1x12=12
11x2=22
The difference between these products is 22-12= 10
A rectangle has been highlighted in the 100 square 3 and 14/13 and 4 are the numbers in the opposite corners product of the number in these opposite corners are
3x14=42
13x4=52
The difference between these products is 52-42=10
A rectangle has been highlighted in the 100 square 7 and 18/17 and 8 are the numbers in the opposite corners product of the number in these opposite corners are
7x18=126
17x8=136
The difference between these products is 136-126= 10
Conclusion:
I have concluded that my prediction was correct and I now know that a 2 by 2 rectangle has a difference of 10
2x4
A rectangle has been highlighted in the 100 square 1 and 14/11 and 4 are the numbers in the opposite corners product of the number in these opposite corners are
1x14=14
11x4=44
The difference between these products is 44-14=30
A rectangle has been highlighted in the 100 square 5 and 18/15 and 8 are the numbers in the opposite corners product of the number in these opposite corners are
5x18=90
15x8=120
The difference between these products is 120-90=30
A rectangle has been highlighted in the 100 square 21 and 34/24 and 31 are the numbers in the opposite corners product of the number in these opposite corners are
21x34=714
24x31=744
The difference between these products is 744-714=30
Conclusion:
I have concluded that my prediction was correct and the investigation told me that a 2 by 4 rectangle will give a difference of 30 in the opposite corners. I now know that a 2 by 2 rectangle will have a difference of 10, and 2 by 3 will have a difference of 20 and a 2 by 4 rectangle will have a difference of 30.
2x5
A rectangle has been highlighted in the 100 square 1 and 15/11 and 5 are the numbers in the opposite corners product of the number in these opposite corners are
1x15=15
11x5=55
The difference between these products is 55-15=40
A rectangle has been highlighted in the 100 square 6 and 20/16 and 10 are the numbers in the opposite corners product of the number in these opposite corners are
6x20=120
16x10=160
The difference between these products is 160-120= 40
A rectangle has been highlighted in the 100 square 22 and 36/32 and 26 are the numbers in the opposite corners product of the number in these opposite corners are
22x36=792
32x26=832
The difference between these products is 832-792=40
Conclusion:
I have concluded that a 2 by 5 rectangle has a difference of 40 and my prediction was correct.
1. 2 x 21 = 42 _
1 x 22 = 22
Diff = 20
2. 80 x 99 = 7920 _
100 x 79 = 7900
Diff = 20
3. 45 x 64 = 2880 _
44 x 65 = 2860
Diff = 20
Prediction:
I predict that next 3 by 2 rectangle will have difference of 20.
Workings:
18 x 37 = 666 _
17 x 38 = 646
Diff = 20
Conclusion:
My prediction was correct and I have proved that a 3 by 2 rectangle has a difference of 20.
3 by 3 Rectangles:
- 73 x 91 = 6643 _
71 x 93 = 6603
Diff = 40
- 25 x 43 = 1075 _
23 x 45 = 1035
Diff = 40
- 10 x 28 = 280 _
8 x 30 = 240
Diff = 40
Prediction:
I predict that the next 3 by 3 Rectangle will have a difference of 40.
Workings:
77 x 95 = 7315 _
75 x 97 = 7275
Diff = 40
Conclusion:
I have concluded that a 3 by 3 rectangle has a difference of 40 and I now know that a 3 by 2 rectangle has a difference of 20 and a 3 by 3 rectangle has a difference of 40.
3 by 4 Rectangles:
1. 50 x 67 = 3350 _
47 x 70 = 3290
Diff = 60
2. 6 x 23 = 138 _
3 x 26 = 78
Diff = 60
3. 54 x 71 = 3834 _
51 x 74 = 3774
Diff = 60
Prediction:
I that the next 3 by 4 rectangle will have a of 60.
Workings:
68 x 85 = 7580 _
65 x 88 = 7520
Diff = 60
Conclusion:
I have concluded that a 3 by 4 rectangle has a difference of 60.
3 by 5 Rectangles:
1. 6 x 22 = 132 _
2 x 26 = 52
Diff = 80
2. 50 x 66 = 3300 _
46 x 70 = 3220
Diff = 80
3. 66 x 82 = 5412 _
62 x 86 = 4332
Diff = 80
Prediction:
I predict that the next rectangle will have a difference of 80.
Workings:
35 x 51 = 1785 _
31 x 55 = 1705
Diff = 80
Conclusion:
I have concluded that a 3 by 5 rectangle has a difference of 80.