Recognizing Patterns

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Students will learn about patterns through physical activities, class discussions, and the use of computer applets.


Upon completion of this lesson, students will:

  • be introduced to patterns in sequences and tessellations
  • have practiced predicting terms in a sequence
  • have practiced creating their own patterns

Standards Addressed:

Textbooks Aligned:

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag.
    • use a browser such for experimenting with the activities.

Teacher Preparation

  • access to a browser
  • access to pencil and paper

Key Terms

patternCharacteristic(s) observed in one item that may be repeated in similar or identical manners in other items
sequenceAn ordered set whose elements are usually determined based on some function of the counting numbers
tessellationA tessellation is a repeated geometric design that covers a plane without gaps or overlaps

Lesson Outline

  1. Focus and Review

    • After the class is seated, ask them to follow along with what you are about to do.
    • Begin rotating between patting your legs and clapping your hands: pat, clap, pat, clap, etc.
    • Once the entire class is following along, ask someone to raise their hand and tell the class how they knew what to do.
    • Ask students if anyone else has a different answer. The answer you are looking for will contain the word "pattern".
    • Tell the students to join in and follow along as soon as they know what you are doing.
    • Begin: clap, pat, tap (on a desk), clap, pat, tap, clap, etc.
    • Once the entire class is following along, ask someone to raise his/her hand and tell the class how they knew what to do.
    • Ask students if anyone else has any different answers. The answer you are looking for will contain the word "pattern".
    • Continue this process making the pattern increasingly more difficult to decipher each time.

  2. Objectives

    Students will be able to recognize patterns and fill in missing segments of patterns.

  3. Teacher Input

    • If the students have not already mentioned the word "pattern", tell them that the exercise they just finished contained various patterns.
    • Ask the class if anyone can come up with a different type of pattern that doesn't involve movement.
    • Call several students to the front of the class and have them share the beginning of their patterns with the class.
    • Ask the class if anyone can complete the patterns provided by their classmates.
    • If none of the students think of any shape patterns place a few of them on the board and have the students complete the patterns.
    • Be sure to ask questions about each pattern.
      • Does anyone see a pattern?
      • What pattern do you see?
      • Is there more than one possible pattern?

  4. Guided Practice

    • Instruct the students to spend about 3-5 minutes playing with the Tessellations applet.
    • After they have had a few minutes to become familiar with the applet, ask if anyone knows what the applet is doing.
      • Did anyone notice any patterns created by the applet?
      • What patterns did you see?
    • Have the students take out a sheet of paper, extend the following number sequences, and explain how they determined the subsequent numbers in the sequences. You may want to do the first one with the students.
      • 0, 1, 2, 3, 4 ...
      • 0, 2, 4, 6, 8 ...
      • 0, 10, 20, 30, 40...
      • 1, 3, 9, 27, 81... (# * 3)
      • 0, 1, 3, 7, 15, 31... (# * 2 + 1)
    • Are these patterns? Why

  5. Independent Practice

    • Have the students open the Patterns applet.
    • Direct the students to complete the sequences provided. You may want to have the students copy a few lines of the computer generated patterns to ensure each student is on task.
    • Now, instruct the students to open the Sequencer applet, and have them begin creating new sequences using the applet.
    • Once the students have created their sequences, have them swap the number sequences with a partner, and instruct their partners to utilize the sequencer applet to help them decipher the sequence patterns.

  6. Closure

    • Discuss patterns and their occurrences in nature, society, school, and math.
    • Answer any remaining questions.

Suggested Follow-Up

You can also use the Coloring Multiples in Pascal's Triangle and the Coloring Remainders in Pascal's Triangle applets to help students recognize number patterns.

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