GCSE Mathematics Tutorial

To run the tutorial, click on the next button. To select individual topics, click on a topic in the contents list below.

On any page of the tutorial, you can click on underlined green words for more information.

Contents

Introduction

Maths Menu

Accessing the Maths Menu

Maths Menu Scores

Setting up Your Course

Selecting Groups of Topics

Selecting a Single Group or Topic

Running Your Course

Selecting a Run Mode

Presentations

The Maths Experts

Running a Presentation

Questions

Question Controls

Answering Questions

Key Steps

Key Step Utility

Numbers, Letters, Symbols and Words

Clicking and Dragging into Input Fields

Typing into Input Fields

Equation Editor

Using the Equation Editor

Displaying Algebraic Fractions

Re-arranging Equations

Menu Bar Options

File

Setting Preferences

Menu

Utilities

Progress

Help

On-screen Utilities


Introduction

This program has been developed as a support to classroom learning - to help you through GCSE Mathematics and get the grade you really deserve.

In normal learning mode, five historical tutors, each an expert in their field, will guide you through the subject, illuminating it with fun, interactive examples.

Although there is a large amount of material in the program, it has been designed to allow you to dip in and have a quick look at any of the individual topics and questions.

When you select the level, or tier, that you require, you will only see material which is appropriate to your tier.


Maths Menu

GCSE Mathematics is divided into four tutorial areas and the exam.

If you select the exam option from the Maths Menu, you will have 45 minutes to answer sets of 16 questions taken at random from all four areas of maths. This is a real test of your ability. You will see no explanations beforehand and there is no help. Each time you select this option, you will see a different exam.

Double clicking on a tutorial area opens it up to show the groups in that area, like this:

As you work down the menu “tree”, each double click expands the level of detail. For example, double clicking on a group opens it up to show all the related sub-groups, and double clicking on a sub-group reveals all the topics you need to cover at your level.

To move back up the menu “tree”, double click on the group or area again.


Accessing the Maths Menu

 The Maths Menu can be accessed by clicking on this button.

The button appears frequently throughout the program.

If the button isn’t on screen when you need it, you can get back to the menu by selecting  Menu from the menu bar at the top of the screen.

Another way of getting back to the menu is to right click on the [image] button, then click on Return to menu.


Maths Menu Scores

A scoring system has been included to help you monitor your progress.  Alongside each topic name you are given your percentage score if you have had a go at the associated question or questions.

When you have attempted to answer at least 30% of the questions in your course, an overall grade is calculated for you. This grade is displayed on the menu screen. As you answer more questions, the grade will change according to your success. This grade will also change if you switch to a different run mode. For example, in learning mode, you will see your learning mode grade, in test mode, you will see your test mode grade.

The grade is intended only as a guide to show how well you are doing, and is not an attempt to predict your grade in the real exam. At foundation level, a grade D is excellent, as this is the highest grade possible at this level. At intermediate level, a grade B is the top grade, while higher level students should be aiming for a grade A.


Setting up Your Course

The program has been designed to allow you to set up your own course. You can choose to:

•	run all the topics in all four areas which are relevant to your tier

•	run all the topics in any one area

•	run all the topics in a group

•	run all the topics in a sub-group

•	run only the specific areas, groups, sub-groups or topics you want to cover

•	run topics and questions individually.

You can set up as many course structures as you want. When you are happy with the structure of your course, you can save it using the File Save option from the menu bar.  When you save your course structure, you must give it a file name so you can load it up again later. You can save your progress in exactly the same way.


Selecting Groups of Topics

From the Maths Menu, you can turn any area, group, sub-group or topic “on” or “off” by clicking on the box next to its name to add or remove the tick [image] .

If you remove a tick to turn an area “off”, this turns off all the topics in that area, so when you Run Maths (see: selecting a run mode) none of the topics from the de-selected area will appear, even though they may still have a tick next to them.

Similarly, if you remove a tick to turn off just a group or sub-group, none of the topics in that group or sub-group will appear when you Run Maths.

If you right click on one of the tick boxes, a menu of options appears on screen as follows.

As well as allowing you to select or de-select all topics, the really useful

features in this menu are options to select all the topics which you haven’t done, and to identify topics where you need to improve.

When you run your course, the topics you select will run in the “top to bottom” order as they appear on the menu.


Selecting a Single Group or Topic

If you have already set up a course, you may want to run a single group or  topic immediately - in other words without having to work through several others first.

There are two ways to do this:

1. Double click on the group or topic title.

2. Click once on the group or topic title and then follow the procedure for running your course.


Running Your Course

When you have finished either setting up your course by selecting groups of topics, or selecting a single group or topic, you are ready to go, so click on the blue Run button


Selecting a Run Mode

Once you have chosen to run your course, a box will appear asking you to select the Run Mode.  You can choose to:

Run Maths

Choose this option to run all of your course from the beginning.

