Maths

Year 9

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 £10 ex VAT

Fractions and ratio (Foundation)


This course is aimed to boost the student’s confidence with fractions and ratio. We start by looking at the basics of fractions by finding equivalent and simplifying, before moving on to adding and subtracting fractions with the same denominator. We then look at what are ratios and look at using that understanding to convert metric measurements.

Recognise, shade and write fractions

To recognise and shade fractions, to recognise and write fractions and to apply understanding to solve fraction word problems.

Recognising that some fractions have the same worth

To identify equivalent fractions and to show fractions on a number line.

Simplifying fractions

To recognise factors and highest common factors and to simplify fractions.

Adding and subtracting fractions when they have the same denominator

To add fractions with the same denominator and to subtract fractions with the same denominator.

Introduction to ratio

To explain what ratio means and to solve problems involving ratio.

Converting metric measurements

To convert metric measurements of length, to convert metric measurements of weight and to convert metric measurements of capacity.

Number method: Part 1 (Foundation)


We start the course with recognition of place value within a number. In the second lesson we look at strategies to add large numbers together, using the place value skills. We then move on to using the same skills to subtract. The next lesson will involve finding what numbers are made of and how to make numbers by looking at multiples and factors. In the last part of the course we will investigate strategies in multiplying and dividing.

Recognising the value of digits in any number

To explore the value of numbers and to read and write numbers.

Develop strategies to add large numbers together

To recognise addition vocabulary and three digit numbers and to apply the column method to add three digit numbers together.

Develop strategies for subtracting

To apply different methods to subtract two digit numbers and to solve word problems by subtracting two digit numbers

Recognising factors, multiples and primes and how to differentiate between them

To identify factors of whole numbers, to identify multiples of whole numbers and to identify prime numbers.

Develop strategies to multiply two numbers together

To recognise multiplication as repeated addition, to apply the grid method for multiplying and to apply the column method for multiplying.

Develop strategies on dividing numbers

To describe division , to apply different methods to divide and to solve word problems by dividing.

Introduction to algebra (Foundation)


This module will focus on the basics of algebra. We will look at creating expressions before simplifying them by collecting like terms, adding and subtracting letters together. We then move on to solving basic equations in the first instance before applying the same method to more difficult ones. Following on from this we will cover substitution which is a skill they will need for science as well. The remaining lessons will be based on co-ordinates in all four quadrants and term to term rule sequences.

Creating expressions

To create an expression, to explain the difference between an expression and an equation and to create an equation.

Simplifying algebraic expressions

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

Solving equations

To solve one step equations and to solve two step equations.

Recognising and calculating with formulae

To use a formula to find a total cost and to explore problems with 2 variables.

Describe and plot 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.

Recognising a pattern in a set of numbers and how to calculate the next one in the sequence

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

Properties of shape including angles and area (Foundation)


In this topic we will start by looking at the properties of shape. The first two lessons will be based around the properties of 2D and 3D shapes before moving onto some angle work where we will be describing and estimating angles. These are useful skills to have especially when trying to find the missing angle and using angle facts, e.g. how many degrees in a straight line? We advance to angles rules within certain 2D shapes and look at symmetry within these shapes. The focus of the final lesson will be on the area of shapes by counting squares before learning about the area of a rectangle.


Recognising and describing 2D shapes

To describe a range of 2D shapes and to solve problems involving 2D shapes.

Recognising and describing 3D shapes

To identify 3D shapes, to describe a range of 3D shapes and to recognise and identify nets of 3D shapes.

Describing, estimating and measuring angles

To describe angles, to measure an angle and to estimate the size of an angle.

Recall and apply basic angle rules

To identify types of angle, to calculate unknown angles around a point, along a straight line or vertically opposite, to calculate unknown angles in a triangle and quadrilateral.

Symmetry of 2D shapes

To identify a line of symmetry, to explain the link between regular polygons and lines of symmetry and to investigate if shapes can have more than one line of symmetry.

Perimeter and area of 2D shapes

To calculate the perimeter by counting, to calculate the perimeter using the dimensions, to calculate area by counting squares and to calculate area using a formula.

