# Maths

## Year 7

#### 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

#### Recognising that some fractions have the same worth

#### Simplifying fractions

#### Adding and subtracting fractions when they have the same denominator

#### Introduction to ratio

#### Converting metric measurements

### 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

#### Develop strategies to add large numbers together

#### Develop strategies for subtracting

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

#### Develop strategies to multiply two numbers together

#### Develop strategies on dividing numbers

### 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

#### Simplifying algebraic expressions

#### Solving equations

#### Recognising and calculating with formulae

#### Describe 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

### 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

#### Recognising and describing 3D shapes

#### Describing, estimating and measuring angles

#### Recall and apply basic angle rules

#### Symmetry of 2D shapes

#### Perimeter and area of 2D shapes

### 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

#### Define percentage and calculate simple percentages of quantities

#### Finding a percentage of a quantity without a calculator

#### Calculating percentage change without a calculator

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

#### Reading timetables to solve problems

### 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

#### Recognising interpreting different types of graphs

#### Reading and understanding line graphs

#### Finding the mode and mean of a set of data

#### Finding the median and range of a set of data

#### Calculating basic probability

### 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?

#### Percentage of an amount without a calculator

#### Percentage of an amount with a calculator

#### Percentage change

#### Compound interest

#### 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

#### Equivalent fractions

#### Fractions of whole numbers and multiplying & dividing

#### Adding & subtracting fractions with different denominators equivalent fractions method

#### Adding & subtracting fractions with different denominators – cross multiplication method

#### Mixed numbers

### 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

#### Cubic graphs

#### Speed, distance & time

#### Graphs of trigonometric functions

#### Solving simultaneous equations graphically

#### Solving Inequalities graphically

### 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

#### Using Pythagoras’ Theorem

#### Congruence & similarity

#### Trig 1

#### Trig 2

#### Trig 3

### 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

#### Formulae

#### Solving harder equations

#### Changing the subject of and equations

#### Trial & improvement

#### Factorising quadratics

### 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

#### Indices

#### Surds 1

#### Surds 2

#### Standard form

#### Upper & lower bounds

### Quick Links

- Fractions and ratio (Foundation)
- Number method: Part 1 (Foundation)
- Introduction to algebra (Foundation)
- Properties of shape including angles and area (Foundation)
- Percentages, money and time (Foundation)
- Introduction to statistics and probability (Foundation)
- Percentages (Higher)
- Further Fractions (Higher)
- Graphs (Higher)
- Pythagoras’ theorem & trigonometry (Higher)
- Further algebraic expressions and equations (Higher)
- Further number (Higher)

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### Safeguarded

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### Professional

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