# Number grid.

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Introduction

Maths coursework number grid In this project, I am going to investigate a number grid. Using a set of instructions, that, have been given to me. The instructions are to find the product of various numbers. Before I start I will like to explain exactly why I have colour coded my work. If you look at my project you will find that there are certain numbers in colour the reason for this is, that it makes it easier to understand what is being multiplied and what is being subtracted. The numbers that were initially given to me were 12, 13, 22, 23 presented in a number grid marked by a two by two box. I was told to find the product of top left, (12) and the bottom right number (23). We then had to do the same to the top right (13) and bottom left (22). Once I we had worked out both products I had to calculate the difference. I am now going to give two examples to show you what I had to do. 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 54 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 ...read more.

Middle

First I took a two by two square, with consecutive multiple numbers in the two times table. I am going to compare it with my original two by two square, where the difference is ten, and my formula below confirms that. d=(b-1)2x10 d=(2-1) 2x10 d=12 x10 d=10 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 4 6 14 16 16 14 Difference x 4 x6 84 84 64 -64 20 X X+2 X+10 X+12 X(X+12) (X+10)(X+2) DIFFERENCE =X2+12X =X2+10X+2X+20 X2+12X+20 = X2+12X+20 -X2+12X = 20 The original general formula is d=(b-1)2x10 Using this formula I can now work out a new formula for consecutive multiples. The formula will have one change to it and that will be, instead of multiplying by ten, we will multiply by ten times the multiple. My new formula which I am going to use to calculate the difference of a four by four square, which numbers are in the four times table, using 'm' for multiples my formula should look like this. four by four two by two d=10m(b-1)2 d=10m(b-1)2 d=(4-1)2x40 d=(2-1)2x20 d=32x40 d=12x20 d=9x40 d=1x20 d=360 d=20 I am now going to use algebra to see if my new formula was correct to calculate the differences for consecutive multiples. X X+4 X+8 X+12 X+10 X+14 X+18 X+22 X+20 X+24 X+28 X+32 X+30 X+34 X+38 X+42 X(X+42) ...read more.

Conclusion

d=(l-1)(b-1)x10 d=10(6X3) d=10x18 d=180 I have now proved that my formula, d=(l-1)(b-1)x10, has worked and will calculate the difference of any sized rectangle. I now do not need to use algebra or number term calculations to find the difference of a rectangle. For the last part of my project I looked at consecutive multiples of the rectangle. Taking the table above and my formula, d=10m(b-1)2 which was used for multiples in squares. I tried d=10m(l-1)(w-1) to obtain a general formula for consecutive multiples of the rectangle. Two by six multiples of five 10 15 20 25 30 35 20 25 10 35 40 45 10 35 Difference x45 x20 700 450 700 450 250 Using the calculations above, I am going to try and prove that my formula d=10m(l-1)(w-1), is accurate in calculating consecutive multiples in the rectangle. d=10m(l-1)(w-1) d=(10x5)(1x5) d=50x5 d=250 X X+25 X+10 X+35 X(X+35) (X+10)( X+25) Difference =X2+35X =X2+25X+250+10X X2+35X+250 =X2+35X+250 - X2+35X =250 My formula is correct as the answer I got is two hundred and fifty, I also got that same answer in my number term working, and also in my algebra. I can therefore be confident that this formula works, and can use it as a general formula. From this project I have seen how interesting it is to investigate a nu,berg id and work out different formulas. All the calculations that I have done in my project are correct. The formulas that I worked out are also correct and may be used as general formulas. Eli rose maths course-work 1 ...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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