Problem
Flipping upward twice returns the shape to its position, so flips cancel in pairs. 7 = 6 + 1 (three cancelling pairs plus one), so 7 upward flips have the same effect as a single upward flip.
An odd number of identical flips acts like just one flip.
4.G.A.3Look For A PatternThe last move was a 90-degree clockwise turn, so to reverse it we turn the shown numeral-4 figure 90 degrees counterclockwise. This puts the figure back to its state right after the flips.
To unwind moves you reverse the order and reverse each move - a clockwise turn is undone by a counterclockwise turn.
4.MD.C.5Work BackwardsWorking backward, the first move to undo is the last one applied - the 90-degree clockwise turn - and it is undone by turning the figure 90 degrees counterclockwise.
To rebuild the start you retrace the moves in reverse, so the newest move (the clockwise turn) is peeled off first, and a turn is peeled off by turning back the same amount the opposite way.
Spinning every point around the center one way and then the same amount the other way carries each point back along its path to exactly where it started.
Clockwise and counterclockwise are opposite directions, so an equal turn each way cancels out and leaves the figure unmoved.
Every move that changes a figure has an opposite move that reverses it, and for a turn the opposite move is an equal turn the other way.
Next undo the flipping. Since 7 upward flips act like one upward flip, and a flip is its own undo, flip the figure upward one time (reflect it across a horizontal line). The result is the original shape.
A flip reverses a flip, so one upward flip undoes the odd number of upward flips.
4.G.A.3Work BackwardsTake the shown numeral-4 figure, turn it 90 degrees counterclockwise, then flip it upward once; draw the resulting shape on the empty left grid. That is the original shape before any moves.
Performing the reversed moves in reverse order reconstructs the start exactly.
4.G.A.3Draw A DiagramTo go back to the start, undo the moves in reverse: turn it back the other way, then flip it once - reversing moves is just Grade 4 flip-and-turn thinking!