Page No.1
Number Grid Investigation
I have been asked to investigate on a number grid 10 wide
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2x2 grids
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. a) My first 2x2 grid is
(6 x 17) - (7 x 16) = -10
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b)My second 2x2 grid is
(18 x 29) - (19 x 28) = -10
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c)My third 2x2 grid is
(2 x 13) - (3 x 12) = -10
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d)My fourth 2x2 grid is
(24 x 35) - (25 x 34) = -10
2. I predict that in the next grid the answer will be -10.
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3 Test prediction- I will use the grid:
(15 x 26) - (16 x 25) = -10
4. Proving the rule
Y
Y+1
Y + 10
Y + 11
(Y x Y + 11) - (Y + 1 x Y + 10)
= (Y2 + 11) - (Y2 + 11)
= 0
` Page No.2
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3x3 grids
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.a) My first 3x3 grid is
(14 x 36) - (16 x 34) = -40
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b) My second 3x3 grid is
(11 x 33) - (13 x 31) = -40
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c) My third 3x3 grid is
(17 x 39) - (19 x 37) = -40
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d) My fourth 3x3 grid is
(23 x 45) - (25 x 43) = -40
2. I predict that in the next 3x3 grid the answer will be -40.
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3. Test the prediction
(8 x 30) - (10 x 28) = -40
4. Proving the rule
Y
Y+1
Y+2
Y+10
Y+11
Y+12
Y+20
Y+21
Y+22
(Y x Y +22) - (Y+2)(Y +20)
= Y² +22Y - (Y² + 2Y + 20Y +40)
= -40
Page No.3
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4x4 grids
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.a) My first 4x4 grid is
(3 x 36) - (6 x 33) = -90
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b) My second 4x4 grid is
(17 x 50) - (20 x 47) = -90
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c) My third 4x4 grid is
(1 x 34) - (4 x 31) = -90
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d) My fourth 4x4 grid is
2. I predict that in the next 4x4 grid the answer will be -90.
3. Test the prediction
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(13 x 46) - (16 x 43) = -90
Y
Y+1
Y+2
Y+3
Y+10
Y+11
Y+12
Y+13
Y+20
Y+21
Y+22
Y+23
Y+30
Y+31
Y+32
Y+33
4. Prove the rule
(Y)(Y+33) - (Y+3)(Y+30)
= (Y² + 33Y) - (Y² + 3Y + 33Y + 90)
= -90
Page No.4
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Number Grid Investigation
I have been asked to investigate on a number grid 10 wide
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3
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5
6
7
8
9
0
1
12
13
4
5
16
17
18
19
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43
44
45
46
47
48
49
50
2x2 grids
6
7
6
7
. a) My first 2x2 grid is
(6 x 17) - (7 x 16) = -10
8
9
28
29
b)My second 2x2 grid is
(18 x 29) - (19 x 28) = -10
2
3
2
3
c)My third 2x2 grid is
(2 x 13) - (3 x 12) = -10
24
25
34
35
d)My fourth 2x2 grid is
(24 x 35) - (25 x 34) = -10
2. I predict that in the next grid the answer will be -10.
5
6
25
26
3 Test prediction- I will use the grid:
(15 x 26) - (16 x 25) = -10
4. Proving the rule
Y
Y+1
Y + 10
Y + 11
(Y x Y + 11) - (Y + 1 x Y + 10)
= (Y2 + 11) - (Y2 + 11)
= 0
` Page No.2
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46
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49
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3x3 grids
4
5
6
24
25
26
34
35
36
.a) My first 3x3 grid is
(14 x 36) - (16 x 34) = -40
1
2
3
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31
32
33
b) My second 3x3 grid is
(11 x 33) - (13 x 31) = -40
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c) My third 3x3 grid is
(17 x 39) - (19 x 37) = -40
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25
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34
35
43
44
45
d) My fourth 3x3 grid is
(23 x 45) - (25 x 43) = -40
2. I predict that in the next 3x3 grid the answer will be -40.
8
9
0
8
9
20
28
29
30
3. Test the prediction
(8 x 30) - (10 x 28) = -40
4. Proving the rule
Y
Y+1
Y+2
Y+10
Y+11
Y+12
Y+20
Y+21
Y+22
(Y x Y +22) - (Y+2)(Y +20)
= Y² +22Y - (Y² + 2Y + 20Y +40)
= -40
Page No.3
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4x4 grids
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26
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.a) My first 4x4 grid is
(3 x 36) - (6 x 33) = -90
7
8
9
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27
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30
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40
47
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b) My second 4x4 grid is
(17 x 50) - (20 x 47) = -90
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4
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4
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31
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c) My third 4x4 grid is
(1 x 34) - (4 x 31) = -90
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7
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9
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7
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9
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28
29
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d) My fourth 4x4 grid is
2. I predict that in the next 4x4 grid the answer will be -90.
3. Test the prediction
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(13 x 46) - (16 x 43) = -90
Y
Y+1
Y+2
Y+3
Y+10
Y+11
Y+12
Y+13
Y+20
Y+21
Y+22
Y+23
Y+30
Y+31
Y+32
Y+33
4. Prove the rule
(Y)(Y+33) - (Y+3)(Y+30)
= (Y² + 33Y) - (Y² + 3Y + 33Y + 90)
= -90
Page No.4
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![number grid investigation]](https://mbt-essays-prod-public.s3.eu-west-1.amazonaws.com/810836/listing/810836_1.jpg)