Run Highlighted Topic(s) Only

Choose this option to run only the group or topic highlighted in blue.

You must then select from the following:

Learning Mode

In this mode each presentation is followed by a question or two to check your understanding.

Test Mode

In this mode you will see only questions. If you need help you can call up a presentation to see the explanation by clicking on [image].

Each time you ask for help in Test Mode you will lose marks.


Presentations

This GCSE Maths program consists of a series of individual presentations - each one covering a particular topic and given by a historical maths expert.  For each presentation, you can choose to have a go at a question or two to check your understanding - but this is not compulsory! If you want to skip the questions, just go back to the menu and select the next topic.

You can see single presentations or set up a course consisting of a whole series of presentations.


The Maths Experts

One of five mathematical experts will guide you through each presentation.

Pythagoras (around 582-500 BC)

Head of the Mathematics Department in the Ultimate Staff Room. Pythagoras was a Greek philosopher and mathematician, famous for his discovery that the square of the hypotenuse on a right-angled triangle is equal to the sum of the squares on the other two sides - Pythagoras’ Theorem.

Charles Babbage (1792-1871)

Specialist in the area of Number in the Ultimate Staff Room.  Babbage was a British mathematician and inventor, famous for designing the Difference Engine and development of the Analytical Engine, the forerunners of today’s computers.

Josiah Willard Gibbs (1839-1903)

Specialist in the area of Shape, Space and Measure in the Ultimate Staff Room.  Gibbs was an American mathematical physicist whose work on vector analysis and statistical mechanics was outstanding.

Blaise Pascal (1623-62)

Specialist in the area of Handling Data in the Ultimate Staff Room. Pascal was a French philosopher, mathematician and physicist who invented the first mechanical adding machine in 1642.

Leonardo Fibonacci (around 1170-1240)

Specialist in Algebra in the Ultimate Staff Room. Fibonacci, also known as Leonardo of Pisa, was an Italian mathematician who contributed to the fields of algebra and number theory. Discoverer of the Fibonacci series (e.g. 1,2,3,5,8,… ) where each number in the series is the sum of the two numbers preceding it.

By right clicking on the characters during a presentation, you are able to repeat speech, turn the character on or off and turn the sound on or off.


Running a Presentation

To find out about on-screen features that appear on such as buttons, tutors, etc., you can right click on the feature you are interested in, then left click on the What’s this? option that appears.

You can move forward through the pages of a presentation by clicking on  [image]. Right clicking on this button gives you another route back to the Maths Menu.

If you want to go back and look at pages again, [image]  will take you to the previous page.

  gives you access to the questions related to each presentation.

By clicking on [image]  you have instant access to the key points in a presentation and the quick page feature, as well as any See also suggestions. By clicking on the headings in this quick page box, you can quickly skip to any page of the presentation, while clicking on an item in the See also list will take you to that topic.

You can click on any words that are in brown and are underlined to reveal definition pop-ups.

At the end of a presentation, if you don’t want to attempt the questions you can simply return to the menu by clicking on Menu on the menu bar.


Questions

Each presentation comes with companion questions.

The questions will appear in different ways depending on which run mode  you have chosen.

In learning mode, the tutor will give a presentation and you can click on [image] at any time to try a question (although it is best to wait until the end of the explanation).

In test mode, the questions will run one after another with no presentations in between.

If you are stuck, you can call up a presentation to help you by clicking on

Alternatively, you can click on [image] to reveal the next part of the answer.

Don’t forget that you will lose marks each time you get help in this way.

In exam mode you will attempt a random selection of 15 questions in 45 minutes. This will really test your ability - there is no help in exam mode!


Question Controls

The control buttons used for the questions are very similar to those used in the presentations. As with presentation screens, you can find out about on-screen features that appear in questions such as buttons, input boxes, etc., by right clicking on the feature you are interested in, then left clicking on the What’s this? option that appears.

Each time you complete a step, confirm your answer by clicking on [image]. This will move the question on to the next step.

If you get stuck, you can click on [image] to reveal the next part of the answer but don’t forget that you will lose marks each time you get help in this way.

In longer questions,  [image] allows you to go back and look at a previous question part and the [image] then allows you to move forward again.

When you have finished a question,  you will see one of the following, depending on the run mode you are in.

 will return you to the course menu when you are looking at individual presentations in learning mode and reach the end of the questions, or when you come to the end of your selected course or exam.

 will take you to the next presentation when you are looking at a series of presentations in learning mode.

 will take you to the next question when you are running in test or exam mode.


