Moves in Parallel
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students practice applying rigid transformations to lines. Each image in this activity has the same starting line and students name the translation, rotation, or reflection that takes this line to the second marked line. Because of their infinite and symmetric nature, different transformations of lines look the same unless specific points are marked, so 1–2 points on each line are marked.
While students have experience transforming a variety of figures, this activity provides the opportunity to use precise language when describing transformations of lines while exploring how sometimes different transformations can result in the same final figures. During the activity, encourage students to look for more than one way to transform the original line.
Launch
Provide access to tracing paper. Give students 2 minutes of quiet work time followed by whole-class discussion.
Student Task
For each diagram, describe a translation, rotation, or reflection that takes line ℓ to line ℓ’.
Then plot and label A’ and B’, the images of A and B.
Sample Response
Sample responses:
-
- Translation in many possible directions, for example, down 3 units
- Reflection over a line parallel to ℓ halfway between ℓ and ℓ’
- Rotation using a point halfway between ℓ and ℓ’ as the center of rotation and an angle of 180∘
-
- Reflection across the vertical line through point A
- Reflection across the horizontal line through point A
- Counterclockwise rotation about point A by the obtuse angle whose vertex is at A
- Clockwise rotation about point A by the acute angle whose vertex is at A
Activity Synthesis (Teacher Notes)
Invite students to share the transformations they chose for each problem. Each diagram has more than one possible transformation that would result in the final figure. If students only found one, pause for 2–3 minutes and encourage students to see if they can find another. For the first diagram, look for a single translation, single rotation, and single reflection that work. For the second diagram, look for a single rotation and a single reflection.
- "Will a translation work for the second diagram? Explain your reasoning." (A translation will not work. Since translations do not incorporate a turn, translations of a line are parallel to the original line or are the same line.)
Standards
- 8.G.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1.a·Lines are taken to lines, and line segments to line segments of the same length.
15 min
15 min
Knowledge Components
All skills for this lesson
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Moves in Parallel
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students practice applying rigid transformations to lines. Each image in this activity has the same starting line and students name the translation, rotation, or reflection that takes this line to the second marked line. Because of their infinite and symmetric nature, different transformations of lines look the same unless specific points are marked, so 1–2 points on each line are marked.
While students have experience transforming a variety of figures, this activity provides the opportunity to use precise language when describing transformations of lines while exploring how sometimes different transformations can result in the same final figures. During the activity, encourage students to look for more than one way to transform the original line.
Launch
Provide access to tracing paper. Give students 2 minutes of quiet work time followed by whole-class discussion.
Student Task
For each diagram, describe a translation, rotation, or reflection that takes line ℓ to line ℓ’.
Then plot and label A’ and B’, the images of A and B.
Sample Response
Sample responses:
-
- Translation in many possible directions, for example, down 3 units
- Reflection over a line parallel to ℓ halfway between ℓ and ℓ’
- Rotation using a point halfway between ℓ and ℓ’ as the center of rotation and an angle of 180∘
-
- Reflection across the vertical line through point A
- Reflection across the horizontal line through point A
- Counterclockwise rotation about point A by the obtuse angle whose vertex is at A
- Clockwise rotation about point A by the acute angle whose vertex is at A
Activity Synthesis (Teacher Notes)
Invite students to share the transformations they chose for each problem. Each diagram has more than one possible transformation that would result in the final figure. If students only found one, pause for 2–3 minutes and encourage students to see if they can find another. For the first diagram, look for a single translation, single rotation, and single reflection that work. For the second diagram, look for a single rotation and a single reflection.
- "Will a translation work for the second diagram? Explain your reasoning." (A translation will not work. Since translations do not incorporate a turn, translations of a line are parallel to the original line or are the same line.)
Standards
- 8.G.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1.a·Lines are taken to lines, and line segments to line segments of the same length.