Illuminations: Patterns That Grow

Patterns That Grow

What’s Next?

Students begin their study of growing patterns by making linear patterns with pattern block shapes using several pattern cores. They extend a partner’s pattern and find the missing element in a pattern.

Learning Objectives
 
Students will:
  • create and read a linear pattern
  • extend a given linear pattern
  • identify the missing element in a linear pattern

Materials
 
Pattern blocks
Shape Tool
Construction paper (optional)

Instructional Plan

Using pattern blocks, make a pattern with at least three repeats of the pattern core (for example, square, trapezoid, hexagon, square, trapezoid, hexagon, square, trapezoid, hexagon).

 

 

Then ask a volunteer to read the pattern. Repeat with other patterns and other volunteers. Next place the students in pairs and give each pair several pattern blocks. (If you do not have pattern blocks, you might supply the students with paper shapes.) Ask each student to make a pattern with at least three repeats. Then call on volunteers to read their patterns and ask if anyone else has a similar pattern. Encourage several students to read their patterns using both descriptive language (square, square, triangle) and generic pattern cores (AAB).

Next have each student make a new pattern with three repeats, trade patterns with their partner and extend the pattern they were given. If students are having difficulty, encourage them to read the patterns aloud using both descriptions (red, blue) and generic pattern cores (AB).

As a challenge, make a pattern and ask the students to hide their eyes while you remove one shape from it. [Doing this successfully requires interpolation, a higher-order thinking skill.] Then have them open their eyes and determine what was removed. Call on students to place the shape that they think was removed back in the pattern and then read the pattern aloud to verify their answer. Repeat this several times. Next ask the students to make a pattern with pattern blocks, leave out one shape, and then show it to their partners to see if the partner can determine the missing piece.

For additional practice, show students the Shape Tool.

Shape Tool Shape Tool

Model how to make a linear pattern with the online shapes. As you demonstrate, you may wish to have the students copy the pattern with pattern blocks or draw it on paper. Allow volunteers to make a pattern on the Web site and read it to the class. Then encourage the students to use the site during math-center or free-choice times.

Finally, ask students to record one pattern by drawing with crayons or gluing pattern block paper shapes on blank pieces of construction paper.

Questions for Students
 

Here are two patterns (for example, triangle, triangle, square and square, square, triangle). How are they alike? How are they different?

[Student responses will depend upon the patterns suggested.]

How can you tell where a pattern core begins and ends?

[Identify which shapes repeat over and over.]

If you wanted to extend your friend’s pattern, how would you decide which shapes to use?

[Student responses may vary.]

Suppose you want to make an AB pattern with pattern blocks. How could you do that? Who could do it a different way?

[Student responses may vary.]

How would you make an ABB pattern with pattern blocks? How is it like an AB pattern? How is it different from an AB pattern?

[Repeat the second shape in the pattern core; the same two shapes are used; the second shape is repeated before beginning again.]

How would you explain to a friend how to find out what is missing in a pattern?

[Student responses may vary.]

Assessment Options
 
  1. At this stage of the unit it is important for students to know how to:
    • make a linear pattern
    • extend a given linear pattern
    • record a linear pattern
    • find the missing element in a linear pattern

Extensions
 
  1. You may wish to direct students who wish to explore patterns with shapes to the Unit Paper Quilts. This Unit looks at geometric patterns set in a quilt context.

Teacher Reflection
 
  • Which students can make a pattern with shapes? What activities are appropriate for those who cannot do so yet?
  • Which students can read a pattern? What activities are appropriate for those who cannot do so yet?
  • Which students can extend a pattern? What activities are appropriate for those who cannot do so yet?
  • Which students can find the missing element in a pattern? What activities are appropriate for those who cannot do so yet?
  • What parts of the lesson went smoothly? Which parts should be modified the next time that I teach this lesson?

NCTM Standards and Expectations
 
Algebra 3-5
  1. Describe, extend, and make generalizations about geometric and numeric patterns.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

 Activities
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