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
realworld understanding of integer concepts and operations. 
How to Buy a Car 101 This article elaborates on the basics of problembased learning units and tips for implementation. The problembased 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 68
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.
