# Mathematics

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The aim of our maths curriculum is to foster pupils’ interest, enjoyment, and curiosity.  We want every pupil to understand the significance of maths so that they can develop the skills and confidence to apply their knowledge across a range of contexts.

Through our curriculum, 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.

Curriculum Overview

Year 6

 Content Skills Number: Place Value and the Four Operations  Know the place values headings up to ten million. Read, write and order numbers up to ten million.  Use formal written methods for addition and subtraction of whole numbers with four or more digits.  Use a formal written division method to divide numbers up to four digits by a two digit number. Number: Factors, Multiples and Primes  Know that a prime number is an integer with exactly two factors.  Know the first 12 square numbers. Identify prime numbers up to 100. Number: Application Understand and use the order of operations including brackets. Geometry: Position and Direction  Know the conventions for a 2D coordinate grid. Use coordinates in all four quadrants. Number: Fractions (Manipulating and Calculating)  Know, and quickly recall, multiplication (and related division facts) up to 12 x 12.  Know the difference between proper fractions, improper fractions and mixed numbers. Write a fraction in its lowest terms by cancelling common factors.  Add and subtract fractions and mixed numbers with different denominators.  Multiply pairs of fractions in simple cases. Number: Decimals and Percentages  Know percentage and decimal equivalents for fractions with a denominator of 2, 3, 4, 5, 8 and 10.  Know that percentage means ‘out of 100’. Multiply and divide numbers with up to three decimal places by 10, 100, and 1000.  Find percentages of quantities. Measurement: Converting Units  Know adjacent measurement facts involving metric units of length, mass, capacity and time. Convert between units of metric measure for length, mass, capacity and time e.g. cm to m, kg to g, hours to mins. Measurement: Perimeter, Area and Volume  Know that the area of a triangle =  × base × height.  Know that the area of a parallelogram = base × perpendicular height.  Know that volume is measured in cubes.  Know that volume of cuboid = length × width × height. Calculate the area and perimeter of rectangles, triangles and parallelograms.  Calculate the volume of cubes and cuboids. Geometry: Properties of 2D and 3D Shapes  Know that vertically opposite angles are equal. Know the angle facts for angles in a triangle, at a point and on a straight line.  Know the names of the special triangles and quadrilaterals.  Know the names of common 3D shapes. Solve missing angle problems involving triangles, quadrilaterals, angles at a point and angles on a straight line.  Classify 3D shapes including cylinders, cones, spheres, prisms and pyramids. Statistics  Know the names of parts of a circle.  Know that the diameter of a circle is twice the radius.  Know that mean = sum of data ÷ number of pieces of data. Calculate and interpret the mean as an average of a set of discrete data. Number: Ratio  Know that the : symbol is used to represent a ratio. Use simple ratios to compare quantities. Number: Algebra  Know that a letter can be used to represent a variable. Use simple formulae expressed in words.

Year 7

 Content Skills Algebraic Thinking: Sequences  Know the Fibonacci sequence. Recognise the difference between a linear and non-linear sequence and describe the term-to-term rule using mathematical language. Algebraic Thinking: Understand and Use Notation  Know basic algebraic notation. Use basic algebraic notation.  Simplify and manipulate simple expressions by collecting like terms.  Substitute positive numbers into expressions. Algebraic Thinking: Equality and Equivalence  Know the meaning of the equivalent (≡) symbol. Solve simple one-step linear equations in one unknown Place Value and Ordering: Place Value  Know the symbols =, ≠,< ,>, ≤, ≥.  Know how to calculate the range of a set of discrete data.  Know how to work out measures of central tendency (the median and mode). Order a set of integers and decimals up to one billion.  Find the median of a set of discrete data.  Find the mode of a set of discrete data.  Find the range of a set of discrete data. Place Value and Ordering: Fraction, Decimal and Percentage Equivalence  Know that a percentage can be greater than 100%.  Know how to enter fractions and mixed numbers into a calculator. Convert fluently between simple fractions, decimals and percentages with a denominator of 2, 3, 4, 5, 8 and 10 without a calculator.  Convert fluently between simple fractions, decimals and percentages with a calculator. Application of Number: Addition and Subtraction  Know when to use a mental strategy, formal written strategy or a calculator. Apply addition and subtraction to decimal numbers. Application of Number: Multiplication and Division  Know that the area of a rectangle = l x w.  Know that the area of a triangle =  bh  Know that the area of a parallelogram = 𝒃𝒉.  Know, and quickly recall, multiplication (and related division facts) up to 12 x 12.  Know the order of operations including brackets and indices.  Know how to work out measures of central tendency (mean). Apply multiplication and division to decimal numbers with up to two decimal places.  Use mental calculation strategies for calculations involving the four operations.  Understand and use the order of operations (including brackets and indices) with positive numbers. Directed Number: Operations and Equations with Directed Number  Know how to enter negative numbers into a calculator. Apply the four operations when working with directed numbers.  Understand and use the order of operations (including brackets and indices) with directed number. Fractional Thinking: Addition and Subtraction of Fractions  Know how to convert between improper fractions and mixed numbers and vice versa. Add and subtract any combination of fractions and mixed numbers. Lines and Angles: Constructing, Measuring and Using Geometric Notation  Know the names and properties of the special triangles and quadrilaterals. Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines.

