# Number Grid Coursework

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Introduction

Index page. Page 1: Title Page. Page 2: Index Page. Page 3: Investigation, 2x2 squares inside a 10x10number grid. Page 4: Investigation, 3x3 squares inside a 10x10 grid. Page 5: Investigation, 4x4 squares inside a 10x10 grid. Page 6: Investigation, 5x5 squares inside a 10x10 grid. Page 7: Formula of a 10x10 grid. Page 8: Investigating Formula of 10x10 grid. Page 9: Investigating, 2x2 and 3x3 squares inside an 8x8 grid. Page 10: Investigating, 4x4 and 5x5 inside an 8x8 grid. Page 11: Formula of an 8x8 grid and investigation of formula. Page 12: Investigating Formula of an 8x8 grid. Page 13: Investigating rectangles 2x3 and 2x4 on a 10x10 grid. Page 14: Investigating rectangles 2x5 and Formula on a 10x10 grid. Page 15: Investigating Formula of rectangles inside a 10x10 grid. Number Grid Coursework. Initial investigation. In this assignment I will look at a 10x10 number grid. I will be looking at different equations and working out the formula for each. Example 1 2 11 12 Equation Total 1 x 12 12 2 x 11 22 I will also find the products and then minus them to get the difference. Equation Total 1 x 12 12 2 x 11 22 Difference 10 The difference is 10. I will investigate further to see if this is always the case for 2x2 squares. 2x2 squares Equation Total 12 x 23 276 13 x 22 286 Difference 10 12 13 22 23 Equation Total 59 x 70 4130 69 x 60 4140 Difference 10 59 60 69 70 81 82 91 92 Equation Total ...read more.

Middle

x 78 1794 28 x 73 2044 Difference 250 12 13 14 15 16 17 22 23 24 25 26 27 32 33 34 35 36 37 42 43 44 45 46 47 52 53 54 55 56 57 62 63 64 65 66 67 Equation Total 12 x 67 804 17 x 62 1054 Difference 250 Using the formula 10x(n-1) 2 the results prove my prediction was correct. Using algebraic equations can also prove these results. x x+5 x+50 x+55 Expression 1 x(x+55)=x2 +55x Expression 2 (x+5) (x+50) = x2 +250x+5x+50 = x2 +55x+250 x2 +55x+250 - x2 +55 = 250 The formula for the 10x10 number grid is 10x(n-1) 2. Is this because it is a 10x10 grid? I am now going to investigate an 8x8 grid and see if the formula will be 8x(n-1). 8x8 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 2x2 Squares 2 3 10 11 Equation Total 2 x 11 22 3 x 10 30 Difference 8 34 35 42 43 Equation Total 34 x 43 1462 35 x 42 1480 Difference 8 45 46 53 54 Equation Total 45 x 54 2430 46 x 53 2438 Difference 8 The difference is always 8 for the 2x2 number squares. ...read more.

Conclusion

2x5 rectangles Equation Total 14 x 28 392 24 x 18 432 Difference 40 14 15 16 17 18 24 25 26 27 28 31 32 33 34 35 41 42 43 44 45 Equation Total 31 x 45 1395 35 x 41 1435 Difference 40 56 57 58 59 60 66 67 68 69 70 Equation Total 56 x 70 3920 66 x 60 3960 Difference 40 I have now investigated the rectangles 2x2, 2x3, 2x4 and 2x5. These are the results. Square size Difference 2x2 10 2x3 20 2x4 30 2x5 40 You can clearly see that the difference goes up in 10. An example is the 2x4 squares. * 4-1=3 * 3x10=30 The formula for the rectangles is n-1x10 Using the formula n-1x10 I am going to predict the difference for a 2x6 square. n-1x10 * 6-1=5 * 5x10=50 Square size Difference 2x6 50 I am now going to investigate to see if my prediction is correct. 2x6 rectangles. Equation Total 4 x 19 76 14 x 9 126 Difference 50 4 5 6 7 8 9 14 15 16 17 18 19 I have proved that my prediction is correct and will investigate further on the 2x6 rectangles to prove that the difference is always 50. Equation Total 32 x 47 1504 42 x 37 1554 Difference 50 32 33 34 35 36 37 42 43 44 45 46 47 53 54 55 56 57 58 63 64 65 66 67 68 Equation Total 53 x 68 3604 63 x 58 3654 Difference 50 I have proved that the difference for 2x6 rectangles is always 50.I have now investigated rectangles on a 10x10 number grid. 1 ...read more.

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