 # Number Grids

explanatory Essay
1600 words
1600 words Number Grids

My task is to find an algebraic rule for different sized squares in a

set sized number grid.

To do this I will establish my algebraic rule by creating a 10×10

square and marking out 3 different sized squares inside this square. I

will then work out the rules for these individual squares and combine

them to create my overall rule.

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I have marked out my smaller squares inside the grid and will now work

out an algebraic rule:

To find my algebraic rule I will times the

#### In this essay, the author

• Explains that their task is to find an algebraic rule for different sized squares in a set-sized number grid.
• Describes 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
• Explains that they will work out an algebraic rule by times the opposite corners in the inset squares and taking the numbers away from each other to find the difference.
• Explains that after multiplying the corners of the 22 squares, they took the lowest away from the highest.
• Explains how they have simplified the rule a2+11a+10 to prove their overall rule.
• Explains that after multiplying the corners of the 33 squares, they took the lowest away from the highest. this number is always 40.
• Explains that they have repeated the stages as before to prove their overall formula for the 44 inset squares.
• Explains that to create their overall formula for the difference they will need to use letters to represent certain numbers.
• Explains that they will subtract the first part of the formula from the other.
• Explains that the number in the 22 squares was 10 so this proves their formula correct.
• Explains that they have marked out individual squares in their original grid and will calculate the formula for them.
• Explains that a2+8a+7 0 +7 =7, 33 117=17, 215=45, 45-17=28, 1026=260, 1224=288,
• Explains that before creating an overall formula, they will create a formula for their 77 grid.
• Explains that they will subtract the first part of the formula from the other part to work out their overall formula.
• Explains that the number in the 22 squares is 7 so this proves their formula correct. to find their final formula, they will multiply the opposite corners like they have in all their previous calculations.
• Explains the formulas to give them their overall formula for the difference.
• Explains that they now know that their formula is correct. to further their work, they will create a rectangle and find the general rule for the difference.
• Describes the requirements for a 50-year-old man.
• Explains that they will create an algebraic rule for the 23 rectangles.
• Explains that they will create an algebraic rule for the 42 rectangles.
• Explains that the general formula for the difference could be: a represents the width of the grid, b represents its length, and y is its width.
• Explains that they will prove this by creating a 75 grid and using the same process.
• Explains that they will create their overall formula for any sized rectangle in any shape.
• Explains that the overall formula for the difference is b(z-1)(a-1).