************************************* MathMagic Cycle 14: Level 4-6 Regular ************************************* 1 2 3 ----- ----- ----- Using small chips, buttons or cutouts labeled K, | | | | L,M, X and Y place them in the squares in this A | | | | order: K in A1; L in A2; X in A3; M in B1 and | | | | Y in B3. ----- ----- ----- | | | | Sliding horizontally (right & left) or vertically B | | | | (up & down) one chip at a time, can you make the | | | | X and the Y change places? ----- ----- ----- You should be able to do it under 20 moves, but probably in more than 12. Use a table like this one to keep track of your moves: |Move#|letter| from | to | Also, use this scale to rate your |-----+------+------+------| results: | 1 | L | A2 | B2 | 12 moves: Extraordinary |-----+------+------+------| - | | | | | 14 moves: Outstanding |-----+------+------+------| - | | | | | 16 moves: Superior |-----+------+------+------| - | | | | | 18 moves: Very Good |-----+------+------+------| - | | | | | 20 moves: Great ************************************** MathMagic Cycle 14: Level 4-6 Advanced ************************************** 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! ==================