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Generate and analyze patterns.
5.
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

• An Introduction to Arithmetic and Geometric Sequences
This lesson plan introduces arithmetic and geometric sequences to students so that they know the terminology and can vary a sequence.
• Chessboard Algebra and Function Machines
This Teaching Channel video shows how students can find the rule that determines the number of chessboard squares. (6 min.)
• Finding Remainders in Pascal's Triangle
This lesson is designed to reinforce division by using clock arithmetic to find remainders and then find patterns in Pascal's triangle by coloring the remainders in colors.
• Flake Maker
This activity allow students to create custom line deformation fractals and practice skills with pattern recognition and plane geometry.
• Floor Tiles
This lesson will help students identify and examine symmetry in geometric figures as well as describe and classify polygons.
• Patterns in Pascal's Triangle
This lesson plan was designed to help students understand Pascal's Triangle and its patterns.
• Recognizing Patterns
This lesson will introduce students to patterns in sequences and tessellations and give them practice in creating their own patterns.
• Tessellate!
This lesson and activity will help the student understand how to classify two-dimensional figures based on properties. The student manipulates shapes to create now polygons.
• USOE Curriculum Guide (4OA5)
This curriculum guide was developed by USOE and Utah educators.
• Venn Diagrams
This is an interactive lesson in which students must place a number into the correct area of a Venn diagram.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Office of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Office of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.