Core Ideas

• Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships.
• Describe and extend patterns of sound, shape, or number and translate from one representation to another.
• Describe and extend growing as well as repeating patterns.
• Use the general principles and properties of operations, such as commutativity, with specific numbers.
• Model problem situations using objects, pictures, and symbols
• Describe change qualitatively, such as students growing taller or the weather turning colder.

Core Ideas

• Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships.
• Describe, extend, and create patterns of sound, shape, and number and translate from one representation to another.
• Describe, extend, and create growing as well as repeating patterns.
• Compare principles and properties of operations, such as commutativity, between addition and subtraction.
• Use concrete, pictorial, and verbal representations to develop an understanding of symbolic notations.
• Describe change quantitatively such as a student's growing two inches in one year.

MARS Tasks

Building Walls

• 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 "Building Walls" Toolkit Packet (large file)

Core Ideas

• Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
• Describe and extend geometric and numeric patterns.
• Represent and analyze patterns using words and/or tables.
• Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
• Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
• Model problem situations with objects and use representations such as graphs and tables to draw conclusions.
• Describe qualitative change (such as students growing taller).
• Describe quantitative change (such as a student's growing two inches in one year).
• Solve simple problems involving a functional relationship (two quantities which vary together, like finding the total cost of multiple items when you know the cost of one).

MARS Tasks

Blob Bugs

• 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 "Blob Bugs" Toolkit Packet (large file)

Core Ideas

• Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
• Represent and analyze patterns and functions using words, tables, and graphs.
• Find the results of a rule for a specific value.
• Use inverse operations to solve multi-step problems.
• Use concrete, pictorial, and verbal representations to solve problems involving unknowns.
• Understand and use the concept of equality.

MARS Tasks

Roger's Rabbits

• 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 "Roger's Rabbits" Toolkit Packet (large file)

Core Ideas

• Understand patterns and use mathematical models such as algebraic symbols and graphs to represent and understand quantitative relationships.
• Represent the idea of a variable as an unknown quantity using a letter or a symbol.
• Express mathematical relationships using equations and graph them on a coordinate grid.
• Investigate how a change in one variable relates to a change in a second variable.
• Identify and describe situations with constant and varying rates of change and compare them.
• Understand and use properties of operations, such as the distributive property of multiplication over addition.

MARS Tasks

Buttons

• 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 "Buttons" Toolkit Packet (large file)
• See Related Classroom Video Visit: Multiple Representations of Numerical Patterning
  Fran Dickinson leads students through a lesson on devising multiple representations of numeric patterning. The multimedia documentation of Dickinson's teaching includes a pre-teaching planning conversation between Dickinson, Margie Trainer, math coach, and Stacy Emory, the curriculum and resource coordinator for the San Carlos Charter Learning Center. The documentation also includes a follow-up faculty debrief with observing teachers, reflections by the coach and the students, and an interview with participating students. VIDEO >>

Pea Soup

• 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 "Pea Soup" Toolkit Packet (large file)