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PART I – MEANINGFUL USE OF SYMBOLS

Reading: Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Meaningful use of symbols. In *Elementary and Middle School Mathematics: Teaching Developmentally*, pg. 262-270

- Why is the symbol = so often misunderstood?

- Why is it important for students to have a proper understanding of it?

- Explain how to solve the open number sentence using RELATIONAL THINKING. How does this differ from solving the number sentence by computation?

- What are the two ways in which variables are usually used? Explain the difference between them, using examples if necessary.

PART II – EQUATIONS AND VARIABLES

Reading: Carpenter, T. E., Franke, M. L., & Levi, L. (2003). Equations with multiple variables and repeated variables. In Thinking Mathematically, pg. 65-77.

On pages 73-74, the authors describe the solution strategies of two students, Susan and Erika.

- For each of the following number sentences and explain in detail how Susan would solve it using her trial-and-error strategy, and then explain in detail how Erika would solve the same problem using her strategy of reasoning with the properties of equality (RELATIONALTHINKING).

- 3×h=20-h
- 25+3×k=5×k-7

- Consider the following number equation: p+4=p+7

How would Susan solve this problem? How would Erika solve this problem? What would each student would conclude about the solution of this problem?

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