Growing Patterns

  • Growing Patterns

    Powerful Patterns
    Grade: 3rd to 5th
    Periods: 1
    Author: Grace M. Burton

    Materials

    Instructional Plan

    Start this lesson by reading a counting book of your choice. (Ten Black Dots by Donald Crews is especially appropriate, but any book which uses a "count on by 1" strategy will work.) Then ask students to tell what happened in the book. Next, tell the students that in this lesson they will explore patterns that grow according to a rule. Display the following growing pattern (without the numbers):

    597 orange dots

    Ask, "What will come next in this pattern?" [Students may find this question easier to answer if they copy the pattern onto paper.] Have the students explain how they got the answer. When someone has given the correct answer, write the number of dots in each row. Solicit student responses to add additional rows to this pattern and label them. Ask the students if they know a name for this pattern and the rule they would use to add more rows to the pattern.

    Next display the pattern below and tell the students this is called an L pattern. Ask students how each L is changing. After students state the answer, or as a hint, write the number of dots used below each L. Ask several students to state the rule they would use to add more figures to the pattern. Call on students to draw the next three L shapes in the pattern.

    597 green dots

    Distribute the Growing Pattern Activity Sheet to students.

    pdficonGrowing Patterns Activity Sheet

    Have them add three more steps in the pattern and write a number pattern to match the figures. Ask students to share their shape and number patterns, explaining how they identified the pattern.

    Assessments and Extensions

    Assessment Option

    Collect students’ Growing Patterns Activity Sheets.

    Extension

    Move on to the last lesson, Looking Back and Moving Forward.

    Questions and Reflections

    Questions for Students

    1. What will come next in this pattern (first growing pattern)? How do you know?

    [There will be 5 dots. I used the counting numbers.]

    2. What is a name for this pattern?

    [Counting on or counting numbers.]

    3. What is the rule?

    [You have to add one more to each row.]

    4. How many dots are in the first figure of the L pattern? How many are in the second figure? The third?

    [The first L figure has 1 dot. The second figure has 3 dots. The third figure has 5 dots.]

    5. How is each L changing?

    [Each L has two more dots.]

    6. What is the rule for the L pattern?

    [Add one dot at the top and add one dot at the bottom of the next L.]

    7. How many dots in the next three L shapes in the pattern?

    [The next L figures will contain 9, 11, and 13 dots.]

    8. Have you ever seen this pattern before?

    [It is the set of odd numbers.]

    9. How long could we continue this pattern?

    [We could keep going forever.]

    10. What will be the next three figures in the triangle growing pattern (from student activity sheet)?

    [They will be 5 triangles, 6 triangles, and 7 triangles.]

    11. What number pattern did you use to describe the pattern?

    [Possible answers include 1, 2, 3, 4, 5, 6, 7 (number of triangles); 3, 5, 7, 9, 11, 13, 15 (number of sides); 3, 4, 5, 6, 7, 8, 9 (number of vertices/corners). Accept all reasonable answers.]

    Teacher Reflection

    • Were students able to analyze and describe growing patterns? If so, what extension activities are appropriate now?
    • Were students able to write number patterns to match the growing patterns?
    • What other examples of growing patterns could I use in this lesson or for continued practice?
    • Did I encourage students to explain and defend their thinking?
     

    Objectives and Standards

    Learning Objectives
    Students will:
    • Extend growing patterns.
    • Describe growing patterns.
    • Analyze how growing patterns are created.
     

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