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Manual
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MATHSBOOK
=========
Designed by award-winning author Marshal Anderson
Programmed by Anthony Benesh
Copyright � 1997 Marshal Anderson
(P) Published 1997 by Topologika Software
SPECIAL NOTE
------------
This extracted is from the MathsBook manual. It does not claim to be error-free or complete. Please see the separate ReadMe file for start-up details and how to purchase the complete pack.
INTRODUCTION
------------
MathsBook is designed to help students with multiplication and division. It is not a teaching pack, but assumes that you have already introduced students to the concepts and skills required for these operations.
After they have been taught an operation, students generally go through what is often quite a long period of rehearsal while they sort the new ideas out in their minds. This period requires a lot of patience from them and from you, as they repeat the same instructions many times until they are fully learned. Even after that there will usually be a period in which students simply continue to build confidence in their own ability rather than make dramatic moves ahead. MathsBook aims to help with the rehearsal and confidence building parts of this process by presenting students with �sums� in a very similar form to the way they are set out in exercise books. The aim - as in all Topologika software - is to help build transferable skills.
As students work their way through each calculation, MathsBook monitors them and provides the kind of help that you would provide, reminding them of each step in these quite complex processes. While this kind of help is quite limited, it is exactly the kind that most students need. They will, of course, continue to make specific kinds of errors due to misunderstandings, and to help you spot these errors, MathsBook records all their attempts so that you can later look for patterns that may require your intervention.
As this part of the learning process can last a long time, MathsBook reacts to the progress by, from session to session, increasing or decreasing the difficulty of the calculations presented - and the level of help it gives - based on performance. This information can be saved on disc for individuals and whole groups of students which makes managing MathsBook in the classroom very straight-forward.
Differentiation
You have control over the level of difficulty and help that MathsBook presents. You can choose students� starting levels and have MathsBook monitor their performance and adjust automatically to their needs. Alternatively you can set it up at an easy level and leave MathsBook to find the correct level for each student. In both cases you have control over the performance required before the difficulty level changes. You don't even have to tell MathsBook the names of your students: it will ask for them and build them into its files when it meets them, tracking and adjusting difficulty levels as appropriate.
As well as keeping track of students' progress, MathsBook can also provide them with a worksheet to take away at the end of each session. This will include calculations they were not able to complete correctly plus a selection of examples from the level they reached during their go.
GETTING STARTED
---------------
MathsBook allows you to prepare files containing data on groups of children. This data is stored in a directory called MFiles_X or Mfiles_�. If you double-click on MFiles_ you will get a menu listing the �dummy� group name or names currently set up. Click on the group you want - any one will do for now - then click on OK. You will see a list of all the students in that group.
Click on one of the boxes next to the names to select that person, then click on OK. (Alternatively you can click on I'm new and enter your name there.)
MathsBook will present you with your first calculation. Note that the student's name - or the name that you entered - appears at the top of the MathsBook window.
THE MAIN IDEA
-------------
This section gives you a quick insight into how MathsBook works. Please note that from now on we�re going to use the word �sum� to mean any calculation set for you by MathsBook.
When the main MathsBook screen appears, you are presented with a �sum� to complete, including all carrying or decomposition, with or without help from the program. What sort of �sum� is presented depends on how the program has been configured - as does the level of help.
When you (think) you have the correct answer, click on the equals sign. MathsBook will tell you whether you are right or wrong and may give you another try or present a new sum. You can rub out numbers you don't want, ask for help, use a calculator, check your score, give up and go onto the next sum - even give up altogether. You can also have any sum saved for printing at the end of your turn. All this happens on the Main Screen.
THE MAIN SCREEN
---------------
Whether you are doing multiplication or division, MathsBook uses exactly the same methods of entering numbers, altering them and accessing the various other functions of the program. These are described in this section.
The Number Line
The number will attach itself to the pointer and can be placed in the sum by moving the number to the position you require, then clicking.
You can only place numbers in sensible positions (ie those we think are sensible).
If you are using one of the help modes a red square will appear on the sum, showing you where the next number should go. At certain help levels you can only place a number there; double clicking on the number on the answer line will put the number straight into the red box.
When doing division, a strike-through character (for decomposition) is available to the right of the digits. Other tools include:
Equals
Rubber
Help
Calculator
Score
Next
Stop
Print
When you have finished your sums you are presented with the results of your work. There are three options:
New go takes you to the Group Menu screen. A new student can now use MathsBook.
Print (see above and Appendix 2 Page 23)
End closes the Results window and stops the session.
You can continue by clicking on the MathsBook icon to bring up the Group Menu.
NOTEBOOK, HELP AND DIFFICULTY LEVELS
------------------------------------
MathsBook can operate in two modes to provide for the needs of your group.
Notebook Mode
In Notebook mode students can place figures anywhere in the calculation in any order; for example, figures will be accepted in carry positions whether they are needed or not. Clicking on the equals icon while in Notebook mode ends that try and tells them whether or not they were right.
Help is never available in Notebook mode which simply mimics what students do in their own note/workbooks.
Help
Help mode provides an ascending scale of help, ranging from reminders about which column should be filled in next up to the calculation being managed entirely by MathsBook. These help levels are described in Appendix 1, page 21, though various other routine checks are carried out on sums, e.g. adding in a subtraction will generate a warning.
Via the Options menu help levels can be set for each student. Help can be of a fixed type or can change automatically depending on the answers given.
Help can also be spoken. See page 23 for details of how to switch this on.
Difficulty Levels
MathsBook can monitor difficulty levels and change them automatically: see Options (page 18) for details.
