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Mathematical Practices Look-fors
MP.1: Make sense of problems and persevere in solving them.
(problem solving)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Analyzes information given
•	 Looks for different ways to
solve the problem (i.e. situation
vs. solution)
•	 Knows and uses different
representations (i.e. equation
vs. table or graph) and/or
manipulative
•	 Evaluates progress and
changes plan if needed
•	 Explains using both pictures
and words
•	 Makes connection to the way
they solved the problem and
how others solved the problem
•	 Uses basic fact fluency or fact
strategies

•	 Promotes visible thinking using
pictures and equations
•	 Gives time for students to
discuss with others or class
•	 Encourages students to keep
trying and builds supportive
math community
•	 Uses explicit and precise
language when using
representations and definitions
and expects students to do the
same in their discussions
•	 Helps students make
connections between
representations, equations, and
student thinking
•	 Engages students in
metacognition
•	 Models problem situation, not
problem solution.

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

MP.3: Construct viable arguments and critique the reasoning of others.
(math talk)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Communicates by using
mathematical reasoning with
objects, drawings, diagrams,
equations …
•	 Justifies solutions
•	 Makes connections between
their own thinking and that of
others
•	 Demonstrates actively listening
by asking questions of others
•	 Makes statements to prove or
disprove concepts or presented
ideas
•	 Students understand different
forms of reasoning (ie.
deductive reasoning) and when
to apply them
•	 Uses accurate vocabulary

•	 Promotes math talk and
the critiquing of presented
solutions
•	 Asks higher-order questions
to facilitate discussion and
presses for justification
•	 Gives time for students to
construct their own ideas
before small or large group
discussions
•	 Expects students to be explicit
and precise when using
representations, definitions,
and symbols
•	 Builds a supportive math
community
•	 Helps make connections
between the reasoning of
students and content standard

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

REGIONAL EDUCATIONAL
SERVICE AGENCY
©2013 St. Clair County RESA

Laura Chambless
Assistant Director, K-8 Math and Science
Mathematical Practices Look-fors
MP.2: Reason abstractly and quantitatively.
(number sense)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer Task
explicitly asks for justification
or explanation

•	 Makes sense of quantities and
their relationship in problem
situations
•	 Recognizes that quantities can
be represented in different
ways
•	 Uses numbers and words to
make sense of a problem
•	 Gives attention to the meaning
of the numbers and knows
which operation to choose
•	 Performs operations flexibly,
accurately, and efficiently
•	 Uses multiple representations
•	 Connects numbers, symbols or
units to quantities
•	 Justifies solutions
•	 Makes connections to how
they solved a problem and how
others solved the problem
•	 Reasons with attributes of
geometric figures

•	 Promotes visible thinking using
pictures and equations
•	 Uses physical representations
(manipulatives, drawings)
to model what happens to a
variable when it changes and
how that effects the other
variable
•	 Gives time for students to
discuss with others or class
•	 Encourages students to keep
trying
•	 Uses explicit and precise
language when using
representations and definitions
and expects students to be the
same in their discussion
•	 Builds a supportive math
community
•	 Helps make connections
between representations,
equations, student thinking,
and content standard

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

MP.6: Attend to precision.
(vocabulary, labeling, answers)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Uses appropriate math
vocabulary
•	 Uses clear definitions in
discussion
•	 Calculates accurately and
efficiently
•	 Explains their reasoning
with accurate mathematical
language
•	 Uses proper unit labels with
measuring
•	 Uses appropriate labels when
graphing and solving story
problems
•	 Determines when different
levels of precision are needed
and how precision affects
results

•	 Communicates precisely using
clear definitions
•	 Emphasizes the importance of
precise communication
•	 Emphasizes the importance of
precision of measurement
•	 Helps make connections
between vocabulary,
student thinking, unit labels,
calculations, and content
standard

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

REGIONAL EDUCATIONAL
SERVICE AGENCY
©2013 St. Clair County RESA

Laura Chambless
Assistant Director, K-8 Math and Science
Mathematical Practices Look-fors
MP.4: Model with mathematics.
(representations and graphs)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Identifies important elements
•	 Expects students to justify their
and quantities needed for a
choice in models
model
•	 Gives students opportunity to
•	 Describes relationships of
evaluate the appropriateness
models and equation
of their model and that of
•	 Chooses a representation
others
•	 Applies formulas/equations
•	 Helps make connections with
•	 Uses models to draw
the relationships between
conclusion
representation, equation,
•	 Explains why it is a good model
answer, student thinking, and
for the problem
content standard
•	 Recognizes and uses parts of a
graph (i.e. title, labels, symbols,
key)

