A solution to the Maths Teacher Shortage

Personal Maths tutor, available 24/7 on all devices

Making maths fun and engaging for all the classroom. Includes the full Teacher and Pupil edition for the whole school


Primary  

Secondary Course Overview

The entire UK National Curriculum for Maths (Key Stage 2, 3 & 4 / GCSE ) is covered in the 12 steps below:

eMathsMaster trains good non-Maths teachers how to teach Maths, giving them confidence to teach Maths up to GCSE level. Starting at the basics, eMathsMaster allows teachers and pupils to build their Maths knowledge, increase confidence in Maths and improve exams results

The Secondary Teacher Edition includes the Pupil Edition plus animated Teaching Techniques for each lesson, with assessments.

The Pupil Edition includes animated lessons with assessments and additional Maths questions.

 

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Topic:

Lesson:

Topic:

Lesson:

Number

Read and write large numbers

Statistics

Range

Number

Identifying values

Geometry and measures           

Naming 2D shapes

Number

Rounding whole numbers

Geometry and measures           

Features of 3D shapes

Number

Rounding to decimal places

Geometry and measures           

Know the terms face, edge and vertex

Number

Rounding to significant figures

Geometry and measures           

Measuring angles using a protractor

Number

Rounding to estimation

Geometry and measures           

Recognising types of angles

Number

Using an empty number line

Geometry and measures           

Angles on a straight line

Number

Column addition and subtraction

Geometry and measures           

Area and perimeter of a rectangle counting squares

Number

Multiply and divide by powers of 10, 100, and 1000

Geometry and measures           

The net of a cube

Number

Standard methods for multiplication

Geometry and measures           

Calculating time intervals

Number

Standard methods for division

Geometry and measures           

Reading units on scales

Number

BIDMAS

Geometry and measures           

Units to estimate length, mass and capacity

Number

Divisibility tests

Geometry and measures           

Identify lines of symmetry on 2D shapes

Number

Introducing negative numbers

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Adding and subtracting decimals

Geometry and measures

Choosing appropriate metric units for measuring

Number

Introducing inequality signs

Geometry and measures

Identifying quadrilaterals

Number

Ordering decimals

Ratio, proportion and rates of change

Translating a shape on a grid

Geometry and measures

Angles around a point

Statistics

Mode

Geometry and measures

Tessellation

Statistics

Calculate median

Geometry and measures

Perimeter of a shape

Statistics

Mean average

Topic:

Lesson:

Topic:

Lesson:

Number

Multiplying decimals

Algebra

Generate terms of a pictorial sequence

Number

Dividing decimals

Probability

Use a probability scale with words

Number

Recognise and use multiples

Probability

Use a probability scale with 0 to 1

Number

Factors

Statistics

Tally charts

Number

Prime numbers

Statistics

Extract data and interpret discrete bar

Number

Common multiples

Statistics

Construct simple bar charts

Number

Common factors

Statistics

Dual bar charts

Number

Knowing simple fraction, decimal and percentage equivalents

Statistics

Pictograms

Number

Convert percentages to fractions out of 100

Statistics

Find range and mode from a bar chart

Number

Convert percentages to decimals

Statistics

Interpret simple pie charts

Number

Convert terminating decimals to fractions

Geometry and measures

Labelling lines, angles, and triangles

Number

Calculate simple percentages

Geometry and measures

Area of squares and rectangles using the formula

Number

Roots of square numbers

Geometry and measures

Use the formula for the area of a triangle

Algebra

Inputs and outputs of more complex functions expressed in words

Geometry and measures

Surface area of a cube using nets

Algebra

Using function machines to find coordinates

Geometry and measures

Perimeter of compound shapes

Algebra

Read values from straight line graphs

Geometry and measures

Properties of triangles

Algebra

Drawing and plotting straight line graphs

Geometry and measures

Properties of quadrilaterals

Algebra

Read and plot coordinates in all four quadrants

Geometry and measures

Rotation around a point

Algebra

Interpret inequalities and show on a number line

Geometry and measures

Begin to estimate the size of angles

Algebra

Generate terms of a simple sequence using term to term rules

Ratio, proportion and rates of change

To identify fractions

Algebra

Generate sequences of square and triangle numbers

Ratio, proportion and rates of change

Simple fraction, decimal and percentage equivalents

Topic:

