Mathematical Reasoning Day 4: Unit Rate and Algebraic Solutions

Overview

A large portion of the Grade 7 algebra standard (MDE) is related to ratio and proportion. This corresponds to the Grade 7 recommendations in the Curriculum Focal Points (NCTM, 2006) that emphasize how the study of ratios and proportions can help students connect arithmetic ideas with algebraic ideas. Equality, function, multiplicative thinking, variable, and structure are all important components of algebraic thinking and make up proportional reasoning.

In This Session Teachers:

•  Will learn to solve problems similar to the Bigfoot MEA and other contextual MEAs. The contexts for these MEAs can vary widely and will be used to discuss the implementation of STEM contexts into the mathematics classroom.
•  Will learn a variety of ways to solve missing-value problems and methods to introduce them to their students. The methods include unit rate, scale factor, fraction, table, graph, equation, and function (Lamon, 2007).
• Will learn how to structure grade appropriate activities that encourage students to use these various methods and develop their abiltity to think proportionally.

Standards Specifically Addressed

Minnesota Academic Standards:
Grade 6 - Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.
Grade 6 - Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.
Grade 7 - Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.
Grade 7 - Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

NCTM Process Standards:

• Problem Solving
• Representation
• Reasoning and Proof
• Communication