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

MP.5: Use appropriate tools strategically.
(calculators, rulers, manipulative)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Uses mental computations
fluently
•	 Knows which tools are
appropriate for the task
•	 Knows when to use a tool
•	 Understands and uses
properties of operations
•	 Uses estimation to find
errors and check answer for
reasonableness
•	 Justifies tool selection

•	 Allows students to choose
appropriate learning tools
•	 Uses appropriate tools to
represent, explore and deepen
student understanding
•	 Models how different
representations are tools
•	 Uses technology tools
to deepen students’
understanding of a concept
•	 Helps make connections
between tool, equation,
student thinking, and content
standard

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

REGIONAL EDUCATIONAL
SERVICE AGENCY
©2013 St. Clair County RESA

Laura Chambless
Assistant Director, K-8 Math and Science
Mathematical Practices Look-fors
MP.7: Look for and make use of structure.
(how numbers and shapes are organized)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Recognizes that quantities can
be represented in different
ways
•	 Uses properties of operations
to make sense of problems
•	 Recognizes how numbers and
shapes are organized
•	 Looks for patterns and
structures in the number
system
•	 Justify strategy for basic facts
•	 Uses models to prove
equations
•	 Recognize how symbols help
represent relationships and can
be applied to new situations

•	 Gives students time to discuss
connections
•	 Brings students back to the
rule or properties being used
•	 Helps students look for
patterns and structures in the
number system
•	 Helps make connections
between the structure used,
equation, student thinking, and
content standard
•	 Helps make connections to real
world

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

MP #8: Look for and express regularity in repeated reasoning.
(number pattern)

The Math Task:

The Student:

The Teacher:

•	 Is an interesting problem
•	 Has more than one
solution path which may be
unpredictable
•	 Creates discussion
•	 Requires cognitive effort
•	 Connects to real world
•	 Relates to grade level CCSS
•	 Builds student understanding
of grade level standard
•	 Leads students to look back
and reflect on answer
•	 Explicitly asks for justification
or explanation

•	 Notices number patterns
•	 Notices if calculations are
repeated
•	 Applies more efficient
computation strategies using
number patterns
•	 Looks both for general
methods and for shortcuts

•	 Encourages students to
connect task to prior concepts
taught
•	 Helps make connections
between pattern, equation,
student thinking, and content
standard

(from: Implementing Standards-Based
Mathematics Instruction; Stein, Smith
Henningsen & Silver, 1998)

REGIONAL EDUCATIONAL
SERVICE AGENCY
©2013 St. Clair County RESA

Laura Chambless
Assistant Director, K-8 Math and Science

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Mathematical practices look fors rev12.2013