Lesson:

Topic:

Lesson:

Number

Multiply 3 digit by 2 digit numbers

Statistics

Calculate the mean from a frequency table

Number

Adding and subtracting simple fractions

Statistics

Compare distributions using mean

Number

Add and subtract from negatives

Statistics

Compound and comparative bar charts

Number

Multiply and divide negative numbers

Statistics

Find range and mode from grouped data

Number

Add and subtract integers from positive and negative numbers

Statistics

Calculate the interval from grouped data containing median

Number

Inverse operations

Statistics

Estimate the mean

Number

Simplifying fractions

Geometry and measures

Interior and exterior angles

Number

Prime factor decomposition

Geometry and measures

Vertically opposite angles

Number

Fractions of quantities and measurements

Geometry and measures

Exterior angles in a triangle

Number

17.5%

Geometry and measures

Calculate the surface area of a cuboid

Number

Index notation

Geometry and measures

Congruent triangles

Number

Ordering negative numbers

Geometry and measures

Plans and elevations

Number

Order fractions, decimals and percentages

Geometry and measures

Solve simple problems with length and area

Algebra

Substitute positive integers into simple formulae

Geometry and measures

Draw diagrams with lines of symmetry

Algebra

Substitute positive and negative integers into simple formulae

Geometry and measures

Rotational symmetry

Algebra

Collecting like terms

Geometry and measures

Identify the order of rotational symmetry

Algebra

Forming expressions from words

Geometry and measures

Solving problems using properties of triangles

Algebra

Plot a simple time distance graph

Geometry and measures

Solving problems using properties of quadrilaterals

Algebra

Plot and draw simple vertical and horizontal line graphs

Geometry and measures

Give a bearing between two points

Algebra

Generate terms of a linear sequence

Ratio, proportion and rates of change

Compare quantities using ratio

Algebra

Simplify by multiplying terms

Ratio, proportion and rates of change

Convert between metric units

Probability

Probabilities sum to 1 whole

Ratio, proportion and rates of change

One number as a fraction of another

Probability

Mutually exclusive outcomes

Ratio, proportion and rates of change

Share quantities in a given ratio

Probability

Probability of something not occurring

Ratio, proportion and rates of change

Proportion

Probability

Experimental and theoretical probabilities

Ratio, proportion and rates of change

Find percentages

Statistics

Interpret frequency tables

Ratio, proportion and rates of change

Find percentages using a calculator

Statistics

Find the mode from frequency tables

Ratio, proportion and rates of change

To increase or decrease a quantity by a percentage

Statistics

Two-way tables

Ratio, proportion and rates of change

Equivalent ratios

Statistics

Produce pie charts

Ratio, proportion and rates of change

Simplify ratio

Statistics

Compare distributions using range and median

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Adding and subtracting fractions with different denominators

