Year 8 maths marks an exciting shift in your learning. You’ll revisit key ideas from Year 7 but go further—tackling more abstract concepts, applying knowledge to unfamiliar problems, and developing the independence expected in Key Stage 3. This year is all about deepening your confidence, sharpening your problem-solving skills, and preparing for the rigour of Year 9 and beyond.
Percentages and Fractions
Developing
Be able to convert mixed numbers to improper fractions and vice versa
Know and recognise equivalence of simple fractions, decimals and percentages (1/2, 1/4, 1/10, 3/4)
Know and recognise proportions of a whole as fractions, decimals and percentages
Be able to calculate a fraction of an amount
Be able to find equivalent fractions
Be able to simplify fractions by cancelling down
Be able to calculate a percentage of an amount
Secure
To be able to use all 4 operations with fractions
To be able to use all 4 operations with mixed numbers
Be able to calculate one quantity as a percentage of another
Be able to increase and decrease by a percentage
Be able to use percentage increase/decrease multipliers
Be able to find percentage change
Mastering (set 1 only)
Be able to work with simple and/or compound interest
Be able to solve reverse percentage problems
Ratio, Proportion and Scaling
Developing
Understand how to write ratios in their simplest forms
Be able to divide a quantity into the ratio of two parts
Be able to divide a quantity in a ratio
Be able to compare two ratios
Secure
Be able to find a distance from a map or drawing with a given scale
Understand how to Express a scale given in different units as a ratio in its simplest form
Use unit cost and unit weight to find which product is cheaper
Mastering (set 1 only)
Recognise and solve problems, using direct or inverse proportion
Complete calculations from a given ratio and partial information
Subject Content
R2 use scale factors, scale diagrams and maps
R4 use ratio notation, including reduction to simplest form
R5 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
R6 understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
R7 relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
R9 Solve problems involving direct and inverse proportion, including graphical and algebraic
Expansion & Factorisation
Developing
Be able to simplify linear expressions by collecting like terms.
Be able to expand a single bracket
Be able to multiply two terms with numbers and letters
Secure
Be able to factorise an expression into a single bracket
Be able to expand and simplify an expression e.g. 5(3x + 2) - 2(x + 4)
Be able to expand a set of double brackets
Mastering (Set 1 only)
Be able to factorise a quadratic expression with x^2 coefficient = 1
Be able to recognise the difference of two squares
Be able to factorise and solve a quadratic equation with x^2 coefficient = 1
Subject Content
A1 use and interpret algebraic notation
A3 understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
A4 simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms, multiplying a single term over a bracket, taking out common factors, expanding products of two or more binomials
A10 interpret mathematical relationships both algebraically and graphically
Forming and solving equations
Developing
Be able to find missing numbers in additions, subtractions, multiplications and divisions
know how to find the missing number in a short equations involving numbers
understand that letters can represent numbers
Be able to solve simple equations using 1 inverse operation
Be able to simplify algebraic expressions by collecting like terms
Be able to solve simple equations
Secure
Be able to solve equations with unknowns on both sides
Be able to solve equations by expanding brackets
Be able to form linear equations
Be able to solve equations involving x squared
Mastering (set 1 only)
Be able to solve equations involving fractions
Be able to solve very basic algebraic fractions
Subject Content
A1 use and interpret algebraic notation
A3 understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
A4 simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms, multiplying a single term over a bracket, taking out common factors, expanding products of two or more binomials
A6 model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
A5 understand and use standard mathematical formulae; rearrange formulae to change the subject
A7 use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
Inequalities
Developing
Know what each inequality symbol means
Be able to solve linear equations including unknowns on both sides
Secure
Know the definition of the word integer
Be able to represent a single inequality on a number line
Be able to represent a combined inequality on a number line
Be able to solve a linear inequality
Mastering (set 1 only)
Be able to solve a combined inequality
Know the effect of dividing/multiplying a negative across an inequality
Subject Content
N2 order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, <, >, <, >
N14 use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x<b
