GO IN DEPTH

A Matter of Pattern

Materials

• Pictures of snowflakes—there are printable images at the Wilson A. Bentley website
• String, 6-8 inches in length
• Paper—you may want to use origami paper since it is thinner than regular paper and it is already square in shape.
• Pre-cut snowflakes

By Wilson Bentley [Public domain], via Wikimedia Commons

Purpose

Students will create and predict patterns formed when making paper snowflakes. Students will construct the understanding that patterns may be predicted based on observation.

Context

Students will explore how shapes can be put together to form repeating sequences or patterns. They will begin by folding paper and making cuts to create different shapes. They will extend this process to a multi-folded piece of paper. Students will predict both shapes and patterns that emerge as they create six-sided snowflakes. The students will also try to predict the pattern of the shape of the entire snowflake.

By doing this activity, students will begin to develop an appreciation of how elements in a pattern relate to one another. At this age, students are very concrete and need focused tasks and multiple representations in order to grasp fundamental concepts. Students will most likely become lost or uninterested if emphasis is placed on abstract ideas, such as the nature of mathematics.

This lesson is designed to give students multiple representations of pattern using a concrete object that fascinates them. Students need to develop an understanding of patterns. For future success, they need to develop the ability to take an initial pattern and extend it to continue the sequence. They need to be able to do this in a variety of ways: shape, color, sound, and number. This allows students to construct real meaning of patterns and sequences that are found throughout life.

See the Materials section. You will need to pre-cut snowflakes for students to use in the activity.

Motivation

Distribute some pictures of snowflakes. Again, there are printable images at the Wilson A. Bentley website.

• What do you see?
• Are there any shapes that you are able to see in the snowflake?
• What shapes do you see? Do any of them repeat?
• Where do you see a pattern?

Give each student, or pair of students, a piece of string. Show students how to lay the string across the snowflake to make a line through the center of the snowflake.

• Now look at the two sides of the snowflake. What do you see?
• Is one side like the other or different? How?
• Do you see a pattern?

Say to students, "Patterns are found everywhere. They are in nature and in man-made things. If we look, we can easily see patterns all around us every day. Today, you are going to design a pattern by creating and cutting out a paper snowflake."

Development

First, have students practice cutting shapes from paper. Have students practice cutting on a piece of paper that is folded in half. Demonstrate cuts both along the fold and on the non-folded sides. Make sure that students attempt to predict the shapes they will see when the paper is unfolded. Students should unfold their paper to determine what shapes emerge from the cuts.

After students have practiced cutting their shapes for about ten minutes, have them clear their paper scraps and discuss their shapes. They should show both the folded and unfolded shapes in their paper. Talk about the differences in the fold cuts and the cuts along the non-folded area.

Next, students should take a piece of paper and make two folds. Students should once again cut shapes from the folded and non-folded portions of the paper. Have students again predict the shapes as they cut the paper. Students should also try to guess how many of each of the shapes they will see. Ask them if the shapes will repeat in a pattern. Make sure that students spend time in thinking both about the shape themselves and the pattern they create as they cut out shapes.

Tell students that they will make a six-sided snowflake using paper you have provided for them. Show students how to fold paper to create a six-sided snowflake. You can refer to the Snowflakes page on the KinderArt website to see how to make a six-sided snowflake.

As students fold their paper, stop them at each fold and ask them what shape they see. Have students discuss the shapes. This will also help to make sure that students are folding the paper in the correct way. After students have folded their paper, assign each student to a partner and have the partners check each others folds to make sure they are correct.

Say to students, "Now we are going to cut out a paper snowflake. You want to make sure that you do not cut completely along a side where there is a fold. Cut out different shapes."

Encourage students to cut out different shapes in their snowflakes. Make sure to remind students that they are to keep their snowflakes folded. After the students have had about ten minutes to cut out their snowflakes, have them set aside their scissors.

• What shapes have you cut into your snowflake?
• Do you think that they will be the same shape when you unfold the paper? Why or why not?
• Do you think that you will see the shape one time or more than once? Why?

Allow students to unfold two folds of their snowflakes. Demonstrate how they are to unfold it. Make sure to instruct students to not completely unfold the snowflake.

• What happened to the shapes that you cut along the fold?
• Is it the beginning of a pattern?
• Do you expect that the shape will repeat more? Why or why not?
• Based on the shape and pattern of the folded snowflake, are you able to predict what will be the pattern of the whole snowflake?

Have students look at their folded snowflakes and sketch the shapes they think they will see when they completely unfold their paper snowflake. Allow students to unfold one more fold of their snowflakes. Have them revise their drawings. Next, students should completely unfold their snowflakes.

• How is the snowflake like your drawing?
• How is the snowflake different than your drawing?
• What shapes do you see?
• Can you see a pattern?
• Is there more than one pattern in the flake?
• How is your snowflake like that of a student near you?
• How is your snowflake different than theirs?
• Pick one pattern on your snowflake. What would be the next three shapes that would come if the pattern were to continue? Compare your pattern to that of a student near you.

Have students go to the Six-sided Snowflake activity (click "Gizmo" to start) on the ExploreLearning website. Here, students are able to create a six-sided snowflake online. As they create the snowflake, they are able to simultaneously watch the actual pattern emerge.

• How is the snowflake you created different than you what expected it to be?
• How is the snowflake similar to what you expected?
• How quickly were you able to see a pattern in the snowflake?
• Is the pattern simpler or more complex than your paper snowflake?
• Do you think that you could re-create your pattern by memory?
• Would using this program before cutting a paper snowflake be useful? How?

Assessment

Divide students into groups of four. Distribute a pre-cut six-sided snowflake to each group. Each group should cut its snowflake in half. Collect one half of each of the group's snowflakes and put them on a table. Allow each group to find the match to its snowflake half.

Discuss with students how they knew that each of their snowflake halves were matches. Have the students point out patterns that helped them to identify their missing half.

Extensions

You can use the Pasta Snowflake activity, found on the Family.com website, as an extension to this lesson.

Say to students, "Today, we looked at patterns of paper snowflakes. Now we are going to create a pattern snowflake out of pasta. On a sheet of paper, you are going to create a snowflake by gluing down pieces of different shaped pasta. Your goal is to create a pasta snowflake that has a visible pattern. You may choose to use different shapes or colors to create the pattern."

Allow students to work on their snowflakes for 20 minutes. Have several students discuss their snowflakes and their choice of patterns.

Have students visit Original Wilson Bentley Images. This is a website with images of actual snowflakes. By double clicking on any of the pictures, the image will enlarge so that students are better able to see it. Have students look for patterns within the different pictures of the snowflakes.

• Do you see any patterns?
• Do you see the pattern repeating in different areas?
• How are the patterns on the real snowflakes different than those on your paper snowflakes?
• How are they similar?

Have students draw half of a snowflake. Then, each student should switch his/her snowflake with another classmate. Have that student complete the snowflake by following the pattern.

Have students visit What Comes Next? and Stars or Hearts?, both found on the Fun Mathematics Lessons website. These are activities that allow students to look at a simple pattern and predict the next in the series.

Allow the students to create patterns using Kid Pix CD. Have them print and describe their patterns.

Have the students play Pattern Parade on the Reader Rabbit and Friends Lets Start Learning CD. This is a fun interactive CD that presents patterns in a variety of ways. It uses sounds, colors, instruments, and sizes to create patterns which parade if completed correctly.

Have students play Rabbit's Rain Dance on the Ready for Math with Pooh CD. This is a pattern quilt that uses the favorite Winnie the Pooh characters. When students successfully complete the pattern, the characters all come out and do a triumphant rain dance.