hour

Writing time

Comparing time
Pupils will be taught the following topics:
2.1 Place Value

Representing numbers to 100

Partwhole model  tens and ones

Count in 3s

Comparing objects and numbers

Ordering objects and numbers
Builds on 1.6
2.2 Addition and subtraction

Bonds to 100 (tens)

Add and subtract 1

10 more and 10 less

Add and subtract 10s

Add and subtracting 2digit and 1digit numbers

Adding and subtracting a 2digit number and a 2digit number
Builds on 1.2 and 1.5
2.3 Measurement (Money)

Counting notes and coins

Comparing money

Find the total

Find the difference

Find change
Builds on 1.12
2.4 Multiplication and division

Recap from 1.8 to prepare for 2.5
2.5 Multiplication and division

Equal groups

Multiplication sentences

2, 5 and 10 timestable

Odd and even numbers

Divide by 2, 5 and 10
Builds on 1.8
2.6 Statistics

Tally charts

Pictograms (1,2, 5 and 10)

Block diagrams
Foundation for future topics.
2.7 Properties of shape

Drawing 2D shapes

Lines of symmetry

Face on 3D shapes

Vertices on 3D shapes

Make patterns with 2D and 3D shapes
Builds on 1.3
2.8 Fractions

Equal parts

A third

Unit fractions

Nonunit fractions

Equivalence of half and 2 quarters

Find three quarters
Builds on 1.9
2.9 Measurement (length and height)

Measure length (cm . m)

Compare lengths

Order lengths

Four operations with length
Builds on 1.7 and 2.2 and 2.5
2.10 Geometry (Position and direction)

Describing movement

Describing turns

Movements and turns
Builds on 1.10
2.11 Measurement (Time)

O’clock and half past

Quarter past and quarter to

Telling time to 5 minutes

Hours and days

Finding and comparing durations
Builds on 1.12
2.12 Measurement (Mass, capacity and temperature)

Comparing mass

Mass in kg and g

Litres and millilitres

Temperature
Builds on 1.8
Pupils will be taught the following topics:
3.1 Place Value

Hundreds

Number to 1,000

100s,10s and 1s

Comparing objects and numbers

Ordering objects and numbers
3.2 Addition and subtraction

Add and subtract 3digit and 1digit numbers (not crossing and crossing 10)

Add and subtract 3digit and 2digit numbers (not crossing and crossing 100)

Add and subtract 100s

Add and subtract 3digit and 2digit numbers (exchanging and no exchange)

Estimating answers
3.3 Multiplication and division

Multiple and divide by 3, 4 and 8

3,4 and 8 timestables
3.4 Multiplication and division

Multiply and divide 2digit and 1digit numbers

Divide 100 into 2,4,5 and 10 equal parts

Remainders

Scaling
3.5 Measurement (Money)

Converting pounds and pence

Add money

Subtract money

Give change
3.6 Statistics

Bar charts

Tables
3.7 Measurement (Length and perimeter)

Equivalent lengths (m and cm)

Equivalent lengths (mm and cm)

Adding and subtracting lengths

Measure and calculate perimeter
3.8 Fractions

Recap from 2.8 to prepare for 3.9
3.9 Fractions

The whole

Tenths

Fractions on a number line

Fractions of objects

Equivalent fractions

Comparing fractions

Ordering fractions

Adding and subtracting fractions with the same denominator
3.10 Measurement (Time)

Months and years

Hours in a day

Time to 5 minutes and the minute

A.m and P.m

24hour clock

Measuring time in seconds
3.11 Geometry (Properties of shape)

Turns and angles

Right angles

Horizontal and vertical

Parallel and perpendicular
3.12 Measurement (Mass and capacity)

Measuring and comparing mass and capacity
Pupils will be taught the following topics:
4.1 Place Value

Round to the nearest 10 and 100

Count in 1,000s

Partitioning

Number Line to 10,000

1,000 more and less

Count in 25s

Negative numbers

Roman numerals
4.2 Addition and subtraction

Subtracting 4digit and 4digit numbers (exchanges and no exchanges)

