• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
• Level: GCSE
• Subject: Maths
• Word count: 2120

# Number Grid

Extracts from this document...

Introduction

Number Grid This investigation is based on finding rules for differences. The investigation: Start with a number grid 10 long. Multiply the top left hand number by the bottom right hand number. Multiply the top right hand number by the bottom left hand number. Find the difference. (This means take away the smallest value from the largest value) Investigate In the grid below; Top left hand number = 13 Bottom right hand number = 24 Top right hand number = 14 Bottom left hand number = 23 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 50 . . . . . . . . . . . . . . . . . . . . So, 13 x 24 = 312 14 x 23 = 322 Difference is largest - smallest = 322 - 312 = 10 Try another 2 x 2 square 56 57 66 67 So, 56 x 67 = 3752 57 x 66 = 3762 Difference is largest - smallest = 3762 - 3752 = 10 (same as above) ...read more.

Middle

3 = 9 x 10 = 90 5 x 5 160 = (5-1=4) 4 = 16 x 10 =160 The size of the square subtract 1, square the answer, multiply it by 10 the pattern continues as w x w = (w-1) x 10 The general rule for the difference using squares of size w on a number grid 10 long is (w-1) x 10 or 10(w-1) Proof for a square w x w Starting position Any number width = w n n+1 n+2 n+3 . . n+(w-1) The amount added n+(1x10) . . . . . . onto n is one less height n+(2x10) . . . . . . than the square (w-1) = w n+(3x10) . . . . . . . . . . . . . . . . . . . . n+10(w-1) . . . . . n+10(w-1) +(w-1) Each row goes up 10, there are one less Need to add a further (w-1) lots of 10 than the height w, so we need to add on to the first square in this row (w-1) lots of 10 (same as the first row) Top left hand number = n Top right hand number n+(w-1) = n+w-1 Bottom left hand number n+10(w-1) ...read more.

Conclusion

. . . . than the square (w-1) = h n+(3xL) . . . . . . . . . . . . . . . . . . . . n+L(h-1) . . . . . n+10(h-1) +(w-1) Each row goes up L, there are one less Need to add a further (w-1) lots of L than the height h, so we need to add on to the first square in this row (h-1) lots of L (same as the first row) Now to find the difference for any size square. Top left hand number = n Bottom right hand number = n+L(h-1)+(w-1) = n+Lh-L+w-1 Top right hand number = n+(w-1) = n+w-1 Bottom left hand number = n+L(h-1) = n+Lh-L Top left hand number x Bottom right hand number n(n+Lh-L+w-1) = n + Lhn-Ln+wn-n Top right hand number x Bottom left hand number (n+w-1) x (n+Lh-L) which gives nxn + nxLh +nx(-L)+ wxn+wxLh+wx(-L)+(-1)xn+(-1)xLh+(-1)x(-L) which gives n + Lhn - Ln +nw +Lwh -Lw - n - Lh + L Difference ( n + Lhn - Ln +nw +Lwh -Lw - n - Lh + L ) - (n + Lhn-Ln+wn-n) Which gives Lwh - Lh - Lw + L = L(wh - h - w + 1) = L(w-1)(h-1) The general rule for rectangles on a L long number grid is L(w-1)(h-1) ...read more.

The above preview is unformatted text

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## What the 'L' - L shape investigation.

I will now prove that my formula works. If I use the same algebraic L-Shape as before I can prove my formula works. L-2g L-1g L L+1 L+2 To enhance my calculations I have replaced the numbers above the L-Number with algebraic notation.

2. ## Number Grid Investigation.

that in a 6 X 6 square, the product difference will be 200. Let's try... 1 2 3 4 5 6 9 10 11 12 13 14 17 18 19 20 21 22 25 26 27 28 29 30 33 34 35 36 37 38 41 42 43 44 45 46 (1 X 46)

1. ## Investigation of diagonal difference.

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 50

2. ## For other 3-step stairs, investigate the relationship between the stair total and the position ...

35 36 1: 21x79-350= 1309 46 47 48 2: 24+35+46+57+68+79+36+47+58+69+70+81+80+ 48+59+60+71+82+72+83+84= 1309 57 58 59 60 68 69 70 71 72 79 80 81 82 83 84 37 Formula: 21x-350 48 49 1: 21x92-350= 1582 59 60 61 2: 37+48+59+70+81+92+49+60+71+82+93+61+72+ 83+94+73+84+95+85+96+97= 1582 70 71 72 73 81 82 83 84

1. ## Maths - number grid

s s+1 s+2 s+10 s+11 s+12 (s+2) (s+10)-s (s+12) = s(s+10) +2 (s+10)- s -12s = s +10s+2s+20- s -12s =20 Furthering my investigation I am going to further my investigation by increasing the size of my rectangle to 5x3.

2. ## Number Grid Investigation

1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 1 x 45 = 45 Difference=160 5 x 41 = 205 My prediction was correct, the difference in this 5 x 5 square is 160

1. ## number grid

a a+2 a+20 a+22 I have used the letter 'a' for the top left number and added how much bigger the other key numbers are away from it. In my investigation I have to find the difference between, the product of the top left number and the bottom right number,

2. ## Mathematics - Number Stairs

it will be: T = 3n + 12 2-Step Staircase/ Grid Width 11 12 1 2 n 1 2 3 4 5 T 15 18 21 24 27 Suspected formula: T = 3n + 12 Prediction / Test: 3 x 20 + 12 = 72 31 20 21 20 +

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work