Reasoning · Grade 2-1 Measurable Lengths
Problem
Subtracting the surviving marks pairwise gives the gaps 1, 2, 3, 4, 5, 6, 7, 9, 10.
The distance between two marks is just the bigger number minus the smaller one - a simple take-away.
2.MD.A.4Make A Systematic ListA pair of marks measures the difference between their numbers, so a broken ruler can still measure anything that matches one of those gaps.
The stretch from the smaller mark to the larger one is the part of the ruler left after the smaller mark's stretch is removed.
An object does not have to start at zero — sliding both of its ends along the ruler by the same amount leaves the length between them unchanged.
The 1 cm clip fits marks 1 and 2, the 4 cm battery marks 2 and 6.
Lining the object's two ends up on two marks lets the ruler measure it even with the middle marks gone.
2.MD.A.1Draw A DiagramThe 3 cm eraser is 11 − 8, so marks 8 and 11.
We test pairs until two marks are exactly 3 apart; 8 and 11 work.
2.MD.A.1Guess And CheckThe 7 cm glue stick spans marks 1 and 8, the 10 cm pencil marks 1 and 11.
Starting both long objects at mark 1 lets the far mark do the measuring; 8 gives 7 and 11 gives 10.
2.MD.A.1Draw A DiagramAll five lengths appear in the gap list, so every object can be measured.
Checking each length against the list makes sure none was missed and confirms every object has a valid pair of marks.
2.MD.A.4Make A Systematic ListA ruler can still measure even with marks erased - just line both ends up on two leftover numbers and subtract to read the length, using only Grade 2 take-away!