Even number of flips returns original
4.G.A.3
Generated variants — 8
Draw the shape that results after flipping the figure to the right 5 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 5 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 5 times in a row. We must draw the shape that results after all 5 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 5 times.
Unknowns
- The appearance of the shape after 5 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 5 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 5 is odd, so the mirror image of the original (a single right-flip) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 6 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 6 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 6 times in a row. We must draw the shape that results after all 6 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 6 times.
Unknowns
- The appearance of the shape after 6 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 6 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 6 is even, so the original shape (unchanged) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 8 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 8 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 8 times in a row. We must draw the shape that results after all 8 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 8 times.
Unknowns
- The appearance of the shape after 8 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 8 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 8 is even, so the original shape (unchanged) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 9 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 9 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 9 times in a row. We must draw the shape that results after all 9 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 9 times.
Unknowns
- The appearance of the shape after 9 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 9 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 9 is odd, so the mirror image of the original (a single right-flip) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 12 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 12 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 12 times in a row. We must draw the shape that results after all 12 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 12 times.
Unknowns
- The appearance of the shape after 12 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 12 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 12 is even, so the original shape (unchanged) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 13 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 13 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 13 times in a row. We must draw the shape that results after all 13 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 13 times.
Unknowns
- The appearance of the shape after 13 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 13 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 13 is odd, so the mirror image of the original (a single right-flip) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 17 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 17 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 17 times in a row. We must draw the shape that results after all 17 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 17 times.
Unknowns
- The appearance of the shape after 17 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 17 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 17 is odd, so the mirror image of the original (a single right-flip) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Draw the shape that results after flipping the figure to the right 20 times.
The starting figure is an asymmetric shape drawn on a grid (shown on the left). Flipping to the right means reflecting the figure across a vertical line. After it has been flipped 20 times, draw the shape that results on the grid to the right.
Show solution
1 · Understandwhat's really being asked
An asymmetric grid shape is flipped to the right (reflected across a vertical line) 20 times in a row. We must draw the shape that results after all 20 flips.
Givens
- A starting asymmetric grid shape (shown on the left).
- The shape is flipped to the right (a reflection across a vertical line) 20 times.
Unknowns
- The appearance of the shape after 20 right-flips.
Constraints
- Each flip is the same right-flip (reflection across a vertical line).
- Flips are applied repeatedly to the result of the previous flip.
2 · Planchoose the strategy
#5 Look for a Pattern
Flipping the same shape across the same line twice brings it back to the start, so the result repeats with period 2. I look at the small cases to find the pattern, then use whether the flip count is odd or even to pick the answer.
3 · Execute4 carry out the plan
1Try the easier case: what does one flip do?
2Flip a second time: back to start
3Use odd/even to count 20 flips
4Draw the result
4 · Reviewdoes it hold up?
The result must be either the original (even flips) or its mirror image (odd flips). 20 is even, so the original shape (unchanged) is the correct outcome.
Standardsmin grade 4
4.G.A.3Recognize a line of symmetry for a two-dimensional figure — Understanding that flipping a figure across a line is a reflection, and that two identical reflections return the original.
Where next?
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