Using Pattern Tasks to Develop Algebraic Thinking

Topic:Using Pattern Tasks to Develop Algebraic Thinking
*Please use the additional files that are uploaded and follow all instructions, thank you.
Reflect on the ways in which the pattern tasks featured in the article “Developing Algebra-Rithmetic in the Elementary Grades” provide a rich opportunity for students to develop algebraic reasoning by making generalizations using words and symbols, and expressing and justifying their thinking. By sharing their methods of problem solving and examining multiple approaches, students develop flexibility in their thinking and learn new ways of describing their mathematical ideas.

In this Discussion, you will study a patterning sequence, and then reflect on the different ways of viewing, describing, and generalizing the pattern.
To begin, examine the S Pattern task illustrated in Fig. 1 (file uploaded). Then, use the prompts below to spark your thinking and record any patterns you notice.
Describe the visual patterns evident in the sequence.
Draw the next two steps in the pattern.
How many total tiles (i.e., squares) will be required for Step 4? Step 5?
Make some observations about the S Pattern that could help you to describe subsequent steps.
Describe two steps in the pattern that are beyond the 10th step.
Devise a method for find the total number of tiles in the 50th step
Translate the visual patterns into a numerical summary. Organize your data in a chart or table.
How might a graph of the change in successive steps of the pattern look?
Write a rule to predict the total number of tiles for any step. Explain how your rule relates to the pattern.
Write a different rule to predict the total number of tiles for any step. How does this rule compare/contrast to the original rule?
Write a description of the patterns you found in the S Pattern task. Include a brief explanation of the different methods you used to determine a generalization, and provide an equation that could be used to define any step in the pattern. Justify the validity of your equation

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