Answering Questions

In your GCSE maths exam, you will get points for using the correct method, as well as for correct answers. This program uses a key steps approach to test that you understand what method to use where this is appropriate.

 shows when you must put in a key step.

 shows when you must put in either numbers, letters, symbols or words.

 shows when you simply click on the box to make a selection.

If you make a mistake when answering a question, the program will put the correct answer in for you and give feedback to explain why the answer is correct.  Each part of a question that you get wrong will be shaded in dark grey to show where you went wrong.

When you complete a question, your score for that topic will be displayed on the Maths Menu.


Key Steps

Key Steps are designed to test that you understand what method to use to answer a question.

 shows when you must put in a key step.

You cannot type key steps in, they must be dragged from various locations in the program and dropped into the answer box.

There are three different ways you can put in a Key Step:

1. By dragging a Key Step in from a presentation.  (Key Steps are shown in green.)

2. By dragging a Key Step in from the presentation “quick page” box.

3. By dragging a Key Step in from the Key Step Utility.

If you change your mind, you can drag a different Key Step into the box to change it.  When you are happy that the Key Step is the one you want to use, click  to move on to the next step.


Key Step Utility

  In test and exam mode, this utility opens automatically to reveal only the key steps that you need to answer the question. If this does not happen you should look in File Preferences to make sure that Auto Open is set to on in the setting section.

If you close the key steps utility down, you can open it up again by double clicking on


Numbers and letters
Numbers, Letters, Symbols and Words

There are several different types of input field or answer box in the program, but they all work in the same way. Some take Key Steps, others take numbers, letters, symbols or words.

There are two main ways to put data into input fields:

Clicking and dragging. This method  can be used for all types of answers.

Typing. This method can only be used for numbers.


Clicking and Dragging into Input Fields

Key Steps, numbers, letters, symbols or words can all be dragged into input fields, or answer boxes, in questions.

You can drag items:

1. from the calculator display

2. from a presentation to a question

3. from the quick page box

4. from the Key Steps utility

5. from the Units utility

6. from label boxes on a question screen.

To click and drag an item:

1. Use the mouse to move the cursor to the item you want to drag.

2. Hold down the left mouse button

3. Drag the item into position

4. Release the left mouse button to drop the item into place.


Typing into Input Fields

To type an answer into an input field (or answer box), simply click on the box to highlight it and type in your number.

Only numbers can be typed in, any other type of input, such as words, symbols, Key Steps or Units must be dragged into the answer. To type in negative numbers, type the number first, then the minus sign.


Equation Editor

The equation editor is mainly used to answer questions in the Algebra section and is only active when it is needed.  It can be used to display numbers which are difficult to type in from the keyboard, such as numbers with indices. It is also used for re-arranging equations.

The equation editor works with a special on-screen input field in questions. This is just a larger box than any of the other input fields. Whatever appears in the editor will also appear in this input field automatically.

To put an equation into the editor quickly, you can click on the equation in the question and drag it into the question input field. The equation will then appear in the equation editor.

The editor looks complicated at first, but it is a handy tool and is quite easy to use as the following sections will explain.


Using the Equation Editor

The equation editor is divided up into cells. The cells in the top half have the same functions as the cells in the bottom half.

Number cells can display numbers, algebraic terms (e.g. x, y) or operators (+ -  × ÷)

To insert a number, click on the number cell to highlight it, then type the number.

To insert an operator or an algebraic term, highlight the number cell as before, then you can either type the symbol from the keyboard, or right click on the cell and select a symbol from the menu that appears.

Index cells are used to display index numbers.

To insert an index number, click on the index cell to highlight it, then type the number. For a negative index number, type the number first, then the negative sign.

You cannot enter a number in an index cell unless there is a number in the number cell below.

Operator cells can display only operators (+ -  × ÷) or the fraction line.

To insert an operator, click on the operator cell to highlight it, then you can either type the symbol from the keyboard, or right click on the cell and select a symbol from the menu that appears.

If you want to use the keyboard to put symbols into number or operator cells:

+ = plus       - = minus          * = multiply         / = divide

If you want to change the = sign to < or >, right click on the = sign and then select the operator you need from the menu that appears.

Each cell holds one symbol or digit.

To delete the contents of a cell, highlight the cell then press delete or backspace.


Displaying Algebraic Fractions

If you enter a term in a number cell in the bottom half of the equation editor when there is a term above it in the top half of the editor, the fraction line appears automatically. This line stretches as far as the = sign, or to the edge of the editor.

To insert an operator into this line, click on the cell you want to use and insert the operator as before.

The fraction line will then be shortened and you can insert another number or fraction after the operator.


Re-arranging Equations

To put an equation into the equation editor you can either:

1. use the keyboard and the right-click menus on the equation editor to enter the equation manually

or:

2. drag the equation into the on-screen input field and it will automatically appear in the equation editor.

