**HALF TERM 1**

**Place Value and Ordering **

- Understand and use place value for decimals, measures and integers of any size.
- Working out and using number lines (fractional sequences)
- Comparing and ordering positive and negative integers, use the number line as a model of ordering of the real numbers; use symbols =, ≠, <, >, ≤, ≥
- Describe and continue sequences in diagram and number forms, both linear and non linear.
- Using one calculation to find the answer to another
- Rounding and measures to an appropriate degree of accuracy
- Applying concepts of ordering numbers and place value to the range and the median.
- Addition and Subtraction
- Use formal methods of addition with positive integers and decimals
- Recognise and use relationships between addition and subtraction including inverse operations.
- Solve problems in the context of perimeter, money and frequency trees and tables
- Choosing when to use mental, written or calculator methods

**Multiplication and Division**

- Multiplying by 10, 100, 1000; Unit conversions
- Formal Methods of multiplication and division of integers and decimals
- Understand the order of operations.
- Calculate and solve problems involving areas in rectangles, triangles and parallelograms.
- Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x ≤b
- Finding the mean.
- Finding simple fractions and percentage of amounts.

**HALF TERM 2**

**Negative Numbers**

- Ordering directed numbers with and without a context
- Revisit four operations to include directed numbers.
- Using a calculator with directed numbers.
- Factors, Multiples, Primes and Powers
- Understanding concepts and vocabulary of prime numbers, factors (or divisors), common factors, highest common factors (HCF) and lowest common multiple (LCM).
- Use integer powers and associated real roots (square, cube and higher).
- Recognising powers of 2, 3, 4, 5 and distinguishing between exact representations and their decimal approximations.
- Find the Prime factor decomposition of a number.
- Find the HCF and LCM of 2 or more numbers - use venn diagrams for larger numbers if students are ready to learn this.
- Solve simple problems involving the HCF and LCM

**HALF TERM 3**

**Fractions, Decimals and Percentages**

- Represent a fraction, decimal and percentage on a variety of diagrams and number lines.
- To understand equivalence and to be able to change between fractions, decimals and percentages for multiples of tenths and quarters.
- To identify and use equivalent fractions as well as simplify a given fraction.
- To be able to convert between any fraction (including mixed numbers and improper fractions), decimal and percentage and to recognise a fraction as a divisor as part of these conversion.
- Expressing one quantity as a fraction or percentage of another.
- Compare and order fractions, percentages and decimals (including using symbols =, ≠, <, >, ≤, ≥ )
- Define percentages as ""number of parts per hundred""
- Compare two quantities using percentage and work with percentages greater than 100%, eg Claire got 16 out of 20 on a test, Simon got 21 out of 25 on a test. Who got the better score?
- Interpret fractions/percentages as operators, with or without a calculator
- Fractional sequences

**HALF TERM 4**

**Notation, Simplifying, Dividing a Quantity**

- Use ratio notation and understand the link between ratio and fractions.
- Represent ratio using diagrams (including the bar model).
- Compare ratios.
- Reduce ratios to their simplest form.
- Dividing a given quantity in to two or more parts.
- Calculating the whole part of other parts having been given information about one part.
- Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction.
- Use ratio to convert between units.
- Use the unitary method to solve proportion problems.
- Work out which product is better value.
- Solve ratio and proportion problems (conversion, comparison, scaling, mixing, concentration).

**HALF TERM 5**

**Notation, Simplifying, Substitution, Expanding Brackets**

- Introduction to algebra:
- Understanding a letter represents a variable.
- Understand the difference between expression, equation, formula, term, function and identity
- Form expressions from situations described in words.
- Pupils should be taught to:
- Use and interpret algebraic notation, including:
- ab in place of a x b
- 3y in place of y + y + y and 3 x y
- a² in place of a x a, a³ in place of a x a x a; a²b in place of a x a x b
- b/a in place of b ÷ a
- Coefficients written as fractions rather than decimals.=
- Simplify and manipulate algebraic expressions to maintain equivalence by;
- Collecting like terms (Involving sums, products and powers)
- Multiplying a single term over a bracket (link back to directed numbers for mutiplying by a negative).
- Expand and simplfy 2 single brakets.
- Using single function machines and series of two function machines with numbers, bar models and letters
- Forming and substituting into expression, including generating sequences.
- Substitute a numerical values in to formulae and expressions, including scientific formulae (including all prior knowledge of fractions, decimals and negatives)

**HALF TERM 6**

**Solving Linear Equations (unknown on one side), Inequalities**

- Use algebraic methods to solve simple linear equations in one variable where the unknown appears on one side of the equation.
- Include simple equations with brackets.
- Include simple fractional equations.
- Understand and use the concepts, vocabulary and notation of inequalities.
- Represent the solution set to an inequality on a number line and vice versa.
- Find the integer solutions of an inequality.
- Solve linear inequalities in one variable.

