Find the relationship between the T-total and the T-number.
T-Totals Aim: In this Investigation I will try and find the relationship between the T-total and the T-number. By changing the size of the grid and translating the T-shape to different positions in the grid I will find the pattern and rule for the T-Total and 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 The Total of the Numbers inside the T-shape is 1+2+3+11+20= 37 The number at the bottom is know as the T-number T-Total The T-number for this T-shape is 20 ) The relationship between the T-total and the T-number. If you take the other Numbers in the T-shape away from the T-number you get a T-shape like this. T-19 T-18 T-17 T-9 T T-Total = T-19+T-18+T-17+T-9+T = 5T-63 2) Testing For T-Total I will use the letter X For T-Number I will use the letter T So X = 5T-63 T=20 X=5x20-63 = 100-63 = 37 For this T-Shape the T-Number is 20 and the T-Total is 37 Here is the difference once more in the T-shape: T-19 T-18 T-17 T-9 T This shows the difference T = T-number The first difference from T is 9 which is also the size of the grid (9x9) W = width number (9) T - (2W+1) T -
Maths GCSE Coursework – T-Total
Maths GCSE Coursework 2000 - T-Total Introduction In this investigation I aim to find out relationships between grid sizes and T shapes within the relative grids, and state and explain all generalizations I can find, using the T-Number (x) (the number at the bottom of the T-Shape), the grid size (g) to find the T-Total (t) (Total of all number added together in the T-Shape), with different grid sizes, translations, rotations, enlargements and combinations of all of the stated. Relations ships between T-number (x) and T-Total (t) on a 9x9 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 From this we can see that the first T shape has a T number of 50 (highlighted), and the T-total (t) adds up to 187 (50 + 41 + 31 + 32 + 33). With the second T shape with a T number of 80, the T-total adds up to 337, straight away a trend can be seen of the larger the T number the larger the total. 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
For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total on a 9x9 grid then change the variables such as grid size.
Maths Coursework By James Lathey For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total on a 9x9 grid then change the variables such as grid size. I will also be looking at what effect rotation has. T number is the number at the bottom of the T shape T Number = blue number To calculate T total add all the numbers inside the T together. T Total = 1+2+3+11+20 = 37 I will represent T number as T and T total as N 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 numbers in red represent all the places were the T shape cant fit. I will ignore these and only use the squares were the t shape fully fits. 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 First I put the T shape onto my 9x9 grid and translated it right by 1 space each time. As shown above I
Maths Coursework T-Totals
Maths GCSE Coursework 2000 - T-Total INTRODUCTION - Tell the reader what the project is all about - get a friend/family member to read it - do they understand what it's all about? Introduction In this investigation I aim to find out relationships between grid sizes and T shapes within the relative grids, and state and explain all generalizations I can find, using the T-Number (x) (the number at the bottom of the T-Shape), the grid size (g) to find the T-Total (t) (Total of all number added together in the T-Shape), with different grid sizes, translations, rotations, enlargements and combinations of all of the stated. EXPLAIN WHAT THE LETTERS STAND FOR Relations ships between T-number (x) and T-Total (t) on a 9x9 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 From this we can see that the first T shape has a T number of 50 (highlighted), and the T-total (t) adds up to 187 (50 + 41 + 31 + 32 + 33). With the second T shape with a T number of 80, the T-total adds up to 337, straight away a trend can be seen of the larger the T number the larger the total. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21
T-Totals. I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another
For this Piece of coursework I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another area of the grid. 7 8 9 3 8 A T-shape consists of five numbers, when added together theses numbers create the T-total. The T-number is the number at the bottom of the T-shape. E.G. - The T-total for this shape would be 7+8+9+13+18 = 55 - The T-number for this shape would be 18 Throughout this Coursework I will refer to the T-total as 'T' and the T-number as 'N'. I started by investigating the relationships on a 5x5 grid, making sure I worked in a systematic way in order to make it easier to compare the results and discover a comparison. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 T-number (n) T-Total (T) 2 25 3 30 4 35 I can see from the table that as N increases by 1, T increases by 5, using this information I can begin to create a formula. Proof I created the T-shape, for this grid, below in order to prove my formula. N-11 N-10 N-9 N-5 N So, T = n-11+n-10+n-9+n-5+n T = 5n - 35 Therefore, according to this T-shape my formula is correct. I then worked out the formula for a 6x6 grid using the same process. 2 3 4 5 6 7 8 9 0
T -Totals. From this 9*9 grid I will collect a number of T Shapes with T Numbers after collecting these I will put them into a table and will investigate to find any relationship between them.