SETTING MATHSBOOK UP FOR YOUR STUDENTS
--------------------------------------
The power of MathsBook lies in the way that you can configure it to react to the performance of each child in a group or even the whole class. It is worth spending some time reading this section in order that you get the most out of the program.
Groups and Group Files
MathsBook can track the progress of individual students in groups of up to 40. information on their levels and facilities available to them are saved in Group files.
Loading an Existing Group
Loading groups can be done in three ways:
Immediately after loading the program, double click on MFiles_, then select the group you want from the menu. This is the method to use straight after loading the program.
If you already have a group loaded you will get the opportunity to save it before loading the new group.
Creating a New Group
Here you can type in the name of each student in the group (see Saving Time, opposite, if you can't face this). Each student has a set of options attached to their name in the file. There's a large number of these options and they're described separately (page 18). To speed things up you can set default options for the whole group and then make minor adjustments for each student. This is described in the next section.
Setting Defaults
Click the Defaults button and you will see the defaults screen. This opens with the defaults we have set. Note that the defaults and options screens look almost identical as they deal with the same set of choices; defaults are applied to all students, options to an individual student. You will be reminded which you are dealing with in the title bar of the screen. The defaults you set form the basis for each individual student's options. When you have set the defaults you want, click on Apply to all. Each time you create a new student, their options will start at the default settings.
There are two other buttons on the defaults screen that change the way they are applied. Close simply closes the defaults screen without making any changes. Apply to new is more complex and is for you to use if you come back to the group and want to apply a different set of defaults to the students you are adding. Clicking Apply to all after you have started setting up your group will reset all the existing students to that default. This may not be what you want as there may be levels and adjustments that you want kept. Clicking Apply to new sets new defaults for students subsequently added without affecting those that are already there.
Setting Options
Once the defaults are set you can adjust the options for each and any individual student. To do this, select the student's name then click on the Options button. The options screen will open with the student's name at the top and the default values entered. You can make any changes to the options for that student then click Finished. You can reset the student's options back to the defaults by clicking Defaults.
From this point on MathsBook will manage students� work, keeping track of progress and adjusting help and difficulty levels based on your options settings.
Saving Time
If you want to set up a group of students and you want them all to do similar work and to have the same facilities, MathsBook can look after that for you.
1 Set up the defaults so that it has the required settings for display, help and session - using estimates, how much help to give and so on.
2 Now enter the name of the first student in the group and close down the Group Editing screen.
When the MathsBook session is started (by clicking on the MathsBook icon), the Student Menu will appear with the first student's name. The only other option will be �I'm new�. After the first student has finished their session, the next simply clicks on �I'm new� and enters their name. MathsBook will start the new student off at the default level that you set and adjust difficulty and help levels to suit that student, recording name and progress in the Group File. This way you can let the students build up the Group File for you.
Changing Options As You Go
There will come a time when you will want to intervene to change the kind of work that MathsBook is presenting to a particular student. There are two ways to do this:
Via the icon bar menu See options entry, access the student�s Options screen and make the necessary changes. This can be done while the student is actually working and will apply the changes immediately. Alternatively, you can access the options for any student in a group by loading the group file and clicking on the See/edit group entry on the icon menu. Clicking on this will bring up the whole group. Click on the name of the student you wish to deal with, then click on Options.
Deleting a group member
To delete a member of a group, load that group then click Menu on the MathsBook icon on the icon bar, and click Select on See/edit group. The group editing screen will appear. Select the person you want to delete by clicking on the Options button to the left of his/her name: the person�s name will be highlighted in white. Use the <Delete> key to remove the name. Click on Finished, then, from the Icon Bar Menu, click Select on Save group. Next time you load that group the name will have been removed.
RESULTS AND RESULTS FILES
-------------------------
MathsBook enables you to keep detailed records of students� performance. Each Results file can hold up to 40 students and 1000 �sums�. Here we explain how Results files work.
MathsBook keeps a record of all the information you need to make judgements about students� progress. This is available via the Results entry in the icon bar menu - slide right over the arrow to see the Results menu.
See Results
This displays in a scrollable window all the results currently held. The information presented looks like this:
Group file name: Class4 Date: 17 Jul 1995
The first line of the results file gives the name of your group file and the date. Each student is then recorded:
Name Timothy Thompson Start levels: add:2 sub:4 Help level:2
The first line details the levels they started at. (If Auto Help is �on�, the Help level refers to the minimum help level.) Following that each calculation is detailed:
Finally you are shown the student's finishing levels:
End levels: add:3 sub:1 100%
This records how the difficulty levels changed during the last session, ie how the student did. The percentage is the percentage of calculations completed correctly. This is calculated on the number of sums actually completed, if the student pressed Stop this will be less than the number you set.
Print Results
Clicking on this menu entry will print out the results.
If a printer driver has not been loaded or the printer has been switched off via the icon menu, this option is not available.
Print Summary
Clicking this will print out just the start and end information for each member of the group. Again, a printer driver must have been loaded.
Save Results
Moving right over the arrow here brings up a standard RISC OS save dialogue box. The file can be re-named and dragged into any directory.
You will notice that the results are saved as a text file so that they can be used with any text editor (like Edit), word processor (like PenDown), or desktop publisher (like Ovation). Once in one of these packages, the results can be edited and presented in whatever form you like.
Auto-save Results
Selecting this puts a tick by it to let you know it's on. When it's on, the Results file is automatically saved into the Results directory that's inside the Mfiles_ directory. The advantage of this is that you don�t have to drag it anywhere. However, the file is saved under the group name, meaning that each new session overwrites the old file. This feature is there in order to stop floppy disc users filling up discs with Results files, but it does mean that they need to transfer, or print out, results before the next session. RISC OS experts can, of course, show off by changing the file name and leaving it in the directory.
