← Reverse the moves to recover original · Work Backwards to Recover a Start Value

Reverse the moves to recover original · 8 practice problems

4.G.A.34.MD.C.5

Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 2 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 2 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 2 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 2 flips behave like 0 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 2 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 2 = 2 x 1 + 0, so 2 upward flips have the same effect as 0 upward flip(s).
2=2×1+02 = 2 \times 1 + 0
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 2 upward flips act like 0 flip, and a flip is its own undo, flip the figure upward 0 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 0 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 2 times = 0 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 2 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 9 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 9 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 9 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 9 flips behave like 1 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 9 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 9 = 2 x 4 + 1, so 9 upward flips have the same effect as 1 upward flip(s).
9=2×4+19 = 2 \times 4 + 1
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 9 upward flips act like 1 flip, and a flip is its own undo, flip the figure upward 1 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 1 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 9 times = 1 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 3 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 7 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 7 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 7 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 7 flips behave like 1 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 7 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 7 = 2 x 3 + 1, so 7 upward flips have the same effect as 1 upward flip(s).
7=2×3+17 = 2 \times 3 + 1
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 7 upward flips act like 1 flip, and a flip is its own undo, flip the figure upward 1 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 1 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 7 times = 1 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 4 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 6 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 6 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 6 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 6 flips behave like 0 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 6 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 6 = 2 x 3 + 0, so 6 upward flips have the same effect as 0 upward flip(s).
6=2×3+06 = 2 \times 3 + 0
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 6 upward flips act like 0 flip, and a flip is its own undo, flip the figure upward 0 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 0 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 6 times = 0 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 5 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 4 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 4 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 4 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 4 flips behave like 0 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 4 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 4 = 2 x 2 + 0, so 4 upward flips have the same effect as 0 upward flip(s).
4=2×2+04 = 2 \times 2 + 0
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 4 upward flips act like 0 flip, and a flip is its own undo, flip the figure upward 0 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 0 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 4 times = 0 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 6 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 3 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 3 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 3 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 3 flips behave like 1 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 3 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 3 = 2 x 1 + 1, so 3 upward flips have the same effect as 1 upward flip(s).
3=2×1+13 = 2 \times 1 + 1
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 3 upward flips act like 1 flip, and a flip is its own undo, flip the figure upward 1 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 1 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 3 times = 1 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 7 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 5 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 5 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 5 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 5 flips behave like 1 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 5 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 5 = 2 x 2 + 1, so 5 upward flips have the same effect as 1 upward flip(s).
5=2×2+15 = 2 \times 2 + 1
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 5 upward flips act like 1 flip, and a flip is its own undo, flip the figure upward 1 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 1 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 1 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 5 times = 1 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!
Variant 8 medium answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.

The figure shown on the right is the result of flipping some shape upward 10 times and then turning it 90°90\degree clockwise. Draw the original shape.

On the empty grid to the left, draw the original shape (before any moves).

Draw original After moves
Show solution
1 · Understandwhat's really being asked

Some original shape was flipped upward 10 times and then turned 90 degrees clockwise, giving the figure shown on the right. We must work backward to draw the original shape.

Givens
  • The final figure on the right grid is shown.
  • The moves applied to the original were: flip upward 10 times, then turn 90 degrees clockwise.
Unknowns
  • The appearance of the original shape (to be drawn on the left grid).
Constraints
  • Flipping upward is a reflection across a horizontal line; doing it twice returns the shape (so 10 flips behave like 0 flip).
  • To reverse a sequence of moves, undo them in the opposite order with each move's inverse.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #5 Look for a Pattern#1 Draw a Diagram

We are given the end state and must find the start, which is the trigger for Work Backwards: undo the last move first. The flip-count pattern simplifies the undo, and a diagram lets us draw each reversed step on the grid.

3 · Execute4 carry out the plan

1Simplify the 10 upward flips

#5 Look for a Pattern 4.G.A.3
Flipping upward twice returns the shape, so flips cancel in pairs. 10 = 2 x 5 + 0, so 10 upward flips have the same effect as 0 upward flip(s).
10=2×5+010 = 2 \times 5 + 0
An odd number of identical flips acts like just one flip; an even number acts like none.

2Undo the last move first: turn back 90 degrees counterclockwise

#11 Work Backwards 4.MD.C.5
The last move was a 90-degree clockwise turn, so to reverse it we turn the shown figure 90 degrees counterclockwise.
undo 90∘ CW=90∘ CCW\text{undo } 90^\circ\,\text{CW} = 90^\circ\,\text{CCW}
To unwind moves you reverse the order and reverse each move.

3Undo the flips

#11 Work Backwards 4.G.A.3
Next undo the flipping. Since the 10 upward flips act like 0 flip, and a flip is its own undo, flip the figure upward 0 time(s) to recover the original.
A flip reverses a flip.

4Draw the original

#1 Draw a Diagram 4.G.A.3
Take the shown figure, turn it 90 degrees counterclockwise, then flip it upward 0 time(s); draw the result on the empty left grid. That is the original shape.
Performing the reversed moves in reverse order reconstructs the start.
Answer: The original shape is obtained by turning the shown figure 90 degrees counterclockwise and then flipping it upward 0 time(s). Drawing those reversed moves on the left grid gives the original shape.
4 · Reviewdoes it hold up?

Applying the original moves (flip up 10 times = 0 flip, then turn 90 degrees CW) to the reconstructed shape returns the shown figure, confirming the work-backwards steps.

Another way: Cut out the shown figure and literally perform the inverse moves in reverse order (turn CCW, then flip up) to see the original take shape.

Standardsmin grade 4
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding flips as reflections and that a flip undoes a flip when reversing the moves.
  • 4.MD.C.5 Recognize angles as geometric shapes formed when two rays share an endpoint — Undoing the 90-degree clockwise turn with a 90-degree counterclockwise turn.
💡Takeaway. To go back to the start, undo the moves in reverse: turn it back the other way, then flip it - reversing moves is Grade 4 flip-and-turn thinking!