Probability

Write probabilities in words, fractions, decimals and percentages

Number

Multiply a fraction by an integer

Probability

Work out probability from a frequency table

Number

Multiply by 0.1 and 0.01

Probability

Work out probabilities from two way tables

Number

Divide by 0.1 and 0.01

Statistics

Recognise misleading graphs and statistics

Number

Adding three or more fractions

Statistics

Design good questions for questionnaires

Number

Add mixed numbers

Statistics

Use grouped frequency tables for continuous data

Number

Work interchangeably with terminating decimals and their corresponding fractions

Statistics

Construct and interpret compound bar charts

Number

Learn fractional equivalents to key recurring decimals

Statistics

Interpret a scatter graph

Number

Find fractions of quantities

Geometry and measures

Alternate and corresponding angles

Algebra

Substitute positive and negative numbers into simple formulae

Geometry and measures

Use angle facts to calculate missing angles

Algebra

Forming expressions from geometry

Geometry and measures

Calculate the volume of a cuboid

Algebra

Use graphs to solve distance time problems

Geometry and measures

Calculate the area of a parallelogram

Algebra

Interpret information from a complex real life graph

Geometry and measures

Construct the perpendicular bisector of a line

Algebra

Plot coordinates in four quadrants

Geometry and measures

Name parts of a circle

Algebra

Plot a graph from the equation

Geometry and measures

Draw a circle

Algebra

Find the nth term of an expression

Ratio, proportion and rates of change

Simple unitary ratio and proportion

Probability

Use probability to estimate the number of outcomes

Ratio, proportion and rates of change

Divide a quantity into more than two parts in a given ratio

Probability

Apply probabilities from experimental data to a different experiment

Ratio, proportion and rates of change

Use a ratio to find one quantity when the other is known

Probability

Identify all mutually exclusive outcomes for successive events

Ratio, proportion and rates of change

Use proportion to solve a problem

Probability

Record outcomes of events in tables and grids

Ratio, proportion and rates of change

Calculate percentage profit and loss

Probability

Find the probability of an event happening using relative frequency

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Calculating upper and lower bounds

Statistics

Recognise when to use mean, median and mode

Number

Write numbers as a decimal number of millions or thousands

Statistics

Frequency polygons

Number

Divide an integer by a fraction

Statistics

Identify and explain outliers in a data set

Number

Understand which part of an expression is raised to a power

Statistics

Quantitative and qualitative data

Number

Calculate average speed, distance and time

Statistics

Sample and population

Number

Multiplying and dividing any number between 0 and 1

Statistics

Primary and secondary data sources

Number

Multiply simple fractions (proper and improper) -

Geometry and measures

Co-interior angles

Number

Divide simple fractions

Geometry and measures

Exterior angles of polygons

Number

Use halving and doubling strategies on fractions to find decimal equivalents

Geometry and measures

Interior angles of polygons

Number

Establish multiplying and dividing index laws for positive powers

Geometry and measures

Area of a trapezium

Number

Index laws for powers of 1 and 0

Geometry and measures

Circumference of a circle

Number

Use an extended range of calculator functions

Geometry and measures

Area of a circle

Algebra

Substitute positive integers into expressions involving powers

Geometry and measures

Construct the bisector of an angle

Algebra

Expanding single brackets

Geometry and measures

Construct a triangle

Algebra

Expanding single brackets and simplifying answers

Geometry and measures

Construct an equilateral triangle

Algebra

Common factors of expressions

Geometry and measures

Construct a hexagon

Algebra

Change the subject of a formula

Geometry and measures

Calculate an angle in a right angled triangle

Algebra

Features of graphs of linear functions

Geometry and measures

Enlarge a shape by a positive scale factor

Algebra

Interpret velocity, time graphs

Geometry and measures

Identify the centre of an enlargement

Algebra

Find the coordinates of the mid-point of a line

Ratio, proportion and rates of change

Ratios in the form of 1: n and n:1

Algebra

Straight line graphs

Ratio, proportion and rates of change

Rough metric and imperial equivalents

Algebra

Whole number values that satisfy an inequality

Ratio, proportion and rates of change

Convert between area measures

Algebra

Position-to-term rules

Ratio, proportion and rates of change

Convert between metric measures of volume and capacity

Probability

Probability tree diagrams

Ratio, proportion and rates of change

Use a unitary method to calculate 100%

Probability

Calculate probability of individual events

Ratio, proportion and rates of change

Percentages in real life

Statistics

Produce back-to-back stem and leaf diagrams

Ratio, proportion and rates of change

Map scales

Topic:

Lesson:

Topic:

Lesson:

