Table of Contents

Unit 4: Modeling and Using Tools (MP4 and MP5)

4.2.2 Middle Grades

In the middle grades, students learn habits and skills that are central to the development of higher-level mathematical thinking.

The habit of problem posing, creating representations, explaining connections, and testing and checking are central to the development of interesting and new mathematics and applications. Real world applications often involve many variables, incomplete information, multiple methods of solution, and answers that vary according to the assumptions, and simplifications made and approach taken. Encounters with such settings dispel students' notion that the trademark of mathematics is the exactness and uniqueness of results. Rather recognition of underlying structure and abstraction become dominant features of the discipline. Teachers must help students become comfortable with uncertainty while striving for clarity in their descriptions and analyses. Students must accept that creativity and clear communication are part of active learning and discovery. Lastly, they must be curious and willing to take risks. Successful students in traditional math classes are rewarded for speed and technical accuracy. A different type of confidence is required when they begin posing problems with no immediate clear method of solution and no guarantee that a solution can be found."

Abrams, 2001

Examples of Grades 6–8 Modeling Activities:

The problems below represent Level 3 modeling tasks:

Problem 1: The Overland Trail — Sublette’s Cutoff
Problem 2: Fermi Estimates