************************************* MathMagic Cycle 14: Level 7-9 Regular ************************************* The ODD TIMES TABLE 1 2 3 4 5 6 7 8 9 10 On an 18X18 grid we are going to create an odd - - - - - - - - - -- times table. Instead of writing the product un- 1 |1 2 3 4 5 6 7 8 9 der the column and across the row, we are 2 |2 4 6 8 1 3 going to write the repeated sum of each number: 3 |3 6 9 3 for 8x6=48 we need to add 4+8=12 and repeat the 4 |4 8 sum until we have one digit: 1+2=3 5 | 6 | 3 Your and your NTP's job is to complete the odd 7 | table and to analyze the result, and come up 8 | with some conclusions that can be turned into 9 | "predictions". Look for lines of symmetry (a 10 | line that creates a mirror image); horizontal vertical or diagonal patterns, and any opera- tion that works with the numbers inside the box. Each "prediction" that you can explain and demonstrate will be called a hypothesis, and will give your team one point. Here is a chance to show all the other MathMagic teams how clever you are! ************************************** MathMagic Cycle 14: Level 7-9 Advanced ************************************** Correcting the "spelling" of an equation Almost any 5th grader should be able to show that the following equation is not true: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 100 Using only + and - signs, change the spacing between the numbers on the left side to allow for bigger numbers, without changing the order of the digits or the result: 123 + 45 - 67 + 89 = 100 Between your team and your NTPs you should be able to create at least six more equations. Can you do the same for the reverse ordered digits? 98 + 76 ... = 100? If each possibility is one point, what was your score? ==================