Year 8

 Content Skills Reasoning with Number: Prime Numbers and Proof  Know, and quickly recall, multiplication (and related division facts) up to 12 x 12.  Know how to write a number as a product of its prime factors. Identify the Highest Common Factor and the Lowest Common Multiple for pairs of numbers (by listing and prime factor decomposition with the use of Venn diagrams). Lines and Angles: Developing Geometric Reasoning  Know the names and properties of the special triangles and quadrilaterals.  Know the angle sum of a quadrilateral is 360 degrees. Solve missing angle problems involving triangles and quadrilaterals. Reasoning with Number: Sets and Probability  Know that probability is measured on a 0- 1 scale.  Know that the sum of all probabilities for a single event is 1. Calculate theoretical probabilities for single events.  List all outcomes for single events systematically.  List all outcomes for combined events systematically. Proportional Reasoning: Ratio and Scale  Know how ratios and fractions are related. Understand the connection between ratio and proportion.  Share a number/amount in a given ratio. Proportional Reasoning: Multiplicative Change Solve problems involving direct proportion Proportional Reasoning: Multiplying and Dividing Fractions  Know how to enter fractions into a calculator. Multiply and divide any combination of fractions and mixed numbers. Developing Geometry: Area of Trapezia and Circles  Know that area of a trapezium =  Know that circumference = 2πr = πd.  Know that area of a circle = πr². Apply the formula for the area of a trapezium.  Apply the formulae for the circumference and area of a circle. Representations: Representing and Analysing Data  Know the difference between discrete and continuous data. Plot and interpret scatter graphs using the concept of correlation.  Represent grouped and ungrouped data in frequency tables. Algebraic Techniques: Brackets and Equations Manipulate algebraic expressions by expanding a single set of brackets.  Factorise an expression by taking out common factors.  Solve two-step equations with an unknown on one side. Algebraic Techniques: Sequences  Know how to find the missing number in a sequence. Find the nth term of a linear sequence. Developing Number: Fractions, Decimals and Percentages  Know how to convert between fractions, decimals and percentages. Solve problems involving percentage change, using a multiplier. Developing Geometry: Angles in Parallel Lines and Polygons  Know how to identify alternate angles.  Know how to identify corresponding angles.  Know how to identify co-interior angles.  Know how to find the angle sum of any polygon. Solve problems involving angles formed between parallel lines. Developing Geometry: Line Symmetry and Reflection  Know how to write a 2D vector. Describe a translation using a 2D vector.  Identify and plot names of lines parallel to the x and y axes.

We teach and assess our curriculum through our curriculum related expectations:

 Year 6 Year 7 Year 8 I can use formal written methods for addition and subtraction of whole numbers. I can recognise the difference between a linear and non-linear sequence and describe the term-to-term rule using mathematical language. I can identify the Highest Common Factor and the Lowest Common Multiple for pairs of numbers. I can use a formal written division method to divide numbers up to four digits by a two-digit number. I can understand and use algebraic notation. I can solve missing angle problems involving triangles and quadrilaterals. I can use coordinates in all 4 quadrants. I can simplify and manipulate expressions by collecting like terms. I can calculate the theoretical probabilities for single events. I can write a fraction in its lowest terms by cancelling common factors. I can convert fluently between simple fractions, decimals and percentages for fractions with a denominator of 2, 3, 4, 5, 8 and 10. I can share a number in a given ratio. I can add and subtract fractions and with different denominators. I can apply addition and subtraction to decimal numbers with up to three decimal places. I can multiply and divide a proper fraction by a proper fraction using an efficient method. I can multiply pairs of fractions in simple cases. I can apply multiplication and division to decimal numbers with up to two decimal places. I can use the formulae for the area and circumference of circles. I can multiply and divide numbers with up to 3 decimal places by 10, 100, 1000. I can use mental calculation strategies for calculations involving the four operations. I can plot and interpret a scatter graph using the concept of correlation. I can find percentages of quantities. I can understand and use the order of operations, including brackets, with positive numbers. I can manipulate algebraic expressions by multiplying a single term over a bracket. I can convert between adjacent units of metric measure e.g. cm to m, kg to g etc I can apply some of the four operations when working with negative numbers. I can solve simple two-step linear equations in one unknown, with whole number, algebraically. I can calculate the area and perimeter of rectangles, triangles and parallelograms. I can add and subtract any combination of fractions and mixed numbers. I can find and use the nth term of a linear sequence. I can calculate the volume of cubes and cuboids. I can understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines. I can solve problems involving percentage change using a multiplier. I can solve missing angle problems involving triangles, quadrilaterals, angles at a point and angles on a straight line. I can solve missing angle problems involving alternate and corresponding angles. I can calculate and interpret the mean as an average of a set of discrete data. I can describe a translation using a 2D vector. I can use simple ratios to compare quantities. I can use simple formulae expressed in words.

• Turing Tumbles Club
• UKMT Mathematical Challenges (Year 7 & 8)
• Maths Clinic
• Numeracy Ninjas competitions
• TT Rockstars competitions