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February 2012, Volume 17, Issue 6


Algebra from Chips and Chopsticks
Jeong Oak Yun and Alfinio Flores
Manipulatives are used to help identify triangular, square, pentagonal, and hexagonal numbers to obtain algebraic representations.

The Value of Debts and Credits
Didem Akyuz
Promote discussions on integers in real life by using positive and negative numbers in the context of net worth.

Why Don’t We Just Divide Across?
Kristie J. Newton and Janice Sands
By exploring algorithms and getting answers to their “Why?” questions, students will gain confidence calculating with fractions.

To Infinity . . . and Beyond!
Jeffrey M. Larson, Michael S. Jacobson, Katherine M. Den Ouden, and Carole G. Basile
Students expand their perspective when they consider counting with large numbers.

Cultivating Algebraic Representations
Leigh A. van den Kieboom and Marta T. Magiera
Teachers learn to appreciate varied student representations of the Flower Bed problem after working through it on their own.

Invest in Financial Literacy
Sarah B. Bush, Maggie B. McGatha, and Jennifer M. Bay-Williams
Budgeting credit card debt and calculating college costs provide real-world mathematical contexts.
Second Look:
Focus Issue - Fostering Mathematical Reasoning

The Write Stuff: Producing a How-To Book
Julie A. Mallia, Don Pawloski, and Peggy Daisey
Help students articulate their mathematical learning through writing.

Using Students’ Interests as Algebraic Models
Kenneth A. Whaley
Incorporate real-life events and hobbies into cross-curriculum writing and mathematics.

Second Look - Focus Issue - Fostering Mathematical Reasoning

The Money Context
An activity taken from a beginning algebra course is used to promote students’ learning of procedures by a conceptual approach.

What Are You Worth?
Use concepts from finance, specifically, assets and debts, to give students a real-world understanding of integer concepts and operations.

How to Buy a Car 101
This article elaborates on the basics of problem-based learning units and tips for implementation. The problem-based learning unit described focuses on the course of action involved in purchasing a new car. Includes the question given to students, one example of student work, and the rubric used for assessment.

Illuminations Lesson: Football Finances
In this activity, students analyze pictures of football stands to make estimates related to the attendance at the Super Bowl. The students will realize that estimates must, at times, be made with little background information and that a range of answers might be correct. Students also make estimates about the television audience.

Illuminations Lesson: The Cost of Being Late
We are bombarded in the media with ads offering 0% interest or teaser rates of 2.9%. These ads are devised to entice us to sign up for these limited time offers that the companies tell us would be crazy to miss. The goal of these ads is to get us to use credit to buy on impulse. If we take the time to analyze the offer, we might realize that if it sounds too good to be true, then it probably is. In this lesson, students will work through a credit card scenario with a teaser rate, minimum payments, fees, and rate increases for being late.

Reasoning and Proof Standard for Grades 6-8

In the middle grades, students should have frequent and diverse experiences with mathematics reasoning as they—

  • examine patterns and structures to detect regularities;
  • formulate generalizations and conjectures about observed regularities;
  • evaluate conjectures;
  • construct and evaluate mathematical arguments.