************************************ MathMagic Cycle 4: Level 7-9 Regular ************************************ CHECKERBOARD MATH Have you ever played the game of checkers? Its played on a board that has squares on it that alternate between 2 colors, usually black and red. The squares are arranged into 8 rows and 8 columns. Answer these questions regarding the checkerboard: 1) How many squares are on a checkerboard? 2) When played, each of 2 players each fills 3 rows with checkers (1 player has black, the other player has red) A) How many checkers are there? B) How many empty squares ore there? C) What fraction of the squares is filled with red squares? 3) There is a story about an inventor who was promised by a king that he would be given 1 grain of rice on the first square, 2 on the second square, 4 on the third, 8 on the fourth, continuing to double the amount on each successive square. A) How many grains of rice would be on the last square in the third row? B) How many grains would be on the last square? C) If each grain is 1/4 inches long (6 mm), how many miles long (kilometers) would the grains be if placed end to end? 4) A domino exactly covers 2 squares. A) How many dominoes will be needed to cover all the squares? B) How many dominoes are needed to cover all the squares except for 1 red and 1 black square? C) How many dominoes are needed to cover all the squares except for 2 red squares? ************************************* MathMagic Cycle 4: Level 7-9 Advanced ************************************* MATH CHAIN A math chain is a series of operations which keeps generating the same result. Start with any number you want and perform the indicated operations to fill in the spaces. When you fill in the [ ] it will be the number you started with. For a greater challenge, start with a number less than 3. [___] -3 = ___ x 6 = ___ + 12 = ___ /6 = ___ + 1 = [___] x 4 = ___ + 8 = ___ /4 = ___ - 2 = [___] + 36 = ___ - 28 = ___ x 4 = ____ - 32 = ____ /4 = [___] Exercise I A) Do the Chain for [ 3 ]. Then do it for [ -2 ]. B) Will the results in [___] always be the same. Explain. C) Is it true for any number x. Prove it! D) Does the chain work in reverse? Start on the end and try it. Explain your results. E) Make your own math chain with at least 3 [___] 's. *********************************************************