Problem
The path's shape decides how many gaps there are
Sculptures are placed at equal intervals along both sides of a path, including one at each end. We need the distance between neighbouring sculptures.
Number systemOperations
Your answer
How to solve
Strategy Draw a Diagram — Two traps sit in a row here. The count is for both sides, so halve it first; and the gaps between objects on a straight line are one fewer than the objects. Draw one side and both become obvious.
1STEP 1
Split the sculptures between the two sides
The 70 is the total for both sides, and the sides are the same, so each side gets half.
70 ÷ 2 = 35
35 sculptures on each side.
4.OA.A.3Identify Subproblems2STEP 2
Count the gaps on one side
Along a straight path with a sculpture at each end, the gaps sit between sculptures, so there is one fewer gap than there are sculptures.
35 - 1 = 34
34 gaps, not 35.
4.OA.A.3Draw A DiagramA straight side with sculptures on it has gaps.
Why?
Every gap sits between two neighbouring sculptures, so each gap pairs with the sculpture just after it and the very first sculpture has no gap before it.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
3STEP 3
Share the length among the gaps
The 42.5 m is split into 34 equal gaps.
42.5 ÷ 34 = 1.25
Each gap is 1.25 m.
6.NS.B.3Solve An Easier Related ProblemAnswer
1.25 m
Multiply back: 1.25 × 34 = 42.5 m, the length of one side.
Takeaway
Objects at both ends of a straight path leave one fewer gap than there are objects.
- Split the sculptures between the two sides
- Count the gaps on one side
- Share the length among the gaps