## Medieval Mathematicians and Whimsical Windows

### Peggy KellyLeon County Schools

#### Description

Open students' minds toward creating a medieval-styled stained glass window. Working as an artist and mathematician on this project demonstrates their mathematical knowledge of symmetry and reflection using congruent geometric shapes.

#### Objectives

The student knows symmetry, congruency, and reflections in geometric figures using concrete materials (for example, pattern blocks, geoboards, mirrors).

#### Materials

-Overhead transparencies (optional – use the worksheets included in the associated file)
-Construction paper
-Large sheets of black paper for window base
-Medieval storybook
-Glue
-Chart paper & markers
-Two sources for looking up definitions (math book, math dictionary, and/or standard dictionary)
-[Magic Tree House Research Guid #2 Knights and Castles] By Will Osbourne and Mary Pope Osbourne, Random House, New York, 2000.

#### Preparations

1. Choose the overhead shapes and/or make the transparencies to use in the beginning activity.
2. Hang the chart paper for recording the student’s math observations.
3. Have dictionaries available for defining these math words.
3. Locate the book: [Magic Tree House Research Guide #2 Knights and Castles].
4. Prepare the large sheets of black paper
5. Prepare (cut in specific sizes depending of the size of the large sheet of black paper) the colored sheets of construction paper for the congruent shapes
6. Prepare a rubric for each student.

#### Procedures

Day 1
1. Use a geometric overhead shapes set to create designs that represent a stained glass window or make transparencies as directed in the Associated File. Spark a class discussion about the mathematics in the window/shapes designs. Through the shape sets designs and/or transparencies, guide students toward an understanding of symmetry, congruent shapes, and reflection. Record their mathematical ideas on chart paper. Refer to their ideas throughout the lesson. Check for misconceptions. Focus on symmetry, congruency, and reflection.

2. Now “Dig for Definitions.- Have the students look up the definitions for symmetry, congruency, and reflection in several sources such as their math books, a math dictionary, and/or a standard dictionary. Compare the actual definitions with their comments that are recorded the chart paper.

3. Read [Magic Tree House Research Guide #2 Knights and Castles]. Discuss the symmetry found in the illustrations throughout this book.

4. Discuss this time period and the way of life.

5. For homework, students research and form an opinion to the following question, “How important was the use of symmetry during the medieval times?” Discuss their findings and opinions at the beginning of the next class session.

Day 2
6. Discuss the homework assignment.

7. Pair students and establish ground rules.

8. Each pair cuts a window design out of a large sheet of black paper then folds in half vertically. This vertical fold is marked in pencil and established as the “line of symmetry."

9. Students cut out congruent pairs of geometric shapes. Each shape pair should be the same color construction paper.

10. The congruent shapes are placed on the black window frame in such a way to show reflective symmetry also known as a "flip."

11. The student pair writes a reflective description of their window to describe the symmetry, reflection, and congruency in their creation.

12. Their work is then placed on display.

#### Assessments

Students will work in pairs to create a stained glass window that shows their knowledge of congruent shapes, symmetry, and reflections. They will use a large sheet of black paper as their base for the window. This sheet is then folded vertically and that fold line represents the line of symmetry.They will use construction paper for their choice of congruent geometric shapes.Their use of color will also reveal reflection in the design. They will write a description that explains their understanding of these geometric ideas.

#### Extensions

Students in older grades may choose to show rotational and/or slide symmetry in their window designs.