Problem
Subtract each mirrored reading from 12:00: 4:52 when he fell asleep and 5:37 when he woke up.
A mirror flips the clock face left-right across the line through 12 and 6, so the mirrored reading and the true time always add up to exactly 12:00 — subtracting the mirrored reading from 12:00 recovers the true time.
Visualize Spatial Relationships2.MD.C.7TimeFrom 4:52 to 5:00 is 8 minutes.
How much is missing from 52 minutes up to a full 60 comes from subtracting 52 from 60 — subtracting reverses adding, so this difference is exactly the number that completes 52 to 60.
Identify Subproblems3.MD.A.1TimeAdd 8 and 37 minutes: Noah napped 45 minutes.
On the clock the two pieces sit end to end — the first ends at 5:00, right where the second begins — so adding them covers 4:52 to 5:37 with no gap and no overlap.
Identify Subproblems3.MD.A.1TimeThe whole nap from 4:52 to 5:37 equals the 8-minute step up to 5:00 plus the minutes from 5:00 to 5:37, added together.
On the clock the two steps sit end to end — the first ends at 5:00, exactly where the second begins — so together they stretch from 4:52 all the way to 5:37 with nothing skipped and nothing counted twice.
When pieces cover a whole span with no gap and no overlap, their lengths add back to the length of the whole span.
The first step is 8 minutes long because 52 needs 8 more to reach a full hour of 60 minutes, and that missing amount is exactly what 60 minus 52 gives.
Taking 52 away from 60 reveals the number that was added to 52 to make 60, because subtracting reverses adding.
A mirrored time becomes real once you subtract it from 12:00. Add the minutes between both true times to get the elapsed time.