T -Totals For this coursework I have been given a task which is to investigate the relationship between the T-total and the T-number. To start my investigation I will do this by working on a 9*9 grid. From this 9*9 grid I will collect a number of T -Shapes with T -Numbers after collecting these I will put them into a table and will investigate to find any relationship between them. 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 Definition of the T -Total and T -Numbers Consider the numbers in the T -Shaped figure shown in the grid by thick lines, redrawn underneath separately for clarity. The integer at the bottom of the T -Shape is 20 this I known as the T -number for the T -Shape: 2 3 1 20 The T -Total is defined as the sum of all the integers shown in the above T -Shaped figure. For example the T -Total for the T -Shape above = 1+2+3+11+20 = 37 I firstly begin the investigation by starting of with a T shape, the following shows 4 T -Shapes collected from the first row: 2 3 4 2 21 T -Number = 21 T -Shape = 2+3+4+12+21 = T -Total = 42 3 4 5 3 22 T -Number = 22 T -Shape = 3+4+5+13+22 = T -Total = 47 4
Step Stairs
Number squares In this investigation I will be looking at 'square step shapes'. These are shapes such as the one pictured below: These shapes are put onto a grid such as the one shown below, the example shown is a 10 x 10 grid: When placed on one of these grids the numbers inside of each box of the step shape are added to give you a total. The number in the bottom left-hand corner of the step shape is the number for that step shape. E.g. This is shape placed on a 10x10 grid. It is shape number one, the first shape, as the number in the bottom left hand corner is 1. All the numbers in the shape added together equals 81. So the total for stair shape 1 on a 10x10 grid is 81. I am going to begin my investigation by trying to find the rule that allows you, if you are given a shape number, to work out the total for a shape on a 10x10 grid. I will begin by putting the shape numbers, numbers inside that shape and shape totals onto a grid. I already know number one from my example and I will use the method I used in my example to work out the subsequent numbers and totals. However, for times' sake I will not draw out each shape. 0x10 grid: Shape number Numbers in shape Shape total ,2,3,11,12,21 50 2 2,3,4,12,13,22 56 3 3,4,5,13,14,23 62 4 4,5,6,14,15,24 68 5 5,6,7,15,16,25 74 6 6,7,8,16,17,26 80 7 7,8,9,17,18,27 86 8 8,9,10,18,19,28 92 1
From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.
T Shape Coursework 9 Grid My teacher gave me a candidate sheet if I add up the total in the T shape I get: 2 3 1 20 T Total=1+2+3+11+20=37 20x5-63=37 I am now going to draw 3 more T shape moving to the right across one on a 9 grid 2 3 4 2 21 T Total= 2+3+4+12+21=42 21x5-63=42 3 4 5 3 22 T Total=3+4+5+13+22=47 22x5-63=47 4 5 6 4 23 T Total=4+5+6+14+23=52 23x5-63=52 Sum Total Increase +2+3+11+20 37 2+3+4+12+21 42 5 3+4+5+13+22 47 5 4+5+6+14+23 52 5 From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five. I am now to investigate the total by moving the T shape down the grid 2 3 1 20 T Total= 1+2+3+11+20=37 20x5-63=37 0 1 2 20 29 T Total= 10+11+12+20+29=82 29x5-63=82 9 20 21 29 38 T Total= 19+20+21+29+38=127 38x5-63=127 28 29 30 38 47 T Total=28+29+30+38+47=172 47x5-63=172 I have noticed that each time I move the T shape down the grid each number increases by nine, as they are five numbers the total increase by 45. Sum Total Increase +2+3+11+20 37 0+11+12+20+29 82 45 9+20+21+29+38 27 45 28+29+30+38+47 72 45 I am going to use algebras to see if on a 9 grid 5t-63 gives you the T total. t-19 t-18 t-17 t-9 T T Total= T+T-19+T-18+T-17+T-9 = 5t-63 3 4 5 23 32 T Total=
T-Totals Investigation.
T-Totals Investigation: In this investigation I will be exploring the different relationships between the letter 'T' and its numbers and totals using a variety of different grid sizes and translations to effectively find any correlations between them. 2 3 1 20 This is the 'T' shape that I will be starting with. The total of the numbers inside the T-shape is: 1+2+3+11+20= 37 This is called the T-total. The number found at the bottom of the whole T-shape is called the T-number. In this case, the T-number for this T-shape is 20. Part 1: Investigate the relationship between the T-total and T-number. Starting with a 9 by 9 grid, a table for T-shapes going horizontally across the grid can be drawn: 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-number 20 21 22 23 24 25 26 T-total 37 42 47 52 57 62 67 +5 +5 +5 +5 +5 +5 A T-shape with the T-number 27 cannot be drawn as this would give an incomplete 'T'. As can be seen above, there is always an addition of 5. Next, I have drawn a table for the T-shapes going vertically down the same 9 by 9 grid: 2 3 4 5 6 7 8 9 0 1 2 3
Mathematics Coursework - T-totals
GCSE MATHEMATICS COURSEWORK T-totals 0/3/'02 Jonathan Briggs INTRODUCTION Introduction The question I have been asked has been set in three parts. The question is about T-shapes on different grids. The bottom number in the T is called the T-number the T-number is the largest number in the T-shape. All the numbers in the T-shape added together are called the T-total. In the whole of the coursework you are not allowed to expand the T-shape but you are allowed to turn it around. In part 1of my coursework I am asked to investigate the relationship between T-totals and T-numbers. At the moment I do not have any notion how the T-total could be calculated in a standard way or of the relationship between the T-number and the other numbers in the T-shape. I did know that they had to be related because they were all numbers with in a sequence. I also knew that the T-total would depend on: ~ * The position of the T-shape on the grid; * The size of the T-shape (for the purpose of this exercise the T-shape is fixed with only five numbers); * The orientation of the T-shape on the grid. These points are fairly obvious as any change to the T-shape will change the numbers within it. From this knowledge I initially experimented practically by putting T-shapes in various positions on a 9 x 9 grid. At this stage (part 1 of this paper) the T-shape was fixed in a normal T position.