It's In The System

  Name change from "Shapes of Algebra"

Topics

Determining solutions to linear equations, systems of linear equations, solving systems of equations, inequalities, solving systems of inequalities, graphing systems of equations and inequalities

Overview of Changes

Name change and extensive change to content

Detailed Description of Changes

This It’s in the System unit is a major revision of the CMP2 Shapes of Algebra unit to reflect experience with teaching of that prior unit and requirements of the Common Core State Standards for Mathematics (CCSSM). To achieve that new focus and meet the CCSSM requirements, we have deleted Investigation 1 of the Shapes of Algebra unit and moved the second investigation of that unit later in the revised and re-purposed unit. The first two investigations now focus on standard grade eight CCSSM. The second half of investigation two and investigations three and four cover material in the CCSSM syllabus for Algebra.

In revising the unit we addressed a common concern that the material on techniques for solving systems of linear equations appearing in Investigation 4 was not presented in the CMP spirit (i. e. too procedural and not enough open problem solving). This concern was elaborated by some teachers with comments to the effect that students didn’t see a need to learn several techniques for solving systems of linear equations. It also could be argued that the CCSSM don’t explicitly call for solving systems by linear combinations or substitution methods (at least not in the grade 8 expectations). We have addressed these concerns by developing a new more contextual and intuitive approach to methods for solving systems. We still include principles and methods for using linear combinations strategies in solving systems of linear equations, since they are explicitly called for by CCSSM for Algebra I and they advance student algebraic understanding and skills more generally.

  • Investigation 1 is essentially Investigation 3;
  • Investigation 2 is a revised and streamlined version of Investigation 4;
  • Investigation 3 draws on and extends the content of Investigation 2;
  • Investigation 4 is basically the same as Investigation 5 from CMP 2, Shapes of Algebra

More intuitive approach to solving systems of equations.

New Investigation Changes in CMP2 Investigations
Investigation 1 Linear Equations With Two Variables Investigation 1 is gone and replaced with a new Investigation. The new Investigation 1 is essentially Investigation 3 from CMP2.
Investigation 2 Solving Linear Systems Symbolically Investigation 2 is a revised and streamlined version of Investigation 4 from CMP2. 
Investigation 3 Systems of Functions and Inequalities Investigation 3 draws on and extends the content of Investigation 2 from CMP2.
Investigation 4 Systems of Linear Inequalities Investigation 4 is basically the same as Investigation 5 from CMP2.