In the article, scientist Philip Ball said some patterns could only be appreciated through repetition. Why do you think that is?

Do you think it's important to understand how and why patterns occur in nature? Why or why not?

According to Ball, the same types of patterns crop up again and again in different places, both in the living and the nonliving world. Do you agree with Ball that what he sees are patterns, or do you think the examples he cites are coincidences? Why?

In the article, Philip Ball said that when he wrote his new book he left the definition of a pattern "slightly ambiguous." Why do you think he did that? How would you define a pattern in nature?

### PROCESS:

- Invite a volunteer to draw a simple picture of a zebra on the board. If you teach grades 9-10, tell the student to draw a stick figure representation of a tree branch.
- As a class, identify the pattern on each drawing. (The zebra has an alternating pattern of black and white stripes. The tree branch has a repeated pattern of two short lines extending from a longer line in the middle. Guide students to recognize that this pattern applies to the entire tree, with the trunk being the main long line.)
- Ask students how they could show the pattern of the zebra's stripes using letters. For example, is it an ABC, ABB, or AB type of pattern? (AB) Guide them to recognize that the tree branch is a fractal. The basic shape of a Y is repeated over and over again.
- Take the class outside or have them look through photos online. Instruct students to identify and classify patterns they see in nature. Challenge them to decode those patterns mathematically, using letters to express each pattern or by identifying the basic geometric shape upon which a fractal is based.
- Once students have identified their pattern, give them time to draw an original piece of art based on the pattern they found in nature.

### ASSESSMENT:

Invite students to share their findings with the class. Challenge them to explain why each example is a pattern and why the mathematical representation they identified is correct. Encourage them to explain how their picture represents the pattern they found in nature.

### CUSTOMIZE THE LESSON:

**Grades 3-4:**

Divide the class into small groups. Instruct each group to find one pattern on a plant and one pattern on an animal. Have groups identify the patterns and explain how they could use letters to represent each. Give them time to draw a picture. After all groups have presented, challenge the class to recognize different examples that show the same type of pattern in nature.

**Grades 5-6:**

Divide the class into pairs. Instruct partners to find one pattern on a plant, one pattern on an animal and one pattern on a non-living item in nature. Have pairs identify the patterns and explain how they could use letters to represent each. Give them time to draw a picture. After all pairs have presented, challenge the class to recognize different examples that show the same type of pattern in nature.

**Grades 7-8:**

Divide the class into small groups. Instruct each group to find two plants that have the same pattern, two animals that have the same pattern and two non-living items in nature that have the same pattern. Have groups identify the different patterns and explain how they could use letters to represent each. Give them time to draw a picture. After all pairs have presented, challenge the class to recognize different examples that show the same type of pattern in nature. Identify the pattern that appears most often.

**Grades 9-10:**

Divide the class into pairs. Tell students to search for patterns on plants, animals and non-living things that they see outside or in the photos they view online. Challenge them to find three examples with the same basic pattern. For example, the pattern of a giraffe's spots matches the patterns found on ripples of water and in dried mud. Instruct students to draw the geometric shape that is the basis for the fractal they see. Give them time to draw a picture. After all pairs have presented, challenge the class to recognize fractals that appear most often in nature.

Read this Smithsonian article to see how snow artist Simon Beck uses his own two snowshoe-clad feet to create masterpieces in the snow.

Sixty years ago, with nothing but numbers, logic and some basic know-how, the inventor of the Turing Test explained how to make a strip. Read this Smithsonian article to learn how Turing’s prediction was finally proven to be true.

An important part of design is learning to look closely at the objects that surround us. In this activity from the Cooper-Hewitt Smithsonian Design Museum, students will have opportunities to observe patterns and symbols across disciplines. They will brainstorm ideas, collect and analyze data and construct graphs and graphic organizers to show what they learned.

Invite upper-level students join Smithsonian experts as they discuss the importance of counting rainforest species and introduce a new way of precisely measuring and mapping biodiversity. In the teleconference, the experts will demonstrate how to use basic spatial statistics to examine distribution patterns of species.

In this activity from the Smithsonian Center for Learning and Digital Access, students will learn how to identify three zebras based on their unique stripe patterns.

A frieze pattern is a mathematical concept to classify designs on two-dimensional surfaces, which are repetitive in one direction, based on the symmetries in the pattern. In this activity from the Cooper-Hewitt Smithsonian Design Museum, students will explore examples of frieze patterns in architecture and art and create an original design using a frieze pattern.