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10.  Calculator Mystery:
 Discovering the order of operations using calculators

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	SREB Readiness Indicator Write, simplify and solve algebraic equations using substitution, the order of operations, the properties of operations and the properties of equality. > Additional indicators
	Skills Explore the way that the order of operations determines the value of an expression Evaluate expressions using the order of operations
	Figure 1: Scientific calculator Figure 2: Four-function calculator

Overview

A scientific calculator (Figure 1) employs the standard algebraic order of operations. If the seven-key sequence 3, x, 2, +, 2, x, 6 is entered on a scientific calculator, it will return the answer 18, the correct value of the expression as prescribed by the algebraic order of operations. On the other hand, a classic four-function calculator (Figure 2) computes values without regard to the algebraic order of operations, typically completing computations as numbers and operations are entered. In this case, the same seven-key sequence entered on a four-function calculator will result in a final answer of 48. In the Calculator Mystery, students use both a scientific and four-function calculator to discover the differences in the ways these calculators compute and to decipher the specific order of operations employed by each calculator.

The Value of This Technology

Since students are likely to know that "calculators don't make mistakes," the inconsistent answers generated in the initial stage of this activity present a conundrum that engages students in discovering the importance of mathematical convention. The activity stimulates thoughtful investigation that results in an understanding of the order of operations and promotes the ability to recall and apply it correctly while manipulating equations.

Look in the Classroom

Mr. Atsalis knows that before students can successfully simplify algebraic expressions or solve equations, they need to have a complete understanding of the algebraic order of operations.
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