Math Tutor 3 is a set of 21 programs that contain introductory tutorials and problem sets on fractions. Each tutorial is followed by a set of problems for the child to answer.

This set of software is built on the basic premise that mathematics, at any level, can only be really understood if it is practiced again and again. Though practicing on a computer can be very helpful, there is no substitute for having the student work out problems with pencil and paper. With this in mind, this distribution contains several activities that generate hardcopy problem sets in PostScript format. (See below for printing PostScript files.)

This package is Freeware and can be freely distributed. This package has no special requirements (e.g. a particular run-time library) and runs under DOS, which means that it can also be run from a DOS window under Windows 3.1 and Windows 9x (though you may have to rezise the DOS window to see the text at the bottom of some pages).

To obtain a copy of this package, simply hold down the left [Shift] key and use the mouse to click on MATH3REG.ZIP. By ensuring that the file transfer is in binary mode, this zip file will be copied to your system. Though I have tried to use unique file names in all of my programs, I would suggest that you download this file to its own directory.

Once this file is downloaded, all of the files can be extracted. The zip file can then be deleted, or moved to a floppy disk for storage. Before running this package, you should first view the file README.TXT to see any additional information. To run this package, simply go to this directory and enter the command

      MATH3

     Activities for Math 3 (Registered Version)
       A = Introduction to Fractions (Level 1)
       B = More Intro. to Fractions Problems (Level 1)
       C = Generate PostScript Intro. to Fract. Prob. (Level 1)
       D = Fractions of a Whole (Level 2)
       E = More Fractions of a Whole Problems (Level 2)
       F = Generate PostScript Fract. of a Whole Prob. (Level 2)
       G = Putting Fractions into Words (Level 3)
       H = More Putting Fractions into Words Problems (Level 3)
       I = Generate PostScript Putting Fract. into Words Prob. (Level 3)
       J = Adding/Subtracting Fractions w/ Common Denominator (Level 4)
       K = More Adding/Subtracting Fractions Problems (Level 4)
       L = Generate PostScript Add./Sub. Fractions Problems (Level 4)
       M = Reducing Fractions (Level 5)
       N = More Reducing Fractions Problems (Level 5)
       O = Generate PostScript Reducing Fractions Problems (Level 5)
       P = Multiplying Two Fractions (Level 6)
       Q = More Multiplying Two Fractions Problems (Level 6)
       R = Generate PostScript Mult. Two Fractions Problems (Level 6)
       S = Simplifying Fractions (Level 7)
       T = More Simplifying Fractions Problems (Level 7)
       U = Generate PostScript Simplifying Fractions Problems (Level 7)
       Z = Nothing (DOS)

When I wrote these tutorials, I assumed that an older person will be working with the young student. Each tutorial screen contains a fair amount of information and is set up so that the older person can carefully discuss this information with the student. In addition, not all of the activities may be appropriate for a given student. It is therefore highly recommended that the older person, or supervisor, first read the file DESCR.TXT. This file contains a general description of the activities and allows for the selection of an appropriate activity.

All of the practice problems use a random number generator to select the numbers. This means that the same activity can be run many times and slightly different problems will be asked. It also means that the same question may be asked more than once, or a relatively hard problem may be followed by a very easy one.

The 21 activities are grouped into seven sets, or levels, with three activities in each level. The first activity within a given level contains a tutorial that introduces a new concept. At the end of the tutorial, the student solves five problems dealing with this concept. The second activity within a level is simply an interactive set of questions on this concept. Up to 20 problems can be given and this allows the student to reinforce their understanding of this concept without having to go through the tutorial again. When the student answers these interactive problems (in the first two activities of any level), they only need to press the correct number key; they never have to press the [Enter] key. The third activity generates a sheet of questions, and an answer key sheet, as separate PostScript files. I have found that my child prefers to answer the questions using pencil and paper, instead of sitting at the computer, and gives practice at handling the tests they receive at school.

These PostScript files can be printed by sending them to a PostScript printer. If such a printer is not available, they can first be read into a PostScript viewer and printed from there. A good PostScript viewer is "ghostview". Versions for DOS, Windows 3.1 and Windows 9x can be obtained by going to http://www.cs.wisc.edu/~ghost/. There you can also get a good Windows interface called GSview. (Please note that I have no involvement with ghostview or GSview, I just find them useful.)