  • 1. Mathematical Practices Look-fors MP.1: Make sense of problems and persevere in solving them. (problem solving) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Analyzes information given • Looks for different ways to solve the problem (i.e. situation vs. solution) • Knows and uses different representations (i.e. equation vs. table or graph) and/or manipulative • Evaluates progress and changes plan if needed • Explains using both pictures and words • Makes connection to the way they solved the problem and how others solved the problem • Uses basic fact fluency or fact strategies • Promotes visible thinking using pictures and equations • Gives time for students to discuss with others or class • Encourages students to keep trying and builds supportive math community • Uses explicit and precise language when using representations and definitions and expects students to do the same in their discussions • Helps students make connections between representations, equations, and student thinking • Engages students in metacognition • Models problem situation, not problem solution. (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) MP.3: Construct viable arguments and critique the reasoning of others. (math talk) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Communicates by using mathematical reasoning with objects, drawings, diagrams, equations … • Justifies solutions • Makes connections between their own thinking and that of others • Demonstrates actively listening by asking questions of others • Makes statements to prove or disprove concepts or presented ideas • Students understand different forms of reasoning (ie. deductive reasoning) and when to apply them • Uses accurate vocabulary • Promotes math talk and the critiquing of presented solutions • Asks higher-order questions to facilitate discussion and presses for justification • Gives time for students to construct their own ideas before small or large group discussions • Expects students to be explicit and precise when using representations, definitions, and symbols • Builds a supportive math community • Helps make connections between the reasoning of students and content standard (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) REGIONAL EDUCATIONAL SERVICE AGENCY ©2013 St. Clair County RESA Laura Chambless Assistant Director, K-8 Math and Science
  • 2. Mathematical Practices Look-fors MP.2: Reason abstractly and quantitatively. (number sense) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer Task explicitly asks for justification or explanation • Makes sense of quantities and their relationship in problem situations • Recognizes that quantities can be represented in different ways • Uses numbers and words to make sense of a problem • Gives attention to the meaning of the numbers and knows which operation to choose • Performs operations flexibly, accurately, and efficiently • Uses multiple representations • Connects numbers, symbols or units to quantities • Justifies solutions • Makes connections to how they solved a problem and how others solved the problem • Reasons with attributes of geometric figures • Promotes visible thinking using pictures and equations • Uses physical representations (manipulatives, drawings) to model what happens to a variable when it changes and how that effects the other variable • Gives time for students to discuss with others or class • Encourages students to keep trying • Uses explicit and precise language when using representations and definitions and expects students to be the same in their discussion • Builds a supportive math community • Helps make connections between representations, equations, student thinking, and content standard (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) MP.6: Attend to precision. (vocabulary, labeling, answers) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Uses appropriate math vocabulary • Uses clear definitions in discussion • Calculates accurately and efficiently • Explains their reasoning with accurate mathematical language • Uses proper unit labels with measuring • Uses appropriate labels when graphing and solving story problems • Determines when different levels of precision are needed and how precision affects results • Communicates precisely using clear definitions • Emphasizes the importance of precise communication • Emphasizes the importance of precision of measurement • Helps make connections between vocabulary, student thinking, unit labels, calculations, and content standard (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) REGIONAL EDUCATIONAL SERVICE AGENCY ©2013 St. Clair County RESA Laura Chambless Assistant Director, K-8 Math and Science
  • 3. Mathematical Practices Look-fors MP.4: Model with mathematics. (representations and graphs) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Identifies important elements • Expects students to justify their and quantities needed for a choice in models model • Gives students opportunity to • Describes relationships of evaluate the appropriateness models and equation of their model and that of • Chooses a representation others • Applies formulas/equations • Helps make connections with • Uses models to draw the relationships between conclusion representation, equation, • Explains why it is a good model answer, student thinking, and for the problem content standard • Recognizes and uses parts of a graph (i.e. title, labels, symbols, key) (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) MP.5: Use appropriate tools strategically. (calculators, rulers, manipulative) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Uses mental computations fluently • Knows which tools are appropriate for the task • Knows when to use a tool • Understands and uses properties of operations • Uses estimation to find errors and check answer for reasonableness • Justifies tool selection • Allows students to choose appropriate learning tools • Uses appropriate tools to represent, explore and deepen student understanding • Models how different representations are tools • Uses technology tools to deepen students’ understanding of a concept • Helps make connections between tool, equation, student thinking, and content standard (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) REGIONAL EDUCATIONAL SERVICE AGENCY ©2013 St. Clair County RESA Laura Chambless Assistant Director, K-8 Math and Science
  • 4. Mathematical Practices Look-fors MP.7: Look for and make use of structure. (how numbers and shapes are organized) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Recognizes that quantities can be represented in different ways • Uses properties of operations to make sense of problems • Recognizes how numbers and shapes are organized • Looks for patterns and structures in the number system • Justify strategy for basic facts • Uses models to prove equations • Recognize how symbols help represent relationships and can be applied to new situations • Gives students time to discuss connections • Brings students back to the rule or properties being used • Helps students look for patterns and structures in the number system • Helps make connections between the structure used, equation, student thinking, and content standard • Helps make connections to real world (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) MP #8: Look for and express regularity in repeated reasoning. (number pattern) The Math Task: The Student: The Teacher: • Is an interesting problem • Has more than one solution path which may be unpredictable • Creates discussion • Requires cognitive effort • Connects to real world • Relates to grade level CCSS • Builds student understanding of grade level standard • Leads students to look back and reflect on answer • Explicitly asks for justification or explanation • Notices number patterns • Notices if calculations are repeated • Applies more efficient computation strategies using number patterns • Looks both for general methods and for shortcuts • Encourages students to connect task to prior concepts taught • Helps make connections between pattern, equation, student thinking, and content standard (from: Implementing Standards-Based Mathematics Instruction; Stein, Smith Henningsen & Silver, 1998) REGIONAL EDUCATIONAL SERVICE AGENCY ©2013 St. Clair County RESA Laura Chambless Assistant Director, K-8 Math and Science