A 5x5 grid has 16 squares on the border.how many squares will be on the border of a 10 x10 grid?

Question

provide two solutions for this question which are appropriate for years 4-6 students in primary school

Answer 1

Secca's answer is right and here's why:

1. (10 + 10) + (10 - 2) + (10 - 2) = 36

Add up two opposite sides (10+10), then add up the other two sides without counting the corners you already counted (10-2) + (10-2), if you factor this it gives the same equation as in number two.

2. (4 X 10) - 4 = 36

There are four sides to a square, so multiply the number of grid squares on one side by four, but you are counting the four corners twice.

Here's my own solutions so I am not totally copying from Secca:

10+(10-1)+(10-1)+(10-2)= Count one side, the count the next side minus the one you already counted, count the next side minus the one you already counted, count the last side minus the two you already counted.

10^2 - (10-2)^2 This solution takes all of the squares (10^2, or 10*10) and subtracts all of the inner squares (10-2)^2.  

Answer 2

Hello,

I hope these are suitable answers:

1. (10 + 10) + (10 - 2) + (10 - 2) = 36

2. (4 X 10) - 4 = 36

Hope these are useful,

Secca

Answer 3

5x5 = 16 squares

10x10 = ‘a’ squares

5x5 =  10x10

16           a

25 x a  = 16 x 100

a = 16 x 100

           25

A = 64 squares