Illuminations: Powerful Patterns

Powerful Patterns

Sorting Time

Students sort objects and symbols and make patterns with sorted objects. They make Venn diagrams and use their sortings to create linear patterns. They extend a pattern created by the teacher. Students will begin identifying pattern cores and reading patterns. A Social Studies connection is suggested as an extension.

Learning Objectives
 
Students will:
  • classify objects according to chosen criteria
  • create a linear pattern
  • name and read patterns
  • extend a pattern

Materials
 
Objects to sort (buttons, pasta, attribute blocks)
Yarn
Chart paper
Index cards
Computer and Internet connection (for Extensions)

Instructional Plan
Show the students a set of objects that can be sorted according to several criteria. Buttons, pretty pasta, and attribute blocks work especially well. Hold up two or three objects and ask the students to describe each one in as many ways as they can. Record the descriptive words on the board or chart paper.

 

 

Now choose two of the descriptive words that are mutually exclusive (for example, red and green), and write each on a separate index card. Next make a Venn Diagram by forming two non-overlapping circles with yarn, and place one index card in each yarn circle. Now hold up an object and ask where it should be placed. Repeat with several more objects. Then remove all the objects and the circles.

Then, choose two of the words that are not mutually exclusive (such as big and red), and write each one on a separate index card. This time, make a Venn Diagram with two overlapping circles with yarn and place one index card in each circle. Hold up an object and ask where it should be placed. Once the students are familiar with the process, give each student an object to place.

Next, remove the objects from the Venn Diagram. Now choose two index cards and place them upside down, one in each yarn circle. Without revealing the sorting rule, place several objects in the circles, then ask the students to try to place objects in the circle. If an object is correctly placed, leave it alone; if it is incorrectly placed, quietly remove it. When several objects have been correctly placed, ask for volunteers to tell how they knew where to place the objects.

When the students have correctly identified the sorting rule, turn over the index cards. Then, remove the items one at a time and create a pattern where all the students can see it. After you have repeated the pattern core (for example, small, big, big) three times, ask for volunteers to place the next object in the pattern. Continue the pattern until all the students are comfortable with the process. Ask a volunteer to read the pattern. Repeat with other patterns, using a different core each time. (A selection of appropriate cores is listed in the Unit Overview at the beginning of this unit.)

Finally, give each student several buttons or attribute blocks or pieces of pretty pasta and ask them to make a pattern. You may wish to use color tiles for younger students. Call on a volunteer to read his or her pattern and ask if anyone else has a pattern that is like that one in some way. Encourage several students to read their patterns, encouraging them to use descriptive words and demonstrating how to use generic pattern descriptions such as AB.

As homework, have students look for patterns in their homes and on their clothing and be ready to describe them tomorrow.

Questions for Students
 
Show me two buttons (or attribute blocks or pieces of pasta) that are alike in some way. How are they alike? How are they different?
[Both buttons are white, but one is a circle and one is a star.]

What labels could you use when you sort this set of (pretty pasta)?

[I could make a group of macaroni and a group of shells.]

How could you describe this pattern to a friend?

[AAB, because I made the first and second objects the same but the third one different. Then I did the same thing again.]

If you wanted to add to a friend’s pattern, how would you know what to do?

[I would look for what she keeps doing over and over again. If she has red and blue, then red and blue, then red and blue, I know I have to put red and blue.]

Assessment Options
 
  1. Ask students to choose one pattern that was shared with the class and record it with crayons for their portfolios. Ask them to label the patterns using a generic pattern description (AB, ABB, etc.).
  2. Record your observations as students are working. Next to each student’s name on a class roster, record the date, the pattern type, the number of iterations the student made, and a check or X to indicate whether the student made any mistakes. This brief scheme allows for easy recording of progress. For example, next to Lucy's name, you might write 3/6 ABB 2 X.Throughout the unit, continue to record students’ pattern types to assess whether students are able to create a variety of patterns.

Extensions
 
  1. Put the students into pairs and have each student choose a pattern core such as AAB and make a pattern with three repeats. Then ask the students to look at their partner’s pattern and see if they can add a repeat to it. Encourage the students to read their patterns aloud using both descriptive words and generic pattern descriptions such as AAB.
  2. Log on to the U.S. Flag Web site. You can see a display of American flags throughout the country’s history. This site also allows access to the state flags of all 50 states. After the students have a chance to examine the flag, call on volunteers to describe any patterns they see. Then encourage the students to discuss why countries have flags. (Teacher background and interesting facts about the American flag are available from the EdSitement lesson Stars and Stripes Forever. Suggest that they make a flag using the flag template available in the Pattern Templates activity sheet.

Teacher Reflection
 
  • Can most of the students sort objects by a given criteria? Which students still find this challenging?
  • Can most of the students read a pattern? What activities are appropriate for those who cannot do this yet?
  • Can most of the students extend a pattern? What activities are appropriate for those who cannot do this yet?
  • Were the materials used for sorting appropriate?
  • What parts of the lesson went smoothly? Which parts should be modified the next time I teach this lesson?

NCTM Standards and Expectations
 
Algebra Pre-K-2
  1. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
  2. Sort, classify, and order objects by size, number, and other properties.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

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