Adding 4digit and 4digit numbers (more than one exchange)

Efficient subtraction

Estimate answers
4.3 Measurement (Length and perimeter)

Kilometres

Perimeter of a rectangle

Perimeter of rectilinear shapes
4.4 Multiplication and division

Multiple and divide by 10 and 100

Multiple by 1 and 0

Divide by 1 and itself

6, 7 and 9 timetables and division facts
4.5 Multiplication and division

11 and 12 timestable

Multiply 3 numbers

Efficient multiplication

Multiplication written methods

Multiply 2digit by 1digit

Multiply 3digits by 1digit

Divide 2digit by 1digit

Divide 2digits by 1digit

Divide 3digits by 1digit
4.6 Measurement (Area)

Introduction to area

Counting squares

Comparing area
4.7 Fractions

Equivalent fractions

Fractions greater than 1

Count in fractions

Add 2 or more fractions

Subtract 2 fractions

Subtract fractions from the whole

Fractions of a quantity
4.8 Decimals

Tenths as decimals

Tenths on a number line

Divide 1 or 2digits by 10

Hundredths

Divide 1 or 2 digits by 100
4.9 Decimals

Write, compare and order decimals

Round decimals

Halves and quarters
4.10 Measurement (Money)

Ordering money

Estimating money
4.11 Measurement (Time)

Hours, minutes and seconds

Years, months, weeks and days

Analogue to digital
4.12 Statistics

Interpret charts

Line graphs
4.13 Geometry (Properties of shape)

Identify angles

Triangles

Quadrilaterals

Symmetry
4.14 Geometry (Position and direction)

Describing positions

Movement on a grid
During Year 4, the pupils will take part in a Multiplication Tables Check, information about this can be found here
Pupils will be taught the following topics:
5.1 Place Value

Numbers to 10,000

Rounding to 10,100 and 1,000

Numbers to 100,000 and a million

Negative numbers

Roman numerals
5.2 Addition and subtraction

Add whole numbers with more than 4digits (formal methods)

Subtract whole numbers with more than 4digits (formal methods)

Round to estimate

Inverse operations
5.3 Statistics

Line graphs

Tables

Twoway tables

Timetables
5.4 Multiplication and division

Factors and multiples

Common Fractions

Prime numbers

Square numbers

Cube numbers

Multiple and divide by 10, 100 and 1,000
5.6 Measurement (Perimeter and area)

Measuring and calculating perimeter

Area of rectangles

Area of compound and irregular shapes
5.7 Multiplication and division

Multiple 4digits by 1digit

Multiply 2, 3 and 4digits by 2digits

Divide 4digits by 1digit
5.8 Fractions

Equivalent fractions

Improper to mixed fractions

Compare and order fractions

Add and subtract fractions

Multiply unit fractions

Fractions of an amount
5.9 Decimals and percentages

Decimals to 2 d.p

Thousandths

Rounding decimals

Fraction, decimal and percentage equivalents
5.10 Decimals

Adding and subtracting decimals

Multiplying decimals by 10,100 and 1,000

Dividing decimals by 10, 100, 1,000
5.11 Geometry (Position and direction)

Measuring angles

Using protractors

Angles on a straight line

Angles around a point
5.12 Measurement (Converting units)

Kgs and Kms

Imperial and metric units

Converting units of time

Timetables
5.12 Measurement (Volume)

Comparing volume

Estimating volume

Estimating capacity
Pupils will be taught the following topics:
6.1 Place Value
 Numbers to 10 million
 Comparing and ordering
 Rounding
 Negative numbers
6.2 Four operations

Consolidation of prior learning

Short and long division

Common factors and multiples

Primes to 100

Order of operations
6.3 Fractions

Simplifying fractions

Comparing and ordering fractions

Adding and subtracting fractions

Multiply and dividing fractions by integers

Fractions of amounts
6.4 Geometry (Position and direction)

First quadrant

Four quadrants

Translation

Reflection
6.5 Decimals

Three decimals places

Multiply and divide by 10,100 and 1,000

Decimals as fractions

Fractions to decimals
6.6 Percentages

Fractions to percentages

Fraction, decimal and percentage equivalent

Percentages of amounts
6.7 Algebra

Forming expressions

Substitution

Formulae

Forming equations

Solving twostep equations
6.8 Measurement (Converting units)