A3 understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
A7 use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
Assessment 1
Angles and Polygons
Developing
to understand half, quarter turn , anticlockwise and clockwise
understand what angle means
understand how many angles there are in a range of shapes (e.g. 3 in a triangle)
Know recognise types of triangles
Know and recognise types of quadrilaterals
Know and recognise types of angles
Secure
Know how to find missing angles in triangles, including right-angled and isosceles triangles
Be able to identify vertically opposite angles
Be able to solve geometrical problems using side and angle properties of a triangle
Be able to identify corresponding, alternate and supplementary angles
Know the formula for the sum of the interior angles of a polygon
Know that the sum of the exterior angles of any polygon is 360°
Be able to find interior and exterior angles of a polygon
Mastering (set 1 only)
Be able to use algebra to solve missing angles of polygons
Subject Content
G5 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
G10 apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
G11 understand the relationship between parallel lines and alternate and corresponding angles
G12 derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and derive properties of regular polygons
Speed & Real Life Graphs
Developing
Be able to draw a set of axes
Be able to recognise coordinates in all 4 quadrants
Secure
Be able to draw and interpret conversion graphs
Be able to plot and interpret graphs of real-life events
Understand converting simple units of measure and time
Be able to calculate Speed, Distance or Time
Mastering
Know how to convert time using a calculator
Subject Content
N12 use standard units of mass, length, time, money and other measures, including with decimal quantities
R9 Solve problems involving direct and inverse proportion, including graphical and algebraic
R10 use compound units such as speed, unit pricing and density to solve problems
A10 interpret mathematical relationships both algebraically and graphically
Pie Charts & Scatter Graphs
Developing
Know how to group data in equal class intervals
Be able to interpret frequency diagrams - including simple pie charts
Secure
Be able to interpret graphs and diagrams, including pie charts
Be able to construct a pie chart by calculating angles
Mastering
Know how to interpret correlation of data using a scatter graph
Know how to draw a line of best fit on a scatter graph
Subject Content
S2 construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
S3 describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs
Distributions
Developing
Be able to represent data in tables
Know how to group data in equal class intervals
Be able to find the mean, median, mode and range
Secure
Be able to calculate the mean from a frequency table
Be able to calculate the mode from a frequency table
Be able to calculate the median from a frequency table
Mastering (set 1 only)
Be able to find the modal class interval from a grouped frequency table
Be able to calculate an estimate of the mean from a grouped frequency table
Subject Content
S1 describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
S2 construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
Transformations
Developing
reflect simple shapes in a mirror line
recognise lines of symmetry
recognise rotational symmetry in shapes
identify all lines of symmetry in 2d shapes
reflect shapes in diagonal mirror lines
rotate shapes through 90 or 180 degrees about a vertex
Secure
Be able to enlarge a shape, given a centre and a positive whole-number scale factor
Know how to find the centre and scale factor of an enlargement from an object and its image
Be able to translate a shape using vectors
Be able to describe and draw a rotation about any point on a coordinate grid
Be able to describe and draw a reflection about x=a or y=b on a coordinate grid
Know that reflections, rotations and translations produce congruent images
Mastering (set 1 only)
Be able to enlarge shapes using a centre and a fractional scale factor
Be able to draw a reflection in the lines y=x and y=-x
Subject Content
G8 identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
G9 identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
Constraction & Loci & Bearings
Developing
Be able to construct a triangle given SSS, ASA, SAS
Secure
To be able to construct perpendicular bisectors
Be able to construct angle bisectors
Be able to measure and draw bearings
Mastering (Set 1 only)
Understand how to construct loci
Be able to construct a 60 and 30 degree angle
Subject Content
G3 draw and measure line segments and angles in geometric figures, including interpreting scale drawings
G4 derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line form/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
Error in Measurement
Developing
be able to use approximation through rounding to estimate answers
know how to use rounding to give solutions to an appropriate degree of accuracy
