Reasoning · Grade 2-1 Measuring Length with Units
Problem
The cat must go 7 right and 7 down, and only two diagonals are useful.
Drawing on the grid and counting the sides is exactly the unit-counting idea from this chapter: a length is just how many one-unit sides you walk along.
1.MD.A.2Draw A DiagramWith no shortcuts every route is the same: 7 + 7 = 14 units.
Splitting the trip into 'rightward steps' and 'downward steps' makes the count easy: no matter the order, you always use 7 of each.
1.MD.A.2Identify SubproblemsEvery route that uses no diagonal has the same length, because it always spends 7 rightward steps and 7 downward steps whatever order they come in.
The route is made of one-unit sides laid end to end with no gaps and no overlaps, so its length is just the number of sides walked.
Reordering the same steps cannot change what they add up to, so two routes made of the same steps in a different order are the same length.
Each diagonal swaps a two-side corner for one line, giving 10 sides + 2 diagonals.
Listing the candidate routes and comparing them is the chapter's core skill: to compare two lengths, count the units of each and see which is fewer.
1.MD.A.1Make A Systematic ListA diagonal beats the two sides it replaces and none are left unused, so this is the shortest.
Seeing how much is saved each time a diagonal replaces a corner is just measuring how much shorter one path is than another.
2.MD.A.4Guess And CheckThis only needs Grade 2 length sense: count the unit-sides, and let the slanted shortcuts cut the corners that head toward the fish!