• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  • Level: GCSE
  • Subject: Maths
  • Word count: 2284

Number grid coursework

Extracts from this document...

Introduction

Number Grid Coursework.

For this coursework I shall investigate and explain thoroughly the
patterns, rules and formulae found in a number grid when placing a
square at any point in the grid, multiplying the top left and bottom
right corners and the top right and bottom left corners and finding
the difference. In the beginning of my investigation I’d like to write the main purpose of it. I want to find one common formula that would help me to find difference on any x by x square on 10 by 10 number grid. Let’s start the investigation!

I have a 2 by 2 square in a 10 by 10 number grid.

I am going to investigate it and find the difference.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

First I shall find the product of the top left number and the bottom right number in the square.

image00.png

I shall find the product of the top right and bottom left numbers.

image01.png

Now I shall find difference between these products.

image26.png

Let’s now move the square and do same calculations.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

...read more.

Middle

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

1)*  image23.pngimage23.png

2)    image24.pngimage24.png

       3)     image25.pngimage25.png

*        The calculations that are being done every time (i.e. multiplying the top left and bottom
right corners and the top right and bottom left corners and finding
the difference) will only be shown by numbers (i.e. 1), 2), 3)) in the further content of the coursework.

I predict that my next 3 by 3 square will result in the answer 40.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

  1. image27.pngimage27.png
  2. image28.pngimage28.png
  3. image29.pngimage29.png

My prediction was correct. There was a difference of 40. This may mean that it doesn't matter which 3 by 3 square you select within a 10 by 10 number grid the difference will still be 40.

I will now prove my conclusion using algebra.

Any top left number will be image07.pngimage07.png, any top right number will be image30.pngimage30.png, any bottom left number will be image32.pngimage32.png, any bottom right number will be image33.pngimage33.png in any 3 by 3 square on a 10 by 10 number grid.

  1. image34.pngimage34.png
  2. image35.pngimage35.png
  3. image36.pngimage36.png

This proves my conclusion and means that all 3 by 3 squares taken from a 10 by 10 number grid result in the answer 40.

I will now investigate 4 by 4 squares in a 10 by 10 number grid.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

  1. image38.pngimage38.png
  2. image39.pngimage39.png
  3. image40.pngimage40.png

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

...read more.

Conclusion

  1. image03.pngimage03.png
  2. image04.pngimage04.png
  3. image05.pngimage05.png

All 5 by 5 squares on a 10 by 10 number grid result in the answer 160.

Now, using algebra I will prove that an x by x square will result in image06.pngimage06.png

Any top left number will be image07.pngimage07.png, any top right number will be image09.pngimage09.png, any bottom left number will be image10.pngimage10.png, any bottom right number will be image11.pngimage11.png in any x by x square on a 10 by 10 number grid.

  1. image12.pngimage12.png
  2. image13.pngimage13.png
  3. image15.pngimage15.png

I can see that image16.pngimage16.png repeats in all parts of equation. To simple equation I will renameimage16.pngimage16.png. It will now be called T.

So image17.pngimage17.png

image18.png

Now I will put image19.pngimage19.png instead of T.

So it is:

image21.png

This means that an x by x square would result inimage21.pngimage21.png. This means my
prediction was correct. This is the result for any x by x grid taken from
a 10 by 10 number grid.

In this investigation I found a formula that can be used to find difference in any x by x square on a 10 by 10 number grid. This was the main purpose of my investigation, so I can say that the investigation passed successfully.

If I were to extend this investigation further, I would experiment with different sized master grids

...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Marked by a teacher

    Number Grid Aim: The aim of this investigation is to formulate an algebraic equation ...

    3 star(s)

    = n2 + 19n + n n + 1(n + 19) = n2 + 19n + n + 19 ? [n2 + 19n + n +19] - [n2 + 19n + n] = 19 My prediction of what the difference would be was correct.

  2. Number Grid Coursework

    Product 2 (TR x BL) Difference (P'duct 2 - P'duct 1) 5 135 175 40 23 1035 1075 40 37 2183 2223 40 52 3848 3888 40 77 7623 7663 40 b) Here are the results of the 5 calculations for 4x4 Box on Width 10 Grid: Top-Left Number Product 1 (TL x BR)

  1. Number Grids Investigation Coursework

    - (top left x bottom right) = 5 x 11 - 1 x 15 = 55 - 15 = 40 To prove that this is the same in all 2 x 5 grids, I will have to use algebra. Let the top left square of my rectangle equal a, and

  2. Algebra Investigation - Grid Square and Cube Relationships

    Because the second answer has +60 at the end, it demonstrates that no matter what number is chosen to begin with (n), a difference of 60 will always be present. Any rectangular box with width 'w', and a height of 3 It is possible to ascertain from the above examples

  1. Number Grid Investigation.

    \ / \ / \ / \ / 24 40 56 ? \ / \ / \ / 16 16 ? We see that 16 is added onto the 1st difference everytime. I can now calculate: 56 + 16 = 72 128 + 72 = 200 Mini prediction I predict

  2. Investigation of diagonal difference.

    51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 But will my previous formula work?

  1. Maths - number grid

    are all multiples of 12 and I suspect this is so because I have used a new 12x12 number grid. Furthering my investigation As I have previously stated, it is possible to see some type of trend forming, I am going to increase my square size to 5x5 and from this I hope to see a trend more clearly.

  2. Maths coursework. For my extension piece I decided to investigate stairs that ascend along ...

    = 300 ? This must mean that my formula Un = 10n + 10g + 10 - where 'n' is the stair number, 'g' is the grid size, and 'Un' is the term which is the stair total - works for all 4-stair numbers on any size grid.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work