Mental Math: The Case of the Unnecessary Calculator

Joanne Sato Rowe, Math, Northwest School of the Arts

Final Unit(pdf)   Implementing Teaching Standards(pdf)


The purpose of this unit is to provide mental math strategies for students to practice “doing the math in their heads”, to develop their numeric sense, and to persevere in problem solving.  Although graphing calculators are useful 21st century tools to help students develop graphical understanding of equation solving, they are often used for calculations that replace the mental practice needed to maintain knowledge of how to add, subtract, multiply, and divide integers,  fractions, and using exponents.  In this unit students train to become detectives by practicing investigative skills and looking at specific cases.  Students will work together to do a “Chalk Talk” to identify what they do and do not know about fractions and exponents and use mental math to critique responses.  Through “Math Deductions” they will practice using numeric clues to deduce the rules used to find another number and describe in writing what they find.  The Cases of the Perfect Square, The Predictable Matrix, and The Deliberate Discount are presented to challenge students to create and test hypotheses by providing mental math multiplication and addition operations with integers that can be extended to polynomials, using percentages and fractions to analyze sales discounts.