# Patterning and Symmetry

**Math Topic:** Patterning and Symmetry

**Grade Levels:** Grades 4 - 6

By: Ann Rule, Ph.D. and Anneke Bart, Ph.D. Saint Louis University

Lesson plan design adapted from: Wigging, G. & McTighe, J. 1998. Understanding by Design. Alexandria,
VA: ASCD.

## Contents |

## Missouri GLEs

Grade | GLE | Description |
---|---|---|

4 | MA 4 1.6 MA 2 3.6 MA 2 1.10 |
describe geometric and numeric patterns. predict the results of sliding/translating, flipping/reflecting or turning/rotating around the center point of a polygon. Create a figure with multiple lines of symmetry and identify the lines of symmetry. |

5 | MA 4 1.6 MA 2 3.6 MA 2 1.6 |
make and describe generalizations about geometric and numeric patterns. predict, draw and describe the results of sliding/translating, flipping/reflecting or turning/rotating around a center point of a polygon. identify polygons and designs with rotational symmetry. |

6 | MA 4 1.6 MA 2 3.6 MA 2 1.6 |
compare various forms of representations to identify patterns. describe the transformation from a given pre-image using the terms reflection/flip, rotation/turn, and translation/slide. create polygons and designs with rotational symmetry. |

Mathematical Context:

- Problem Solving
- Reasoning
- Communication
- Making Connections
- Designing and Analyzing Representations

## Identify Desired Results

Understandings:

- Students will understand the connection between patterns in art and patterns in mathematics.
- Students will understand the visual effects of patterns.
- Students will understand the key components of symmetry.
- Students will understand the properties of border patterns and their relationships to mathematics.

Essential Questions:

- Why is it important to explore patterns in the real world?
- What are the relationships between patterns in art and patterns in math?
- How can learning about patterns in different pieces of artwork develop a heightened sense of patterns in mathematics?

## Planned Learning Experiences

Objectives:

- Through exploration of border patterns in pieces of artwork, students will be able to identify the properties of patterns.
- Through exploration of border patterns in pieces of artwork, students will be able to describe symmetries.

## Assessment Evidence

After exploring border patterns, students will complete the attached worksheet on Border Patterns in Greek Art. Students are expected to accurately complete the worksheet with 90% accuracy.

## Learning Activities

Motivator:

- A field trip to the St. Louis Art Museum to explore Greek Art

Procedures (what will students do?)

- Students will be directed to chosen pieces of artwork in the museum, where they are given background on the artwork e.g., a Greek Amphora, c. 530 BC, painted by Antimenes, etc.
- Students will explore the patterns on the vase looking for lines of symmetry.
- On the handout (attached) students will be asked to fill in the appropriate information as they explore the amphora.
- Students will design their own border patterns based on vertical lines of symmetry
- Students will design their own border patterns based on horizontal lines of symmetry.

Closure:

- Ask students key questions about what they’ve learned about border patterns and how they relate to both mathematics and art.

## Border Patterns in Greek Art Worksheet

**Objective:** Explore properties of border patterns and describe symmetries

There are several border patterns on this beautiful vase. Let’s explore some of their properties:

1. There is a fairly broad pattern at the top of the Amphora:

A. Do you see mirror lines in this pattern? If so draw them on the image above.

B. Does the pattern have rotational symmetry? (in other words: does it look the same upside-down as it does right-side up?)

2. Towards the bottom of the amphora we see several more border patterns. Let’s look at one of them:

A. Does this border have any mirror lines?

B. Does this pattern have rotational symmetry? (in other words: does it look the same upside-down as it does right-side up?)

3. Draw a border pattern that has a vertical mirror line, but no horizontal mirror line.

4. Draw a border pattern that has a horizontal mirror line, but no vertical mirror line.