Louisiana School Math Resources
created by J. Bradford Burkman (email)
Instructor in Mathematics
Louisiana School for Math, Science, and the Arts www.lsmsa.edu
made freely available for use and adaptation in all educational settings under the terms of the GNU General Public License.
Feedback Appreciated


Ideas Behind this Collection.
1. Even in this age of hand-held CAS, students still benefit from learning to do mathematics by hand.
2. Exercises that come out nicely when worked by hand are much harder to write than ones requiring a calculator, and (ironically), finding the best paper-and-pencil exercises requires a computer.
3. Students will do their homework together, so curriculum materials should be designed to encourage productive cooperative learning. Many of these exercise sets have a page for each student, with similar but different exercises.
4. The coming of educational cyberinfrastructure allows teachers access to curriculum materials that do not fit in a printed textbook.
5. All of the programs required to use and revise these curriculum materials (C++, TeX, pdf) are available for free. The C++ files that generated most of these exercises are written to work on most IDE's.


Fraction-Addition Mistakes: Practice in finding mistakes in the addition of fractions.
Worksheets, with explanatory materials.
WARNING: The above document is 111 pages. Print selectively.
Generating C++ code
TeX code for introductory pages
TeX fonts used (primitive, I know)
permutations20m.txt, a file used in running the C++.
Permutations Lecture, a prototype PDF slide presentation.
Slides will not advance automatically if opened in a web browser. Save and open as PDF for the full-screen effect.


The above set of exercises in Fraction-addition mistakes is the model for a three-year project whose approval for funding is pending at the National Science Foundation. The project will develop similar exercises in proofreading for Intermediate-Algebra topics. As they are developed and updated, these curriculum materials will be added to this collection.

Completing-the-Square Mistakes: Practice in finding mistakes in quadratics equations, functions and relations.
Level One: Quadratic equations of the form x² + 2bx + (b² - c²) = 0, b, c ε {1, 2, 3, ... 12}.
Each of 100 worksheets has twelve worked-out "solve-for-x" exercises, one of which is correct, and eleven of which have a different type of mistake.
In Fall 2007 I plan to expand to more interesting equations, with factoring, rational coefficients, and non-integer roots.
Plans are sketched at Quadratic Plans 21 May 2007, and exercises in Mistake #1 for b, c ε {1, 2, 3, ... 100} are at Quadratic 1 Details.

Teachers are welcome to anonymously download and use these materials freely in all educational settings. There is no mechanism included in the download that seeks registration, names, email addresses, or other identifying information.

Feedback from teachers is greatly appreciated, in three areas:
    Utility of the materials to your classes and students
    Experiences using them in the classroom
        Note: Please do not include students' names or identifying information, as their anonymity should be respected.
    Suggestions for revisions or new versions

Send feedback to bburkman@lsmsa.edu

Participation is voluntary. We may email with follow-up questions, but response is voluntary, and withdrawl from participation at any time will be respected. Email not being a secure mode of communication, privacy of the information sent cannot be guaranteed, but the investigators will not use contributors' names or identifying information in print or online publications without their consent.

Questions or concerns about the research may also be sent to Brad Burkman
    bburkman@lsmsa.edu
    Office: 318-357-3174 x130
    Fax 318-357-3299
    Louisiana School for Math, Science, and the Arts
    715 University Parkway
    Natchitoches, LA 71457

Copies of the NSF project description, summaries of feedback, and summaries of results of the project, will be posted here.

Two Radicals: 28,044 Equations in one variable with two radicals, of the form √(ax + b) + √(cx+d) = e, with integer solutions. Some sets have extraneous solutions, one has double solutions, one has no actual solutions.
Introduction
Set 1 PDF format, TeX format Addition, one actual, one extraneous solution. (2404 exercises)
Set 2 PDF format, TeX format Subtraction, one actual, one extraneous solution. (2960 exercises)
Set 3 PDF format, TeX format Addition, two different solutions. (3356 exercises)
Set 4 PDF format, TeX format Addition, one double solution. (430 exercises)
Set 5 PDF format, TeX format Addition, no actual solutions. (18894 exercises)
Generating C++ code.

Proportions: Similar-triangle exercises involving proportions, systems of two equations in two variables, and factorable quadratic equations with extraneous solutions.
Worksheets Being revised for wide distribution. This version has my students' names on the worksheets.
Generating C++ code


Triangle Ratios 15: The ratios of the lengths of the sides of all triangles with angles whose measures are multiples of 15°. Instructions on how to make "Law of Sines," "Ambiguous Law of Sines," and "Law of Cosines" exercises. The .pdf file is given, along with the .TeX file for adaptation.
.pdf file
.TeX file

Three Methods for Approximating √2: Shows the first few iterations of three methods of approximating √2: Bracket-and-halving, Linear interpolation (secant lines), and Newton's method (tangent lines).
Most dramatically, it illustrates the speed with which the three sequences converge to six significant digits of accuracy: Newton in four iterations, linear interpolation in seven, but seventeen for bracket-and-halving.
I stopped the Newton's method after four iterations, because the numbers get too big for my C++ IDE to support.
.pdf file
.TeX file
Generating .cpp code