Secure
be able to calculator possible rounding errors in a calculation
Find the limits of accuracy of numbers that have been rounded to different degrees of accuracy
To review factors multiples and primes
Mastering (set 1 only)
Combine limits of two or more variables together to solve problems
To understand upper and lower bounds
To be able to use numbers in index form
Subject Content
N14 use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x<b
Standard Form
Developing
Be able to multiply by powers of 10
Know the powers of 10
Secure
Be able to multiply and divide with powers
Be able to change a number into standard form
Be able to change a number back into normal form
Be able to use standard form with negative powers
Mastering
Be able to calculate using standard form
Subject Content
N5 use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
N8 interpret and compare numbers in standard form A x 10^n 1< A < 10, where n is a positive or negative integer or zero
Decimal calculations:
Developing
Add, subtract, multiply and divide decimals
Solve money problems
Secure
Solve harder word problems involving decimals
Rational & Real Numbers
Developing
be able to recognise rational numbers, reciprocals, terminating decimals and recurring decimals
Secure
know how to convert terminal decimals to fractions
know how to convert fractions to recurring decimals
be able to find reciprocals of numbers or fractions
know how to simplify surds
Mastering
be able to calculate and manipulate surds, including rationalising a denominator
Subject Content
N16 appreciate the infinite nature of the sets of integers, real and rational numbers
Circles
Developing
Know the parts of a circle
Know how to square numbers
Be able to substitute numbers into formulae
Secure
Know how to find the circumference of a circle
Know how to find the area of a circle
Know how to find the diameter or radius from circumference
Know how to find the radius of a circle if you know the area
Mastering (set 1 only)
Be able to find the area of a compound shape with circles
Be able to find perimeter or area of a semi-circle or quarter circle
Be able to find the area or perimeter of a sector
Subject Content
G2 calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes
G7 derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
Pythagoras' Theorem
Developing
Understand the properties of a right angled triangle
be able to square numbers
be able to find square root
be able substitute into formulae
Secure
Be able to calculate the length of the hypotenuse in a right-angled triangle.
Be able to calculate the length of a shorter side in a right-angled triangle.
Mastering (set 1 only)
Be able to solve real life problems using Pythagoras’ theorem.
Be able to solve problems using Pythagoras’ theorem with coordinates.
Subject Content
G14 Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
Volume, Surface Area & Density
Developing
be able to find the area of a rectangle/square
Know the units for area & volume
be able to find the area of a triangle
be able to find the volume of a cube/cuboid
Secure
be able to find the surface area of a cuboid
be able to find the volume of a prism
be able to find the surface area of a triangular prism
be able to find the volume of a cylinder
Know and use the formula for density
Mastering
be able to find the surface area of a cylinder
be able to convert between metric units of area and volume
Subject Content
R1 change freely between related standard units [for example time, length, area, volume/capacity, mass]
R10 use compound units such as speed, unit pricing and density to solve problems
G1 derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids and other prisms (including cylinders)
G2 calculate and solve problems involving: perimeters of 2D shapes (including circles), areas of circles and composite shapes
G15 Use properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3D
G16 interpret mathematical relationships both algebraically and geometrically
N12 use standard units of mass, length, time, money and other measures, including with decimal quantities
Straight Line Graphs
Developing
be able to use and interpret coordinates in all four quadrants
be able to plot and interpret simple linear graphs (y=x, y=2x, y=x+1)
know the equations for lines parallel to the x and y axes
Secure
be able to plot graphs of linear functions
be able to recognise that graphs of the form y=mx+c are straight-line graphs
Mastering (set 1 only)
Be able to find the gradient of a graph
Be able to find the gradient and y-intercept from the equation of a linear graph
Be able to identify parallel and perpendicular lines from their equations
Subject Content
A8 work with coordinates in all four quadrants
A9 recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
A10 interpret mathematical relationships both algebraically and graphically
A11 reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
Algebraic Graphs
Developing
Be able to substitute numbers into formulae
be able to plot graphs of linear functions
Secure
