Number Grid Coursework
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 2 1 2 Equation Total x 12 2 2 x 11 22 I will also find the products and then minus them to get the difference. Equation Total x 12 2 2 x 11 22 Difference 0 The difference is 10. I will investigate further to see if this is always the case for 2x2 squares. 2x2 squares Equation Total 2 x 23 276 3 x 22 286 Difference 0 2 3 22 23 Equation Total 59 x 70 4130 69 x 60
Number Stairs Investigation
Number Stairs Investigation Introduction: This is a 3-step stair taken from a 10 x 10 grid. The total of the numbers inside the stair shape is: 25+26+27+35+36+45 = 194 We can write this as T = 194 Part 1 Working: For other 3-step stairs investigate the relationship between the stair total and the position of the stair shape on the 10 x 10 grid (given by the label x in Tx) Results Table: X T (total) 1 T = 50 25 T = 194 26 T = 200 27 T = 206 28 T = 212 78 T = 512 As the x number rises by one, the total number rises by six. This is because there are six numbers in the 3-step stair, and if x increases by one then so do the rest of the numbers. E.g. 45 46 35 36 36 35 25 26 27 26 27 28 As we can see, each of the six numbers has increased by one. Therefore; x 6 = 6. So far the equation stands like so; X = 6X??? We can discover the remainder of the equation by using examples. X 6X Total (Tx) 6 +44 50 25 150 +44 194 26 156 +44 200 27 162 +44 206 28 168 +44 212 78 468 +44 512 or we can find it algebraically; x + 20 x + 10 x + 11 x x + 1 x + 2 The formula for the 3-step stair on a 10 x 10 grid is Tx = 6x + 44 The letter "g" represents the grid number, in this case 10. Using this formula I will predict that T = (6 x 4) + 44 T = 24 + 44 T
Investigate the relationship between the T-total and the T-number
T-Total and T-Number Coursework INTRODUCTION PART 1: INVESTIGATE THE RELATIONSHIP BETWEEN THE T-TOTAL AND THE T-NUMBER T-NUMBER T-TOTAL 20 37 21 42 22 47 23 52 24 57 The table above shows the difference between the consecutive T-Totals as the T-Number increases by one. On grid sheet 1, the T-Shapes can be seen being translated across the 9 x 9 grid by one square each time. There is a pattern between the T-Totals as the T-Shape is translated each time, as each time the T-Total increases by 5, as shown in the table above. Each T-Total on the diagrams increases by 5 each time it is translated one square across. This is because each square in the T-Shape increases by one each time it is translated, and as there are 5 squares in the T-Shape, a total increase of 5 is calculated for the T-Total. Already from this, I can begin to create a formula for working out the T-Total for any T-Shape on a 9 x 9 grid. n-19 n-18 n-17 n-9 n The formula shown in the T-Shape above should work out the T-Total for any T-Shape on a 9 x 9 grid. I now plan to test this theory, by taking a few random sample T-Numbers from the 9 x 9 grid and using the formula to work out the T-Total. I think that my formula is correct, and that it will give the correct T-Total each time, but I will check it anyway. 24 25 26 34 43 The T-Number of the T-Shape is 43. Using my formula, I can work
Investigate the relationship between the T-total and the T-number.
GCSE Math's Investigation Introduction In this investigation I'm going to investigate the relationship between the T-total and the T-number. What I'm going to do is use different sizes of grids for example 9*9, 8*8, 7*7, 6*6, 5*5 and 4*4. To compare the answers I will have to investigate each grid for a few times for example 9*9 grid will be investigated for at list three times. I will have to make predictions for each of the grids. I will also have to translate and compare different positions of the T-shape and the T-numbers. After I have finished the investigation I will then evaluate and compare the relationships between different sizes of grids. The first grid I will investigate will be the 9*9 grid. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 2 3 1 20 T-number = 20 T-Total = 1+2+3+11+20=37 T20=37 n-19 n-18 n-17 n-9 n T-number = n T-Total = n+n-9+n-17+n-18+n-19 Tn = 5n-63 T-number = 20 Tn = 5n-63 20 * 5 = 100 -63 37 Here is another 9*9 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the
Investigation into T-shapes.
Investigation into T-shapes Looking at the 9-9 grid below and the T-shape drawn on it, The total number of the numbers on the inside of the T-shape is called the T-total 2 3 4 5 6 7 8 9 0 11 12 13 14 15 16 17 18 9 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 The t-total for this T-shape is: +2+3+11+20=37 so 37 = T-total The number at the bottom is the T-number, so the T-number for this shape is 20 Aims: ) Investigate the relationship between the T-total and the T-number 2) Use the grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T-number and the grid size. 3) Use grids of different sizes again, try other transformations and combinations of transformations. Investigate relationships between the T-total and the T-number and the grid size and the transformations. Aim 1- the solution 2 3 4 5 6 7 8 9 0 11 12 13 14 15 16 17 18 9 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 T69= 50+51+52+60+69 =282 T22=3+4+5+13+22 =47 in the diagram below it