T- total T -number coursework
PART 1 I have a grid nine by nine with the numbers starting from 1 to 81. There is a shape in the grid called the t-shape. This is highlighted in the colour red. This is shown below: - 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 The number 20 at the bottom of the t-shape will be called the t-number. All the numbers highlighted will be called the t-total. In this section there is an investigation between the t-total and the t-number. 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 For this t-shape the T-number is 20 And the T-total is37 For this t-shape the T-number is 21 and the T-total is 42 As you can see from this information is that every time the t-number goes up one the t-total goes up five. Therefore the ratio between the t-number and the t-total is 1:5 This helps us because when we want to translate a t-shape to another position. Say we move it to
ICT Coursework: Data Management Systems
Identify My mum is part of a company that sells cards. She works from home. At present, she only has hand written records, showing what she has bought from the company, and what she has sold to customers. These records are very untidy, and are always getting lost, or muddled up. She would like a better way to keep this information, and so I offered to make a spreadsheet on the computer, that would help her to do this. However, she is not very good with computers, and can only do basic things, therefore, I need to keep it as simple and easy to use as possible. The only other alternative solution to this is to continue making manual records, but to keep them in a filing cabinet. This is not such a good idea though, as it is time consuming, and takes up a lot of room. Using a computer is therefore the best way to store this information, as it saves a lot of time, and space, and keeps all records together where they can be accessed quickly and easily. Even though my mum is not very good with computers, by keeping the spreadsheet easy to use, it will be easy to teach her to use it. The result of this will mean that a lot of time is saved, and the business can run more efficiently. The advantages of using an ICT solution are that a lot of space is saved (there is no need for lots of loose paper), time is saved (all calculations are done automatically), and the business
T-Shape investigation.
T-Shape Firstly, I am going to look at the relationship between the t-number and the t-total. I am going to refer to these terms using the letters N and Z: n = t-number z = -total I will take the first t-shape at the top left of a 9 x 9 size grid. 2 3 4 0 1 2 3 9 20 21 22 28 29 30 31 37 38 39 40 I predict that if I move the t-shape to a different location the t-total will be the t-number + 17 (n+17) 2 3 4 5 6 7 0 1 2 3 4 5 6 9 20 21 22 23 24 25 28 29 30 31 32 33 34 37 38 39 40 41 42 43 If my prediction is correct, t-total should equal 40 (23 + 17 = 40) Z = 4+5+6+14+23=52 My prediction is not correct. I will move the t-shape to the right and tabulate my results to see if there is a pattern. n 20 23 26 z 37 52 67 The t-total is in creasing by 15. Using first differences I will try to find a formula. n 20 23 26 5n 300 345 390 -263 -293 -323 z 37 52 67 I cannot find a formula for this. However, I have noticed that my n value is increasing by 3 every time. I will re-tabulate my results so it increases by 1 each time. This will make the numbers smaller and closer together and easier to spot a pattern. n 20 21 22 23 24 25 z 37 42 47 52 57 62 There is a definite pattern. The z value is increasing by 5 each time. I will try and find a formula. n 20 21 22 23 24 25 5n 00
Investigate how to calculate the total number of Winning Line
GCSE Mathematics Coursework: Connect 4: Investigate how to calculate the total number of Winning Lines Task In my investigation I am going to look at change in grid size and winning line length. From this I am aiming to be able to predict the number of winning lines in any size square grid with any winning line length I am planning to do this through modelling situations and finding links in my results when in a results table so I can calculate working algebraic formulae. I will achieve this by first devising a rule to calculate the total number of horizontal winning lines, vertical winning lines and diagonal winning lines in a square grid. In my investigation I am making the following assumptions; * The grid is a square * Winning line length is known * Grid size is known * The Winning line length is equal or less than the Grid side length, because if not the total number of winning lines is zero. * 1 is not a valid line length because it is only one point of the grid. * The grid below is a 4x4 grid. . . . . . . . . . . . . . . . . I will investigate the following: * Number of horizontal winning lines in any size square grid with any winning line length. * Number of vertical winning lines in any size square grid with any winning line length. * Number of diagonal winning lines in any size square grid with any winning line
Maths Investigation- Grids
Karen Ng 10H Maths Investigation- Grids The first part of my task was to investigate the number of squares, which can be drawn on grids made from 11 lines. I used 11 lines to make different grids on paper, alternating the use of lines. Starting with 1 horizontal and 10 vertical lines I work up (or down) so my grid then is 2 horizontal and 9 vertical. I counted the number of squares by outlining the shape of the square; this is shown in diagram 3. Here is my table of results using 11 lines only. Lines Down Lines Across x1 square 2x2 Square 3x3 square 4x4 square Total Squares 0 0 0 0 0 0 0 0 0 0 0 0 0 9 2 8 0 0 0 8 8 3 4 6 0 0 20 7 4 8 0 4 3 35 6 5 20 2 6 2 40 5 6 20 2 6 2 40 4 7 8 0 4 3 35 3 8 4 6 0 0 20 2 9 8 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 As you can see, after the 6x5 result comes up, the rest of the results are exactly the same as the ones at the top, because 6x5 is the same as 5x6 and etc. After a while of studying the table, I found out the rule was, say if you were trying to find out how many 1x1 squares were in a 6x5 grid, you would do 6-1=5 and 5-1=4, then, you times the answer ( 5 and 4 ) together, and that number will be the amount of 1x1 squares you will get in the grid. To find out how many 2x2 squares are in a grid, you do exactly the same thing, except you
The aim of this investigation is to find a relationship between the T-total and T-numbers. First by using a 9 by 9 number grid and then by changing the grid size.