Wipe results
This clears out the current Results file in memory (not on disc), and starts again.
OTHER BITS
----------
There are four more entries on the icon bar menu:
Save group
Save group leads to a RISC OS save dialogue box with the current group file in it. This is automatically set to be saved in the Mfiles_+- directory. There's no need to save it there as it's been constantly up-dated by MathsBook. However, this option allows you to drag the group file to anywhere on the filing system, for what ever reason you see fit.
Enable Printer
MathsBook takes account of the settings in Options and Defaults when offering students the Print option. It also checks to see if a printer driver is loaded. When the printer is enabled, students with the printer option switched on in their options will be able to print, but those with it off will not. With Enable Printer not ticked no printing will be allowed.
Whole Screen
When Whole screen is switched on, the main screen will fill the entire screen with no scroll bars etc. This means that the students do not have access to the desktop while they are working (quite possibly a Good Thing).
To get to the icon bar so that you can quit, change options etc. press <Shift> and <F12> at the same time.
The whole screen setting is saved as part of your group file.
Quit
Here is the official way to leave MathsBook:
Select Quit from the icon menu. If you have not saved the Results and/or Group files you will be warned. (It is likely that you will not want to save the results as you will have seen them or printed them out, but we thought we would just remind you.)
THE OPTIONS MENU
----------------
This is where you can set up MathsBook to work in the best way to suit any given user. Because there will be so many different needs within any group, MathsBook is able to have different options for up to 40 users saved as part of a group - and you can create as many groups as you like. You can change an individual's options from the icon bar menu while they are working. To access the icon bar while you are in Whole Screen mode press <Shift> and <F12> at the same time.
Automatic Level, when selected, automatically raises or lowers the difficulty level.
You can set the number of right or wrong answers after which the level is changed. (See also Force right answer, page 20).
The Use decimals option sets MathsBook up to produce sums with two decimal places. All sums will then be presented with decimals to two places, with trailing positions filled with zeros (eg 2.3 is always shown as 2.30) for work on money.
MathsBook does not go beyond two decimal places.
With Own sum selected, Automatic level is, of course, automatically switched off, but help is available, if it is turned on for that student.
Session
You can set the number of questions in each session and the number of tries that will be given. An answer is only considered wrong if it was still wrong at the last try. (But see Force right answer) A time limit in minutes can be set for each student�s go.
Help
Here you choose either Notebook mode (where there is no help and total freedom to place numbers anywhere), or Active mode (in which MathsBook can help with completion of calculations). The Level of help is the current help level MathsBook is using.
Note that if Automatic level is switched on, the level of help could change with each calculation.
Switching on Automatic level means that MathsBook will increase the level of help for each incorrect try and reduce it for each correct try. Once a student reaches help level 5 - where they cannot get the answer wrong - the level will always move back down to 4. The minimum level of help you want MathsBook to present must always be set in order to prevent students getting into situations where they are getting less help than you think they need.
When Force right answer is on, each time the last try on a calculation is incorrect an additional try will be given at help level 5. This level only allows the correct figures to be entered and the extra try is not counted for scoring purposes. This feature works independently of the current level of help. When the calculation is finished MathsBook will return to the previous level of help.
Display
This allows you to control what is seen and what is available while MathsBook is running. You can switch off the Calculator, Score, Next and Stop buttons. You can have the columns titled and have the Estimate request on or off (see below). The Print option will be greyed out unless a printer driver has been loaded or if printing has been turned off. Speech is also switched on and off from here.
This box will be superimposed on top of the main MathsBook work screen when Allow estimate is configured �on� in the Options menu. The estimate is entered using the usual number line, and completed by clicking on the equals sign in the estimate box. The estimated answer is not checked by the program, but is displayed as soon as the student finishes the main calculation.
Keep results records students� work in the Results file. As the Results file can hold a huge amount of data for a session it may be that you only want to keep the results of those you think might be having particular problems.
APPENDIX 1 - DIFFICULTY LEVELS
---------------------------------------
Note that the number of figures is the maximum possible in a calculation.
Numbers used in �sums� are chosen randomly by the computer. The levels actually represent the hardest calculations that will be presented at a particular level. However, the choice of calculation is purposely skewed to give a high chance of the most difficult calculations being presented.
Division DIFFICULTY LEVELS
Level 1 Divisor 2, 3 or 4. Number to divide 3-5 figures, no carry, no remainder.
Level 2 Divisor 2 - 5. Number to divide 3 figures. Carrying but no remainder.
Level 3 Divisor up to 9. Number to divide 5 figures. Carrying but no remainder.
Level 4 As level 3 but with remainders.
Level 5 Long division. Divisor 11 - 19. Number to be divided 3 - 4 figures.
Level 6 Divisor 11 - 50. Number to be divided 4 - 5 figures.
Level 7 Divisor 20 - 99. Number to be divided 4 - 5 figures.
HELP LEVELS
Level 1 Red square marks column to be done next.
Level 2 Clicking Help give type of operation to be done next.
Level 3 Figures must be placed at the position of the red square.
Level 4 Gives type of operation with specific figures.
Level 5 Forces right answer.
Multiplication Difficulty Levels
Level 1 2 figures times 1 figure.
Level 2 3 figures times 1 figure.
Level 3 3 figures times 10.
Level 4 3 figures times 2 figures. One of the two figures in the multiplier will always be 1. Switches to long multiplication layout.
Level 5 3 figures times two figures. No restrictions on multiplier.
