Number Grid Coursework
My task is to investigate a 2x2 box on a 100 square
I will take a 2x2 square on a 100 square grid and multiply the two
corners together. I will then look at the relationship between the two
results, by finding the difference.
Test 1
======
54 55 54 x 65= 3510
64 65 55 x 64= 3520
3520-3510= 10
DIFFERENCE = 10
Test 2
======
5 6 5 x 16= 80
15 16 6 x 15= 90
90-80= 10
DIFFERENCE = 10
Test 3
======
18 19 18 x 29= 522
28 29 19 x 28= 532
532-522= 10
DIFFERENCE = 10
Prediction
==========
I predict that in a two by two square the difference will always be 10
Proof
=====
83 84 83 x 94= 7802
93 94 84 x 93= 7812
7812-7802= 10
DIFFERENCE = 10
Algebraic Explanation
=====================
[IMAGE]I will assign a letter to the first number in the 2 x 2 square,
n.
The next number to the right will therefore be n+1
The number directly below it will then be n+10
The number diagonally across from it will be n+11
I will then times the corners together, like In did on the above
examples.
Top Left hand corner x bottom right hand corner = n(n+11) = n² + 11n
Top right hand corner x bottom left hand corner = n² +1n+10n+10
n² +11n+10
(n² +11n+10) - (n² + 11n) = 10
Therefore the difference between the corners multiplied together will
always be 10.
Expanding the Task
==================
I now feel it will be interesting to look at a 3x3 number square on a
100 grid. I will take a 3x3 square on a 100 square grid and multiply
the two corners together. I will then look at the relationship between
On the second day of class, the Professor Judit Kerekes developed a short chart of the Xmania system and briefly explained how students would experience a number problem. Professor Kerekes invented letters to name the quantities such as “A” for one box, “B” for two boxes. “C” is for three boxes, “D” is for four boxes and “E” is for five boxes. This chart confused me because I wasn’t too familiar with this system. One thing that generated a lot of excitement for me was when she used huge foam blocks shaped as dice. A student threw two blocks across the room and identified the symbol “0”, “A”, “B”, “C”, “D”, and “E.” To everyone’s amazement, we had fun practicing the Xmania system and learned as each table took turns trying to work out problems.
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