Term

What are we learning


1

Decimal Manipulation
Estimation and Limits of Accuracy
Related Calculations
HCF and LCM of Large Numbers
Fraction Calculations

 Adding, subtracting, multiplying and dividing integers and decimals.
 Manipulation of Decimals e.g. 2.54 ÷ 4, using one calculation to perform another, ordering decimals (including use of inequality symbols).
 Calculations involving money and correct use of units.
 Order of operations (BIDMAS): use conventional notation for priority of operations, including brackets, powers, roots and reciprocals.
 Rounding number to the nearest 10, 100, 1000, and to a given number of decimal places
 Rounding to significant figures
 Estimate answers to one or two step calculations
 Apply sensible rounding depending on the calculation
 Recognise and use relationships between operations
 Prime numbers, prime factor decomposition, LCM, HCF (of large numbers)
 Add and subtract fractions and mixed numbers with different denominators
 Multiply and divide fractions and mixed numbers. Simplify calculations by cancelling first
 Fraction of an amount
 Identify and work with fractions in ratio problems
 Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
 Find the reciprocal of an integer, decimal or fraction

2

Algebraic Manipulation
Index Laws
Expanding and Factorising
Expression and Substitution

 Collect like terms
 Multiply together two simple algebraic expressions, e.g. 2a × 3b
 Simplify expressions by cancelling, e.g. = 2x
 Add and subtract fractions with an algebraic numerator including with powers
 Multiply, divide and simplify algebraic fractions including with powers
 Simple laws of indices
 Use index notation when multiplying or dividing algebraic terms
 Use index notation for integer powers of 10, including negative powers
 Simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, negative powers and powers of a power
 Understand the term reciprocal
 Expand single brackets
 Factorise  single brackets
 Expanding double brackets
 Factorising quadratics of the form x2 + bx + c
 Difference of two squares
 Use algebra to show expressions are equivalent
 Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

3

Percentages with a Calculator
Proportion
Probability

 Percentage of an amount (including of a measurement) with and without a calculator
 Percentage increase and decrease
 Finding the original amount (reverse percentage) with and without a calculator
 Work with percentages greater than 100%
 Compare two quantities using percentages
 Express one quantity as a percentage of another
 Use percentages in reallife situations e.g. price after VAT, value of profit or loss, simple interest, income tax
 Best buy
 Recipes
 Currency
 Unitary method
 Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
 Solve problems involving direct and inverse proportion, including graphical and algebraic representations
 Interpret equations and graphs that describe direct and inverse proportion
 Conversion graphs
 Apply systematic listing strategies
 Describe probability using the probability scale, tables and frequency trees
 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
 Calculate expected outcomes
 Mutually exclusive events sum to one
 Experimental and theoretical probability
 Venn diagrams and appropriate notation
 Possibility spaces/sample spaces
 Find a missing probability from a list or table including algebraic terms
 Unbiased samples and effects of increasing sample size
 Sets and combinations of sets using Venn diagrams

4

Linear Equations
Linear Inequalities
Sequences
Pythagoras

 Solve linear equations in one unknown algebraically, with unknowns on one side e.g. 5x  7 = 18
 Solve linear equations which contain brackets, fractional coefficients, negative signs, negative solutions
 Substitute into a formula, and solve the resulting equation
 Solve linear equations in one unknown algebraically, with unknowns on both sides
 Form and solve algebraic equations and interpret the solution
 Solving linear equations that require algebraic fraction manipulation
 Solve linear inequalities in one variable e.g. 5x  7 > 18
 Represent and interpret solution sets to inequalities on a number line
 Solve two inequalities in x, find the solution sets and compare them to see which value of x satisfies both
 Fibonacci sequences and simple geometric progressions (r^n where n is an integer, and r is a rational number > 0)
 Continue a geometric progression and find the termtoterm rule, including negatives, fraction and decimal terms
 Use finite/infinite and ascending/descending to describe sequences
 Recognise and use simple geometric progressions
 Calculate with roots, and with integer indices
 Pythagoras’ theorem
 Leave answers in surd form
 Given 3 sides of a triangle, justify if it is rightangled or not
 Apply Pythagoras’ Theorem with a triangle drawn on a coordinate grid
 Calculate the length of a line segment AB given pairs of points

5

Interior and Exterior Angles
Parallel Lines
Basic Vectors
Basic Transformations

 Interior and exterior angles, angle sums
 Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices
 Explain why some polygons fit together and others do not
 Alternate and corresponding angles on parallel lines
 Solve missing angle problems, giving reasons for answers
 Apply properties of angles in parallel lines to an algebraic context
 Describe translations as 2D vectors
 Translate a given shape by a vector
 Addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
 Be able to represent information graphically given column vectors
 Identify two column vectors which are parallel
 Reflection and rotation symmetry
 Transformations  rotation, reflection, translation, enlargement (with a positive scale factor)
 Identify the equation of a line of symmetry
 Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides, simple integer scale factors, or simple fractions

6

Plans and Elevations
Circles
Surface Area

 Identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
 Draw sketches of 3D solids
 Interpret Plans and elevations of 3D shapes
 Construct plans and elevations of 3D shapes
 Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid
 Circle definitions  centre, radius, chord, diameter, circumference
 Use Circumference of a circle = 2πr = πd and area of a circle = πr2
 Circle definitions including tangent, arc, sector and segment
 Arc lengths, angles and areas of sectors of circles
 Calculate exactly with multiples of π
 Use rearranging to calculate missing lengths given the area or circumference
 Estimate surface areas by rounding measurements to 1 significant figure
 Sketch nets of cuboids and prisms
 Surface area of spheres, pyramids, cones and composite solids (hemispheres, frustums)

Links

https://corbettmaths.com/contents/ https://www.mathsgenie.co.uk/