Help levels
Level 0 The red square shows the column. No message.
Level 1 Help gives message about column.
Level 2 As level 1 but reminder about carry is also given if relevant.
Level 3 Red square goes to carry position. Column message or carry message.
Level 4 Gives details of what to multiply/add or what to carry.
Level 5 Force right answer.
In complex situations, for instance when a student is correcting a large subtraction sum with several decomposition errors, MathsBook does not offer help beyond indicating errors in the answer line, ie. wrong digits in the answer given. This is because there are so many possible sequences available and we don't want the program to force any particular way of working.
APPENDIX 2 - SAMPLE WORKSHEET
Three types of sums appear on MathsBook worksheets which are made up as follows:
When a student clicks on the Print button on the main screen the current sum is saved
for printing.
When a sum is not completed correctly it is saved for printing.
Once these have been assembled on the worksheet further sums are added, using
the student's current difficulty levels and chosen operators, to fill the page.
The result looks like this:
(ends) 00000000 4d 41 54 48 53 42 4f 4f 4b 0a 3d 3d 3d 3d 3d 3d |MATHSBOOK.======| 00000010 3d 3d 3d 0a 0a 44 65 73 69 67 6e 65 64 20 62 79 |===..Designed by| 00000020 20 61 77 61 72 64 2d 77 69 6e 6e 69 6e 67 20 61 | award-winning a| 00000030 75 74 68 6f 72 20 4d 61 72 73 68 61 6c 20 41 6e |uthor Marshal An| 00000040 64 65 72 73 6f 6e 0a 50 72 6f 67 72 61 6d 6d 65 |derson.Programme| 00000050 64 20 62 79 20 41 6e 74 68 6f 6e 79 20 42 65 6e |d by Anthony Ben| 00000060 65 73 68 0a 43 6f 70 79 72 69 67 68 74 20 a9 20 |esh.Copyright . | 00000070 31 39 39 37 20 4d 61 72 73 68 61 6c 20 41 6e 64 |1997 Marshal And| 00000080 65 72 73 6f 6e 0a 28 50 29 20 50 75 62 6c 69 73 |erson.(P) Publis| 00000090 68 65 64 20 31 39 39 37 20 62 79 20 54 6f 70 6f |hed 1997 by Topo| 000000a0 6c 6f 67 69 6b 61 20 53 6f 66 74 77 61 72 65 0a |logika Software.| 000000b0 0a 53 50 45 43 49 41 4c 20 4e 4f 54 45 0a 2d 2d |.SPECIAL NOTE.--| 000000c0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 54 68 69 73 |----------..This| 000000d0 20 65 78 74 72 61 63 74 65 64 20 69 73 20 66 72 | extracted is fr| 000000e0 6f 6d 20 74 68 65 20 4d 61 74 68 73 42 6f 6f 6b |om the MathsBook| 000000f0 20 6d 61 6e 75 61 6c 2e 20 49 74 20 64 6f 65 73 | manual. It does| 00000100 20 6e 6f 74 20 63 6c 61 69 6d 20 74 6f 20 62 65 | not claim to be| 00000110 20 65 72 72 6f 72 2d 66 72 65 65 20 6f 72 20 63 | error-free or c| 00000120 6f 6d 70 6c 65 74 65 2e 20 50 6c 65 61 73 65 20 |omplete. Please | 00000130 73 65 65 20 74 68 65 20 73 65 70 61 72 61 74 65 |see the separate| 00000140 20 52 65 61 64 4d 65 20 66 69 6c 65 20 66 6f 72 | ReadMe file for| 00000150 20 73 74 61 72 74 2d 75 70 20 64 65 74 61 69 6c | start-up detail| 00000160 73 20 61 6e 64 20 68 6f 77 20 74 6f 20 70 75 72 |s and how to pur| 00000170 63 68 61 73 65 20 74 68 65 20 63 6f 6d 70 6c 65 |chase the comple| 00000180 74 65 20 70 61 63 6b 2e 0a 0a 0a 49 4e 54 52 4f |te pack....INTRO| 00000190 44 55 43 54 49 4f 4e 0a 2d 2d 2d 2d 2d 2d 2d 2d |DUCTION.