Problem
Start with the easiest cases. With 1 cut the rope becomes 2 pieces. With 2 cuts it becomes 3 pieces. With 3 cuts it becomes 4 pieces.
Fourth graders can cut paper or draw short ropes and just count the pieces, so the small cases are easy to trust.
4.OA.C.5Solve An Easier Related ProblemThe pairs (1,2), (2,3), (3,4), (4,5) show pieces always running 1 ahead of cuts.
Listing the two patterns side by side makes the +1 relationship jump out, just like comparing two number patterns.
5.OA.B.3Make A Systematic ListSo the rule is pieces = cuts + 1, the extra one being the rope before any cut.
Each cut splits exactly one piece into two, adding one piece each time, so the count of pieces stays one ahead of the count of cuts.
5.OA.A.2Look For A PatternThe number of pieces is always one more than the number of cuts.
Each cut lands inside one piece and splits it into two, so every single cut raises the piece count by exactly one.
The rope is already one piece before any cut is made, so the count starts at one and then climbs by one for each cut.
The pieces are the whole rope divided up with nothing lost and nothing overlapping, so they always add back to the same rope.
Put ○ = 10 into the rule △ = ○ + 1 to get △ = 10 + 1 = 11.
Once the rule is found, big numbers are no harder than small ones — just substitute and add.
5.OA.A.2Look For A PatternEvery cut adds one piece, so the rope always has one more piece than the number of cuts: △ = ○ + 1.