Problem
Small cases: 1 sheet needs 4 tacks, 2 sheets need 6, 3 sheets need 8. Each new sheet after the first adds 2 tacks.
Looking at one, two, then three sheets makes the steady jump of 2 easy to spot.
3.OA.D.9Solve An Easier Related ProblemAfter the first sheet there are 25 - 1 = 24 extra sheets, each adding 2 tacks, on top of the starting 4.
The first sheet sets the 4, and every later sheet contributes the same 2 tacks.
3.OA.D.8Look For A PatternThe thumbtacks needed for 25 sheets can be written as 4 + (25 - 1) x 2.
The tacks on the board split with no overlap into the first sheet's 4 and the extra tacks the later sheets bring, so the total is 4 plus those extras.
Every sheet after the first brings the same 2 extra tacks, so all the extras together come to (25 - 1) x 2.
The number of sheets after the first is what is left when the one already-counted first sheet is taken away from 25, which is 25 - 1 = 24.
Twenty-four later sheets each adding the same 2 tacks is 24 equal groups of 2, and that repeated same-size adding is exactly 24 x 2.
Compute the extra tacks then add the starting 4.
Twenty-four added sheets bring 48 tacks, plus the original 4 makes 52.
3.OA.A.3Look For A PatternFind how much the count grows each step, start from the first one, then multiply and add: 4 + 24 times 2 = 52!