Building and Expanding Patterns

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Content Area(s):  
Grade Level(s):  
Oregon Common Core State Standards: 
6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs, words and when possible, symbols
Lesson Plan Details
Duration: 
60 minutes
Objective: 
Students will learn to generate a number or shape pattern that follows a given rule. Students will learn to identify apparent features of the pattern that were not explicit in the rule itself.
Resources: 
SMART Board, netbooks, math manipulatives (tile pieces), paper, pencil
Preparation: 

In this lesson the teacher will introduce the common core state standard of 4.5A, which is equivalent of this year's Oregon state standard of 6.3.5, brainstorm definitions, give examples of use, review the definition, explore different websites that allow students to practice working with patterns, work with partners to create/solve patterns, and to test each other on predicting what the pattern will be at a targeted pattern figure. Teacher will have already introduced SMART Board basics and the ability to navigate to websites on the netbooks.

Instruction: 

Direct Instruction:

Teacher Talk:

Today we are covering the common core standard of 4.5A: Generalize and Analyze Patterns.

Does anyone know what a pattern is?  What do patterns do? Where do you see patterns in school  The real world?  Everyday life?  Can you think of a reason why we need patterns?  How about in a job that you may have in the future?

Let’s come up with a definition of what a pattern is? -----

Now let’s compare our definition of what a PATTERN is to what is the given definition is.

Definition of Pattern  (taken from icoachmath.com)

A Pattern constitutes a set of numbers or objects in which all the members are related with each other by a specific rule.  A pattern is also known as sequence. There can be finite or infinite number of members in a pattern.

On the SMART Board :

 Create a  pattern which contains 2 identical groups with each group having 3 different images, a star followed by a bar, which is followed by 3 dots.  How would you extend this pattern.

Create other problems equivalent to the one below:

 Find the next three terms of the following pattern.

81, 79, 77, ___, ___, ___,...

Choices:

A. 79, 81, and 83

B. 83, 81, and 79

C. 75, 73, and 71

D. 79, 77, and 75

Correct Answer: C

Have students pair/share their thinking about the rule.  For example:

Step 1: The rule for the pattern is to count down by 2 repeatedly and continue the sequence to find the next 3 terms.

Step 2: So, the next three terms in the sequence are 75, 73, and 71.

 (Other terns that may need to be defined or explained: number, rule, sequene)

 Guided Practice:  Have students work in pairs on a netbook at the following websites to reinforce discovering rules about patterns.

http://www.learner.org/teacherslab/math/patterns/word.html

http://www.mathplayground.com/logicgames.html

http://www.mathsisfun.com/definitions/pattern.html

 Check for Comprehension: (Using Bridges Student Workbook pages)

Now that we have experienced some different types of patterns, I want each of you to work with your math partner(s) to solve these patterns.  Remember, you need to figure out the rule by testing several patterns and then quiz each other by seeing if you and your partner can predict/design/demonstrate what the “tenth” pattern will look like.  Be sure to question each other: how do you know that this is the tenth pattern representation? How can you prove it?  What was the rule that you figured out?  Does it work?  Did you both get the same answer?  What if you both decide to determine what the twentieth pattern would be?  Hand out Bridges worksheet from student workbook pages 149-150 and pages 152-153.

Assessment: 

As a method to check for student understanding and an exit ticket: have students team up with their math partner, use tile pieces to design their own pattern and create the first three shapes.  Have each student determine the next two shapes to their partner's pattern.

Remind students to create the first three shapes of their pattern so their partner has the visuals to build from.  Once each set of partners have shared, created and discussed their outcomes, have students sketch the FIVE shapes that were created from their own individual pattern.  Write the definition of a pattern and the rule to solve their pattern.  Use sketches and words to explain the definition.

ATTACHMENTS
Oregon Educational Technology Standards
Creativity and Innovation: 
1A. Apply existing knowledge to forecast possibilities and generate new ideas, products or processes.
1B. Create original works as a means of personal or group expression.
1C. Develop or apply models and simulations to explore complex systems, issues and trends.
Communication and Collaboration: 
2A. Interact and collaborate with peers, experts, or others employing a variety of digital environments and media.
2D. Contribute to project teams. Produce original works or solve problems in a team setting.
Research and Information Fluency: 
3A. Plan strategies to guide inquiry.
3B. Locate, organize and use information ethically from a variety of sources and media.
Critical Thinking, Problem Solving and Decision Making: 
4D. Use multiple processes and diverse perspectives to explore alternative solutions.
Digital Citizenship: 
5A. Advocate and practice safe, legal, and responsible use of information and digital technology.
5B. Model and practice a positive attitude toward using digital technology that supports collaboration, learning, and productivity.
5C. Demonstrate personal responsibility for lifelong learning.
Career Related Learning Standards
Personal Management: 
CR1A. Identify tasks that need to be done and initiate action to complete the tasks.
CR2A. Plan, organize, and complete projects and assigned tasks on time, meeting agreed upon standards of quality.
CR3A. Take responsibility for decisions and actions and anticipate consequences of decisions and actions.
CR4A. Maintain regular attendance and be on time.
Problem Solving: 
CR2A. Identify problems and locate information that may lead to solutions.
CR2D. Select and explain a proposed solution and course of action.
CR2F. Assess results and take corrective action.
Communication: 
CR3A. Locate, process, and convey information using traditional and technological tools.
CR3B. Listen attentively and summarize key elements of verbal and non-verbal communication.
CR3C Give and receive feedback in a positive manner.
CR3F. Speak clearly, accurately and in a manner appropriate for the intended audience when giving oral instructions, technical reports and business communications.