• 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: 1581

Number grid algebraic course work

Extracts from this document...

Introduction

Number grid algebraic course work

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

Firstly I was given this number grid, the intrusions were…

  • A box is drawn round four numbers.
  • Find the product of the top left number and the bottom left in this box.
  • Do the same with the top right and bottom left numbers.
  • Calculate the difference between these products.
  • Investigate further.

The first thing I did was follow these instructions. Then I changed the box size and looked for patterns.

A two by two box…

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

12×23=276                 286-276= 10

13×22=286                

I tested a two by two box two more times to ensure each time I got the answer of 10, also to ensure that the answer was the same in different areas of the grid. I will do this for each different size boxes.

78×89=6942

79×88= 6952

9×20=180               10×19= 190

6952-6942 =10

190-180=10

...read more.

Middle

46

52

53

54

55

56

12×56=672

16×52=832

1×45=45

5×41=205

96×60=5760

100×56=5600

832-672=160

205-45=160

5760-5600=160

I have noticed that all these numbers are divisible by ten. I’m going to divide by 10 to see what answers I get…

box

Difference

Divide by 10

answer

2×2

10

10÷10=

1

3×3

40

40÷10=

4

4×4

90

90÷10=

9

5×5

160

160÷10=

16

I have notice that when I divide by 10 I get all square numbers as my answers. These answers are all less than the box size chosen. Eg 2×2    2-1=1     1²

box

Difference

Divide by 10

answer

Square no

2×2

10

10÷10=

1

3×3

40

40÷10=

4

4×4

90

90÷10=

9

5×5

160

160÷10=

16

So from this I can make an equation to test any box…

10 (n-1)(n-1)=10 (n-1)²

Now I will test rectangle boxes to further my investigation. I predicted that this formula would not work on the rectangles. I will have to alter the formula later.  

A three by two box…

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

  12×24=288               308-288=20

  22×14=308

I tested the three by two box twice more in different places to see if it would be the same answer…

5×17=85

7×15=105

67×79=5293

69×77=5313

105-85=20

5313-5293=20

Now I will test the box as a two by three and see if this will alter my answer…

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

128

4293-4165=128

I can use the same formula on this grid except I have to change it slightly… this was my formula for the 10 grid

10(c-1)(r-1)

as this is a 8 grid and all my difference are divisible by 8 I will change my formula to

8(c-1)(r-1)

I can check my answers using this formula

8(5-1)(5-1)=128                  8(2-1)(2-1)=8

I now know that I can use my formula to find my difference of rectangles in this grid. Eg.

A two by three grid…

11

12

13

19

20

21

11x21=231           247-231=16

13x19=247

 8(2-1)(3-1)=16

The answers are the same so I think it is more efficient to use the formula to find the answers…

8(2-1)(4-1)=24        8(4-1)(2-1)=24

8(2-1)(5-1)=32        8(5-1)(2-1)=32

I will now further my investigation using algebra…

If I know that it’s a two by grid…

            2

X    

2

TL=X  TR=X+1

BL=X+10   BR=X+11

TL X BR         TRXBL

(X)(X+11)        (X+1)(X+10)

X²+11X         X²+10+X+10X   X²+10+11X           

This helps to p

...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)

    78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 1. 1 x 13 = 13 2 x 12 = 24 ?

  2. Number Grid Investigation.

    Formula 2. 10 (n-1) for squares such as 3 X 2, 4 X 2 etc... Will it be 7 (n-1) for a 3 X 2 square in a 7 wide grid? Formula 3. 10 (n-1)(d-1) Will this be 7 (n-1)(d-1) for random boxes in a 7 wide grid? Let's see...

  1. Investigation of diagonal difference.

    the amount of G's needed in the bottom two corners of a cutout. The height of the cutout takeaway 1 defines the amount of G's needed in the bottom two corners, and since this is a trend for all the different size cutouts I can now substitute this number with an algebraic expression.

  2. Maths - number grid

    Chapter Four So I have now investigated squares and rectangles in a 10x10 number grid and squares in a new 12x12 number grid. With my new 12x12 grid I have noticed my results are all multiples of 12. I am now going to repeat my processes from chapter two, except

  1. Number Grid Investigation

    69= 966 Difference = 19 x 64= 1216 250 The difference is 250 as I predicted, I will now do the same using a different set of numbers. 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 32

  2. number grid

    a a+3 a+30 a+33 In my investigation I have to find the difference between, the product of the top left number and the bottom right number, and the product of the top right number and the bottom left number. So therefore I will multiply 'a' by 'a+33' and also I will multiply 'a+3' by 'a+30' and find the difference.

  1. Mathematical Coursework: 3-step stairs

    Nevertheless using the annotated notes on the formula my formula would look like this now: > 6N =6n x 1= 6 > 6+b=54 Now I would need to find the value of b in order to use my formula in future calculations.

  2. The patterns

    22 x 13 = 286 286 - 276 = 10 I shall now use letters to prove this correct X X+1 X+10 X+11 X(X+11) = X� + 11X (X+1)(X+10) = X�+11x+10 (X�+11x+10) - (X�+11X) = 10 Square Size 2x2, Grid Width 9 1 2 3 4 5 6 7 8

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