**HALF TERM 1**

**Fractions**

- Adding and subtracting any fraction:
- Fractions with the same denominator
- Fractions with a denominator that is a multiple of the other (eg quarters/eights, thirds/sixths)
- Fractions with different denominators
- Multiply and divide proper, improper fractions and mixed numbers (both positive and negative)
- Find a fraction of an amount.
- Finding the whole amount given a fraction of the amount
- Find a fractional increase and decrease

**HALF TERM 2**

**Percentages**

- Interpret percentages and percentage changes as fractions or a decimals.
- Work with percentages greater than 100% (Recapping on prior knowledge from year 7).
- Solve problems involving percentage change including:
- Calculating percentage increase/decrease (using non calculator and calculator methods).
- Original value problems using reverse percentage methods
- Simple interest in financial mathematics.
- VAT (Value Added Tax)

**HALF TERM 3**

**Factorise, Solving linear equations**

- Simplify and manipulate algebraic expressions to maintain equivalence by taking out common factors (explore the language of factorising linking back to prior knowledge of HCF, with discussions based around HCF being a number or a variable)
- Expanding products of two or more binomials.
- Rearrange formulae to change the subject, where the subject appears once.
- Use algebraic methods to solve 2 step equations including x on both sides (including all forms that require rearrangement) - including equations with fractions and brackets.
- Area and Perimeter, 2D Shapes, Compound Shapes
- Derive and apply formulae to calculate the area and perimeter of 2D shapes (Rectangles, Parallelograms, Triangles, and Trapezia).
- Calculate the missing length of a shape given the area or perimeter.
- Calculate the area and perimeter of compound shapes, made up of squares, rectangles, triangles and trapezia.
- Solve problems involving area and perimeter of 2D shapes (including lengths, areas an costs).
- Convert between cm² and m².

**HALF TERM 4**

**Circles**

- To be able to recognise key parts of a circle and label.
- To derive and apply formulae to calculate and the area and circumference of a circle.
- To calculate the area of composite shapes involving circles.
- To calculate the radius or diameter of a circle given the area or circumference.
- To solve problems involving the area or circumference of a circle; Including part of a circle (semicircle, quarter of a circle - this is to act as an early introduction to sectors of a circle and so allow students to make this link and refer to the semi-circle and quarters of a circle as a sector).
- Including leaving your answer in terms of ∏

**HALF TERM 5**

**3D Shapes **

- Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D shapes.
- To recognise and be able to draw the Plans and Elevations of a 3D shape.
- Derive and apply formulae to solve problems involving the surface area of 3D shapes (cuboids and prisms - not cylinders).
- Derive and apply formulae to calculate and solve problems involving the volume of 3D shapes and prisms (including cylinders - not pyramids, cones or spheres)
- To convert between cm³ and m³
- Know the fact that 1 litre = 1000cm³

**Lines and Angles **

- Describe sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons and other polygons that are reflectively and rotationally symmetric .
- Derive and illustrate properties of triangles, quadrilaterals (square, rectangle parallelogram, trapezia, kite, rhombus), circles and other plane figures (for example, equal lengths and angles), using appropriate language and technologies.
- Use a protractor to measure and draw angles.
- Apply the properties of angles at a point, angles at a point on a straight line and vertically opposite angles.
- Understand and use alternate and corresponding angles on parallel lines.
- Find missing angles using corresponding and alternate angles.
- Derive and prove angles sum of a triangle and quadrilateral.
- Derive and use the sum of angles in a triangle and a quadrilateral to solve problems.
- Derive and use the sum of angles in a triangle and use it to deduce angle sum in any polygon, and to derive properties of a regular polygons. (This is a great opportunity to allow students to explore how to find angles in a polygon, do not direct them to split the polygon in to (n-2) triangles, allow them to come up with methods and concepts for themselves).
- Calculate the interior angle of a regular polygon.
- Calculate the exterior angle of a regular polygon.

**HALF TERM 6**

**Statistics 1**

- Understand the data handling cycle.
- Understand the different types of data.
- Collect, organise and interpret data:
- Tally Charts
- Frequency Tables.
- Two Way Tables (include worded versions)
- Stem and Leaf diagrams, including back to back stem and leaf diagrams.
- Pie Charts
- Consider outliers.
- Draw and interpret bar charts, pictograms and line graphs.

**HALF TERM 1**

**Higher Tier**

- Basic angle facts (triangles, lines, around a point, vertically opposite, angles in quadrilaterals)
- Measuring and drawing angles
- Angles on parallel lines
- Angles in polygons
- Exterior angles of polygons
- Interior angles of polygons
- Tessellation using polygons

**Lower Tier**

- Basic angle facts (triangles, lines, around a point, vertically opposite, angles in quadrilaterals)
- Measuring and drawing angles
- Angles on parallel lines
- Angles in polygons

**HALF TERM 2**

**Higher Tier**

- Plotting straight line graphs, finding the equation of a line from the graph
- Finding the equation of a line from two coordinates
- Finding the rule for the nth term (sequences)
- Plotting quadratic equations, solving quadratic functions graphically
- Parallel and perpendicular lines
- Finding approximate solutions using line graphs
- Direct and Inverse proportion

**Lower Tier**

- Plotting straight line graphs, finding the equation of a line from the graph
- Finding the equation of a line from two coordinates
- Finding the rule for the nth term (sequences)
- Plotting quadratic equations, solving quadratic functions graphically