Aim: The aim of this investigation is to find a relationship between the T-total and T-numbers. First by using a 9 by 9 number grid and then by changing the grid size. Method: I will first draw out a 9 by 9 grid and put Ts within it. I will place my results into a table and attempt to find a relationship between the two. I will incorporate this relationship into a rule using letters and numbers only. I will then do the similar thing for a 4 by 4, 5 by 5, 6 by 6 and 7 by 7 grid also. I will then try to find an overall rule to work out any grid size T-totals: I am going to do some T-totals and put the answers into tables. The first grid I am going to do is a 9 by 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 Table: This table shows all the T-numbers and T-totals possible in a 9 by 9 grid up to a T-number of 40. I have worked the T-totals out by drawing Ts in the grid and adding up the numbers within each T. T-number T-total 20 37 21 42 22 47 23 52 24 57 25 62 26 67 29 82 30 87 31 92 32 97 33 02 34 07 35 12 38 27 39 32 40 37 Prediction: I have found that there is a
This project consists of the investigation between patterns between T-numbers and T-totals.
* Investigation * Introduction This project consists of the investigation between patterns between T-numbers and T-totals. My investigation consists of different aims, but all of these aims have to do with this mathematical "T". I believe that there is a direct link between these two, as the T-total increases depending on the T-number. I think that there is nth sequence relating the T-number and the T-total, and therefore I will try and investigate this. First, I will use a 9 by 11 grid and find the relationship between the T-number, and the T-total in this grid. I will draw other girds and also find out the correlation between the translation of T-numbers, T-totals and the gird size. After this, I will go back to my initial 9 by 11 grid, and rotate the "T" and try to find the possible relationship of T-numbers and T-total of the rotated "T". I believe that there is a formula for the T-total of T-shapes in any grid and in any rotation. Subsequent to this investigation, I will use and enlargement of my initial "T" and use different examples to show the relationship between the enlargement and the T-number and T-total. From all my different investigations I will draw my conclusions giving explications for these. * Method: Task I. . I will draw a 9 by 11 grid, where I will select a T-shape, and transform it to form as many T-numbers and T-totals as possible, to see a
T-Totals. To figure out an equation for different grid sizes, I have to find the relationship between grid sizes and the T total. I will now let S= Grid Size.
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 T-Totals Part 1 By using algebra I can find the equation for T Total for grid size 9 T Total= n-19+n-18+n-17+n-9+n= 5n-63 T Total= 5n-63 is the relationship between the T total and the T number. This means for example that if the T number is 20 my formula predicts a T Total of 5× 20- 63= 37 which agrees with my earlier calculations. Part 2 Equation for different grid sizes To figure out an equation for different grid sizes, I have to find the relationship between grid sizes and the T total. I will now let S= Grid Size. I get this T T Total= n+n-S+n-2S+n-2S+1+n+2S-1= 5n-7S This means that the equation is T total= 5n-7S where S is the grid size so if for example the T number is 24 and the grid size is 11 then the T total will be (5× 24- 11× 7)= 43. I can check whether this works. 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
Maths Coursework- Borders
Joanna Burton 10s 23rd June 2004 Maths Coursework- Borders QUESTION Figure below shows a dark cross-shape that has been surrounded by white squares to create a bigger cross-shape; The bigger cross-shape consists of 25 small squares in total. The next cross-shape is always made by surrounding the previous cross-shape with small squares. Part 1- Investigate to see how many squares would be needed to make any cross-shape built in this way. Part 2- Extend your investigation to 3 dimensions. Introduction - I am doing an investigation to see how many squares would be needed to make any cross-shape built up in this way. Each cross-shape is made by using the previous cross-shape and adding another layer of white squares, making all the inner squares black. The first cross-shape in the sequence is a single black square. To start my investigation I must draw the first 7 cross-shapes. This will enable me to see a pattern in the shapes so I can make a table and record how many black and white squares there are in each cross-shape I have drawn. From my table I must use the results to work out formulae for black, white and total number of squares. After this I will test the formulae on a pattern I have already drawn and on one I have not already drawn. I will be working systematically in my investigation
T-totals, Relationships between the T-number and the T-total on a 9 x 9 grid.
Mathematics GCSE T-totals Alex Pavlou ). Relationships between the T-number and the T-total on a 9 x 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 82 83 84 85 86 87 88 89 90 T-totals T-numbers 21 42 26 67 42 47 66 267 80 337 86 367 The difference in each T-shape is: N-19 N-18 N-17 N-9 N If we take the T-shape: 2 3 4 12 21 we can create the sum: t=21+(21-9)+(21-19)+(21-18)+(21-17) As there are 5 numbers in the T-shape we need 5 lots of 21, the number above 21 is 12, which is 9 less than 21, the other numbers are 2,3 and 4 which is 9 less than 21. Therefore we arrive to the conclusion: N-19 N-18 N-17 N-9 N To prove this we use the T-shape: 61 62 63 71 80 T=80-19+80-18+80-17+80-9+80 T=337 We can do the same for the T-shape: 47 48 49 57 66 T=66-19+66-18+66-17+66-9+66 T=267 To find the formula of the relationship between the T-number and the T-total we use N for the T-number. T=N+(N-9)+(N-19)+(N-18)+(N-17) T=5N-9-54 T=5N-63 Examples of this formula are : In the case of the T-shape: 52 53 54 64 71 T=5(71)-63 T=355-63 T=292 When we add the