**Bibliographic Information:**

Woodward, Ernest and Hamel, Thomas. Geometric Constructions and

Investigations with a Mira. Maine: J. Weston Walch, 1992.

**Mathematical Concept:** Reflection and using Mira’s

**Grade Levels:** 6th – 8th

NCTM Standards and Principles of School Mathematics• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

• Use geometric models to represent and explain numerical and algebraic relationships.

• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

**Materials:**

Graphing Paper

Colored Pencils

Sharp Writing Pencils

Mira’s

Copies of pages 3 and 5 from Geometric Constructions and Investigations

**Detailed Description:**

Completion of the following activities will allow students to learn the language associated with reflections and draw a reflected image of a figure over a line of reflection. Students will also be able to perform two-dimensional reflections while using a Mira, as well as recognize when a figure is not symmetrical. By the end of this lesson, students should realize that if the reflective figure looks reversed from its original, it is not symmetrical.

**Procedure:**

1. Activity One:

a. Hand out graphing paper to each student.

b. Have the students divide a piece of graph paper into four quadrants by drawing the axis lines.

c. In any one quadrant, create a pattern of polygons from the lines on the paper and diagonals.

d. Have students to copy the patterns into the other three quadrants by reflecting the pattern over the axis lines.

2. Activity Two:

a. Divide the class into working partners.

b. Hand each student a piece of graphing paper.

c. Divide the graph paper into four quadrants by drawing the axis lines.

d. Have each student draw a pattern in any one of the quadrants.

e. Each student should pass their graph paper to their partner.

f. The partner is to reflect the pattern over the axis lines.

3. Activity Three:

a. Pass out copies of page 3 from Geometric Constructions and Investigations

b. Pass out a mira to each student. Direct students to find the beveled edge (the edge that seems to cut inward) and that this beleved edge should be placed down.

c. Allow students to practice using the mira as they complete page 3 from Geometric Constructions and Investigations.

d. Students should use the mira to find the line of reflection which puts the boy on the swing.

e. Have students to trace the line of reflection.

f. Finally, students will trace the boy on the other side of the Mira while looking through it as the teacher monitors the activity and gives assistance as necessary.

4. Activity Four:

a. Pass out copies of page 5 from Geometric Constructions and Investigations

b. Instruct students to complete this activity the same way as Activity 3 was completed. They are to follow the handouts instructions to place the hats on the woman’s head.

c. Remind students to trace the line of reflection onto the handout

**Attachment: ** Worksheet/Activity Student Page

Geometric Constructions and Investigations page 3

Geometric Constructions and Investigations page 5