Reasoning · Grade 3-2 Applications of Division
Problem
174 ÷ 6 gives 29 gaps per side.
Each 6 ft step is one gap, so 174 ft makes 29 equal gaps.
3.OA.A.3Solve An Easier Related ProblemEnds included makes 30 a side, so 60 trees.
Posts beat gaps by 1 on an open line, and there are two identical sides.
4.OA.A.3Draw A DiagramThe loop closes, so the oaks match the gaps at 30.
On a circle the last gap returns to the first oak, so posts and gaps match exactly.
3.OA.A.3Draw A DiagramAround a closed loop the last gap comes back to the first tree, so the number of trees equals the number of gaps.
Walking all the way round returns you to where you started, so the loop has no loose end to add an extra tree.
Each tree owns exactly the gap that follows it, so trees and gaps pair off with none left over on either side.
Two maples per gap makes 30 + 60 = 90.
Each of the 30 oak-to-oak gaps gets 2 maples, and adding the 30 oaks gives the grand total.
4.OA.A.3Identify SubproblemsCount the gaps first: on a straight road add 1 for the end post, but on a loop the trees just equal the gaps -- the circle quietly saves you that extra tree!