Maths

Year 9 (Higher)

Tute’s team of experienced teachers have planned our lessons to work alongside what students are studying in school; to enable catch-up, to consolidate something that was difficult to master in class or to help revise for exams. To make is easy to choose lessons for different subjects, year groups and levels, we have organised lessons into topics that are fully aligned with the National Curriculum ensuring a comprehensive coverage of the curriculum that makes sense!

All you need to do is select the topic and then the level you feel is appropriate and you will find a list of suitable lessons that you can book for just £12 inc. VAT

Fractions, decimals and percentages (Higher)


This topic will be covering different applications of fractions a and percentages which can be used in other subjects. The first lessons will cover simplifying fractions and applying the four operations to them. We will then move on to ordering fractions, decimals and percentages before finishing with percentages with a calculator.

Ordering fractions

To identify equivalent fractions, to express a fraction in its simplest form and to order fractions.

Adding and subtracting fractions with different denominators

To add and subtract same denominator fractions, to add or subtract fractions with different denominators and to add and subtract mixed number fractions.

Multiplying and dividing fractions

To multiply fractions, to calculate a fraction of a number and to divide fractions.

Converting fractions to percentages and percentages into fractions

To work out simple fractions as percentages, to work out fractions, that simplify, as percentages and to work out fractions as a percentage using a calculator.

Ordering fractions, decimals and percentages

To convert between fractions, decimals and percentages and to order numbers in mixed formats.

Calculating a percentage and percentage change with a calculator

To find a percentage multiplier, to find a percentage with a calculator and to calculate the percentage change.

Further number methods (Higher)


This topic will look at more complex number work. The first half will focus on multiplying and dividing techniques extending to decimals. The fourth lesson will focus on rounding numbers, a skill which is used in other subjects often. The final two lessons will be based on prime index form and applying it to finding the highest common factor and lowest common multiple of two or more numbers.

Different strategies of multiplying two digit numbers

To multiply using the Egyptian method, to multiply using the Russian method and to multiply using the Chinese stick method

Division methods including long division

To apply the short division method and to apply the long division method.

Multiplying and dividing decimals with whole numbers

To multiply decimals using Napier’s bones and to divide decimals using a short division method.

Rounding numbers including decimal places

To round numbers to nearest 10,100 and whole number, to round numbers to given amount of decimal places and to round numbers to given amount of significant figures.

Prime index form

To explain what is meant by a prime number, to use a prime number as a factor and to express a number in its prime index form.

Finding the highest common factor and lowest common multiple using prime index form

To express a number as a product of its prime factors, to use prime factors to determine the HCF of two or more numbers and to use prime factors to determine the LCM of two or more numbers.

Expressions, equations and graphs: Part 1 (Higher)


We begin by looking at the coordinates on a graph and how to plot them which will go on to using it with 2D shapes.
During the next 4 lessons we look in depth at expressions and equations. Simplifying them to start before looking at solving equations and moving on to expanding and factorizing expressions. We end by focusing on patterns and sequences, finding the term to term rule and describing how the sequence is formed.

Coordinates in all four quadrants

To identify coordinates in the first quadrant, to plot coordinates to draw a range of 2D shapes and to recognise and plot coordinates in all four quadrants.

Simplifying expressions

To simplify algebra expressions involving 1 term, to simplify algebraic expressions with multiple terms and to collect like terms.

To simplify algebra expressions involving 1 term, to simplify algebraic expressions with multiple terms and to collect like terms.

To solve one step equations, to solve two step equations and to create equations out of a sentence.

Expanding expressions

To expand single brackets, to expand and simplify multiple brackets in an expression

Factorising algebraic expressions

To factorise with a numerical common factor and to factorise with an algebraic common factor.

Sequences and n-th term

To create patterns that repeat according to a rule, to describe the way patterns grow and to write a rule that describes a pattern.

Mensuration and Pythagoras’ theorem (Higher)


In the first three lessons we concentrate on area, looking at the formula for triangles, parallelograms and circles before ending with the area of compound shapes. We move on in lesson 4 and 5 to 3D shapes. Firstly, finding the volume of a prism then the surface area of a prism. We end with dealing with the Pythagoras Theorem, finding the size of the length of any side of a right angle triangle

Calculating the area of triangles and parallelograms

To recall and apply the formula for the area of a rectangle, to calculate the area of a triangle and to calculate the area of a parallelogram.

Calculating the area and perimeter (circumference) of a circle

To calculate the circumference of a circle and to calculate the area of a circle.

Calculating the area of compound shapes

To calculate the perimeter of a shape, to calculate the area of a rectangle and to calculate the area of a compound shape.

Volume of cuboids and prisms

To calculate the volume of a cuboid, to calculate the volume of a prism and to calculate the volume of a cylinder.

Calculating the surface area of 3D shapes

To identify and draw nets of 3D shapes, to calculate the surface area of a cube or cuboid and to calculate the surface area of a triangular prism.

Using Pythagoras’ Theorem to calculate the length of a side of

and to calculate the shorter lengths of a right angled triangle.

Angles and transformations (Higher)


Some angle facts should be known at the start because in the first lesson we look at angles in a parallel line and in a triangle. In the second lesson we look at how many degrees these are in any polygon and see if there is a formula we can use. The next three lessons we look at transformations, looking at reflecting and rotating, transformation and enlargement, with one lesson using the ray method of enlargement. We end this section by looking at similar and congruent shapes.

Calculating the missing angle when dealing with parallel lines

To find missing angles on a straight line and at a point, to recognise and calculate alternate, corresponding and interior angles and to find a missing angle in a triangle.

Calculating missing angles from any 2D shape

To calculate the sum of angles in a polygon, to calculate the exterior angle of a regular polygon and to calculate the interior angle of a regular polygon.

Reflecting and rotating shapes

To perform and describe a rotation and to perform and describe a reflection.

Translation and enlargement

To perform and describe a translation and to perform and describe an enlargement.

Using the ray method to enlarge shapes

To enlarge a shape by a scale factor and to enlarge a shape by a scale factor from a centre of enlargement

Recognising the difference between similar and congruent shapes

To find the scale factor of enlarged shapes, to identify congruent shapes, to find missing lengths of similar shapes and to identify similar shapes.

Further statistics and probability (Higher)


In the first lesson we will look at averages from raw data we will find the mode mean and median and look at the range of the data. In the second lesson we will expand on this knowledge to finding all the averages in grouped data or in a table. During the next two lessons we will be dealing with charts and graphs, reading drawing and constructing pie charts, before looking at frequency polygons and scatter graphs. We will move on to probability; starting with calculating the probability of a single event happening and then the probability of more than one event.

Finding averages and the range from a set of data

To find the mode of a set of numbers, to calculate the mean in a set of numbers, to explain how the median of a set of data is calculated and to explain how the range of a set of data is calculated.

Calculating averages from tables

To calculate averages and range from a table and to calculate averages and range from grouped data.

Reading and constructing pie charts

To interpret pie charts and to solve pie chart problems.


Displaying continuous data

To draw a frequency diagram, to draw a frequency polygon and to draw a scatter graph.

Calculating the probability of an event happening

To use the vocabulary of probability correctly and to calculate the probability of an event.

Calculating the probability of two events happening

To calculate the probability of a single event happening, to find the probability of two events and to calculate the expected frequency.

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