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Often, patterns given in tables are assumed to have a unique description. This session makes the point that patterns in tables, separate from contexts or situations, can be described in multiple ways. If, however, the pattern is associated with a specific context (such as the toothpick problem in Part B), the description is more uniquely defined.
Another goal of this session is to use variables to describe situations both in and out of context. The staircase and toothpick problems motivate us to think about using variables to describe what happens "down the line" in stages where it would be difficult to extend the table or the drawings.
Materials Needed:
Thirty-five blocks or cubes for individuals working alone or per group if not doing the Counting Stairs interactive activity
Review Previous Session
Begin by reviewing the main idea of Session 1: Reasoning about situations and then describing how quantities in those situations are related is one of the big ideas in algebraic thinking. In Session 1, although we were thinking algebraically, we may not have been using variables. In Session 2, we will explore situations in which variables may be more useful in describing patterns and relationships.
Homework Review
Groups: Discuss any questions about the homework. Consider discussing everyone's reactions to the "Algebra for Everyone" readings, particularly Bob Moses's assertion that algebra is part of a civil rights agenda. Also, react to Richard Riley's argument about algebra for all in the eighth grade.
Groups: Consider discussing Problem H3 from the homework. It is challenging to make the connection between the sloped sides of the container and the curve of the graph. This picture may help explain the situation better.
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