IMP 1 POW #3 (Checkerboard Squares)

Expectations Rubric:

Please attach this rubric to your POW

Note: In order to earn an A, the work must include all five required sections of the POW:

Problem Statement - The problem statement must provide enough information so that a reader unfamiliar with the textbook can understand and solve the problem without referring to the text. Be sure to clearly state what you are being asked to do, to solve or to find. Remember: You may have more than one task!

Process - This may be a journal or narrative format. You should include all diagrams, equations, tables, etc. that you used - even if you eventually discarded the idea! Remember: “Mistakes” help us learn!

Solution - This section may be included in the Process section. Whether a separate section or part of the Process section, your Solution must be clearly labeled and clearly stated.

Extensions – These are questions that ask, “What would happen if . . .?” The questions should make the problem more mathematically challenging not just longer.

Please label each section.

General Grading Rubric:

100% - The work includes all five sections of the POW. The work indicates conceptual understanding: The mathematics is complete and correct, fully explained and fully justified. The work clearly indicates that the student has a full conceptual understanding of the problem, the solution and its process. The work includes a generalized solution (in the form of a verbal rule, equation or a clearly stated step by step process). (For a 100% - use this hint: see HW#11) The mechanics of the writing do not hinder the flow of the work. The organization of the work clarifies the process and solution. The work is neat with all headings included. The work meets the criteria for Expert in all categories.

95% Like 100% but mechanics hinder flow of the work OR minor organizational problems hinder the reader’s ability to understand the work the first time through OR headings are not included OR the student’s work includes one minor counting error that does not affect the reasoning and result. The work meets the criteria for Expert in Problem Solving, Representation and Reasoning. The work meets hte criteria for Practitioner in Communication and Connections.

85% - The student’s work includes a mathematically correct and complete explanation of the number of squares in an 8x8 checkerboard. The work also includes a reasonable attempt to generalize the pattern for all square checkerboards. OR The work is like a 100% with missing extensions. The work clearly meets the criteria for Practitioner in all categories.

75% - The work indicates procedural understanding only: The work is partially correct with full explanations and justifications for the given partial solution. The work may include a correct answer for the 8x8 checkerboard but the work indicates that the student has further investigation to do before they will arrive at a complete solution including a generalization of the solution. OR The work is incorrect but the process indicates understanding that, with further investigation, could easily lead to a complete and correct solution. The work clearly meets the criteria for Apprentice in all areas except communication which should be at Practitioner level.

65% - The work shows full effort on the part of the student but indicates that procedural and conceptual understanding are in progress. OR The work states a partially correct answer with little to no explanation of the process or justification of the given solution. The work meets the criteria for Apprentice and/or Novice in all categories.

50% - Incorrect work. Incomplete work is treated as a late grade.


Checklist:

 I wrote a correct and complete problem statement.

 I was able to find the number of 3x3 squares in the 8x8 checkerboard.

 I was able to find all other sized squares in the 8x8 checkerboard.

 I explained how I found the correct number of squares.

 I included any diagrams or tables or equations I used or developed.

 I clearly wrote my solution and boxed or highlighted it.

 I extended the problem.

 My writing uses complete sentences and correct grammar.

 Someone else reading my POW could recreate my process without having to ask me questions.

 I labeled each required section of my POW.

 I put my Name, the Due Date and my Class Period on my POW – either in the upper right hand corner of the first page or on a cover sheet.

 I put a complete label “POW #3” on the first page of my POW or on a cover sheet.