Reflections over parallel or intersecting lines (Day 2 of 2)

Objective

SWBAT draw and identify images of figures over composites of two reflections.

Big Idea

Students discover that consecutive reflections results in a translated or a rotated figure. In this lesson they perform transformations hands-on, and using technology.

Launch

10 minutes

To begin Day 2 of this lesson, I pair up students with a different partner than each had in Day 1. Each pair gets a copy of Why aren't the figures rotations or translations. I allow a few minutes for students to work on the worksheet. As they work, I walk around reminding students to think carefully about the properties of different kinds of transformations. I encourage the students to look in their notebooks or textbooks if necessary.

Some common answers that I expect to see for Parts a - d are:

a) "Size is not preserved"; "the figures aren't congruent"; "side lengths are different"

b) "Orientation is not preserved"; "one goes clockwise and the other counterclockwise".

c) same as (b)

d) "Size is not preserved"; "Not congruent"; "angle measure is not preserved"

An alternative method of launching the lesson is projecting the figures one at a time on the smartboard, asking student pairs to discuss and jot down their answers, and then calling on volunteers. Either way, I would always ask more than 1 pair of students to share their response, and write these responses on the board for all to see. The idea is to reinforce the properties of translations and rotations which they have seen in past lessons.

Activity

25 minutes

After our Launch discussion, I hand each pair of students the Composite Reflection Task Day 2 handout, a piece of tracing paper, and a ruler. One handout per pair is fine. Both students can share it and do their reflections together.

I walk around assessing students making sure that they are drawing their lines and performing their constructions correctly and with clarity.  I check that the students have good clean erasers so when they reach the step where they have to erase the intermediate figure, their paper does not look messy.

Once all students are done with their reflections, they will compare and note that the resulting figure E''L''A'' is a rotation of figure ELA.

I then ask the class the following questions:

1. What is the center of rotation?

2. How can we prove that this really is a rotation?

3. Find the magnitude of rotation:

4. Write a concluding statement summarizing this activity:

Closure

15 minutes

Once students are finished with the activity and have answered and discussed the questions, I point out to the class that two co-planar lines can either be parallel or intersecting and there are only two possible composites for reflections over two lines in a plane, a translation, or a rotation. To close the lesson we will validate our hands-on activity with technology using our Geometer's Sketchpad tools.

Ask students to open a blank Sketchpad document. I have the students draw two intersecting lines similar to those they drew on their trace paper in the activity section. I then ask that they draw a figure L, and label it ELA, just like in the activity. Then, I ask them to reflect Figure ELA over the two lines. Students should then measure the magnitude of rotation using any two corresponding points and the intersection of the lines.  Finally, using the rotate feature, rotate pre-image ELA that same number of degrees.

After students explore the transformation using Sketchpad, we will discuss the results by comparing the final images. I always have my students save their work in their folder.

This video narrative demonstrates the closure activity.

Homework

Some students may be led to think that the magnitude of rotation of an image after being reflected over intersecting lines, is the actual angle formed between the two lines. Questions 3 in this HW assignment will clear this up. I always make sure students take home two sheets of trace paper if they don't have any, so they can perform the construction to question 3.

Homework day 2 Composite reflections.pdf