Teaching and PracticingMental Math Strategies

in Applied and Mathematical Contexts56th Annual Math Teachers Conference

Eastern Illinois UniversityApril 9, 2013

Jim OlsenWestern Illinois University

http://www.wiu.edu/users/mfjro1/wiu/index.htmEmail: JR-Olsen@wiu.edu

Cathy Seeley, NCTM President 2004-2006What does it mean to know mathematics? This is a complex question, but there is strong agreement that facility with numbers and skill in problem solving play important roles. Principles and Standards for School Mathematics calls for students to be proficient with tools that include pencil and paper and technology, as well as mental techniques. I would like to make a case for raising the importance of mental math as a major component in students’ tool kits of mathematical knowledge. Mental math is often associated with the ability to do computations quickly, but in its broadest sense, mental math also involves conceptual understanding and problem solving.

From The Final Report of the National Mathematics Advisory Panel

To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, each facilitating learning of the others. Teachers should emphasize these interrelations; taken together, conceptual understanding of mathematical operations, fluent execution of procedures, and fast access to number combinations jointly support effective and efficient problem solving.

First example mental math worksheet

• 8th Grade:– Seventh worksheet: Compatible Numbers for Addition

(8.7)• This is 1 of 30 available worksheets• (more later)

Five Keys for Learning Mental Math

• Prezi (presentation)• http://prezi.com/3azgqq64xedo/keys-for-ment

al-math-learning-in-7-12/

How to teach strategies

• Prezi (presentation)• http://prezi.com/nu6cynqs58w-/teaching-men

tal-math-strategies/

Second example mental math worksheet

• 8th Grade: – 28th worksheet: Multiplying Decimals by dropping

the decimal and putting it back in later (8.28)• This is 1 of 30 available worksheets

Lists of the

• 30 mental math strategies for 8th Grade• 30 mental math strategies for Algebra I

These are designed so that they can be used– Together (8th grade then Algebra I) or– Independently.

There is some (not a lot of) overlap from one grade to the next. They more important strategies are taught in multiple grades.

(yellow sheets)

How it works (flexible)

• 15 worksheets in the fall semester (one per week)

• 15 worksheets in the spring semester. • Each worksheet teaches one mental math

strategy and practices previous strategies. • Practice the mental math strategies, but

practice in a context of a math problem or a real-world problem.

Everything is available on the websiteDownload, unzip, and print for classroom use.

Third example mental math worksheet

• Algebra I: – 17th worksheet: Multiplying a Fraction Times a

Number by Dividing and Multiplying (9.17)• This is 1 of 30 available worksheets

How to unzip files from the website

Thank you