Reasoning · Grade 2-2 Bars and Length
Problem
Laid down as they are, the bars give 1, 3, 8.
Each single piece is itself a length we can mark off, so its size is automatically measurable.
2.MD.B.5Make A Systematic ListAdding end to end gives 4, 9, 10, 11, 12, 13.
Lining bars up nose to tail simply stacks their lengths, so each new sum is a length we can span.
2.OA.A.1Draw A DiagramReading the leftovers fills in 2, 5, 6, 7.
Overlapping two pieces and measuring the part that sticks out gives the difference of their lengths.
2.MD.A.4Make A Systematic ListOverlapping two bars and reading the part that sticks out measures the difference of their lengths.
The longer bar is the shorter bar plus the sticking-out piece laid end to end, so those two parts add back to the longer bar.
Knowing the whole and one part, taking that part away returns the other, because taking away undoes putting together.
Together that is 1 through 13 with no gaps — 13 lengths.
Counting the distinct values in the ordered list gives the total, and seeing every number 1–13 appear confirms nothing is missing or repeated.
2.NBT.A.2Make A Systematic ListBy adding and comparing the bars (and their 1 cm thickness!), you can make every length from 1 to 13 cm — just Grade 2 add-and-compare thinking!