Illuminations: Calculating Patterns

Calculating Patterns


Connecting Numbers and Patterns

This lesson accommodates multiple learning styles by having students create patterns using different forms. Students use knowledge and skills in new situations to develop a solid understanding of the process for creating patterns, recognizing pattern sequences, and representing patterns in different ways, and connecting numbers with patterns.

Learning Objectives

 

Students will:

  • recognize and describe patterns
  • use sound and movement to create patterns
  • represent patterns in multiple ways
  • connect numbers with patterns

Materials

 
Pencils and crayons
Connecting cubes
Connecting links
Pattern blocks
Buttons
Models of fruits and vegetables
Geometric shapes (rectangle, hexagon, circle, triangle)
Grid Paper
Hundred Chart Activity Sheet
Calculator and Hundred Board Applet

Instructional Plan

Conduct an oral assessment of the students' knowledge from the previous lesson by asking them to give you a pattern using words (such as blue, blue, white), letters (such as AAB), or objects (such as pencil, crayon, scissors).

Review the four patterns created in the previous lesson. Call attention to the multiple ways the pattern was represented (with movements, letters, numbers, objects, and pictures). Explain to the students that they will create more patterns in different ways today.

Have the students move to an open area where it is acceptable to make noise. Once there, have the students move by following a patterned sequence of motions, such as walk, stop, stamp. Remember to repeat these motions at least three times so that the students can identify the repeat.

Ask students to tell you how they would label this pattern with numbers, such as one, two, three. Then invite a volunteer to create a different pattern that uses movement--for example, wave, wave, clap.

Ask the students to use numbers to label that pattern (one, one, two). A third pattern might be winter (standing with hands stretched down along side the body), spring (chirping like a bird), summer (moving as if swimming), fall (gently bending to the ground to imitate falling leaves). Again, invite the students to tell how to label these patterns with numbers.

Divide the students into two groups. Have one group act out a repeating pattern while the other takes turns calling out numbers that could be used to label the pattern.

Return to the classroom and discuss what the students did while in the open area and what it looked like. It may be helpful to reenact some of the patterns.

Model ways to record various patterns using numbers, pictures, and words.

Provide a variety of materials so that the students can select a method for recording the movement patterns. Materials might include:

  • Crayons
  • Connecting cubes
  • Pattern blocks
  • Connecting links
  • Buttons
  • Models of fruits and vegetables

Students might use the Grid Paper and crayons to record a walk, stop pattern. Students might use geometric shapes as a second way of representing the seasons of the year: rectangle, hexagon, circle, and triangle.

For each recording, have the students add numbers if their original representation uses elements other than numbers.

Turn the students’ attention to visualizing and predicting patterns that feature numbers.

Introduce them to the calculator from NCTM’s E-Standards Web site.

Calculator and Hundred Board Applet Calculator and Hundred Board Applet

Show them how to display a number pattern in the calculator window.

It will accommodate three full repeats of "1, 2, 3" and two numerals of a fourth repeat of a three-numeral pattern. See the screen shot below for an example.

Note that during the exercise, nothing will happen in the corresponding online hundred chart. However, this applet displays counting sequences that use the constant function feature of the calculator, such as 5 + 5 =, =, = or 2 + 2=, =, =. You could use the constant function feature to show the third number of a three-part pattern and the sixth number.

 

Ask the students how they might translate the pattern in the calculator window to a colored pattern on the Hundred Chart activity sheet.

Distribute copies of Hundred Charts and crayons, and have the students use a different color for each numeral in the pattern to color a pattern on the chart.

For example, if they were coloring a 1, 2, 3 pattern using blue, green, and yellow respectively, each numeral on the chart representing “1” in the pattern would be colored blue, each numeral on the chart representing “2” in the pattern would be colored green, and each numeral on the chart representing “3” in the pattern would be colored yellow.

This activity also works well with a four-numeral pattern, such as 1, 2, 3, 4. The sample below illustrates how such a pattern would look on the calculator and the hundred chart.

Group the students so that as many of them have access to online calculators as possible, and have them create their own number patterns and record these in color on hundred charts. Keep the students’ work from this activity for future reference.

Questions for Students

 

What happens when you color a number pattern?

Tell me some other ways you could show me the patterns you created.

How does counting help you remember the pattern?

What other repeating patterns can you find in our classroom or school?

If I were to clap, clap, snap; clap, clap, snap; and clap, clap, snap, how could you use numbers to describe that pattern?

Assessment Options

 
  1. Documenting what the students know and are able to do with repeating patterns on the Class Notes Teacher Resource Sheets helps you plan for needed remediation, enrichment activities, and future instructional experiences.

Teacher Reflection

 
  • Which students could recognize but not describe patterns?
  • What misunderstandings prohibit students from describing patterns?
  • What different representations did students most frequently use when translating patterns in multiple ways? How can I help them identify the pattern core and recognize different ways to represent it?
  • Which students experienced difficulty in understanding that numbers could represent core elements of the pattern? What learning experiences would help them understand this concept and apply with using numbers and other objects?

NCTM Standards and Expectations

 
Algebra Pre-K-2
  1. Sort, classify, and order objects by size, number, and other properties.
  2. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
This lesson was developed by Carol W. Midgett.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

Web Sites


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