Percentages, money and time (Foundation)


There are many connections between percentages and money and we start in this topic by looking at them separately and building the students confidence and skills. Many people get mixed up with money at times so we start by making sure that they are able to deal with money. In the second lesson we move on to finding simple percentages before working out more complicated percentages without a calculator. We end this course with time related problems by converting between 12 hour and 24 hour time and looking at solving problems that involve timetables.

Use of money to calculate change from a pound

To calculate the total cost of a range of items and to calculate change from worded problems.

Define percentage and calculate simple percentages of quantities

To define percentage, to calculate 50%, 25% and 10% and to calculate 1%.

Finding a percentage of a quantity without a calculator

To find simple percentages of quantities without a calculator ,and to find any percentage of a quantity without a calculator.

Calculating percentage change without a calculator

To calculate percentage increase, to calculate percentage decrease and to solve real-world examples.

Reading time on a 12-hour clock and a 24 hour clock

To tell the time on an analogue clock to the nearest five minutes, to calculate how long until the next hour on an analogue clock and to tell the time in hours and minutes on a 12-hour digital clock using a.m. and p.m. convention.

Reading timetables to solve problems

To solve word problems using time and to follow timetables to answer time related questions.

Introduction to statistics and probability (Foundation)


This topic will cover the basics of statistics and probability. We will start by learning about classifying objects into a Venn diagram before extracting information from different types of graphs such as bar charts and pictograms. In the third lesson we look at being able to read the information from a line graphs. The next lessons will focus on finding averages in data, ie calculating the mean and finding the median and mode with a little bit of the range of the data. In the last lesson we have a chance to look at probability and ways of finding the probability of something happening.

Construct and interpret Venn diagrams

To sort into one Venn diagram circle.


Recognising interpreting different types of graphs

To draw and interpret bar graphs and to draw and interpret pictograms.

Reading and understanding line graphs

To interpret line graphs and correlation and to solve problems relating to line graphs.

Finding the mode and mean of a set of data

To find the mean in a set of numbers and to find the mode of a set of numbers.

Finding the median and range of a set of data

To explain how the range of a set of data is calculated, to arrange numbers in the ascending order and to explain how the median of a set of data is calculated.

Calculating basic probability

To express probability as a word, to show probability on a scale and to express probability as a fraction.

Percentages (Higher)


This topic will be covering different applications of percentages using knowledge from methods used in factions (non-calculator) decimals (calculator) and percentage change. The topic concludes with repeated percentage change in compound interest and looking at the method to reverse percentage change to find original amount.

What is a percentage?

To identify percentages, to express a fraction as a percentage, and to express a percentage as a fraction

Percentage of an amount without a calculator

To relate percentage as a fraction, to calculate 10%, 50%, 1%, and to calculate any percentage using10%, 50%, 1%,

Percentage of an amount with a calculator

To relate percentage as a decimal multiplier, to calculate percentage using decimal multiplier, and to solve percentage problems using calculator.

Percentage change

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.

Compound interest

To express multiple percentage changes as a single multiplier, to calculate compound interest, and to solve growth and decay problems.

Reverse percentages

To calculate percentage increase and decrease, to use percentage multipliers, and to calculate reverse percentages.

Further fractions (Higher)


This topic will look at more complex work with fractions, beginning with simplifying and equivalence. It will then look at adding & subtracting fractions with different denominators using equivalent fractions and highest common factor. An alternative method of adding & subtracting fractions using cross multiplication is also covered. The topic finishes with arithmetic with mixed numbers.

Simplifying fractions

To recognise factors and highest common factors, and to simplify fractions

Equivalent fractions

To identify equivalent fractions and to put fractions in order.

Fractions of whole numbers and multiplying & dividing

To multiply fractions together, to divide fractions together, and to multiply a fraction by a whole number.

Adding & subtracting fractions with different denominators equivalent fractions method

To add two or more fractions with different denominators, and to subtract two or more fractions with different denominators.

Adding & subtracting fractions with different denominators – cross multiplication method

To add two or more fractions with different denominators, and to subtract two or more fractions with different denominators.

Mixed numbers

To convert between an improper fraction and a mixed fraction and to add two or more mixed fractions with different denominators. Also, to subtract two or more mixed fractions with different denominators.

