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MathMagic Cycle 14: Level 7-9 Regular
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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!
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MathMagic Cycle 14: Level 7-9 Advanced
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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?
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