Number

Find the reciprocal of a number

Geometry and measures

Area and perimeter of semicircles and quadrants

Number

Compound measures

Geometry and measures

Congruent triangles

Number

Index laws and negative powers

Geometry and measures

Construct a perpendicular from a point

Number

Write numbers in standard index form

Geometry and measures

Loci about a point, line, or corner

Number

Calculating compound interest

Geometry and measures

Construct angles of 90º, 60º, 30º, and 45º

Algebra 

Find an unknown where it is not the subject of the formula

Geometry and measures

Pythagoras theorem

Algebra

Identify parallel lines from their equation

Geometry and measures

Describe a translation

Algebra

Quadratic functions

Geometry and measures

Describe an enlargement

Algebra

Construct a table of values of x

Geometry and measures

Describe a rotation

Algebra

Re-arrange linear functions in terms of x

Geometry and measures

Describe a reflection

Algebra

Linear inequalities

Ratio, proportion and rates of change

Find best value using ratio and proportion

Algebra

Trial and improvement to solve equations

Ratio, proportion and rates of change

Convert between currencies

Algebra

Multiplying brackets by a negative number

Ratio, proportion and rates of change

Direct proportion with algebra

Algebra

Multiplying double brackets

Ratio, proportion and rates of change

Inversely proportionate expressions

Algebra

Substituting into expressions involving powers

Statistics

Venn diagrams

Algebra

Factorising expressions into single brackets

Statistics 

Median, mode and range from stem and leaf diagrams

Geometry and measures

Volume of a prism

Statistics

Comparing data in pie charts

Geometry and measures

Surface area of a prism

Statistics

Random sampling

Geometry and measures  

Calculate lengths and area of a prism given the volume

Statistics

Scatter graphs and line of best fit

Geometry and measures

Volume of a cylinder

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Multiply mixed fractions

Algebra

Triangular numbers

Number

To manipulate and simplify surds

Algebra

Solve simultaneous equations graphically

Number

Write numbers less than 1 in standard form

Algebra

Solve simultaneous equations where neither or one equation needs multiplying

Number

Order numbers in standard form

Algebra

Setup and solve a pair of simultaneous equations in two variables

Number

Calculations involving numbers in standard form

Algebra

Solve simultaneous equations representing a real-life situation

Number

Multiply and divide numbers in standard form

Algebra

Add and subtract vectors

Algebra

Find the equation of a line from its graph

Geometry and measures

Find the surface area and volume of compound solids

Algebra

Graphs of inverse

Geometry and measures

Recognise the formula for length of arc of a circle

Algebra

Interpret distance time graphs

Geometry and measures

Recognise the formula for area of a sector of a circle

Algebra

Interpret gradients

Geometry and measures

Enlarged areas and volumes

Algebra

Identify and interpret roots, intercepts and turning points of a quadratic graph

Geometry and measures

Calculate the short side of a triangle using Pythagoras theorem

Algebra

Calculate the length of AB from their given coordinates

Geometry and measures

Use trigonometry to find missing sides of a right-angle triangle

Algebra

Plot & draw graphs of straight lines without using a table of values

Geometry and measures

Use trigonometry to find missing angle of a right-angle triangle

Algebra

Recognise a quadratic function from its equation

Statistics

Use tree diagrams to calculate the probability of two dependent events

Algebra

Solve more complex inequalities

Statistics

Construct cumulative frequency tables

Algebra

Use algebra to support proofs

Statistics

Interpret box plots

Algebra

Identify which terms cannot be in a sequence

Statistics

Produce box plots from raw data

Algebra

Recognise and use simple geometric progressions

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Use inequality notation to specify simple error intervals

Algebra

Cube a linear expression and simplify

Number

Estimate powers and roots of a positive number

Statistics

Interpret cumulative frequency graphs

Number

Recall that n0 = 1 and n-1 = 1/n for any positive number n

Statistics

Compare the measures  between a pair of box plots/cumulative frequency graphs

Algebra

Change the subject of a complex formula that involves fractions

Statistics

Select and justify a sampling scheme and a method to investigate a population

Algebra

Identify and interpret gradient from ax+by=c

Geometry and measures

Prove and use the fact that the angle in a semicircle is a right angle

Algebra

Quadratic equation from the graph of the corresponding quadratic function

Geometry and measures

Prove and use the fact that angles in the same segment are equal

Algebra

Graphs of simple cubic functions

Geometry and measures

Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180°

Algebra

Reciprocal graphs

Geometry and measures

Prove and use facts about the angle subtended at the centre and at the circumference;