To edit individual cells click on the cell to highlight it, then enter the new number or symbol. To delete the contents of a cell, highlight the cell then press delete or backspace.

To move the equals sign - if the equation has an equals (=) sign and you need to move it, you can do this by clicking on the equals sign and dragging it to its new position.

To change the equals sign to < or >, right click on the = sign and then select the operator you need from the menu that appears.

When you have finished re-arranging your equation, you will see that it is displayed in the on-screen input field. All you have to do now is to click on

Always make sure you give your answer in its simplest form, unless the question instructs you otherwise.


Menu Bar Options

The menu bar has the following options.

File

Menu

Utilities

Progress

Help


File

New

Allows you to start again with a new maths course. All previous results and settings are cleared. This option also allows you to switch to a different tier.

Open

Allows you to open a previously saved course, so you can carry on from where you left off.

Save

Allows you to save your progress. When you save for the first time, you will have to enter a file name. This means you can return to a course later and carry on from where you left off.

Save As...

Also allows you to save your progress, so you can return to a course later and carry on from where you left off. When you select Save As… you will have to enter a file name.

Print set-up

Allows you to set up a printer.

Print

Allows you to print screens.

Preferences

Allows you to adjust appearance, scoring and sound settings.

Exit

Allows you to leave the program.


Setting Preferences

Appearance allows you to turn the tutor on or off. If you turn this feature off, the tutor will not appear on the screen again until you return to preferences and turn it on.

You can also turn the sound and the background colour on or off from here.

Setting allows you to turn synchronised text on or off. When this feature is turned on, the text for each page builds in synchrony with the audio. When it is turned off, all the text for a page is displayed at once.

If you turn masked presentation on, this ensures that the question window masks the presentation window, so making the questions more difficult to answer.

In test or exam mode, auto open automatically opens utilities such as the calculator and key steps box when they are needed. You can turn this feature off if you wish.

Scoring lets you set your target grade. The grades used in this program are intended only as a guide to show how well you are doing, and is not an attempt to predict your grade in the real exam.


Menu

This option allows you to return to the main menu at any time.


Utilities

This menu gives you access to the following utilities. These are also accessible by clicking the buttons on the right hand side of the screen.

Calculator

This is an extremely useful on-screen calculator. You can drag numbers from the calculator display into your answers to save you typing them in again, but be careful! Sometimes you are instructed to give answers to a certain number of decimal places or significant figures!

You can put numbers into the calculator either by clicking on the calculator buttons or by using the number keys on the keyboard. Similarly, you can use the operator (+-/*) buttons either on the calculator or on the keyboard.

To put numbers with index notation into the calculator from the keyboard:

1. type the number

2. type x

3. type the index number

4. if the index number is negative, type -

Units

Some questions ask you to add units to your answer. This option allows you to click and drag units into your answer.

Equation Editor

The equation editor is mainly used in the Algebra section and will open automatically when it is needed.  It is used to display numbers which we could not easily type in from the keyboard, such as numbers with indices. It is also used for re-arranging equations.

Key Steps

When answering questions in Test or Exam mode, you can gain access to the relevant Key Steps by selecting this option.

Notepad

You can use the keyboard to make notes on the notepad. You can also drag numbers from the calculator display and key points into the notepad.

Index

The index lets you look at any topic in the program at any time, except when you are in exam mode, when the index is switched off.


Progress

By selecting this option, you will be able to see how much of the course you have covered.


Help

This option gives you access to this tutorial and other information about the program.


On-Screen Utilities

These utilities are also available from the Utilities menu bar.

 This is an extremely useful on-screen calculator. You can drag numbers from the calculator display into your answers to save you typing them in again. But be careful! Sometimes you are told to give answers to a certain number of decimal places or significant figures!

You can put numbers into the calculator either by clicking on the calculator buttons or by using the number keys on the keyboard. Similarly, you can use the operator (+-/*) buttons either on the calculator or on the keyboard.

To put numbers with index notation into the calculator from the keyboard:

1. type the number

2. type x

3. type the index number

4. if the index number is negative, type -

 Some questions ask you to add units to your answer. This option allows you to click and drag units into your answer.

 The equation editor is mainly used in the Algebra section and will open automatically when it is needed.  It is used to display numbers which we could not easily type in from the keyboard, such as numbers with indices. It is also used for re-arranging equations.

 When answering questions in Test or Exam mode, you can gain access to the relevant Key Steps by selecting this option.

 You can use the keyboard to make notes on the notepad. You can also drag numbers from the calculator display and key points into the notepad.

 The index lets you look at any topic in the program at any time, except when you are in exam mode, when the index is switched off.