The Mathematics of Wallpaper

Classroom Activities

Before the unit starts, give each student a pre-assessment (See Appendix). After the assessment, I activate students' prior knowledge to find out what they already know about symmetry and geometry. The students complete a KWL chart. Then I read a picture book about symmetry to provide additional knowledge. There are several books you can read that I mention on the student bibliography page.

Lesson 1 (Parts: A, B, & C): Introduction to Symmetry

Objectives: Students will be able to find and identify lines of symmetry on objects.

Materials:

Cut-Out Objects (Shapes, Alphabets, Flags, Leaves)

Pencil

Overhead Projector

Math Journal

Vocabulary: Line of Symmetry

Part A: Distribute a cut-out heart to each student. Ask students to fold the heart in half vertically. Then draw a line on the folded line. Ask students, what do you notice about both sides? Are they the same? (Possible response: Both sides of the heart have exactly the same shape and the same size). Explain that when the halves on both sides of a line match in shape and size, we can say that figure is symmetric and we can call that line a line of symmetry. I define line of symmetry as a line drawn through a figure that creates two halves that are mirror images of each other. I give students cut-outs of other objects such as, a butterfly, square, triangle, circle, snowflake, and a person. I hold up each object and ask students if it has a line of symmetry. Based on student's answers, I fold each object to check for lines of symmetry. If an object does have a line of symmetry, explain to students that an object can possess more than one line of symmetry, such as the square or circle. Use the overhead to show students how to draw lines of symmetry. Now explain to students that not all objects will have line symmetry. Demonstrate this concept by giving each student a cut-out of a leaf/ another object (find one without line symmetry). Ask students to fold the leaf across the center. What do you see? Students notice that the leaf does not have a line of symmetry. The top and bottom parts of the leaf do not match. During this lesson the students can answer the following questions in groups.

What do you notice about the two sides of the object?

What is symmetry?

Does this object possess a line of symmetry?

How many lines of symmetry are there?

Part B

Symmetry in Alphabets

Objectives: Students will be able to identify the letters of the alphabet that have lines of symmetry.

Materials

1 bag of cut-out alphabets (3 students per bag)

Math Journals

Pencils

Give each group of students a bag of cut-out alphabets. Before students explore with the letters, review symmetry with the class. Allow students the opportunity to explain what symmetry means. Students can come to the board and provider an example.

After each group has the letters, students need to find the number of symmetrical letters. Students will put the letters in two piles: symmetrical and non symmetrical letters. Students record results in their math journal.

Challenge Activity

Students will find out the number of symmetrical letters in their first and last name.

Part C

Symmetry in Art

Objective: Students will create a butterfly with at least one line of symmetry.

Materials:

White Construction Paper

Liquid Paint (Different Colors)

Teaspoon

Give each student a piece of white construction paper folded in half. Have students open the paper and place two or three teaspoons of different colored liquid paint on their paper. The students need to close the paper and rub the top. Demonstrate first, showing students how to rub the paper carefully and thoroughly. Once students open their paper, they will see asymmetrical butterfly. Display the art work around the room.

Lesson 2: Symmetry Around Us!

Objective: Students will be able to identify symmetry found in nature and architecture. Students will observe and draw at least 5 different objects that have symmetry.

Materials:

Math Journal/Sketch Pad

Pencil

Camera

Photographs of Chicago Buildings

Book: Symmetry (My Path to Math)

Part A: This activity requires a field trip around the neighborhood/city looking for symmetry. During the walk, students observe and sketch objects, such as flowers, insects, and buildings. Some students are chosen to take pictures on the trip. Students include the line/lines of symmetry in their drawings. Students must label their drawings. I point out different buildings or architecture as we walk around the city. Questions are asked about the symmetry observed. I also give students important facts about the buildings. After the walk, students write a paragraph in their math journal about the trip. Students share their paragraph and drawings with the class. Once the pictures have been developed, students discuss the symmetry in the pictures. As the teacher, you must remind students that math is all around us; allow students to see the connection.

Part B: The teacher reads aloud Symmetry (My Path to Math). This story provides real world symmetry examples. On every page of this book, the author challenges students to complete symmetry related problems. For example, students must find and list all the symmetrical objects in their house or create a building that has a line of symmetry. After I read the book, students must complete one activity challenge and share with the class.

Lesson 1 and 2 provide students with a solid background of identifying line of symmetry. Students are aware that symmetry is found everywhere in nature and architecture. Lesson 3 focuses more on teaching students about the types of symmetries: reflections, rotations, translations, and glides.

Lesson 3: Frieze Patterns

Objectives: Students will be able to identify 5 out of the 7 frieze patterns. Students will be able to create their own frieze pattern designs.

Materials:

Pictures of the 7 Frieze Patterns

Math Journal

Pencil

Art Supplies (Markers, Crayons, or Paints)

Construction Paper

Frieze Pattern Templates

Overhead Projector

Vocabulary:

Frieze Pattern

Reflections & Glide Reflection

Rotations

Translation

Part A: I will show (Use Overhead & Pictures) and tell students about the frieze patterns. I will explain how frieze patterns are found on buildings, clothes, vases, and other objects. Students will get the opportunity to look at several examples of the pattern. Using the overhead, I will show students all 7 patterns, discussing them one at a time. I will model how the patterns have translations, reflections, rotations, and glides as symmetries. I define the symmetry vocabulary and write them on chart paper. Students record the same information in their journals. In groups, students identify the different types of frieze patterns.

Part B: I review symmetry vocabulary: reflection, rotations, translation, and glides by using frieze patterns from previous activity (Part A). Today students will apply Conway's' footprint movements to each frieze pattern. Pattern 1-Hop, Pattern 2-Jump, Pattern 3-Sidle, Pattern 4-Spinning Hop, Pattern 5-Spinnng Jump, Pattern 6-Step, and Pattern 7-Spinning Sidle. First I model how the movements look. As I move, students guess which pattern the movement represents. Then students will perform the movements.

Part C: Student Choice. In order to demonstrate an understanding of frieze patterns, the students can do one of the following: Option 1: Create five different frieze pattern designs using art supplies. Label each pattern. Option 2: Create five frieze footprint patterns using your feet, paint, and butcher paper. Label each pattern.