Metric measures

Converting and calculating metric measures

Miles and Kilometres

Imperial measures
6.9 Measurement (Perimeter, area and volume)

Area and perimeter

Area of triangles

Volume of a cuboid
6.10 Ratio

Calculating ratio

Calculating scale factors
6.11 Statistics

Line graphs

Circles
Pie charts 
The mean
6.12 Geometry (Properties of shape)

Protractors

Vertically opposite angles

Angles in a triangle

Angles in regular polygons
This year serves as the bridge between Primary education and Secondary, and so we focus on checking the understanding of students with regards to their KS2 mathematics skills. We are then able to reinforce and extend the prior learning of our pupils.
Pupils are unlikely to have used the calculator in their Maths lessons in their primary schools and so the aim of our curriculum in year 7 is to revisit and reinforce, whilst extending their number work from KS2 and gradually introduce them to solving simple algebraic equations and deepen their knowledge of calculating averages and representing data through charts.
Pupils will be taught the following topics:
Number:

Use positive integer powers and associated real roots

Apply the four operations with decimal numbers

Write a quantity as a fraction or percentage of another

Add, subtract, multiply and divide with fractions and mixed numbers

Check calculations using approximation, estimation or inverse operations
Algebra:

Simplify and manipulate expressions by collecting like terms

Simplify and manipulate expressions by multiplying a single term over a bracket

Substitute numbers into formulae

Solve equations in one unknown

Understand and use lines parallel to the axes, y = x and y = x
Ratio, proportion and rates of change:

Use multiplicative reasoning to interpret percentage change
Geometry and measures:

Calculate the volume and surface area of cubes and cuboids

Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines

Convert between metric and imperial measures
Probability and Statistics topics will be taught in year 8.
Pupils who meet age related expectations will be able to demonstrate:

Fluency in their knowledge and understanding of the mathematical rules relating to each topic area

Be able to reason mathematically by applying their knowledge to justifying answers and solving problems relating to each aspect covered.
In year 8, we build on the content that had been covered in year 7. Students will cover units that fall broadly under Number, Algebra, Shapes and data handling. The emphasis on this year is to consolidate their previous learning in year 7, as well as introducing new concepts like Real Life graphs and Straight Line graphs. By the end of year 8, we expect all students to be confident in solving two step algebraic equations, as well as expand a term over a single bracket and factorising algebraic expressions
Pupils will be taught the following topics:
Number:

Apply the four operations to negative numbers

Convert numbers to and from standard form

Apply the multiplication and division power laws of indices

Convert between terminating decimals and fractions
Algebra:

Factorise an expression by taking out common factors

Change the subject of a formula when two steps are required

Find and use the nth term for a linear sequence

Solve linear equations with unknowns on both sides

Plot and interpret graphs of linear functions
Ratio, proportion and rates of change:

Find a relevant multiplier when solving problems involving proportion

Solve problems involving percentage change, including original value problems
Geometry and measures:

Apply the formulae for circumference and area of a circle

Find the volume of prisms
Probability:

Calculate theoretical probabilities for single events
Statistics:

Find the mean, modes, range and mean of both discrete and continuous data and use these to compare at least 2 different sets of data
Pupils who meet age related expectations will be able to demonstrate the following (in relation to each topic):

Fluency in their knowledge and understanding of the mathematical rules relating to each topic area

Be able to reason mathematically by applying their knowledge to justifying answers and solving problems relating to each aspect covered.
This year serves as the bridge between our KS3 and KS4 and so it is an opportunity for students to get themselves ready for their GCSE years. At the end of this academic year, students will sit an exam; the outcome of these assessments in conjunction with their overall attitude towards learning will be used to determine their GCSE maths tier of entry. Students will still have the opportunity in the course of the following academic year to switch tiers. So the overarching objective of our curriculum in year 9 is to reinforce students learning in KS3 as well as starting with preparations for their GCSE’s.
Pupils will be taught the following topics:
Number:

