Table Patterns Essay, Research Paper
Table Patterns Q1.
For the first part of this investigation into table patterns I am
going to see what happens when you add the two numbers in opposite corners of
squares which have a side 3 (which are drawn around nine numbers). Then I will
investigate what happens when you subtract the smaller answer from the larger
answer. After this we will take this investigation further. The squares are
taken from the following ?Multiplication Tables Grid?. X 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100 Example: Add the two numbers in the opposite corners. 8 10 12 12 15 18 16 20 24 8+24=32
and
12+16=28 Now, subtract the smaller answer from the
larger answer. 32-28=4 Now, I will investigate this theory three times by picking
out random number square and then I will make a hypothesis. Square 1: 48 56 64 54 63 72 60 70 80
<48+80=128
and
60+64=124 2000 Maths GCSE Coursework
Ben Blackmore 10 Shirley
Mr. Wellings Page 2 Therefore, 128-124=4 Well, we have the answer 4. I will try again
and see whats answer will come out this time. Square 2:
6 9 12 8 12 16 10 15 20 6+20=26
and
10+12=22 Therefore, 26-22=4 Okay, I am hoping that 4 is the next answer so I can make
the hypothesis that I want to. Square 3: 4 6 8 6 9 12 8 12 16 4+16=20
and
8+8=16 Therefore, 20-16=4 I am now in a position to make my hypothesis and then I
will attempt to prove it using algebra. Hypothesis When you add the
two numbers in opposite corners and subtract the smaller number from the larger
number the answer is always 4. I have also found that the top left and
bottom right numbers, when added up, is the larger number (this is the number
is pink). I am now going to try to prove this statement by using algebraic
terms. 2000 Maths GCSE Coursework
Ben Blackmore 10 Shirley
Mr. Wellings Page 3 This is my drawn hypothesis: TL T TR ML M MR BL B BR (TL+BR)-(BL+TR)=4