Content Rubric (Focus on Overarching Habits of Mind): Student Implementation
4 Student-work indicates the use of complex and non-algorithmic thinking, problem solving or exploring and understanding
the nature of mathematical concepts, procedures, and/or relationships
Student-work indicates evidence of at least four of the behaviors defined by student’s engagement in the overarching habits
of mind of a productive mathematical thinker:
 Understand the meaning of the problem and look for entry points to its solution
 Analyze information (givens, constraints, relationships, goals)
 Make conjectures and plan a solution pathway
 Monitor and evaluate the progress and change course as necessary
 Check answers to problems and ask, “Does this make sense?”
 Communicate precisely using clear definitions
 State the meaning of symbols, carefully specifying unites and measure and providing accurate labels
 Calculate accurately and efficiently, expressing numerical answers with a degree of precision
 Provide carefully formulated explanations
 Label accurately when measuring and graphing.
Student work includes an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
3
Student work indicates that students engaged in problem-solving or in creating meaning for mathematical procedures and
concepts BUT the evidence of students thinking or reasoning is incomplete (no explanation, justification, or explicit
connections).
Student-work indicates evidence of at least three of the behaviors defined by student’s engagement in the overarching habits
of mind of a productive mathematical thinker (see above);
Student work may or may not include an accurate and mathematically sound solution that reflects a deep, conceptual
understanding for procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect
solution with minor flaws)
2
Students engage with the task/item at a procedural level. Students apply a demonstrated or prescribed procedure. Students
may be required to show or state the steps of their procedure, but are not required to explain or support their ideas. Students focus
on correctly executing a procedure to obtain a correct answer.
Student-work indicates evidence of no more than two of the behaviors defined by student’s engagement in the overarching
habits of mind of a productive mathematical thinker (see above);
Student work may or may not include an accurate solution that reflects procedural fluency. (For example; solutions developed
by procedures without connections OR an incorrect solution with major flaws)
1
Students engage with the task/item at memorization level. Students are required to recall facts, formulas, or rules (e.g., students
provide answers only), OR
Even though a procedure is required or implied by the task/item, only answers are provided in students’ work; there is not
evidence of the procedure used by the students.
Student-work indicates no evidence of the behaviors defined by student’s engagement in the overarching habits of mind of a
productive mathematical thinker (see above);
Student does not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License
Content Rubric (Focus on Reasoning and Explaining): Student Implementation
4 Student-work indicates the use of complex and non-algorithmic thinking, problem solving or exploring and understanding
the nature of mathematical concepts, procedures, and/or relationships
Student-work indicates evidence of at least four of the behaviors defined by students’ reasoning and explaining;
 Make sense of quantities and relationships in problem situations
 Represent abstract situations symbolically and understand the meaning of quantities
 Create a coherent representation of the problems at hand
 Consider the units involved
 Flexibly use properties of operations
 Use definitions and previously established causes/effects (results) in constructing arguments
 Make conjectures and use counterexamples to build a logical progression of statements to explore and support their ideas
 Communicate and defend mathematical reasoning using objects, drawings, diagrams, and/or actions
 Listen to or read the arguments of others
 Decide if the arguments of others make sense and ask probing questions to clarify or improve the arguments.
Student work includes an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
3
Student work indicates that students engaged in problem-solving or in creating meaning for mathematical procedures and
concepts BUT the evidence of students thinking or reasoning is incomplete (no explanation, justification, or explicit
connections).
Student-work indicates evidence of at least three of the behaviors defined by students’ reasoning and explaining (see
above);
Student work may or may not include an accurate and mathematically sound solution that reflects a deep, conceptual
understanding for procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect
solution with minor flaws)
2
Students engage with the task/item at a procedural level. Students apply a demonstrated or prescribed procedure. Students
may be required to show or state the steps of their procedure, but are not required to explain or support their ideas. Students focus
on correctly executing a procedure to obtain a correct answer.
Student-work indicates evidence of no more than two of the behaviors defined by students’ reasoning and explaining (see
above);
Student work may or may not include an accurate solution that reflects procedural fluency. (For example; solutions developed
by procedures without connections OR an incorrect solution with major flaws)
1
Students engage with the task/item at memorization level. Students are required to recall facts, formulas, or rules (e.g., students
provide answers only), OR
Even though a procedure is required or implied by the task/item, only answers are provided in students’ work; there is not
evidence of the procedure used by the students.