--------| 000001a0 2d 2d 2d 2d 0a 0a 4d 61 74 68 73 42 6f 6f 6b 20 |----..MathsBook | 000001b0 69 73 20 64 65 73 69 67 6e 65 64 20 74 6f 20 68 |is designed to h| 000001c0 65 6c 70 20 73 74 75 64 65 6e 74 73 20 77 69 74 |elp students wit| 000001d0 68 20 6d 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e |h multiplication| 000001e0 20 61 6e 64 20 64 69 76 69 73 69 6f 6e 2e 20 49 | and division. I| 000001f0 74 20 69 73 20 6e 6f 74 20 61 20 74 65 61 63 68 |t is not a teach| 00000200 69 6e 67 20 70 61 63 6b 2c 20 62 75 74 20 61 73 |ing pack, but as| 00000210 73 75 6d 65 73 20 74 68 61 74 20 79 6f 75 20 68 |sumes that you h| 00000220 61 76 65 20 61 6c 72 65 61 64 79 20 69 6e 74 72 |ave already intr| 00000230 6f 64 75 63 65 64 20 73 74 75 64 65 6e 74 73 20 |oduced students | 00000240 74 6f 20 74 68 65 20 63 6f 6e 63 65 70 74 73 20 |to the concepts | 00000250 61 6e 64 20 73 6b 69 6c 6c 73 20 72 65 71 75 69 |and skills requi| 00000260 72 65 64 20 66 6f 72 20 74 68 65 73 65 20 6f 70 |red for these op| 00000270 65 72 61 74 69 6f 6e 73 2e 20 0a 0a 41 66 74 65 |erations. ..Afte| 00000280 72 20 74 68 65 79 20 68 61 76 65 20 62 65 65 6e |r they have been| 00000290 20 74 61 75 67 68 74 20 61 6e 20 6f 70 65 72 61 | taught an opera| 000002a0 74 69 6f 6e 2c 20 73 74 75 64 65 6e 74 73 20 67 |tion, students g| 000002b0 65 6e 65 72 61 6c 6c 79 20 67 6f 20 74 68 72 6f |enerally go thro| 000002c0 75 67 68 20 77 68 61 74 20 69 73 20 6f 66 74 65 |ugh what is ofte| 000002d0 6e 20 71 75 69 74 65 20 61 20 6c 6f 6e 67 20 70 |n quite a long p| 000002e0 65 72 69 6f 64 20 6f 66 20 72 65 68 65 61 72 73 |eriod of rehears| 000002f0 61 6c 20 77 68 69 6c 65 20 74 68 65 79 20 73 6f |al while they so| 00000300 72 74 20 74 68 65 20 6e 65 77 20 69 64 65 61 73 |rt the new ideas| 00000310 20 6f 75 74 20 69 6e 20 74 68 65 69 72 20 6d 69 | out in their mi| 00000320 6e 64 73 2e 20 54 68 69 73 20 70 65 72 69 6f 64 |nds. This period| 00000330 20 72 65 71 75 69 72 65 73 20 61 20 6c 6f 74 20 | requires a lot | 00000340 6f 66 20 70 61 74 69 65 6e 63 65 20 66 72 6f 6d |of patience from| 00000350 20 74 68 65 6d 20 61 6e 64 20 66 72 6f 6d 20 79 | them and from y| 00000360 6f 75 2c 20 61 73 20 74 68 65 79 20 72 65 70 65 |ou, as they repe| 00000370 61 74 20 74 68 65 20 73 61 6d 65 20 69 6e 73 74 |at the same inst| 00000380 72 75 63 74 69 6f 6e 73 20 6d 61 6e 79 20 74 69 |ructions many ti| 00000390 6d 65 73 20 75 6e 74 69 6c 20 74 68 65 79 20 61 |mes until they a| 000003a0 72 65 20 66 75 6c 6c 79 20 6c 65 61 72 6e 65 64 |re fully learned| 000003b0 2e 20 45 76 65 6e 20 61 66 74 65 72 20 74 68 61 |. Even after tha| 000003c0 74 20 74 68 65 72 65 20 77 69 6c 6c 20 75 73 75 |t there will usu| 000003d0 61 6c 6c 79 20 62 65 20 61 20 70 65 72 69 6f 64 |ally be a period| 000003e0 20 69 6e 20 77 68 69 63 68 20 73 74 75 64 65 6e | in which studen| 000003f0 74 73 20 73 69 6d 70 6c 79 20 63 6f 6e 74 69 6e |ts simply contin| 00000400 75 65 20 74 6f 20 62 75 69 6c 64 20 63 6f 6e 66 |ue to build conf| 00000410 69 64 65 6e 63 65 20 69 6e 20 74 68 65 69 72 20 |idence in their | 00000420 6f 77 6e 20 61 62 69 6c 69 74 79 20 72 61 74 68 |own ability rath| 00000430 65 72 20 74 68 61 6e 20 6d 61 6b 65 20 64 72 61 |er than make dra| 00000440 6d 61 74 69 63 20 6d 6f 76 65 73 20 61 68 65 61 |matic moves ahea| 00000450 64 2e 20 4d 61 74 68 73 42 6f 6f 6b 20 61 69 6d |d. MathsBook aim| 00000460 73 20 74 6f 20 68 65 6c 70 20 77 69 74 68 20 74 |s to help with t| 00000470 68 65 20 72 65 68 65 61 72 73 61 6c 20 61 6e 64 |he rehearsal and| 00000480 20 63 6f 6e 66 69 64 65 6e 63 65 20 62 75 69 6c | confidence buil| 00000490 64 69 6e 67 20 70 61 72 74 73 20 6f 66 20 74 68 |ding parts of th| 000004a0 69 73 20 70 72 6f 63 65 73 73 20 62 79 20 70 72 |is process by pr| 000004b0 65 73 65 6e 74 69 6e 67 20 73 74 75 64 65 6e 74 |esenting student| 000004c0 73 20 77 69 74 68 20 90 73 75 6d 73 91 20 69 6e |s with .sums. in| 000004d0 20 61 20 76 65 72 79 20 73 69 6d 69 6c 61 72 20 | a very similar | 000004e0 66 6f 72 6d 20 74 6f 20 74 68 65 20 77 61 79 20 |form to the way | 000004f0 74 68 65 79 20 61 72 65 20 73 65 74 20 6f 75 74 |they are set out| 00000500 20 69 6e 20 65 78 65 72 63 69 73 65 20 62 6f 6f | in exercise boo| 00000510 6b 73 2e 20 54 68 65 20 61 69 6d 20 2d 20 61 73 |ks. 