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