• 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
• Level: GCSE
• Subject: Maths
• Word count: 1095

Number Grids

Extracts from this document...

Introduction

Number Gridss 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 Use the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and top right numbers in the square. Calculate the difference between these numbers. INVESTIGATE! To start this assignment I randomly selected an area in the matrix to put boxes of size; (2x2) ...read more.

Middle

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 Z 92 93 94 95 96 97 98 99 Q I came up with: X=X Y=X + (n-1) Z=X + ((n-1) x 10) Q=X + ((n-1) x 10) + (n-1) I used this to formulate the equation: X x X+11(n-1)) - ((X+ (n-1)X+10(n-1))) This cancels down to: (X2+11X(n-1))-(X2+11X(n-1) +10(n-1)2) To work out my overall formula I will subtract the first part of the Formula from the other: X2+11X(n-1) - X2+11X(n-1)) +10(n-1)2 0 + 0 + 0 +10(n-1)2 =10(n-1)2 Rectangles Solving the puzzle of rectangles in a grid came quite quickly to me as I realized that n was just for use in a square because the dimensions were the same. I labeled the vertical length now as m, but keeping the horizontal length as n. I adapted the equation from 10(n-1)2 into 10(n-1)(m-1). ...read more.

Conclusion

However, it should work with a rectangular grid as well. I tried a 3x4 inner grid in a 6x7 outer 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 (3-1)(4-1)7 =2x3x7 =42 The formula still works. 4x23 = 92, 2x25 = 50, 92-50 = 42 so I have found a formula which will work whatever of the size, inner or outer grid. Conclusion I have now found three equations, from these I can find any size of rectangle or square in any size of number grid. They are: * 10(n-1)2, for any square inside a 10x10 grid * 10(n-1)(m-1), for any rectangle inside a 10x10 grid * g(n-1)(m-1), for any rectangle or square inside any grid Josef Jeffrey Math's G.C.S.E coursework ...read more.

The above preview is unformatted text

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

Related GCSE Number Stairs, Grids and Sequences essays

1. Number Grids Investigation Coursework

I can predict that, in my formula for any size rectangle, D = 10 (m - 1) (n - 1), the 10 will equal the width, and therefore my theory for the formula for any size rectangle in any size grid is: D = w (m - 1)

2. Number Grid Coursework

Fig 3.1 shows examples of the varying box sizes, except that they can be rectangular. a) Here are the results of the 5 calculations for 2x4 Box on Width 11 Grid: Top-Left Number Product 1 (TL x BR) Product 2 (TR x BL)

1. Algebra Investigation - Grid Square and Cube Relationships

= n+ Increment size (s) x (Width -1) It is also evident from the examples calculated that the bottom left number is also linked with the height, w, of the box using a formula that remains constant: Formula 3: Bottom Left (BL)

2. Maths - number grid

are not in any particular order, I feel to establish a major trend I would have needed to start with a 3x2 and move up one each time, yet I feel this would be very time consuming and that through more investigating I will still be able to reach my

1. Investigate The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted.

7 8 9 10 2 x 6 Grid 1 2 3 4 5 6 7 8 9 10 11 12 Now I have put this data in a table to look for patterns. Grid size Answer Difference column 1 2 x 3 4 2 2 x 4 6 2 2

2. Maths Grids Totals

the number underneath the square is "x" added to (9 multiplied by "the squares length"-1). The bottom-right number is "x+ 10(n-1)" because it is "x+ 9(n-1) added to another (n-1), so therefore this becomes "x+ 10(n-1). n n x x+ (n-1)

1. number grid

product of the top right number and the bottom left number in any 4 X 4 grid inside a 10 X 10 grid will always be 90. Now I will draw a 4 X 4 grid to test if my theory is correct.

2. 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=46 Now I would need to find the value of b in order to use my formula in future calculations.

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