Layers investigation
Layers I am carrying out an investigation to find out the different arrangements of cubes on a specified grid size. I will first start off with a two by three grid size which means there are six squares in the grid. On these six squares I will put five cubes. Each cube must fit exactly onto one square. During the course of my investigation I will display and describe my work and findings. I first investigated how many different arrangements of the five cubes there were on a 2 by 3 grid. The 2 by 3 grid obviously has 6 squares; as one square always has to stay blank, the other five squares will be filled in. Because there are six squares and one square is always blank, there are six different variations. For the second layer, there are only five squares, one of which has to stay blank. Because of this four squares can be filled, and this produces 5 different arrangements. As you can see the total number of different combinations is 30. This can also be worked out by saying that there are five different arrangements on the second layer and there are six different arrangements on the first layer. So if you calculate 5*6 you get the answer 30. There is a theory behind this to find out the number of different arrangements without drawing the layers: "The number of squares filled in is always -1 of the number of arrangements and the number of possible empty squares." To
The Weight of Your School Bag
Statistics Coursework The Weight of Your School Bag Introduction: My Chosen Topic is The Average Weight of the School Bag of Students in Year Ten at the Start of the week and just before it ends, as it seems to be a topic that no one actually thinks about all that much, but students sometimes complain how heavy there bags seem to be. Hypothesis: The Hypotheses I present on my topic are: * The Weight of the Bag will be Slightly Heavier as it is the start of the week, and students have a lot of work to turn in * The Weight of the Bag will be Slightly Lighter as it is just before the end of the week. * The Weight will also depend on the Miscellaneous Items the Student is carrying, so it is hard to determine which gender will have the Heavier bag but it should be about the same Questionnaire: There was a little bit of difficulty in making the questionnaire for me, as I wanted specific results whilst keeping the questionnaire as simple as possible. First I had decided upon using Monday and Friday to compare but a lot of students have similar classes on both days so there wouldn't much to compare whereas Thursday was just before the end of the week, and I decided to use it instead. There was also another problem that students did not have a scale to measure the weight of the Bag in Kilograms (Kg) and/or Pounds (Lbs) and /or Stone (St,), so I had to decide what scale to use,
Maths Investigative task on perimeter of a rectangle and volume of shapes
MINIMUM PERIMETER . Your task is to find the value of dimension that minimizes the perimeter. By using technology, list all the possible values of length, width, and perimeter with area 1000m2. Data attached at the back. Color code: Yellow shows the best value that matches the requirements, red matches with red and green matches with green. Here is some sample data: Length (m) Width (m) Perimeter (m) Area (m2) 1 1000 2002 1000 2 500 1004 1000 3 333.333 672.667 1000 4 250 508 1000 5 200 410 1000 6 166.667 345.333 1000 7 142.857 299.714 1000 8 125 266 1000 9 111.111 240.222 1000 10 100 220 1000 11 90.909 203.818 1000 12 83.333 190.667 1000 13 76.923 179.846 1000 14 71.429 170.857 1000 15 66.667 163.333 1000 16 62.5 157 1000 17 58.824 151.647 1000 18 55.556 147.111 1000 19 52.632 143.263 1000 20 50 140 1000 21 47.619 137.238 1000 22 45.455 134.909 1000 23 43.478 132.957 1000 24 41.667 131.333 1000 25 40 130 1000 26 38.462 128.923 1000 27 37.037 128.074 1000 28 35.714 127.429 1000 29 34.483 126.966 1000 30 33.333 126.667 1000 31 32.258 126.516 1000 32 31.25 126.5 1000 33 30.303 126.606 1000 34 29.412 126.824 1000 35 28.571 127.143 1000 36 27.778 127.556 1000 37 27.027 128.054 1000 38 26.316 128.632 1000 39 25.641
T-Total Maths coursework
Maths Coursework T Total Introduction In my maths casework I am investigating the relationship between the T-Number and the T-Total, throughout a range of different size grids. I am going to work out the rule for any size grid that is by 10, below is a 9 by 10 grid, the t is the coloured in bit and the red number is the T-Number. So the T-Number is 50 in this 9X10 grid is 50. The T-Total for this T is all the numbers in the T added up 50+41+31+32+33=187 The T-Total would be 187 as this is all the coloured in squares added up. So in my coursework I am going to use different grid sizes to translate the T-Shape to different positions .I will then investigate the relationship between the T-Number and the T-Total, and the grid size. I am then going to use different size grids to try to work out Ts in all different ways. Like the grid below, I am going to work out rules for all the T-Numbers with the T standing different ways. This grid shows the ways in which I am going to work out the T- Number in different ways. Looking for patterns and predicting the next T 9X10 Grids I am first going to work out the T-Total for 5 consecutive Ts, starting at 20 and going up to 24. T-Number = 20 T-Total = 37 T-Number = 21 T-Total = 42 T-Number = 22 T-Total = 47 T-Number = 23 T-Total = 52 T-Number = 24 T-Total = 57 T-Number T-Total 20 37 21 42 22 47 23 52 24 57
Number grids
NUMBER GRIDS 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 The aim of my investigation is to find the cross product difference of various grid sizes and see what I notice about this. I will try to find out a pattern from when I change the grid sizes. I will get a 10 by 10 table ranging from 1-100 and start off using squares, i.e. 2x2, 3x3, 4x4 e.c.t. I will take the two opposite corners and multiply them together doing the same on both sides, I will take the two final numbers and subtract them from one another, this will leave me with a number, which should be the same for each of the same sized grid shapes. I will place my results into a table and see if I can work out a formula for finding out all the results. 2x2 2 3 22 23 (13x22) - (12x23) = 286-276 = 10 5 6 25 26 (16x25)-(15x26) = 400-390 = 10 77 78 87 88 (78x87)-(77x88) = 6786-6776 = 10 81 82 91 92 (82x91)-(81x92) = 7462-7452 = 10 33 34 43 44 (34x43)-(33x44) = 1462-1452 = 10 In all of the small 2x2 number grids above I have found out that the product of the