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As the Res| 00005120 75 6c 74 73 20 66 69 6c 65 20 63 61 6e 20 68 6f |ults file can ho| 00005130 6c 64 20 61 20 68 75 67 65 20 61 6d 6f 75 6e 74 |ld a huge amount| 00005140 20 6f 66 20 64 61 74 61 20 66 6f 72 20 61 20 73 | of data for a s| 00005150 65 73 73 69 6f 6e 20 69 74 20 6d 61 79 20 62 65 |ession it may be| 00005160 20 74 68 61 74 20 79 6f 75 20 6f 6e 6c 79 20 77 | that you only w| 00005170 61 6e 74 20 74 6f 20 6b 65 65 70 20 74 68 65 20 |ant to keep the | 00005180 72 65 73 75 6c 74 73 20 6f 66 20 74 68 6f 73 65 |results of those| 00005190 20 79 6f 75 20 74 68 69 6e 6b 20 6d 69 67 68 74 | you think might| 000051a0 20 62 65 20 68 61 76 69 6e 67 20 70 61 72 74 69 | be having parti| 000051b0 63 75 6c 61 72 20 70 72 6f 62 6c 65 6d 73 2e 20 |cular problems. | 000051c0 20 0a 0a 41 50 50 45 4e 44 49 58 20 31 20 2d 20 | ..APPENDIX 1 - | 000051d0 44 49 46 46 49 43 55 4c 54 59 20 4c 45 56 45 4c |DIFFICULTY LEVEL| 000051e0 53 0a 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |S.--------------| 000051f0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 00005200 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 4e 6f 74 65 20 |---------..Note | 00005210 74 68 61 74 20 74 68 65 20 6e 75 6d 62 65 72 20 |that the number | 00005220 6f 66 20 66 69 67 75 72 65 73 20 69 73 20 74 68 |of figures is th| 00005230 65 20 6d 61 78 69 6d 75 6d 20 70 6f 73 73 69 62 |e maximum possib| 00005240 6c 65 20 69 6e 20 61 20 63 61 6c 63 75 6c 61 74 |le in a calculat| 00005250 69 6f 6e 2e 0a 0a 4e 75 6d 62 65 72 73 20 75 73 |ion...Numbers us| 00005260 65 64 20 69 6e 20 90 73 75 6d 73 91 20 61 72 65 |ed in .sums. are| 00005270 20 63 68 6f 73 65 6e 20 72 61 6e 64 6f 6d 6c 79 | chosen randomly| 00005280 20 62 79 20 74 68 65 20 63 6f 6d 70 75 74 65 72 | by the computer| 00005290 2e 20 54 68 65 20 6c 65 76 65 6c 73 20 61 63 74 |. The levels act| 000052a0 75 61 6c 6c 79 20 72 65 70 72 65 73 65 6e 74 20 |ually represent | 000052b0 74 68 65 20 68 61 72 64 65 73 74 20 63 61 6c 63 |the hardest calc| 000052c0 75 6c 61 74 69 6f 6e 73 20 74 68 61 74 20 77 69 |ulations that wi| 000052d0 6c 6c 20 62 65 20 70 72 65 73 65 6e 74 65 64 20 |ll be presented | 000052e0 61 74 20 61 20 70 61 72 74 69 63 75 6c 61 72 20 |at a particular | 000052f0 6c 65 76 65 6c 2e 20 48 6f 77 65 76 65 72 2c 20 |level. However, | 00005300 74 68 65 20 63 68 6f 69 63 65 20 6f 66 20 63 61 |the choice of ca| 00005310 6c 63 75 6c 61 74 69 6f 6e 20 69 73 20 70 75 72 |lculation is pur| 00005320 70 6f 73 65 6c 79 20 73 6b 65 77 65 64 20 74 6f |posely skewed to| 00005330 20 67 69 76 65 20 61 20 68 69 67 68 20 63 68 61 | give a high cha| 00005340 6e 63 65 20 6f 66 20 74 68 65 20 6d 6f 73 74 20 |nce of the most | 00005350 64 69 66 66 69 63 75 6c 74 20 63 61 6c 63 75 6c |difficult calcul| 00005360 61 74 69 6f 6e 73 20 62 65 69 6e 67 20 70 72 65 |ations being pre| 00005370 73 65 6e 74 65 64 2e 0a 0a 44 69 76 69 73 69 6f |sented...Divisio| 00005380 6e 20 20 44 49 46 46 49 43 55 4c 54 59 20 4c 45 |n DIFFICULTY LE| 00005390 56 45 4c 53 0a 20 4c 65 76 65 6c 20 31 20 44 69 |VELS. Level 1 Di| 000053a0 76 69 73 6f 72 20 32 2c 20 33 20 6f 72 20 34 2e |visor 2, 3 or 4.