# Maths - Number grid.

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Introduction

Planning What is your task about? What do you have to do? My task is to take a number grid, draw a square around four numbers, and work out the product of the top left corner and bottom right corner. I am to do the same for the top right and bottom left corner. I must then work out the formula for my calculations so it can apply to any four numbers in a square on that size grid. Have you got any questions you would like to add to the original tasks? After each section of results I will do an Analysis of my results to look for any kind of relationship forming. What will you do first? To begin with I will plan my results table and then begin work on my task analysis. What information or data will you need to collect in order to complete the task? The information I need to collect is the product of the top right and bottom left numbers in a two-by-two square on a ten-by-ten number grid. I will also need to find the product of the top right and bottom left numbers. I will then use these numbers to calculate an nth term. How much information do you think you will need to collect? I will need to take 3, 4 or 5 readings (depending on grid size) ...read more.

Middle

99 100 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 2, 11, 12 1 x 12 = 12 2 x 11 = 22 10 26, 27, 36, 37 26 x 37 = 962 27 x 36 = 972 10 58, 59, 68, 69 58 x 69 = 4002 59 x 68 = 4012 10 73, 74, 83, 84 73 x 84 = 6132 74 x 83 = 6142 10 89, 90, 99, 100 89 x 100 = 8900 90 x 99 = 8910 10 n, n + 1, n + 10, n + 11 n(n + 11) = n2 + 11n (n + 1)(n + 10) = n2 + 11n + 10 10 1.2 - Seven-by-Seven Grid, Two-by-Two Square 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 2, 8, 9 1 x 9 = 9 2 x 8 = 16 7 12, 13, 19, 20 12 x 20 = 240 13 x 19 = 247 7 25, 26, 32, 33 25 x 33 = 825 26 x 32 = 832 7 30, 31, 37, 38 30 x 38 = 1140 31 x 37 ...read more.

Conclusion

1, 3, 15, 17 1 x 17 = 17 3 x 15 = 45 28 4, 6, 18, 20 4 x 20 = 80 6 x 18 = 108 28 23, 25, 37, 39 23 x 39 = 897 25 x 37 = 925 28 33, 35, 47, 49 33 x 49 = 1617 35 x 47 = 1645 28 n, n + 2, n + 14, n + 16 n(n + 16) = n2 + 16n (n + 2)(n + 14) = n2 + 16n + 28 28 2.3 - Five-by-Five Grid, Three-by-Three Square 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 3, 11, 13 1 x 13 = 13 3 x 11 = 33 20 13, 15, 23, 25 13 x 25 = 325 15 x 23 = 345 20 n, n + 2, n + 10, n + 12 n(n + 12) = n2 + 12n (n + 2)(n + 10) = n2 + 12n + 20 20 Results Analysis Two In this set of results I have realised that the difference between the two products is 4 times the grid size, i.e. on a 7x7 grid, with a 3x3 square, the difference will be 4x7. On a 5x5 grid with a 3x3 square, the difference will be 4x5. ...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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