to be able to recognise and draw sketch graphs of quadratic functions
to be able to recognise cubic, exponential and reciprocal graphs
To understand time series and real life graphs
Mastering (set 1 only)
to be able to sketch transformations of quadratic functions
to be able to draw cubic, exponential and reciprocal graphs
Subject Content
A12 use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
A13 find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
Simultaneous Equations
Developing
Be able to solve a linear equation
Be able to substitute into expressions
Secure
Be able to solve a simple simultaneous equation by elimination
Be able to solve a simultaneous equation by manipulating one or both equations
Be able to form and solve a simultaneous equation
Mastering (set 1 only)
Be able to solve simultaneous equations graphically
Subject Content
A10 interpret mathematical relationships both algebraically and graphically
A12 use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
Rearranging Formulae
Developing
Be able to solve linear equations
Secure
Be able to change the subject of a formula
Extension Objectives (set 1 only)
Be able to change the subject of a formula when the letter appears twice
Subject Content
A5 understand and use standard mathematical formulae; rearrange formulae to change the subject
A7 use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
Probability & Venn Diagrams
Developing
be able to describe how likely an event is to happen
to understand and use the vocabulary relating to probability
to recognise the like hood of outcomes or events
Be able to understand and use the probability scale from 0 to 1
Secure
Be able to find probabilities based on equally likely outcomes
Know how to systematically list all possible outcomes of compound events
Know how to know the sum of all possible outcomes is 1
understand relative frequency as an estimate of probability and use this to compare outcomes of an experiment
Extension Objectives (set 1 only)
Know the meanings of mutually exclusive, complementary and exhaustive events
Understand the meaning of intersection and union
Be able to calculate probabilities from grids, tables and Venn diagrams
Subject Content
P1 record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
P2 understand that the probabilities of all possible outcomes sum to 1
P3 enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
P4 generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities
Trigonometry
Developing
Be able to use Pythagoras' Theorem to find the length of any side of a right angled triangle
Be able to identify opposite, adjacent and hypotenuse
Secure
Be able to use the trigonometric ratios to find lengths of right-angled triangles
Be able to use the trigonometric ratios to find angles of right angled triangles
Mastering (set 1 only)
Be able to solve problems using the trigonometric ratios
Subject Content
G13 apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem and use known results to obtain simple proofs
G14 Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
Congruence & Similarity
Developing
to recognise congruent and similar shapes
know how to describe the difference between congruent and similar shapes
Secure
be able to show that two triangles are congruent
be able to show that two triangles are similar
Mastering
know how to work out the scale factor between similar triangles
Subject Content
G6 use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence in triangles
G13 apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem and use known results to obtain simple proofs
Investigation and Problem Solving
Developing
To be able to solve problems by applying mathematics to a variety of routine and non-routine problems.
To know how to break down maths problems into a series of simpler steps
To understand how to model situations mathematically
To be able to develop mathematical knowledge by solving multistep problems and evaluating outcomes
Sequences
Developing
● Recognise simple sequences including at the most basic level odd, even, triangular, square and cube numbers and Fibonacci-type sequences;
● Generate sequences of numbers, squared integers and sequences derived from diagrams;
● Describe in words a term-to-term sequence and identify which terms cannot be in a sequence;
● Generate specific terms in a sequence using the position-to-term rule and term-to-term rule;
● Find and use (to generate terms) the nth term of an arithmetic sequence;
● Use the nth term of an arithmetic sequence to decide if a given number is a term in the sequence, or find the first term above or below a given number;
● Identify which terms cannot be in a sequence by finding the nth term;
Secure
Generate sequences of numbers from quadratic formula
Find nth term of a quadratic formula
Mastering
Recognise and generates geometric sequesce
Algebra
Developing
Be able to simplify algebraic expressions by collecting like terms
Be able to solve simple equations
Secure
Be able to solve equations involving fractions
Mastering (set 1 only)
Be able to solve basic algebraic fractions