Student-work indicates no evidence of the behaviors defined by students’ reasoning and explaining (see above);
Student does not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License
Content Rubric (Focus on Modeling and Using Tools): Student Implementation
4 Student-work indicates the use of complex and non-algorithmic thinking, problem solving or exploring and understanding
the nature of mathematical concepts, procedures, and/or relationships
Student-work indicates evidence of at least four of the behaviors defined by students’ modeling and using tools;
 Apply prior knowledge to solve real world problems
 Identify important quantities and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts,
and/or formulas
 Use approximations to make a problems simpler
 Check to see if an answer makes sense within the context of a situation and change a model when necessary
 Make sound decisions about the use of specific tools (Examples might include: calculator, concrete models, digital technologies,
pencil/paper, ruler, compass, protractor)
 Use technological tools to visualize the results of assumptions, explore consequences, and compare predications with data
 Identify relevant external math resources (digital content on a website) and use them to pose or solve problems
 Use technological tools to explore and deepen understanding of concepts.
Student work includes an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
3
Student work indicates that students engaged in problem-solving or in creating meaning for mathematical procedures and
concepts BUT the evidence of students thinking or reasoning is incomplete (no explanation, justification, or explicit
connections).
Student-work indicates evidence of at least four of the behaviors defined by students’ modeling and using tools (see above);
Student work may or may not include an accurate and mathematically sound solution that reflects a deep, conceptual
understanding for procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect
solution with minor flaws)
2
Students engage with the task/item at a procedural level. Students apply a demonstrated or prescribed procedure. Students
may be required to show or state the steps of their procedure, but are not required to explain or support their ideas. Students focus
on correctly executing a procedure to obtain a correct answer.
Student-work indicates evidence of no more than three of the behaviors defined by students’ modeling and using tools (see
above);
Student work may or may not include an accurate solution that reflects procedural fluency. (For example; solutions developed
by procedures without connections OR an incorrect solution with major flaws)
1
Students engage with the task/item at memorization level. Students are required to recall facts, formulas, or rules (e.g., students
provide answers only), OR
Even though a procedure is required or implied by the task/item, only answers are provided in students’ work; there is not
evidence of the procedure used by the students.
Student-work indicates no evidence of the behaviors defined by students’ modeling and using tools (see above);
Student does not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License
Content Rubric (Focus on Seeing Structure and Generalizing): Student Implementation
4 Student-work indicates the use of complex and non-algorithmic thinking, problem solving or exploring and understanding
the nature of mathematical concepts, procedures, and/or relationships
Student-work indicates evidence of at least three of the behaviors defined by student’s seeing structure and generalizing;
 Look for patterns or structure, recognizing that quantities can be represented in different ways
 Recognize the significance in concepts and models and use the patterns or structure for solving related problems
 View complicated quantities both as single objects or compositions of several objects and use operations to make sense of
problems
 Notice repeated calculation and look for general methods and shortcuts
 Continually evaluate the reasonableness of intermediate results (comparing estimates), while attending to details, and make
generalizations based on findings.
Student work includes an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
3
Student work indicates that students engaged in problem-solving or in creating meaning for mathematical procedures and
concepts BUT the evidence of students thinking or reasoning is incomplete (no explanation, justification, or explicit
connections).
Student-work indicates evidence of at least two of the behaviors defined by student’s seeing structure and generalizing (see
above);
Student work may or may not include an accurate and mathematically sound solution that reflects a deep, conceptual
understanding for procedural fluency. (For example; solutions developed by procedures without connections OR an incorrect
solution with minor flaws)
2
Students engage with the task/item at a procedural level. Students apply a demonstrated or prescribed procedure. Students
may be required to show or state the steps of their procedure, but are not required to explain or support their ideas. Students focus
on correctly executing a procedure to obtain a correct answer.
Student-work indicates evidence of no more than one of the behaviors defined by student’s seeing structure and generalizing
(see above);
Student work may or may not include an accurate solution that reflects procedural fluency. (For example; solutions developed
by procedures without connections OR an incorrect solution with major flaws)
1
Students engage with the task/item at memorization level. Students are required to recall facts, formulas, or rules (e.g., students
provide answers only), OR
Even though a procedure is required or implied by the task/item, only answers are provided in students’ work; there is not
evidence of the procedure used by the students.
Student-work indicates no evidence of the behaviors defined by student’s seeing structure and generalizing (see above);
Student does not include an accurate and mathematically sound solution that reflects a deep, conceptual understanding for
procedural fluency.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License