This what I found out:
My theory for working out the number of squares in a border is counting the outsides of the grids and since there are 4 sides and the grids are 10by10 you have to multiply the 10 by 4 so its 4x10 and the answer will be 40 and since you count the corner twice you have to take away 4 and the answer will 36
Methods:
10+10+10+10 - 4 = 36
(4x10)-4 = 36
Algebra: N(n) = 10
(n+n+n+n-4)
(4n - 4) = (answer)
Other Methods:
The other theory for working out the number of squares in a border is multiplying the outside of the grids which is the 10x10 and the answer will be 100 and the inside squares will be 8x8 and the answer will be 64 and once you get both answers you subtract them together(100-64) and the answer will be 36.
Methods: 100 - 64 = 36
10x10 =100
8x8 = 64
Algebra: N(n) = 10
(n x n = 100)
( n-2 x n-2 =64)
There also other methods or formula on how to calculate. First, you have to count the top which is 10 and count the 2 sides of the outside grids which are 9, it's 9 because we already count the top and we are not gonna count it again and the bottom grids will be 8 because of we already count the sides.
In this method you have to do is 10 + 9 + 9 + 8 = 36.
Example:
10+9+9+8 = 36
Algebra:
(n + n-1 + n-1 + n-2 = 36)
n + 2(n-1) + n-2 = 36
Proof of 6 ways of doing it.
Did you understand the example?
Hi Jhermaine! It's Summer.
ReplyDeleteI really like how you've explained and described the theories and how to calculate the number of squares outside of a grid.
I really like how interesting the 10 x 10 - 8 x 8 one is. Isn't the algebra for that one meant to be 2n - 2n-2, or am I just reading it wrong?
G'day Jhermaine. I like how you have explained this really good and it is very understandable. You have added great descriptive words and you've used good punctuation. You have also added in the algebra way of doing it and that way seems very easier. Keep up the good work!
ReplyDeleteHi Jhermaine, I really like how you've explained the different ways on how to solve the squares outside a grid. Maybe next time you could make an example to really show that it can work with any types of grid, it could be 20 by 20 grid or 50 by 50. Overall, Good Job!
ReplyDeleteHe JhermaineI like your description of how to calculate the grids but i think your equation for the area one doesen't make sense to me. Whenyou use n*n that can be equal to n^2 (squared) you might want to revisit this and then have a go again
ReplyDeleteHello Jhermaine, I really like the way you've explained how to calculate the numbers of the squares outside the grid and I really like your work, keep it up!
ReplyDelete