Number Stairs - Up to 9x9 Grid

Number Stairs 91 92 93 94 95 96 97 98 99 00 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 This is a 3-step stair. The total of the numbers inside the stair shape above is: * 1st Line: 25+26+27 * 2nd Line: 35+36 * 3rd Line: 45 T=Total T=194 The stair total for this 3-step stairs is 194. Part 1 * 1st Line: 25+26+27 * 2nd Line: 35+36 Going up by 1 * 3rd Line: 45 45 46 47 35 36 37 25 26 27 Hypothesis: The number from left to right are going up by 1 and the numbers going from bottom to top are going up by 10, therefore if I was given the bottom left hand corner on a 10 by 10 square grid, I would know the rest of the number stair digits. E.g. Bottom left hand corner number. 88 89 90 78 79 80 68 69 70 On a different number square grid, e.g. 4 by 4 number square grid, the theory would be the same, except that the number above the bottom left hand corner number is going to go up by 4. 3 4 5 6 9 0 1 2 5 6 7 8 2 3 4 The total of the numbers inside the stair shape is: * 1st Line: 1+2+3 * 2nd Line: 5+6 * 3rd Line: 9

  • Word count: 2284
  • Level: GCSE
  • Subject: Maths
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Investigate the difference between the products of the numbers in the opposite corners of a rectangle that can be drawn on a 100 square. We were giving as the first rectangle to compare was this

Maths Coursework Opposite Corners April 2005 Investigate the difference between the products of the numbers in the opposite corners of a rectangle that can be drawn on a 100 square. We were giving as the first rectangle to compare was this A. 54 55 56 64 65 66 So we have to do B. 54 × 66 = 3564 64 × 56 = 3584 Then; C. 3584 - 3564 = 20 The different in this is 20. I am going to investigate if the differences will change if I change the numbers involved. a. 1 2 3 11 12 13 b. 1 × 13 = 13 11× 3 = 33 c. 33-13=20 The different in this rectangle is 20, the same as the starter rectangle. From this I am going to try another rectangle the same size as this one and the original. 2a. 84 85 86 94 95 96 b. 84 × 96 = 8064 94 × 86 = 8086 c. 8084 - 8064 = 20 The different in this rectangle is 20 as well. From this it is starting to build up a picture, that all the rectangles this size have the same different of 20. however I will do one more rectangle in this size (2×3) 3a. 81 82 83 91 92 93 b. 81 × 93 = 7533 91 × 83 = 7553 c. 7553 - 7533 = 20 The different in this rectangle is also 20. this indicates that all rectangles of this size will have the difference of 20. Now I am going to do a rectangle of 2×4 squares. I think that these rectangles different will be 30. 4a. 34 35

  • Word count: 2569
  • Level: GCSE
  • Subject: Maths
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The Open Box Investigation

The Open Box Investigation Part 1 The aim of this investigation is to find the largest volume within for an open box with any size square cut out I will be increasing the square cut out by 1cm until I reach a point where the volume decreases. At this point I will decrease the square cut out by 0.1cm until I reach the maximum volume. This will be done on several different grids until I see a pattern which I will then use to create a formula. I will record my results in a table for the different grids and record the peaks to try and establish a pattern. My initial grid size will be 12cm x 12cm and I will increase this as I continue my investigation. The volume will be calculated by multiplying the length by the width by the height. When I appear to reach a maximum volume I will try cut sizes 0.1cm smaller and larger than the cut size that appears to give the maximum volume. If the volume increases then I will make the cut size smaller or larger by 0.1cm again. I will repeat this for grid sizes of 18cm x 18cm and 24cm x 24cm. I have found the following results: Grid Size: 12cm x 12cm Cut Size Calculation Volume cm 0 x 10 x 1 00cm3 2cm 8 x 8 x 2 28cm3 3cm 6 x 6 x 3 08cm3 .9cm 8.2 x 8.2 x 1.9 27.8cm3 2.1cm 7.8 x 7.8 x 2.1 27.8cm3 Grid Size: 18cm x 18cm Cut Size Calculation Volume cm 6 x 16 x 1 256cm3 2cm 4 x 14 x 2 392cm3 3cm 2 x 12 x 3 432cm3

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  • Level: GCSE
  • Subject: Maths
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Open box. In this investigation, I will be investigating the maximum volume, which can be made from a certain size square piece of card, with different size sections cut from their corners. The types of cubes I will be using are all open topped boxes.