Algebra

Find the coordinates of the midpoint of a line

Geometry and measures

Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle

Algebra

Solve linear inequalities graphically

Geometry and measures

Use the appropriate ratio to find a length or angle

Algebra

Solve two simultaneous inequalities algebraically

Geometry and measures

Find angles of elevation and angles of depression

Algebra

Answer simple proof and 'show that' questions using consecutive integers

Geometry and measures

Know that the tangent on a circle is perpendicular to the radius at that point.

Algebra

Continue a quadratic sequence and use the nth term to generate terms

Geometry and measures

Know that the perpendicular from the centre to the chord bisects the chord.

Algebra

Use finite/infinite and ascending/ descending to describe sequences

Geometry and measures

Complete a formal geometric proof of similarity of two triangles

Algebra

Arithmetic and geometric sequences

Ratio, proportion and rates of change

Use expressions of the form y α x²

Algebra

Continue geometric progression and find term to term rule

Ratio, proportion and rates of change

Identify direct proportion from a table of values by comparing ratios of values

Algebra

Expand double brackets and simplify

 

 

Topic:

Lesson

Topic:

Lesson:

Number

Use the product rule for counting

Probability

Use a tree diagram to calculate conditional probability

Number

Convert a recurring decimal to a fraction in simple cases

Statistics

Appropriate use of Histograms

Number

Understand a recurring decimal to fraction proof

Statistics

Compare distributions and make inferences

Number

Value of calculations using indices

Statistics

Compare median and inter-quartile range of two distributions

Number

The inverse operation of raising a positive number to a power n 

Statistics

From a cumulative frequency graph

Number

Simplify surd expressions involving squares

Statistics

Estimate the mean from a histogram

Number

Use fractions, surds and pi in exact calculations, without a calculator

Statistics

Stratified sampling

Algebra

Use function notation

Geometry and measures

Prove and use the alternate segment theorem

Algebra

Deduce turning points by completing the square

Geometry and measures

Use congruence to show that translations, rotations and reflections preserve length and angle

Algebra

Sketch a graph of a quadratic by factorising, identifying roots and y-intercept

Geometry and measures

Use Pythagoras' theorem in 3-D problems

Algebra

Find the equation of the line through two given points

Geometry and measures

Calculate the length of a diagonal of a cuboid

Algebra

The equation of the line through one point with a given gradient

Geometry and measures

Enlarge 2D shapes, given a negative, fractional scale factor

Algebra

A line perpendicular to the line y = mx + c, will have a gradient of -1/m

Geometry and measures

Apply the sine rule a/sin A = b/sin B = c/sin C to find unknown lengths and angles

Algebra

Write  the equation of a line perpendicular to a given line

Geometry and measures

Apply the cosine rule a² = b² + c² - 2bc cos A to find unknown lengths

Algebra

Analyse a straight-line graph

Geometry and measures

Area of a triangle given the length of two sides and the included angle

Algebra

Solve quadratic inequalities in one variable

Geometry and measures

Magnitude of a vector

Algebra

Simplify and manipulate algebraic expressions

Geometry and measures

Calculate, the sum of, and the difference of two vectors and a scalar multiple of a vector

Algebra

Solve exactly linear/quadratic simultaneous equations

Geometry and measures

Calculate the resultant of two vectors

Algebra

Find approximate solutions to simultaneous equations

Ratio, proportion and rates of change

Solve problems involving inverse proportion using graphs

Probability

Calculate conditional probability

Ratio, proportion and rates of change

Solve problems involving inverse proportionality

Probability

Use a tree diagram to calculate conditional probability

Ratio, proportion and rates of change

Calculate an unknown quantity

Probability

Use Venn diagrams to calculate conditional probability

Ratio, proportion and rates of change

Set up and use equations to solve word and other problems involving direct or inverse proportion