| 000053b0 20 4e 75 6d 62 65 72 20 74 6f 20 64 69 76 69 64 | Number to divid| 000053c0 65 20 33 2d 35 20 66 69 67 75 72 65 73 2c 20 6e |e 3-5 figures, n| 000053d0 6f 20 63 61 72 72 79 2c 20 6e 6f 20 72 65 6d 61 |o carry, no rema| 000053e0 69 6e 64 65 72 2e 0a 20 4c 65 76 65 6c 20 32 20 |inder.. Level 2 | 000053f0 44 69 76 69 73 6f 72 20 32 20 2d 20 35 2e 20 4e |Divisor 2 - 5. N| 00005400 75 6d 62 65 72 20 74 6f 20 64 69 76 69 64 65 20 |umber to divide | 00005410 33 20 66 69 67 75 72 65 73 2e 20 43 61 72 72 79 |3 figures. Carry| 00005420 69 6e 67 20 62 75 74 20 6e 6f 20 72 65 6d 61 69 |ing but no remai| 00005430 6e 64 65 72 2e 0a 20 4c 65 76 65 6c 20 33 20 44 |nder.. Level 3 D| 00005440 69 76 69 73 6f 72 20 75 70 20 74 6f 20 39 2e 20 |ivisor up to 9. | 00005450 4e 75 6d 62 65 72 20 74 6f 20 64 69 76 69 64 65 |Number to divide| 00005460 20 35 20 66 69 67 75 72 65 73 2e 20 43 61 72 72 | 5 figures. Carr| 00005470 79 69 6e 67 20 62 75 74 20 6e 6f 20 72 65 6d 61 |ying but no rema| 00005480 69 6e 64 65 72 2e 0a 20 4c 65 76 65 6c 20 34 20 |inder.. Level 4 | 00005490 41 73 20 6c 65 76 65 6c 20 33 20 62 75 74 20 77 |As level 3 but w| 000054a0 69 74 68 20 72 65 6d 61 69 6e 64 65 72 73 2e 0a |ith remainders..| 000054b0 20 4c 65 76 65 6c 20 35 20 4c 6f 6e 67 20 64 69 | Level 5 Long di| 000054c0 76 69 73 69 6f 6e 2e 20 44 69 76 69 73 6f 72 20 |vision. Divisor | 000054d0 31 31 20 2d 20 31 39 2e 20 4e 75 6d 62 65 72 20 |11 - 19. Number | 000054e0 74 6f 20 62 65 20 64 69 76 69 64 65 64 20 33 20 |to be divided 3 | 000054f0 2d 20 34 20 66 69 67 75 72 65 73 2e 0a 20 4c 65 |- 4 figures.. Le| 00005500 76 65 6c 20 36 20 44 69 76 69 73 6f 72 20 31 31 |vel 6 Divisor 11| 00005510 20 2d 20 35 30 2e 20 4e 75 6d 62 65 72 20 74 6f | - 50. Number to| 00005520 20 62 65 20 64 69 76 69 64 65 64 20 34 20 2d 20 | be divided 4 - | 00005530 35 20 66 69 67 75 72 65 73 2e 0a 20 4c 65 76 65 |5 figures.. Leve| 00005540 6c 20 37 20 44 69 76 69 73 6f 72 20 32 30 20 2d |l 7 Divisor 20 -| 00005550 20 39 39 2e 20 4e 75 6d 62 65 72 20 74 6f 20 62 | 99. Number to b| 00005560 65 20 64 69 76 69 64 65 64 20 34 20 2d 20 35 20 |e divided 4 - 5 | 00005570 66 69 67 75 72 65 73 2e 20 0a 0a 20 20 48 45 4c |figures. .. HEL| 00005580 50 20 4c 45 56 45 4c 53 0a 20 4c 65 76 65 6c 20 |P LEVELS. Level | 00005590 31 20 52 65 64 20 73 71 75 61 72 65 20 6d 61 72 |1 Red square mar| 000055a0 6b 73 20 63 6f 6c 75 6d 6e 20 74 6f 20 62 65 20 |ks column to be | 000055b0 64 6f 6e 65 20 6e 65 78 74 2e 0a 20 4c 65 76 65 |done next.. Leve| 000055c0 6c 20 32 20 43 6c 69 63 6b 69 6e 67 20 48 65 6c |l 2 Clicking Hel| 000055d0 70 20 67 69 76 65 20 74 79 70 65 20 6f 66 20 6f |p give type of o| 000055e0 70 65 72 61 74 69 6f 6e 20 74 6f 20 62 65 20 64 |peration to be d| 000055f0 6f 6e 65 20 6e 65 78 74 2e 0a 20 4c 65 76 65 6c |one next.. Level| 00005600 20 33 20 46 69 67 75 72 65 73 20 6d 75 73 74 20 | 3 Figures must | 00005610 62 65 20 70 6c 61 63 65 64 20 61 74 20 74 68 65 |be placed at the| 00005620 20 70 6f 73 69 74 69 6f 6e 20 6f 66 20 74 68 65 | position of the| 00005630 20 72 65 64 20 73 71 75 61 72 65 2e 0a 20 4c 65 | red square.. Le| 00005640 76 65 6c 20 34 20 47 69 76 65 73 20 74 79 70 65 |vel 4 Gives type| 00005650 20 6f 66 20 6f 70 65 72 61 74 69 6f 6e 20 77 69 | of operation wi| 00005660 74 68 20 73 70 65 63 69 66 69 63 20 66 69 67 75 |th specific figu| 00005670 72 65 73 2e 0a 20 4c 65 76 65 6c 20 35 20 46 6f |res.. Level 5 Fo| 00005680 72 63 65 73 20 72 69 67 68 74 20 61 6e 73 77 65 |rces right answe| 00005690 72 2e 0a 0a 4d 75 6c 74 69 70 6c 69 63 61 74 69 |r...Multiplicati| 000056a0 6f 6e 20 44 69 66 66 69 63 75 6c 74 79 20 4c 65 |on Difficulty Le| 000056b0 76 65 6c 73 0a 20 4c 65 76 65 6c 20 31 20 32 20 |vels. Level 1 2 | 000056c0 66 69 67 75 72 65 73 20 74 69 6d 65 73 20 31 20 |figures times 1 | 000056d0 66 69 67 75 72 65 2e 0a 20 4c 65 76 65 6c 20 32 |figure.. Level 2| 000056e0 20 33 20 66 69 67 75 72 65 73 20 74 69 6d 65 73 | 3 figures times| 000056f0 20 31 20 66 69 67 75 72 65 2e 0a 20 4c 65 76 65 | 1 figure.. Leve| 00005700 6c 20 33 20 