Reasoning · Grade 2-1 Measuring Length with Units
Problem
One loop traces a rectangle, so it uses two base edges and two heights.
Drawing the loop shows it is just the outline of a rectangle wrapped around the box, and a rectangle's outline uses each side twice.
2.MD.A.1Draw A DiagramCounting: ㉠ is 2L+2W+4H, ㉡ is 4W+4H, ㉢ is 4L+4H, ㉣ is 2W+2H.
Splitting each wrap into separate loops turns a confusing picture into a simple parts list I can add up.
2.MD.A.1Identify SubproblemsWith equal counts the box using more long edges wins: ㉢, then ㉠, then ㉡.
When two paths use the same number of heights, the one that goes around the longer side wins; swapping a long edge for a short edge always makes the string shorter.
2.MD.A.4Organize Information In More Ways㉣ has only one loop and just two heights, so it is the shortest.
One loop must be shorter than two loops of the same kind, so the box wrapped just once uses the least.
2.MD.A.4Organize Information In More WaysPutting it together, the order is ㉢, ㉠, ㉡, ㉣.
Chaining the pairwise comparisons lines all four boxes up in one clear order.
2.MD.B.5Organize Information In More WaysComparing the boxes two at a time is enough to line all four up in one order from most string to least.
Each comparison only says which of two boxes uses more, yet those separate verdicts link together into a single ranking of all four.
If the first uses more than the second and the second more than the third, the first must use more than the third, so no comparison ever has to be redone.
Each single comparison is settled without measuring, because trading a long edge for a short one always shortens the wrap by the same difference.
You don't need any numbers — just count the loops and remember that going around the longer side uses more string!