Probability

Understand  probabilities to decide if two events are independent

Ratio, proportion and rates of change

Calculate the new area of a shape after enlargement

Probability

Understand selection with or without replacement

 

 

Topic:

Lesson:

Topic:

Lesson:

Number

Calculate the upper and lower bounds of 2-D measurements

Statistics

Use and understand frequency density

Number

Calculate the upper and lower bounds of other compound measurements

Statistics

Construct and interpret histograms from class intervals with unequal width

Number

Write (3 - √3) ² in the form a + b√3

Statistics

From a histogram complete a grouped frequency table

Number

Rationalise a denominator

Statistics

From a histogram understand and define frequency density

Algebra

Apply transformations to the graph of y = f(x) for linear, quadratic, cubic, sine and cosine functions

Statistics

Estimate the median from a histogram with unequal class width

Algebra

Apply to the graph of y = f(x) the transformations

Geometry and measures

Use the formulae for length of arcs and area of sectors of circles to solve problems.

Algebra

y = f(x) + a

Geometry and measures

Give reasons for angle sizes using mathematical language

Algebra

y = f(ax)

Geometry and measures

Give reasons for angle and length calculations involving the use of tangent theorems

Statistics

y = f(x + a)

Geometry and measures

Understand and use the fact that tangents from an external point are equal in length

Statistics

y = af(x) for linear, quadratic, cubic, sine and cosine functions f(x)

Geometry and measures

Apply the cosine rule a² = b² + c² - 2bc cos A to find unknown angles

Algebra

Construct the graphs of simple loci including the circle x² + y² = r²

Geometry and measures

Apply Area = 1/2 ab sin C to calculate the sides or angles of any triangle

Algebra

Find the gradient of the radius that meets the circle at a given point

Geometry and measures

Prove lines are parallel / co linear

Algebra

Find the nth term of a quadratic sequence of the form n² ,an², an² ± b, an² ± bn ± c,

Ratio, proportion and rates of change

Recognise sketch and interpret graphs of exponential functions y = kx

Algebra

Solve linear/x² + y² = r² simultaneous equations

Ratio, proportion and rates of change

Find points that divide a line in a given ratio, using the properties of similar triangles

Topic:

Lesson:

Topic:

Lesson:

Algebra

Interpret the gradient of linear or non-linear graphs, and estimate the gradient of a quadratic or non-linear graph at a given point

Geometry and measures

Solve problems for areas and volumes

Algebra

Find the equation of a tangent to a circle at a given point

Geometry and measures

Use the trigonometric ratios to solve 3-D problems

Algebra

Interpret coordinates for trigonometric graphs

Geometry and measures

Find the angle between a line and a task

Algebra

Plot graphs of the exponential function y = abx

Geometry and measures

Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

Algebra

Use iteration with simple converging sequences

Geometry and measures

Use the sine and cosine rules to solve 2-D and 3-D problems

Geometry and measures

Solve problems involving more complex shapes and solids

Geometry and measures

Apply vector methods for simple geometrical proofs

Geometry and measures

Find the area of a segment of a circle

Ratio, proportion and rates of change

Calculate the new volume of a shape after enlargement

Secondary Edition
KS2 to GCSE

Primary Edition
KS2 + Advance Primary

Pupil Edition
KS2 to GCSE Revision

Schools

News & Events

"As a non-specialist, eMathsMaster has given me more confidence with the mathematics, along with teaching ideas to use with my classes. Of the Year 11 pupils that have been introduced to the pupil version, several have really engaged with the course since we introduced it. I believe that this will really benefit the pupil in that they can monitor their own progress which also builds confidence. It is an intuitive and easy to use platform. I highly recommend it."

- Roger Hutchinson, Biology Teacher, Barnsley Academy, UK

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