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

Objectives

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:

Grade 3

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 4

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Grade 5

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

Fifth Grade

Operations and Algebraic Thinking

Analyze patterns and relationships.

Fourth Grade

Operations and Algebraic Thinking

Generate and analyze patterns.

Functions

Linear, Quadratic, and Exponential Models

Construct and compare linear, quadratic, and exponential models and solve problems

Geometry

Congruence

Experiment with transformations in the plane

Understand congruence in terms of rigid motions

Grades 3-5

Algebra

Analyze change in various contexts

Understand patterns, relations, and functions

Use mathematical models to represent and understand quantitative relationships

Grade 3

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 5: The learner will recognize, determine, and represent patterns and simple mathematical relationships.

Grade 5

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 5: The learner will demonstrate an understanding of patterns, relationships, and elementary algebraic representation.

Technical Mathematics I

Number and Operations

Competency Goal 1: The learner will apply various strategies to solve problems.

3rd Grade

Algebra

The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time.

4th grade

Algebra

Standard 4-3: The student will demonstrate through the mathematical processes an understanding of numeric and nonnumeric patterns, the representation of simple mathematical relationships, and the application of procedures to find the value of an unknown.

5th grade

Algebra

The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

Geometry

Geometry

Standard G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

3rd Grade

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

4th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

5th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

6th Grade

Algebra

Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

7th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

8th Grade

Algebra

The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.

Algebra I

Algebra

Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real world problem solving.

Algebra II

Algebra

Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.

Geometry

Algebra

Students will recognize, extend, create, and analyze a variety of geometric, spatial, and numerical patterns; solve real-world problems related to algebra and geometry; and use properties of various geometric figures to analyze and solve problems.

Grade 3

Patterns, Relationships, and Algebraic Thinking

6. The student uses patterns to solve problems.

Grade 5

Patterns, Relationships, and Algebraic Thinking

5. The student makes generalizations based on
observed patterns and relationships.

3rd Grade

Patterns, Functions, and Algebra

3.24 The student will recognize and describe a variety of patterns formed using concrete objects, numbers, tables, and pictures, and extend the pattern, using the same or different forms (concrete objects, numbers, tables, and pictures).

3.25a The student will investigate and create patterns involving numbers, operations (addition and multiplication), and relations that model the identity and commutative properties for addition and multiplication.

4th Grade

Patterns, Functions, and Algebra

4.21 The student will recognize, create, and extend numerical and geometric patterns, using
concrete materials, number lines, symbols, tables, and words.

5th Grade

Patterns, Functions, and Algebra

5.20 The student will analyze the structure of numerical and geometric patterns (how they change or grow) and express the relationship, using words, tables, graphs, or a mathematical sentence. Concrete materials and calculators will be used.

6th Grade

Patterns, Functions, and Algebra

6.21 The student will investigate, describe, and extend numerical and geometric patterns, including triangular numbers, patterns formed by powers of 10, and arithmetic sequences.

7th Grade

Patterns, Functions, and Algebra

7.19 The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships.

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

pattern

Characteristic(s) observed in one item that may be repeated in similar or identical manners in other items

sequence

An ordered set whose elements are usually determined based on some function of the counting numbers

tessellation

A tessellation is a repeated geometric design that covers a plane without gaps or overlaps

Lesson Outline

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.

Objectives

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

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?

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.

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.

Closure

Discuss patterns and their occurrences in nature, society, school, and math.