In this investigation, I will be investigating the maximum volume, which can be made from a certain size square piece of card, with different size sections cut from their corners. The types of cubes I will be using are all open topped boxes. The size sections that I will be cutting from the square piece of card will all be the same size. The section sizes will go up to half of the original size of card. I will only go up to this size, because it is physically impossible to cut square sections, with sides over half the length of the original shape. During this investigation, I will not account for the 'tabs', which would normally be needed to hold the box sides together. I predict that when the size of the square I cut out is very small, the volume of the box will also be very small. Secondaly, I predict that when the size of the square I cut out is almost half the size of the square I start with, then the volume of the box would be very small aswell. Thirdly, I predict that as the size of the square I cut out increases, then the volume of the box will increase to a maximum and then decrease again. cm by 1cm, piece of square card. Length of the section (cm) Height of the section (cm) Depth of the section (cm) Width of the section (cm) Volume of the cube (cm3) 0.1 0.1 0.8 0.8 0.064 0.2 0.2 0.6 0.6 0.072 0.3 0.3 0.4 0.4 0.048 0.4 0.4 0.2 0.2 0.016

  • Word count: 1826
  • Level: GCSE
  • Subject: Maths
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An investigation into Number Grids.

An investigation into Number Grids We are investigating the effect of number grids and to try and explain the pattern between a 2x2 selection grid on a 10x10 grid. We found that if you multiply the bottom left number and the top right number and the bottom right number and top left number, then subtract one from the other you will find that the difference is 10. As is shown in the below table and number 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 91 92 93 94 95 96 97 98 99 00 If we multiply 3x 14 we get 42 and if we multiply the sum of 4x13 we get 52. 42 subtracted from 52 equals 10. This occurs for any selection square sized grids ie 3x3, 4x4 etc in a 10x10 grid as is shown in the table below.(Blue minus Red) Due to the fact that the difference is always 10 we have decided to show this in a table algebraically. If we multiply the bottom left digit by the top right digit and the top left digit by the bottom right digit we can see that the N's disappear to leave just 10 which is the difference. As is shown below. N(n+1)=n2+1 =see below N(n+21)=n2+21 =N2+21-N2+1

  • Word count: 2630
  • Level: GCSE
  • Subject: Maths
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In this piece course work I am going to investigate opposite corners in grids

Mathematics Course Work Opposite Corners Introduction In this piece course work I am going to investigate opposite corners in grids. I will start by investigating a 7x7 grid. Within this grid I will use 2x2, 3x3, 4x4, 5x5, 6x6 and a 7x7 grid. I will do this to find whether I can find a pattern. I will do this by multiplying the two opposite corners together then subtracting them. I will try to find the patterns and do a formula that will work for all grid sizes and shapes. I will experiment shapes and sizes of all different grids. Prediction I predict that in a 7x7 grid all the opposite corners will be a multiple of 7 and in an 8x8 grid they will be a multiple of 8 and so on. They will only do this if I multiply the two opposite corners then subtract the two from each other. To check my hypothesis I will use 6x6, 7x7, 8x8 and maybe if I have time I will do a 9x9 and 10x10 grid. Also I will be looking at all different shapes and sizes. I hope to find a formula for all grids and all shapes and sizes. 7x7 Grid Here is a grid of numbers in sevens. It is called a seven grid. In this section I will multiply the opposite corners and then subtract them. 2x2 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 In my 7x7 grid I have highlighted three 2x2

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  • Level: GCSE
  • Subject: Maths
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The analysis of number patterns on various types of number grids.

The analysis of number patterns on various types of number grids The main objective of this mathematics coursework is to analyse the various number patterns that emerge from carrying out a very simple mathematical operation on the set of numbers found in a number grid of natural integers. The number grid is arranged in the form of a square grid as 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 The above diagram shows the method that needs to be done to make the calculations so that the number pattern can be found out. The calculation would have to be carried out for all the other number grids and patterns so that the rule which applies to one number pattern should also apply to another number pattern. Once all the calculations have been carried out the results are analysed to find out if any specific number pattern can be seen or not and whether a formula can be written down to find out the results for any other similar number grid pattern. The Rule that would have to be applied to the above numbers is as follows: A box is drawn

  • Word count: 1582
  • Level: GCSE
  • Subject: Maths
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The Magic of Vedic Mathematics.

