Chapter 20: Adding Square Roots: Situation 14 From the MACMTL-CPTM Situations Project
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Published:2015
Amy Hackenberg, Eileen Murray, Heather Johnson, Glendon Blume, M. Kathleen Heid, 2015. "Adding Square Roots: Situation 14 From the MACMTL-CPTM Situations Project", Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations, M. Kathleen Heid, Patricia S. Wilson, Glendon W. Blume
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Mr. Fernandez was concerned about his ninth-grade algebra students’ responses to a recent quiz on radicals, specifically those in response to a question about square roots, in which students added and and obtained as a result.
The mathematical basis for determining the appropriateness of the students’ work is that the sum of the square roots of two numbers is not, in general, equal to the square root of the sum of the two numbers. Establishing that a statement is not true can be accomplished in different ways, including finding a counterexample and constructing an indirect proof. The students’ statement, , can be disproved using numeric, geometric, and symbolic representations. Connections are also made to linear transformations.
