Lesson 3

Repeating Pattern

Est. Class Sessions: 1–2

Developing the Lesson

Part 1: Repeating Patterns with Kids

The lesson Repeating Patterns is meant for students who are unfamiliar with pattern concepts, but remains interesting to those who worked with patterns in kindergarten. Students explore repeating patterns with the teacher drawing on the knowledge of more-experienced students to extend the knowledge of less-experienced students.

Introduce Repeating Patterns. Explain to students that they are going to make "kid patterns." Direct five students to line up in a girl, boy, girl, boy pattern. Ask students to describe patterns they see in this line. Students may name the girl, boy pattern or other patterns represented by clothing, body positions, and so forth. When all the patterns have been mentioned, select a group of six different students to represent a girl, boy, boy, girl, boy, boy pattern. Ask students to identify patterns they see. Create new patterns for students to identify. Some ideas are listed below. See Figure 1 for an example.

  • hands up, hands down
  • plain shirt, patterned shirt
  • eyes open, eyes shut
  • buttons, no buttons
  • sitting, standing
  • arms crossed, arms hanging down, arms in back
  • socks, no socks
  • facing front, facing back
  • gym shoes, sandals
  • smiling, frowning

Extend Repeating Patterns. After students have practiced identifying kid patterns, encourage them to extend the patterns. Create a smile, smile, frown pattern. Use Sample Dialog 1 to guide your discussion of extending patterns.

Invite three or more volunteers to extend the line by adding more repeating units, smile, smile, frown. Have the students extend other patterns.

Use this Sample Dialog to discuss extending the smile, smile, frown pattern.

Teacher: Look at this pattern. What do you think comes next? [Points to the smile, smile, frown pattern.]

Grace: I think frown comes next.

Teacher: Why do you think that?

Grace: Because I think the pattern will be smile, smile, frown, frown.

Teacher: Good thinking, Grace! Does anyone have a different answer?

Benjamin: I think smile comes next because the pattern could be smile, smile, frown, smile, smile, frown.

Teacher: That's a good answer, also. Both of you showed good thinking. In a repeating pattern, the pattern unit is the part that gets repeated. If the pattern unit is smile, smile, frown, what do you think comes next?

Javier: If smile, smile, frown is the pattern unit, then smile would be next.

Teacher: Great answer, Javier! So we have to know what the pattern unit is to decide what comes next. How do we know when we should start over?

Brenda: I looked for a pattern. If the pattern unit is smile, smile, frown, then after we use the pattern unit once, we start all over again with the same pattern and keep repeating it.

Teacher: Excellent thinking, Brenda! It's important to know the pattern unit so we can continue with the pattern.

Most students will focus on repeating patterns. However, encourage and discuss growing patterns suggested by students.

Some examples of growing patterns are:

  • 2, 4, 6, 8
  • 10, 20, 30, 40, 50

Explain to students that they have been making repeating patterns. The part that gets repeated is the pattern unit—in this case, smile, smile, frown. Encourage students to find repeating patterns in the classroom.

Students might notice patterns on clothing, on the calendar, or in the tiles on the floor or walls. Frequently, students will assume that any ordered design is a pattern. Use their examples to introduce the difference between a pattern and a design. See the Mathematics in this Unit section and the Content Note about Patterns and Designs for further information.

Patterns and Designs. A repeating pattern, as used here, refers to a predictable repetition, a regular or repetitive form, order, or arrangement. A design refers to a group of elements—sometimes repeated but not necessarily—placed in a pleasing array and usually used for decoration. A design may include a repeating pattern, but it does not have to.

An example of a pattern
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