Number Grids Coursework.

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Number Grids Coursework (MA1)

Experiment 1

Part 1

Grid Size = 10*10

Box Size = 2*2

Experiment

)

2 * 23 = 276

3 * 22 = 286

286 - 276 = 10

2)

9 * 20 = 180

0 * 19 =190

90 - 180 = 10

3)

89 * 100 = 8900

90 * 99 = 8910

8910 - 8900 = 10

4)

* 12 =12

2 * 11 = 22

22 - 12= 10

5)

81 * 92 = 7452

91 * 82 = 7462

7462 - 7452 = 10

Table Of Results

Equation

Sum A Answer

Sum B Answer

Difference

276

286

0

2

80

90

0

3

8900

8910

0

4

2

22

0

5

7452

7462

0

Conclusion

Whatever the answers are of the two sums the difference between the difference between them is 10.

X

X+1

X+10

X+11

This box is how the numbers lay out in the box of a 2*2 box

The algebra to explain this is below;

(x+10) (x+1) - (x) (x+11) = d (difference)

Therefore x squared +10x + 10 + x - x squared + 11x = d

Therefore 10 + x - x = d

Therefore d=10

Prediction

43

44

53

54

I predict when multiplied in the same way the difference between the two sums will be 10, I will now test this to check that I am correct;

Prediction)

43* 54 = 2322

44 * 53 = 2332

2332 - 2232 = 10 I Was Correct

Experiment 1

Part 2

Grid Size = 10*10

Box Size = 3*3

Experiment

)

* 23 = 23

3 * 21 = 63

63 - 23 = 40

2)

8 * 30 = 240

0* 28 = 280

280 - 240 = 40

3)

71 * 93 = 6603

73 * 91 = 6643

6643 - 6603 = 40

4)

78 * 100 = 7800

80 * 98 = 7840

7840 - 7800 = 40

5)

45 * 67 = 3015

47 * 65 = 3055

3055 - 3015 = 45

Table Of Results

Equation

Sum A Answer

Sum B Answer

Difference

23

63

40

2

240

280

40

3

6603

6643

40

4

7800

7840

40

5

3015

3055

40

Conclusion

Whatever the answers are of the two sums the difference between the difference between them is 40.

X

X+2

X+20

X+22

This box is how the numbers lay out in the box of a 3*3 box

The algebra to explain this is below;

(x+20) (x+2) - (x) (x+22) = d (difference)

Therefore x squared + 2x + 40 + 20x - x squared + 22x = d

Therefore x squared + 22x + 40 - x squared + 22x = d

Therefore 40 + 22x - 22x = d

Therefore d=40

Prediction

(NB: These Are ONLY The Numbers In The Corners)

4

6

24

26

I predict when multiplied in the same way the difference between the two sums will be 40, I will now test this to check that I am correct;

Prediction)

4* 26 = 104

6 * 25 = 144

44 -104 = 40 I Was Correct

Experiment 1
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Part 3

Grid Size = 10*10

Box Size = 4*4

Experiment

)

* 34 = 34

4 * 34 = 124

24 - 34 = 90

2)

7 * 40 = 280

0 * 37 = 370

370 - 280 = 90

3)

61 * 94 = 5734

91 * 64 = 5824

5824 - 5734 = 90

4)

67 * 100 = 6700

97 * 70 = 6790

6790 - 6700 = 90

5)

34 * ...

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