The Magic of Vedic Mathematics All the students nowadays use a calculator for working out even some of the easiest calculations. You may wonder what the people did when there was no calculator. Well, in India there was Vedic Mathematics. It originated from the Vedas of Hindu. I am going to illustrate some examples of how Vedic Mathematics works. You will be astonished at how fast you can do some of the calculations. Let us start with some easy stuff. Finding the square of adjacent numbers: (a) Say you know the square of 60 = 3600, then the square of 61 will be given as (60)^2 + (60 + 61) = 3600 + 121 = 3721. (b) If you want to find the square of 26, (25)^2 + (25 + 26) = 625 + 51 = 676. Apply it to find the square of a number which is 1 more than the number whose square is known. Suppose you want to find the square of a number which is one less than the number whose square is known, you can use the following method: Square of 79 will be given as, (80)^2 - (80 + 79) = 6400 - 159 = 6241. Finding the square of a number near 50. Now, if you want to find the square of 51, the formula will be, (5)^2+1/ (1)^2 = 25 + 1/ 01 = 2601. This is what you do: The LHS of the answer is given as (5)^2 + 1 and the RHS is given as the square of the difference of the number from 50. The RHS of the answer should always contain 2 digits. Square of a number having all digits 1.

  • Word count: 834
  • Level: GCSE
  • Subject: Maths
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Mathematics - Number Stairs

Ben Foster -------- School--------- Centre Number -------- GCSE Coursework: Number Stairs Teacher: ------- Table of Contents Aim 3 First Part 3 3 Step-Staircase / Grids of width 10 3 Second Part 4 3 Step-Staircase 4 3 Step-Staircase / Grid Width 8 4 3 Step-Staircase / Grid Width 9 5 3 Step-Staircase / Grid Width 11 6 3 Step-Staircase / Grid Width 12 6 2 Step-Staircase 7 2-Step Staircase/ Grid Width 8 7 2-Step Staircase/ Grid Width 9 8 2-Step Staircase/ Grid Width 10 8 2-Step Staircase/ Grid Width 11 9 2-Step Staircase/ Grid Width 12 10 Step-Staircase 11 4 Step-Staircase 11 4 Step-Staircase / Grid Width 8 11 4 Step-Staircase / Grid Width 9 12 4 Step-Staircase / Grid Width 10 13 4 Step-Staircase / Grid Width 11 14 4 Step-Staircase / Grid Width 12 15 5 Step-Staircase 16 5 Step-Staircase / Grid Width 8 16 5 Step-Staircase / Grid Width 9 17 5 Step-Staircase / Grid Width 10 18 5 Step-Staircase / Grid Width 11 19 5 Step-Staircase / Grid Width 12 20 The Final Formula 21 Finding the "n" term of the formula 21 Finding the "g" term of the formula 22 Finding the number term of the formula 23 Aim In this investigation, I will be aiming to find out the formulas of the combinations of the size of number stairs and the size of grid widths. Eventually I will convene a formula connecting the stair totals and other steps on other number grids. First Part

  • Word count: 4455
  • Level: GCSE
  • Subject: Maths
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O-X-O investigation

O-X-O Investigation In this investigation I will investigate the game noughts and crosses. My aim is to find out how many winning lines in a game. I will find out a rule for a regular game on a 3 by 3 grid using 3 in a row as the winning line. After I have a rule for the first grid I will then go on to find rules for several other grids and come up with a general rule. To further my investigation I will change the shape of the grid by changing the length and width and changing the number needed for a winning line. I also may investigate 3D grids and make an overall comparison between all my general rules to see if there is an overall rule for all lengths, widths, winning lines and shapes. In this investigation on the grids the black is the outline of the grid and the red is to show how many winning lines there are. Also I will use some abbreviations in this investigation. W=Width L=length T= Number of squares needed for a winning line S= Number of winning lines. Investigation 1 I will start off by investigating square grids with the number of squares that the length and width is will be the number needed for a winning line i.e. L=W=T 3x3 8 winning lines 4x4 0 winning lines 5x5 2 winning lines Size of grid WxL N.o of squares needed for a winning line 'T' N.o of winning lines 'S' 3x3 3 8 4x4 4 0 5x5 5 2 Rule WxW W 2W+2 I got this rule because

  • Word count: 1184
  • Level: GCSE
  • Subject: Maths
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