Core Ideas

• Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change
• Represent, analyze, and generalize a variety of functions including linear and simple exponential relationships
• Relate and compare different forms of representation for a relationship including words, tables, graphs in the coordinate plane, and symbols
• Express mathematical relationships using expressions and equations
• Develop conceptual understanding of different uses of variables
• Use symbolic algebra to represent situations to solve problems
• Identify and describe situations with constant or varying rates of change and compare them

MARS Tasks

Odd Numbers

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Odd Numbers" Toolkit Packet (large file)

Core Ideas

• Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change
• Identify functions as linear or nonlinear, and contrast their properties from tables, graphs, or equations
• Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope
• Recognize and generate equivalent forms of simple algebraic expressions and solve linear equations
• Model and solve contextualized problems involving inequalities
• Use graphs to analyze the nature of changes on quantities in linear relationships
• Recognize, represent and solve contextualized problems involving polynomials and their factors

MARS Tasks

The Cog Railway

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "The Cog Railway" Toolkit Packet (large file)

Picking Apples

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Picking Apples" Toolkit Packet (large file)

• Video