Math Tutor 4 is a set of 21 programs that continue the 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 MATH4REG.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

      MATH4

     Activities for Math 4 (Registered Version)
       A = Tutorial on Adding/Subtracting Fractions 2 (Level 8)
       B = More Adding/Subtracting Fractions 2 Problems (Level 8)
       C = Generate PostScript Add/Sub Fract. 2 Prob. (Level 8)
       D = Tutorial on Multiplying/Dividing Fractions 2 (Level 9)
       E = More Multiplying/Dividing Fractions 2 Problems (Level 9)
       F = Generate PostScript Mult/Div Fract. 2 Prob. (Level 9)
       G = Tutorial on Adding/Subtracting Fractions 3 (Level 10)
       H = More Adding/Subtracting Fractions 3 Problems (Level 10)
       I = Generate PostScript Add/Sub Fract. 3 Prob. (Level 10)
       J = Change a Number to a Product of Primes Tutorial (Level 11)
       K = More Number to Product of Primes Problems (Level 11)
       L = Generate PostScript Product of Primes Problems (Level 11)
       M = Tutorial on Greatest Common Factor of Two Numbers (Level 12)
       N = More Greatest Common Factor Problems (Level 12)
       O = Generate PostScript Greatest Common Factor Prob. (Level 12)
       P = Tutorial on Least Common Multiple of Two Numbers (Level 13)
       Q = More Least Common Multiple Problems (Level 13)
       R = Generate PostScript Least Common Multiple Prob. (Level 13)
       S = Tutorial on Advanced Fractions Problems (Level 14)
       T = More Advanced Fractions Problems (Level 14)
       U = Generate PostScript Advanced Fractions Problems (Level 14)
       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 daughter prefers to answer the questions using pencil and paper, instead of sitting at the computer, and they give her practice at handling the tests she receives 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) Tutorial on Adding/Subtracting Fractions 2 (Level 8)
(B) More Adding/Subtracting Fractions 2 Problems (Level 8)
(C) Generate PostScript Add/Sub Fract. 2 Prob. (Level 8)

In the Level 5 activities (M, N and O) of the Registered Version of Math Tutor 3, the student learned how to convert an improper fraction into a "mixed" proper fraction that contains an integer and a fraction. In this tutorial, the student is shown how to add and subtract two mixed fractions by first changing them to improper fractions. The result is then converted to a reduced, proper fraction. In the interactive problems, Activities A and B, the student is shown two mixed fractions that should be added or subtracted. Four possible answers are shown (labeled A through D) and the student only has to type the letter of the correct answer. In the PostScript questions, the student must add or subtract two mixed fractions.

(D) Tutorial on Multiplying/Dividing Fractions 2 (Level 9)
(E) More Multiplying/Dividing Fractions 2 Problems (Level 9)
(F) Generate PostScript Mult/Div Fract. 2 Prob. (Level 9)

In the Level 6 activities (P, Q and R) of the Registered Version of Math Tutor 3, the student learned how to multiply two fractions together. In this tutorial, the student is shown how to multiply an integer times a fraction, and how to divide one fraction by another. The result is then converted to a reduced, proper fraction. In the interactive problems, Activities D and E, the student is shown an integer times a fraction divided by a fraction. Four possible answers are shown (labeled A through D) and the student only has to type the letter of the correct answer. In the PostScript questions, the student must simplify expressions containing an integer times a fraction divided by a fraction.

(G) Tutorial on Adding/Subtracting Fractions 3 (Level 10)
(H) More Adding/Subtracting Fractions 3 Problems (Level 10)
(I) Generate PostScript Add/Sub Fract. 3 Prob. (Level 10)

The tutorial describes how to add and subtract two fractions with slightly different denominators. Since this is the first time that this subject is treated, one denominator is simply a small number times the other. Once the fractions are placed under a common denominator and added or subtracted, the result is then converted to a reduced, proper fraction. In the interactive problems, Activities G and H, the student is shown a mixed fraction plus or minus another fraction. Four possible answers are shown (labeled A through D) and the student only has to type the letter of the correct answer. In the PostScript questions, the student must simplify expressions containing a mixed fraction plus or minus another fraction.

