Transformations Lesson 2
Develop an understanding of reflections in the coordinate plane, and determine general rules for reflections through exploration.
Using the image below, have students “I see, I think, I wonder” about the reflection below. Have a discussion to start students thinking about what happens during a reflection.
Ask students to compare the distance and direction of each figure to the line of reflection. They should notice the distance from the line of reflection for each figure is the same, but in opposite directions. Introduce the formal vocabulary to describe this transformation as a reflection on the coordinate plane. Students should notice that in each reflection the size and shape are preserved. The orientation and location will change with a reflected image. They may also notice that the figures are congruent.
There are multiple options to develop student understanding in reflections, including the use of Miras and patty paper.
If using a Mira, place the Mira, beveled edge facing you and pointed down, on the line of reflection, and trace what you see in the Mira on the other side of the line of reflection.
To use patty paper, trace the pre-image and line of reflection on the patty paper. Fold the paper on the newly traced line of reflection and trace the pre-image on the other side. A reflection image will be created.
Possible questions to ask include:
Have students look at their Activity Sheet Part I. In pairs or small groups, they will explore and draw reflections using a manipulative (e.g. Mira, patty paper, etc.). As the pairs complete their drawings, ask them to discuss and provide observations in the space provided. As a whole class, share and chart observations. Highlight student observations that lead to the creation of rules for reflection.
Example questions to prompt creation of rules:
What are rules to describe the changes in coordinates when the image is reflected over the x-axis? The y-axis? The line y = x?
What is the rule for a line of x = a, where a is any number on the plane? A line of y = b where b is any number on the plane?
In Part II Students will work in groups or pairs to explore what happens when they reflect a shape over a line of reflection of their choosing. The students will identify a line of reflection and record the coordinates before and after a reflection. Using the table, students should begin to identify patterns.
After students have completed the second part of the worksheet, work as a class to determine a set of rules for performing a reflection.
Note that (1) some of the rules described are specific to certain lines of reflection and (2) that reflections preserve size and shape; that is, the resulting figure will have the same side lengths and interior angle measures as the original figure.
Leave your thoughts in the comments below.
Develop an understanding of translations in the coordinate plane and determine general rules for translations through exploration.
Explore rotations on a coordinate plane where (0,0) is the center; determine general rules for rotations.
Students will develop an understanding of dilations on the coordinate plane and general rules for dilating an image through exploration.
Please note: the answers for Reflections Part I #3 do not match the student activity sheet.
CCSS, Content Standards to specific grade/standard
CCSS, Standards for Mathematical Practices
PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS