1. By Sanjar Hekmati

2. Standard: Students will understand algebraic concepts and applications 9-12 Benchmark.A.1: Represent and analyze mathematical situations and structures using algebraic symbols. 9-12.A.1.1 Use the special symbols of mathematics correctly and precisely. 9-12 Benchmark A.3: Use mathematical models to represent and understand quantitative relationships. Standard 9: Understand how mathematical ideal build on one another Standard 10: Use representations to solve problems 9-12 Benchmark D.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

3. To identify matrices and their elements To organize data into matrices To solve certain matrix equations To multiply two matrices To use inverse matrices in solving matrix equations To use real-world connection

4. A graphing calculator a. TI-83, TI-84 series Game set 1, 2, and 3 Video on Cryptography Video on matrix multiplication Internet access (or any graphing calculator- homework)

5. Algebra 1 Knowledge of using a graphing calculator Be able to scramble letters to make words Be able to use logic, strategy, work well with a group

6. Essential questions: a.What is Cryptography? b.Writing activity- Construct a “Frayer Model” on Cryptography c.What is matrix multiplication d.Solve varies matrix multiplications The students (groups of 3 to 4) will start by solving simple system of equations to obtain a information on which game set (1,2,3) to try first The students will use the encoding matrix to decode another matrix The students will use the new matrix to obtain numbers that correspond to certain letters from a table (hints will be given) The students will scramble(decode) the letters to make out certain words and phrases

7. The Matrix

8. A = 26, 0 = INDICATES A BREAKN = 13 B = 250 = 12 C = 24P = 11 D = 23Q = 10 E = 22R = 9 F = 21S = 8 G = 20T = 7 H = 19U = 6 I = 18V = 5 J = 17W = 4 K = 16X = 3 L = 15Y = 2 M = 14Z = 1

10. # 4. Hint – Part of a parabola 6.5 16.5 20.5 23.5 15 1 Matrix C = 1.75 2.25 1.25 4.75 -3.5.5 2.5 4.5 -2 -3.5 -7 0 8 21 14 7 8 0 S F M T S o = 2 0 9 26 0 2 = Y o R A o Y= AXIS OF SYMMETRY 3 12 18 14 22 0 X O I M E o

11. The game is designed for students to learn through problem based learning, the teachers role is to proctor the groups as their solving the puzzles In order for fairness, the teacher will not help the groups with errors and give extra help Individual assessment will take place at home or outside of the classroom where students are required to visit the teacher website to play the game and turned in a hard copy of the puzzles they finished.

14. Proficiency with the use of graphing calculators raises test scores Students are allowed to use graphing calculators on SBA When graphing calculators are effectively used in the mathematics classroom, they are a powerful tool to assist teachers in providing their students with an environment to help them construct their mathematical knowledge and understanding A graphing calculator is one of the most portable and affordable(only on ebay) technology in mathematics education A graphing calculator quickens the mechanical procedure in solving mathematical problems and creates a highly interactive learning environment, which makes learning a seemingly difficult subject, easy The game of cryptography is something new to students and interesting enough to keep them engaged while learning math.

15. PLAY THE GAME USING MATRIX MULTIPLICATION PLAY THE GAME USING MATRIX INVERSES PLAY THE GAME USING LOGIC, PLAY THE GAME USING HINTS TO CONNECT TO MATH CONCEPTS PLAY THE GAME CONNECTING SOLUTIONS TO REAL-WORLD SITUATIONS MAKE THE CONNECTION BETWEEN THE GAME AND THE MATH CONCEPT

16. Secondary school teachers’ conceptions and their teaching practices using graphing calculators, Jane A. Lee and Douglas E. McDougall, International Journal of Mathematical Education in Science and Technology, 2010. Effects of the application of graphing calculator on students’ probability achievement, Choo-Kim Tran, Computers and Education, May of 2012 Instructional efficiency of the integration of graphing calculators in teaching and learning mathematics, Wan Zah Wan Ali, International Journal of Instruction, July 2009. Fostering positive attitude in probability learning using graphing calculator, Lau Siong-Hoe and Madhubula Bava, November 2011

17. Game on line http://hekmati.bhs.beleneagles.org Free graphing calculators online http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCal c.html http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCal c.html http://www.calculator-grapher.com/calculators/matrix-calculator.html http://www.numberempire.com/matrixcalculator.php Help on matrix multiplication http://www.youtube.com/watch?v=_fFj4NbLcTU http://www.prenhall.com/divisions/esm/app/calc_v2/ http://www.prenhall.com/divisions/esm/app/graphing/ti83/Home_Screen/ Menu_Keys/Matrix/matrix.html http://www.prenhall.com/divisions/esm/app/graphing/ti83/Home_Screen/ Menu_Keys/Matrix/matrix.html