**HALF TERM 3**

**Higher Tier**

- Mean, median, mode and range
- Different types of data
- Comparing mean and range of data
- Grouped data, estimating the mean, modal class interval
- Sampling
- Bias

**Lower Tier**

- Mean, median, mode and range
- Different types of data
- Comparing mean and range of data
- Grouped data, estimating the mean, modal class interval
- Sampling
- Bias

**HALF TERM 4**

**Higher Tier**

- Mean, median, mode and range
- Different types of data
- Comparing mean and range of data
- Grouped data, estimating the mean, modal class interval
- Sampling
- Bias

**Lower Tier**

- Mean, median, mode and range
- Different types of data
- Comparing mean and range of data
- Grouped data, estimating the mean, modal class interval
- Sampling
- Bias

**HALF TERM 5**

**Higher Tier**

- Transformations
- Enlargement
- Translations
- Reflections
- Rotation
- Volume and surface area of 3D (not prism) shapes
- Congruence and smiliarity
- Scale factors

**Lower Tier**

- Transformations
- Enlargement
- Translations
- Reflections
- Rotation
- Volume and surface area of 3D (not prism) shapes

**HALF TERM 6**

**Higher Tier**

- Pythagoras
- Trigonometry

**Lower Tier**

- Scale factors, drawing diagrams to scale
- Scale on maps and diagrams
- Congruent triangles (SSS,ASA,SAS,RHS triangles)
- Bisecting lines and angles
- Loci

**HALF TERM 1**

**Higher Tier**

- Four operations with integers
- Directed numbers
- Estimations
- Factors multiples and primes
- Index laws
- HCF/LCM
- Sequences (nth term)
- Standard form
- Inequalities

**Lower Tier**

- Four operations with integers
- Directed numbers
- Estimations
- Factors multiples and primes
- Index laws
- HCF/LCM
- Sequences (nth term)
- Standard form
- Inequalities

**HALF TERM 2**

**Higher Tier**

- Inequalities
- Simultaneous equations
- Recap of linear graphs
- Plotting inequalities graphically
- Iterative processes

**Lower Tier**

- Inequalities
- Simultaneous equations

**HALF TERM 3**

**Higher Tier**

- Transformations
- Area and circumference of circles
- Labelling circles
- area and perimeter of sectors and arc lengths
- Vector arithmetic
- Adding and subtracting vectors
- Angles and circle theorems

**Lower Tier**

- Area and circumference of circles
- Labelling circles
- area and perimeter of sectors and arc lengths
- Vector arithmetic
- Adding and subtracting vectors
- multiplying vectors

**HALF TERM 4**

**Higher Tier**

- Proportionality
- Fractions, decimals and percentages
- increase and decrease of percentages
- Compound interest
- Speed/distance/time
- Pressure and density
- Probability of independent events
- Probability tree diagrams

**Lower Tier**

- Fractions, decimals and percentages
- increase and decrease of percentages
- Compound interest
- Speed/distance/time
- Pressure and density
- Probability of independent events
- Probability tree diagrams

**HALF TERM 5**

**Higher Tier**

- Limitations of data
- Time series graphs
- Scatter graphs
- Frequency polygons
- Comparing distribution
- Frequency density
- Histograms

**Lower Tier**

- Limitations of data
- Time series graphs
- Scatter graphs
- Frequency polygons
- Comparing distribution

**HALF TERM 6**

**Higher Tier**

- Algebraic fractions
- Further Pythagoras and trigonometry

**Lower Tier**

- Congruence and similarity
- Pythagoras

**HALF TERM 1**

**Higher Tier**

- Plotting coordinates
- Plotting straight line graphs
- Finding the equation of a line given the graph
- Finding the equation of a line from two coordinates
- Plotting and solving quadratic equations
- Real life graphs (exchange rates etc)
- Pythagoras
- Trigonometry

**Lower Tier**

- Plotting coordinates
- Plotting straight line graphs
- Finding the equation of a line given the graph
- Finding the equation of a line from two coordinates
- Plotting and solving quadratic equations
- Real life graphs (exchange rates etc)

**HALF TERM 2**

**Higher Tier**

- Trig graphs
- Transformations of graphs
- Expanding and factorising linear functions
- Changing the subject of a formula
- Functions

**Lower Tier**

- Expanding and factorising linear and quadratic equations
- Solving inequalities
- Changing the subject of a formula
- Functions

**HALF TERM 3**

**Higher Tier**

- Multiplicative reasoning
- Geometric reasoning
- Algebraic reasoning
- Transformations
- Constructions
- Volume and Surface area of 3D shapes

**Lower Tier**

- Multiplicative reasoning
- Geometric reasoning
- Algebraic reasoning
- Transformations
- Constructions

**HALF TERM 4**

**Higher Tier**

- Ratio and Fractions

**Lower Tier**

- Organising and listing (venn diagrams, lists)
- Plans and elevations
- Congruence and similarity

**HALF TERM 5**

**Higher Tier**

- Revision

**Lower Tier**

- Revision

**HALF TERM 6**

**Higher Tier**

- Revision

**Lower Tier**

- Revision