33 20 66 69 67 75 72 65 73 20 74 69 |l 3 3 figures ti| 00005710 6d 65 73 20 31 30 2e 0a 20 4c 65 76 65 6c 20 34 |mes 10.. Level 4| 00005720 20 33 20 66 69 67 75 72 65 73 20 74 69 6d 65 73 | 3 figures times| 00005730 20 32 20 66 69 67 75 72 65 73 2e 20 4f 6e 65 20 | 2 figures. One | 00005740 6f 66 20 74 68 65 20 74 77 6f 20 66 69 67 75 72 |of the two figur| 00005750 65 73 20 69 6e 20 74 68 65 20 6d 75 6c 74 69 70 |es in the multip| 00005760 6c 69 65 72 20 77 69 6c 6c 20 61 6c 77 61 79 73 |lier will always| 00005770 20 62 65 20 31 2e 20 53 77 69 74 63 68 65 73 20 | be 1. Switches | 00005780 74 6f 20 6c 6f 6e 67 20 6d 75 6c 74 69 70 6c 69 |to long multipli| 00005790 63 61 74 69 6f 6e 20 6c 61 79 6f 75 74 2e 0a 20 |cation layout.. | 000057a0 4c 65 76 65 6c 20 35 20 33 20 66 69 67 75 72 65 |Level 5 3 figure| 000057b0 73 20 74 69 6d 65 73 20 74 77 6f 20 66 69 67 75 |s times two figu| 000057c0 72 65 73 2e 20 4e 6f 20 72 65 73 74 72 69 63 74 |res. No restrict| 000057d0 69 6f 6e 73 20 6f 6e 20 6d 75 6c 74 69 70 6c 69 |ions on multipli| 000057e0 65 72 2e 20 0a 0a 20 20 48 65 6c 70 20 6c 65 76 |er. .. Help lev| 000057f0 65 6c 73 0a 20 4c 65 76 65 6c 20 30 20 20 20 54 |els. Level 0 T| 00005800 68 65 20 72 65 64 20 73 71 75 61 72 65 20 73 68 |he red square sh| 00005810 6f 77 73 20 74 68 65 20 63 6f 6c 75 6d 6e 2e 20 |ows the column. | 00005820 4e 6f 20 6d 65 73 73 61 67 65 2e 0a 20 4c 65 76 |No message.. Lev| 00005830 65 6c 20 31 20 20 20 48 65 6c 70 20 67 69 76 65 |el 1 Help give| 00005840 73 20 6d 65 73 73 61 67 65 20 61 62 6f 75 74 20 |s message about | 00005850 63 6f 6c 75 6d 6e 2e 0a 20 4c 65 76 65 6c 20 32 |column.. Level 2| 00005860 20 20 20 41 73 20 6c 65 76 65 6c 20 31 20 62 75 | As level 1 bu| 00005870 74 20 72 65 6d 69 6e 64 65 72 20 61 62 6f 75 74 |t reminder about| 00005880 20 63 61 72 72 79 20 69 73 20 61 6c 73 6f 20 67 | carry is also g| 00005890 69 76 65 6e 20 69 66 20 72 65 6c 65 76 61 6e 74 |iven if relevant| 000058a0 2e 0a 20 4c 65 76 65 6c 20 33 20 20 20 52 65 64 |.. Level 3 Red| 000058b0 20 73 71 75 61 72 65 20 67 6f 65 73 20 74 6f 20 | square goes to | 000058c0 63 61 72 72 79 20 70 6f 73 69 74 69 6f 6e 2e 20 |carry position. | 000058d0 43 6f 6c 75 6d 6e 20 6d 65 73 73 61 67 65 20 6f |Column message o| 000058e0 72 20 63 61 72 72 79 20 6d 65 73 73 61 67 65 2e |r carry message.| 000058f0 0a 20 4c 65 76 65 6c 20 34 20 20 20 47 69 76 65 |. Level 4 Give| 00005900 73 20 64 65 74 61 69 6c 73 20 6f 66 20 77 68 61 |s details of wha| 00005910 74 20 74 6f 20 6d 75 6c 74 69 70 6c 79 2f 61 64 |t to multiply/ad| 00005920 64 20 6f 72 20 77 68 61 74 20 74 6f 20 63 61 72 |d or what to car| 00005930 72 79 2e 0a 20 4c 65 76 65 6c 20 35 20 20 20 46 |ry.. 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Once these | 00005c00 68 61 76 65 20 62 65 65 6e 20 61 73 73 65 6d 62 |have been assemb| 00005c10 6c 65 64 20 6f 6e 20 74 68 65 20 77 6f 72 6b 73 |led on the works| 00005c20 68 65 65 74 20 66 75 72 74 68 65 72 20 73 75 6d |heet further sum| 00005c30 73 20 61 72 65 20 61 64 64 65 64 2c 20 75 73 69 |s are added, usi| 00005c40 6e 67 20 0a 20 20 20 20 20 20 74 68 65 20 73 74 |ng . the st| 00005c50 75 64 65 6e 74 27 73 20 63 75 72 72 65 6e 74 20 |udent's current | 00005c60 64 69 66 66 69 63 75 6c 74 79 20 6c 65 76 65 6c |difficulty level| 00005c70 73 20 61 6e 64 20 63 68 6f 73 65 6e 20 6f 70 65 |s and chosen ope| 00005c80 72 61 74 6f 72 73 2c 20 74 6f 20 66 69 6c 6c 20 |rators, to fill | 00005c90 74 68 65 20 70 61 67 65 2e 20 0a 0a 54 68 65 20 |the page. ..The | 00005ca0 72 65 73 75 6c 74 20 6c 6f 6f 6b 73 20 6c 69 6b |result looks lik| 00005cb0 65 20 74 68 69 73 3a 0a 0a 28 65 6e 64 73 29 |e this:..(ends)| 00005cbf
.