Graphs (Higher)


We begin by visualising functions with squared terms in quadratic graphs and then cubic and reciprocals. The graphs of the Sin, Cos & Tan functions are studied next followed by real world graphs of speed distance & time. Finally, we look at simultaneous equations and finding the solution by plotting a pair of straight line graphs then at the regions of graphs made by straight line graphs when solving inequalities graphically.

Quadratic graphs

To draw a quadratic graph and to solve quadratic equations graphically

Cubic graphs

To create and analyse a cubic graph and to create and analyse a reciprocal graph.

Speed, distance & time

To draw and interpret travel graphs and to use the speed, distance, time formula.

Graphs of trigonometric functions

To recognise common values for Sin, Cos & Tan, to plot graphs of Sin, Cos & Tan, to read values from Sin, Cos & Tan curves.

Solving simultaneous equations graphically

To evaluate methods of drawing straight line graphs and to create and solve a pair of simultaneous equations.

Solving Inequalities graphically

To plot straight line graphs, to understand regions bounded by graphs and to solve Inequalities.

Pythagoras’ theorem & trigonometry (Higher)


In the first two lessons, we concentrate on Pythagoras Theorem, finding the size of the hypotenuse then the length of any side of a right-angle triangle. We then investigate congruence and similarity in triangles. We begin to understand trigonometry by looking at congruence and the ratio of side and how this affects the size of angles, then we label and select Sin Cos & Tan. We then use trig ratios to find missing sides and angles and finish off by looking at the case when the functions need to be rearranged and also exam style problems.

Recognise Pythagoras’ Theorem

To label the hypotenuse of a right angles triangle and to explain the link between the sides of a right-angled triangle.

Using Pythagoras’ Theorem

To calculate the length of the Hypotenuse and to calculate the shorter sides of a right-angled triangle.

Congruence & similarity

To identify congruent triangles, to label corresponding angles and sides of congruent shapes and to calculate the lengths of corresponding sides on similar shapes.

Trig 1

To analyse the ratios of sides in congruent triangles and to correctly label a triangle, to select the correct trigonometric function.

Trig 2

To find a missing length and to find a missing angle.

Trig 3

To change the subject, to find missing lengths and angles in right angle triangle problems.

Further algebraic expressions and equations (Higher)


In this series of topics, we will look at methods in algebra focusing on quadratic expressions, initially looking at multiplying a pair of expressions in brackets. We then compare and contrast expressions, formulae and equations before learning methods of solving more complex equations. Our algebraic skills are further extended in changing the subject and trial and improvement methods and concludes with factorising quadratics.

Expanding double brackets

Expanding brackets using FOIL method and expanding brackets using table method

Formulae

To substitute numbers into formulae, to change the subject of a formula and to discriminate between expressions, equations, and formulae.

Solving harder equations

To solve equations with brackets, to solve equations with x on both sides and to solve equations involving fractions.

Changing the subject of and equations

Rearrange simple formula, and rearrange formulae with brackets or fractions, rearrange quadratic formulae.

Trial & improvement

To understand the trial and improvement process and to be able to use trial and improvement to solve quadratic equations.

Factorising quadratics

To factorise quadratic expressions with positive coefficients and to factorise quadratic expressions with positive and negative coefficients.

Further number {Higher)


In the first lesson, we will look at the most familiar indices of powers and roots before extending this in our second lesson about indices which focusses on the laws of indices. Our first lesson on surds combines laws of indices and roots with square number.

Powers & roots

To investigate square and cubic numbers and to investigate square and cubic roots

Indices

To multiply and divide indices, to find the power of indices and to calculate with zero, negative and fractional powers.

Surds 1

To relate square numbers and laws of indices to surds and to simplify surds.

Surds 2

To add and subtract with surds,, to multiply brackets with surds and to rationalise surds.

Standard form

To convert numbers into standard form, to convert numbers out of standard form and to calculate with numbers in standard form.

Upper & lower bounds

To find the most significant digit, to write numbers to a certain number of significant figures and to find upper and lower limits of a number.

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* Promotion ends 31st March 2017