One final point before describing the concepts introduced in each level is that all questions are generated "on the fly" using a random number generator. This means that the same activity can be run many times with slightly different questions being asked. This also (unfortulately) means that the same question may be asked more than once and that a relatively hard question may be followed by a very easy one.

(A) Introduction to Fractions (Level 1)
(B) More Intro. to Fractions Questions (Level 1)
(C) Generate PostScript Intro. to Fractions Questions (Level 1)

The tutorial introduces the student to the concept of fractions, and the terms "numerator" and "denominator". In the interactive problems, Activities A and B, the student is shown a group of blocks, some of them are red and others are yellow, and is asked to enter the fraction of blocks that are red. In the PostScript questions, some of the blocks are empty and some are filled, and the student needs to enter the fraction of the blocks that are filled.

(D) Fractions of a Whole (Level 2)
(E) More Fractions of a Whole Questions (Level 2)
(F) Generate PostScript Fractions of a Whole Questions (Level 2)

The tutorial builds on the concept introduced in the preceeding level by showing them how you can measure the fraction of a single object that is divided into equal sections. In the interactive problems, Activities D and E, the student is shown an object that is divided into several sections, some of the sections are red and others are yellow, and is asked to enter the fraction of the object that is red. In the PostScript questions, some of the sections are empty and some are filled, and the student needs to enter the fraction of the object that is filled.

(G) Putting Fractions into Words (Level 3)
(H) More Putting Fractions into Words Problems (Level 3)
(I) Generate PostScript Putting Fractions into Words Problems (Level 3)

The tutorial describes how to put a fraction into words, and intorduces the correct way of writing the denominator (half, third, fourth, etc). In the interactive problems, Activities G and H, the student is shown a a fraction in words (e.g. three-fifths) and they are asked to enter the corresponding numerical fraction. In the PostScript questions, three different types of problem sheets can be generated. The first shows a column of fractions in words and a column of numerical fractions, and is asked to match the number with the words. The second lists fractions in words and they have to write the numerical fraction, and the third lists numerical fractions and they have to write each fraction in words.

(J) Adding/Subtracting Fractions with a Common Denominator (Level 4)
(K) More Adding/Subtracting Fractions Questions (Level 4)
(L) Generate PostScript Adding/Subtracting Fractions Questions (Level 4)

The tutorial introduces the term "common denominator" and shows the student how to add or subtract two fractions with a common denominator. The problems shown/generated in each of these activities display two fractions with a common denominator and the student must add or subtract these fractions. (Please note that the concept of a negative number has not been introduced yet, so in all subtraction problems the first fraction is always larger than the second.)

(M) Reducing Fractions (Level 5)
(N) More Reducing Fractions Problems (Level 5)
(O) Generate PostScript Reducing Fractions Problems (Level 5)

The tutorial introduces the student to "improper fractions", where the numerator is larger than the denominator, and teaches them how to reduce them. The problems shown/generated in each of these activities display an improper fraction and ask the student to reduce it.

(P) Multiplying Two Fractions (Level 6)
(Q) More Multiplying Two Fractions Problems (Level 6)
(R) Generate PostScript Multiplying Two Fractions Problems (Level 6)

The tutorial first describes how the word "of" is used to mean multiply (i.e. "one-half of one-half" means "one-half times one-half") by means of an example. It then shows the student how to multiply two fractions together. The problems shown/generated in each of these activities display two fractions and asks the student to multiply them.

(S) Simplifying Fractions (Level 7)
(T) More Simplifying Fractions Problems (Level 7)
(U) Generate PostScript Simplifying Fractions Problems (Level 7)

The tutorial uses the concept introduced in the preceeding level to show the student how to reduce a fraction. In other words, it shows them that "two-fourths" is the same as "one-half". The problems shown/generated in each of these activities display a fraction that the student must simplify.

I hope this set of programs is useful and you will let me know if you have any suggestions to make them better.

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� 1998 Brian T. Luke, Ph.D.