Estimate the powers and roots to any given positive number to include work on surds

Calculate with numbers in standard form and know how to adjust answers accurately

Choose appropriate degrees of accuracy when rounding numbers and understand how these have limits in accuracy

Use inequality notation to specify simple error intervals
Algebra:

Understand and us the concepts of inequalities and identities

Solve linear inequalities

Multiplying out and double brackets and factorising expressions in the form ax^{2} + bx + c

Finding the difference of two squares

Solve simultaneous and quadratic equations algebraically and using a graph

Recognise, sketch and interpret graphs of simple quadratic functions
Geometry and measures:

Geometry of triangle; Pythagoras theorem and trigonometry

Shape constructions, including plans and elevations of 3D shapes

Calculating arc lengths, angles and areas of sectors of circles
Probability:

Listing outcomes using tree diagrams

Understand how experimental probability tends towards theoretical probability with an increased sample size

Calculate the probability of independent and dependent events

Straight line graphs finding the equations of lines through coordinates and finding the gradient
Statistics:

Interpret and construct tables, charts and diagrams

Scatter graphs, correlation and suing lines of best fit to make predictions
Pupils who meet age related expectations will be able to demonstrate the following (in relation to each topic):

Fluency in their knowledge and understanding of the mathematical rules relating to each topic area

Be able to reason mathematically by applying their knowledge to justifying answers and solving problems relating to each aspect covered.
Our aim and objective is to teach all our year 10 and 11 students the GCSE syllabus to develop their knowledge, confidence and competence of the curriculum. All students will be taught the core aspects of the curriculum while Higher pupils content will extend to areas that will support their further learning at KS5 if the wish to study A’ level mathematics. Higher tier students will follow the Edexcel GCSE specification and the foundation tier students will be taught in line with the OCR GCSE specification.
Pupils will be taught the following topics:
Number:

Estimate the powers and roots to any given positive number to include work on surds

Calculate with numbers in standard form and know how to adjust answers accurately

change recurring decimals into their corresponding fractions and vice versa

Choose appropriate degrees of accuracy when rounding numbers and understand how these have limits in accuracy

Use inequality notation to specify simple error intervals

calculate exactly with fractions, surds and multiples of π: simplify surd expressions involving squares and rationalise denominators
Algebra:

Understand and us the concepts of inequalities and identities

Solve linear inequalities

Multiplying out and double brackets and factorising expressions in the form ax2+ bx + c

Finding the difference of two squares

Solve simultaneous and quadratic equations algebraically and using a graph

Recognise, sketch and interpret graphs of simple quadratic functions

interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’.

identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square

recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/ x with x ≠ 0, exponential functions y= kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sinx, y = cosx and y = tanx for angles of any size

sketch translations and reflections of a given function
Geometry and measures:

Geometry of triangle; Pythagoras theorem and trigonometry

Shape constructions, including plans and elevations of 3D shapes

Calculating arc lengths, angles and areas of sectors of circles

describe the changes and invariance achieved by combinations of rotations, reflections and translations

identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

describe translations as 2D vectors

apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs
Probability:

Listing outcomes using tree diagrams

Understand how experimental probability tends towards theoretical probability with an increased sample size

Calculate the probability of independent and dependent events

Straight line graphs finding the equations of lines through coordinates and finding the gradient
Ratio, proportion and rates of change:

use ratio notation, including reduction to simplest form

divide a given quantity into two parts in a given part: part or part: whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

express a multiplicative relationship between two quantities as a ratio or a fraction

understand and use proportion as equality of ratios 8. relate ratios to fractions and to linear functions

interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.
Statistics:

Interpret and construct tables, charts and diagrams

Scatter graphs, correlation and using lines of best fit to make predictions

construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use
Pupils who meet age related expectations will be able to demonstrate the following (in relation to each topic):

develop fluent knowledge, skills and understanding of mathematical methods and concepts

acquire, select and apply mathematical techniques to solve problems

reason mathematically, make deductions and inferences and draw conclusions

comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.