- Students will recognize that a rotation is an isometry.
- Students will apply matrix multiplication to rotations.
- Students will draw in new rotations on a coordinate grid.
IV.NotesonAssessment
- Collect student work.
- Compare the matrix multiplication to the triangles on the coordinate grid.
- Does the work match up?
- If not, what is missing?
- Offer correction/feedback as needed.
- This could be graded as a classwork or homework assignment.
Composition
I.SectionObjectives
- Understand the meaning of composition.
- Plot the image of a point in a composite transformation.
- Describe the effect of a composition on a point or polygon.
- Supply a single transformation that is equivalent to a composite of two transformations.
II.ProblemSolvingActivity-GlideRotations
- Students are going to draw a glide rotation of their own choosing.
- Tell students that the figure is going to be reflected in the x axis.
- Then tell students to draw in their figure.
- Next, they need to use matrix multiplication to design a reflection of that figure.
- Finally, they can move it 4 units to the right and one up.
- Students draw in the final figure.
- Allow time for them to share their work when finished.
- Solution:
- Because the figure is reflected in thexaxis, students will multiply the coordinates of the figure by
[
1 0
0 − 1
]
- Then they use( 4 , 1 )to add to the product of the first two steps.
- Finally, the students can draw in the figure.
III.MeetingObjectives
- Students will understand the meaning of composition.
- Students will plot the image of a point in a composite transformation.
- Students will describe the effect of a composition on a point or polygon.
- Students will supply a single transformation that is equivalent to a composite of two transformations.
- Students will share their work with their peers.
IV.NotesonAssessment
- Collect student work.
- Be sure to collect the diagram and the written work.
- Check it for accuracy.
- Provide feedback/correction as needed.
5.12. Transformations