# Mathematics

## 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 well-designed 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.

**Special Educational Needs Disability (SEND) / Pupil Premium / Higher Attainers**

All children will have Quality First Teaching. Any children with identified SEND or in receipt of pupil premium funding will have reasonable adjustments made that are additional to or different from their peers in order to support them to access the curriculum. All reasonable adjustments made are based around the individual and their needs.

As well as this, our school offers a demanding and varied curriculum, providing children with a range of opportunities in order for them to reach their full potential and consistently achieve highly from their starting points.

### Year Group Content

## Reception

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

Maths is taught through adult-led 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 child-initiated 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.

## Year 1

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

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)**

- Part-whole model
- Fact families
- Number bonds within 10
- Number bonds to 10
- Addition introduction
- Subtraction introduction

**1.3 Geometry (Shape)**

- Recognise and name 3-D shapes
- Recognise and name 2-D shapes
- Patterns with 2-D and 3-D 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

## Year 2

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

Pupils will be taught the following topics:

**2.1 Place Value**

- Representing numbers to 100
- Part-whole 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 2-digit and 1-digit numbers
- Adding and subtracting a 2-digit number and a 2-digit 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 times-table
- 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 2-D shapes
- Lines of symmetry
- Face on 3-D shapes
- Vertices on 3-D shapes
- Make patterns with 2-D and 3-D shapes

*Builds on 1.3*

**2.8 Fractions**

- Equal parts
- A third
- Unit fractions
- Non-unit 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*

## Year 3

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

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 3-digit and 1-digit numbers (not crossing and crossing 10)
- Add and subtract 3-digit and 2-digit numbers (not crossing and crossing 100)
- Add and subtract 100s
- Add and subtract 3-digit and 2-digit numbers (exchanging and no exchange)
- Estimating answers

**3.3 Multiplication and division**

- Multiple and divide by 3, 4 and 8
- 3,4 and 8 times-tables

**3.4 Multiplication and division**

- Multiply and divide 2-digit and 1-digit 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
- 24-hour 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

## Year 4

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

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 4-digit and 4-digit numbers (exchanges and no exchanges)
- Adding 4-digit and 4-digit 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 time-tables and division facts

**4.5 Multiplication and division**

- 11 and 12 times-table
- Multiply 3 numbers
- Efficient multiplication
- Multiplication written methods
- Multiply 2-digit by 1-digit
- Multiply 3-digits by 1-digit
- Divide 2-digit by 1-digit
- Divide 2-digits by 1-digit
- Divide 3-digits by 1-digit

**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 2-digits 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

## Year 5

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

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 4-digits (formal methods)
- Subtract whole numbers with more than 4-digits (formal methods)
- Round to estimate
- Inverse operations

**5.3 Statistics**

- Line graphs
- Tables
- Two-way 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 4-digits by 1-digit
- Multiply 2, 3 and 4-digits by 2-digits
- Divide 4-digits by 1-digit

**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

## Year 6

Please see our long-term plan below, including curriculum objectives:

### Mathematics

Mathematics Long Term Plans (Primary)Updated: 13/02/2024 80 KB

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 two-step 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

## Year 7

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.

## Year 8

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.

## Year 9

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 over-arching 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.

## KS4

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.