# I'm going to investigate the difference between products on a number grid first I'm going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then

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Introduction

Introduction:

I'm going to investigate the difference between products on a number grid first I'm going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then I'm going to do the same with the top right, bottom right numbers in the box. I'll will then calculate the difference between these products. Not only I am going to investigate squares, but also rectangles, I'll use algebra to try and find a formula or a general rule that will give me this difference for any size shape.

I'm going to draw a box round four numbers then I will find the product of

Middle

76

77

78

85

86

87

88

The difference between 4930 and 4840 is 90 because 4930 - 4840 = 90.

58 x 85 = 4930

55 x 88 = 4840

I predicted that the difference for all 4 by 4 spares will be 90, I'll do another 4 by 4 grid to confirm that my prediction is correct.

51 | 52 | 53 | 54 |

61 | 62 | 63 | 64 |

71 | 72 | 73 | 74 |

81 | 82 | 83 | 84 |

The difference between 4930 and 4940 is 90 because 4930 - 4940 = 90.

54 x 81 = 4374

51 x 84 = 4284

This shows that my prediction is correct, that all 4 by 4 will equal to 90.

5 by 5

I'm going to draw a box round twenty five numbers then I will find the product of top left, bottom right numbers, and then I'm going to do the same with the top right, bottom right numbers.

1 | 2 | 3 | 4 | 5 |

11 | 12 | 13 | 14 | 15 |

21 | 22 | 23 | 24 | 25 |

31 | 32 | 33 | 34 | 35 |

41 | 42 | 43 | 44 | 45 |

The difference between 205 and 45 is 160 because 205 - 45 = 160.

5 x 41 = 205

1 x 45 = 45

55 | 56 | 57 | 58 | 59 |

65 | 66 | 67 | 68 | 69 |

75 | 76 | 77 | 78 | 79 |

85 | 86 | 87 | 88 | 89 |

95 | 96 | 97 | 98 | 99 |

The difference between 5605 and 5445 is 160 because 5605 - 5445 = 160.

59 x 95 = 5605

55 x 99 = 5445

42 | 43 | 44 | 45 | 46 |

52 | 53 | 54 | 55 | 56 |

62 | 63 | 64 | 65 | 66 |

72 | 73 | 74 | 75 | 76 |

82 | 83 | 84 | 85 | 86 |

The difference between 3772 and 3612 is 160 because 3772 - 3612 = 160.

46 x 82 = 3772

42 x 86 = 3612

I predicted that the difference for all 5 by 5 spares will be 160, I'll do another 5 by 5 grid to confirm that my prediction is correct.

35 | 36 | 37 | 38 | 39 |

45 | 46 | 47 | 48 | 49 |

55 | 56 | 57 | 58 | 59 |

65 | 66 | 67 | 68 | 59 |

75 | 76 | 77 | 78 | 79 |

Conclusion

24

25

26

31

32

33

34

35

36

41

42

43

44

45

46

51

52

53

54

55

56

61

62

63

64

65

66

71

72

73

74

75

76

The difference between 1846 and 1596 is 250 because 1846 - 1596 = 250.

26 x 71 = 1846

21 x 76 = 1596

1 | 2 | 3 | 4 | 5 | 6 |

11 | 12 | 13 | 14 | 15 | 16 |

21 | 22 | 23 | 24 | 25 | 26 |

31 | 32 | 33 | 34 | 35 | 36 |

41 | 42 | 43 | 44 | 45 | 46 |

51 | 52 | 53 | 54 | 55 | 56 |

The difference between 306 and 56 is 250 because 306 - 56 = 250.

6 x 51 = 306

1 x 56 = 56

33 | 34 | 35 | 36 | 37 | 38 |

43 | 44 | 45 | 46 | 47 | 48 |

53 | 54 | 55 | 56 | 57 | 58 |

63 | 64 | 65 | 66 | 67 | 68 |

73 | 74 | 75 | 76 | 77 | 78 |

83 | 84 | 85 | 86 | 87 | 88 |

The difference between 3154 and 2904 is 250 because 3154 - 2904 = 250.

38 x 83 = 3154

33 x 88 = 2904

I predicted that the difference for all 6 by 6 spares will be 250, I'll do another 6 by 6 grid to confirm that my prediction is correct.

14 | 15 | 16 | 17 | 18 | 19 |

24 | 25 | 26 | 27 | 28 | 29 |

34 | 35 | 36 | 37 | 38 | 39 |

44 | 45 | 46 | 47 | 48 | 49 |

54 | 55 | 56 | 57 | 58 | 59 |

64 | 65 | 66 | 67 | 68 | 69 |

The difference between 1216 and 966 is 250 because 1216 - 966 = 250.

19 x 64 = 1216

14 x 69 = 966

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

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