Problem
The white stones make an n by n block in figure n.
Reading the small figures in order shows the white side length matches the figure number, a pattern a 5th grader can spot.
5.OA.B.3Look For A PatternThe black border is the (n+2) by (n+2) square less that white block, which comes to 4n + 4.
Counting the border as 'whole square minus inside' on the easy first figures gives a clean rule without counting every stone.
5.OA.A.2Solve An Easier Related ProblemThe black border of the n-th figure holds 4 x n + 4 stones.
The border is exactly what is left when the inner white square is taken out of the whole square, with no stone missed and none counted twice.
That leftover can also be counted straight off the picture as four sides of n stones plus the four corner stones.
Each side runs n stones between two corners, and the corners belong to no side, so every stone is matched to exactly one place in the count.
Apply each rule at n = 30. White is 30 x 30 = 900 stones. Black is 4 x 30 + 4 = 124 stones.
Each correspondence is its own little machine; feed 30 in and read each count out.
4.OA.C.5Look For A PatternThere are more white stones than black, so the difference is white minus black: 900 - 124 = 776.
Picture the big inner block of white dwarfing the thin black frame, so the gap is large and positive.
5.OA.A.2Draw A DiagramWhen one picture has two things changing, make a separate rule for each, then use both.