##### Problem Solving Scoring Guide with categories for reasoning and proof, communication, representation, attitude or habits of mind, and mathematical understanding
Descriptor   OK, good try, unclear Pretty good, gets the job done

Exceptional, awesome, goes beyond

Problem solving

• Does not use a systematic approach to solving problems
• Randomly tries different strategies
• Selects numbers semi randomly to use in different operations to solve the problem

• Begins to use a systematic approach to solving the problem by reading and attempting to understand the problem
• Finds most of the important parts of problem - some less important are missing
• Chooses a strategey that will not successfully solve the problem
• Uses a systematic method for solving the problem (hueristic)
• Selects appropriate strategies
• Knows all important parts of problem
• Checks the solution with reasoning and proof

• Uses a systematic method for solving the problem (hueristic)
• Selects appropriate strategies
• Knows all important parts of problem
• Checks the solution with reasoning and proof
Reasoning and proof Randomly uses different numbers with different operations without providing a reason why.
• Uses many ways to show thinking like diagrams, charts, graphs, manipulatives, equations, step by step explanation
• May experiment, design, analyze
• May compare problem to other similar or different known or unknown problems
• Experiments with multiple solutions to achieve similar solutions
• Use multiple solutions as proof and reasoning.
• Solves the problem in multiple ways
• Describes a solution for infinite or all possible values
• Compares problem to other similar or different known or unknown problems
• Doesn't explain thinking
Communication No explanation beyond answer Writes for minimal communication to arrive at a solution and communicate it.
• Writes for others
• Has a clear, convincing, thoughtful solution
• Solution missing or incomplete - representations, reasoning and proof, or mathematical information

• Writes for others
• Has a clear, convincing, thoughtful solution
• Solution includes - representations, reasoning and proof, with mathematical information
Representation Attempts to represent, solve, and explain the problem by comparing it to similar problems conceptually or procedurally, but the solution isn't accurate and the explanation isn't appropriate. Attempts to represent, solve, and explain the problem by comparing it to similar problems conceptually or procedurally, but can't explain why either way seems to work. Can represent, solve, and explain the problem conceptually, but not procedurally Can represent, solve, and explain the problem conceptually and procedurally
Attitude or Habits of mind

• Makes no or little effort.
• Doesn't seem motivated to want to discover how to solve the problem.
Listens to challenging problems and will persist in watching others as they attempt to solve the problem offering minimal suggestions. Is fascinated and challenged by problems and engages in openminded attempts and persists until a solution and proof is presented that seems reasonable. Is fascinated and challenged by problems and engages in openminded attempts and persists until a solution and proof is adequate enough to overcome his or her skepticism and gain his or her confidence.
Mathematical understanding

• Has little understanding of problem
• Focuses on less important ideas of the problem, may identify bits and pieces of math needed
• Doesnâ€™t indicate an understanding of the problem
• May or may not solve the problem
• Seems to randomly or inaccurately select an operation to plug numbers in to arrive at an answer.
Accurately uses mathematical concepts and procedures
• Accurately uses mathematical concepts and procedures
• Will probably use a non standard mathematical process that is thought to be creative and not a traditional algorithm