(J) Change a Number to a Product of Primes Tutorial (Level 11)
(K) More Number to Product of Primes Problems (Level 11)
(L) Generate PostScript Product of Primes Problems (Level 11)

In order for the student to solve more advanced fractions problems, it is first necessary to show them how to break up a number into a product of primes. This tutorial (Activity J) introduces the concept of "prime numbers". It lists the first seven prime numbers and explains that the only way to tell if a number is prime is to see if it can be evenly divided by smaller prime numbers. The tutorial then proceeds to show the student "tricks" to determine whether a number is evenly divisible by 2, 3, 5 or 11. This activity then reviews the information by asking the student to enter the first five prime numbers. This is followed by a set of questions asking if certain numbers are evenly divisible by a 2, then 3, then 5, then 11. Here the student only has to press the "Y" key for yes or the "N" key for no for each number. The tutorial continues by showing the student how to break up a number into a product of primes. The student is then asked to find the prime factors of five numbers. Here, the student only has to enter a prime factor (without pressing the [Enter] key) and the program automatically lists all other factors. In Activity K, the student is asked to break up numbers into products of primes using the same procedure described above. Activity L generates a sheet of numbers and the student must write down the product of primes. (Please note that the answer key lists the prime factors in ascending order but the Commutative Property of Multiplication states that they can be listed in any order.)

(M) Tutorial on Greatest Common Factor of Two Numbers (Level 12)
(N) More Greatest Common Factor Problems (Level 12)
(O) Generate PostScript Greatest Common Factor Prob. (Level 12)

The tutorial (Activity M) uses the information in the previous level to introduce the student to the "Greatest Common Factor" (GCF) between two numbers. After a couple of examples, the student is asked to determine the GCF for five pairs of numbers. The tutorial continues to show how this information is used to reduce a fraction to its simplest terms (e.g 24/60 = 2/5). The student is then asked to reduce five fractions to their simplest terms. In Activity N, you have the option of having the program ask up to 20 questions on finding the GCF of two numbers and/or reducing a fraction to its simplest terms. In Activity O, you have the option of generating a problem sheet (and answer key) on either finding the GCF of pairs of numbers or reducing fractions to their simplest terms.

(P) Tutorial on Least Common Multiple of Two Numbers (Level 13)
(Q) More Least Common Multiple Problems (Level 13)
(R) Generate PostScript Least Common Multiple Prob. (Level 13)

The tutorial (Activity M) uses the information in Level 11 to introduce the student to the "Least Common Multiple" (LCM) between two numbers. After a couple of examples, the student is asked to determine the LCM for five oairs of numbers. The tutorial continues to show how this information is used to add or subtract fractions with different denominators. The student is then asked to add/subtract five pairs of fractions, giving the answer as a proper, reduced fraction. In Activity N, you have the option of having the program ask up to 20 questions on finding the LCM of two numbers and/or adding or subtracting two fractions. In Activity O, you have the option of generating a problem sheet (and answer key) on either finding the LCM of pairs of numbers or adding/subtracting two fractions.

(S) Tutorial on Advanced Fractions Problems (Level 14)
(T) More Advanced Fractions Problems (Level 14)
(U) Generate PostScript Advanced Fractions Problems (Level 14)

The tutorial (Activity S) uses the concepts presented in the preceeding levels to show the student how to simplify complex expressions involving fractions. In general, the numerator of these expressions contains the sum or difference of two fractions with different denominators, and the denominator is a third fraction. At the end of the tutorial, the student is asked to simplify five expressions, giving the result as a proper, reduced fraction. Activity T lets the student simplify up to 20 expressions, and Activity U generates a sheet of complex expressions 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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� 1999 Brian T. Luke, Ph.D.