OCEAN COUNTY MATH
CURRICULUM
Content Area: Standards for Mathematical Practices
Course Title: Mathematics / Grade Level: K-5
Standards for Mathematical Practice 1
Make sense of problems and preserves in solving them. / All of the Content Specific Standards should be developed through the processes and proficiencies identified in the Standards for Mathematical Practice. This is ongoing and embedded in all mathematical instruction.
Standards for Mathematical Practice 2
Reason abstractly and quantitatively.
Standards for Mathematical Practice 3
Construct viable arguments and critique the reasoning of others.
Standards for Mathematical Practice 4
Model with mathematics.
Standards for Mathematical Practice 5
Use appropriate tools strategically.
Standards for Mathematical Practice 6
Attend to precision.
Standards for Mathematical Practice 7
Look for and make use of structure.
Standards for Mathematical Practice 8
Look for and express regularity in repeated reasoning.
OCEAN COUNTY Math CURRICULUM
Overview of Mathematical Practices
Content Area: Mathematics Grades K-5
Domain (Unit Title): Mathematical Practices
Summary
·  These practices consist of a variety of capabilities that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
Content Standards
Number / Common Core Standard for Mastery
GMP 1 / Make sense of problems and preserve in solving them.
GMP 2 / Reason abstractly and quantitatively.
GMP 3 / Construct viable arguments and critique the reasoning of others.
GMP 4 / Model with mathematics.
GMP 5 / Use appropriate tools strategically.
GMP 6 / Attend to precision.
GMP 7 / Look for and make use of structure.
GMP 8 / Look for and express regularity in repeated reasoning.
Unit Essential Questions
·  How do you articulate mathematical understands?
·  What is the balance between “procedure” and “understanding” in mathematics? / Unit Enduring Understandings
Students will understand that…
·  Mathematically proficient students:
o  Persevere in problems solving in a variety of situations using various tools and strategies,
o  Use numbers, words, pictures, symbols, tables and/or concrete objects to mathematically represent problems and solutions,
o  Communicate clearly about their mathematical ideas,
o  Connect mathematical ideas to “real-world “situations”,
o  Use appropriate tools efficiently to solve problems,
o  Attend to precision in communicating about mathematics, and in procedural aspects of mathematics,
o  Use patterns and structure as a means of solving problems.
OCEAN COUNTY Math CURRICULUM
Evidence of Learning
Formative Assessments
·  Teacher observation
·  Homework
·  Daily classwork
·  Games / ·  Anecdotal records
·  Student participation
·  Exit slips
Summative Assessments
·  Tests
·  Quizzes
·  State / District assessments
Modifications (ELLs, Special Education, Gifted and Talented)
·  Differentiation of instruction based on the specific needs of the students
·  Follow all IEP modifications/504 plan
Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources:
Teacher Notes:
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 1: Make Sense of problems and persevere in solving them.
Mathematical Practice Summary
·  explain the main elements of a problem
·  look for an entry point to the solution
·  analyze constraints, relationships, and goals of the problem
·  monitor and evaluate their progress changing course if necessary
·  check answers to ensure that the solution makes sense
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
Common Core Standard for Mastery
·  Make sense of problems and persevere in solving them.
GMP 1 / The student can…
1.1  Work to make sense of a problem
1.2  Make a plan for solving the problem
1.3  Try different approaches when necessary
1.4  Solve the problem in more than one way
1.5  Check for reasonableness of a solution
1.6  Connect mathematical ideas and representation to one another
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 2: Reason abstractly and quantitatively
Mathematical Practice Summary
·  Make sense of quantities and their relationships in problem situations
·  Decontextualize - Abstract a given situation and represent it symbolically
·  Contextualize – Pause as needed in order to probe into the symbols/words/phrases involved
·  Create a coherent representation of a problem
·  Know and are able to use different properties of operations and objects
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 2 / Can the student:
2.1 Represent problems and situations mathematically with numbers, words, pictures, symbols, gestures, tables, and concrete objects.
2.2 Explain the meanings of the numbers, words, pictures, symbols, gestures, tables, and concrete objects you and others use.
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 3: Construct viable arguments and critique the reasoning of others
Mathematical Practice Summary
·  Understand and use stated assumptions, definitions, and previously established results in constructing arguments.
·  Make conjectures and build a logical progression of statements to explore their truth
·  Analyze situations
·  Justify their conclusions, communicate them to others, and respond to the arguments of others
·  Reason inductively about data, make plausible arguments
·  Compare the effectiveness of two reasonable arguments, distinguish correct logic or reasoning from flawed reasoning
·  Construct solutions using concrete objects, drawings, diagrams, actions, etc. that make sense and are correct
·  Decide whether the solutions of others made sense and ask useful questions to clarify or improve the arguments
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 3 / Can the student:
3.1 Explain both what to do and why it works
3.2 Work to make sense of others’ mathematical thinking
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 4: Model with mathematics
Mathematical Practice Summary
·  Apply mathematics to problems arising in everyday life, society and the workplace
·  Make assumptions and approximations to simplify a complicated situation, realizing that these may need revision later
·  Identify important quantities in a practical situation and map their relationships using tools such as diagrams, two-way tables, graphs, flowcharts and formulas and draw conclusions from the data
·  Reflect on the reasonableness of their results
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 4 / Can the student:
4.1 Apply mathematical ideas to real-world situations
4.2 Use mathematical models such as graphs, drawings, tables, symbols, and diagrams to solve problems.
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 5: Use appropriate tools strategically
Mathematical Practice Summary
·  Consider the appropriate tools when solving problems (pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, dynamic geometry software, etc.
·  Detect possible errors by strategically using estimation and other mathematical knowledge
·  Recognize the usefulness and the limitations of tools in order to make appropriate choices
·  Use appropriate technology to explore and deepen their understanding of a concept
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 5 / Can the student:
5.1 Choose appropriate tools for your problem
5.2 Use mathematical tools correctly and efficiently
5.3 Estimate and use what you know to check the answers you find using tools
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 6: Attend to precision
Mathematical Practice Summary
·  Communicate precisely to others about their mathematical thinking
·  Use clear definitions in their reasoning and conversation with others
·  Sate the meaning of mathematical symbols consistently and appropriately
·  Specify units of measure and label axes to clarity the correspondence with quantities in a problem
·  Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context
·  Give carefully formulated explanation to each other
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 6 / Can the student:
6.1 Communicate your mathematical thinking clearly and precisely
6.2 Use the level of precision you need for your problem
6.3 Be accurate when you count, measure, and calculate
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 7: Look for and make use of structure
Mathematical Practice Summary
·  Discern patterns and structure
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 7 / Can the student:
7.1 Find, extend, analyze, and create patterns
7.2 Use patterns and structure to solve problems
OCEAN COUNTY MATHEMATICS CURRICULUM
GMP 8: Look for and make use of structure
Mathematical Practice Summary
·  Notice if calculations are repeated,, and look for general methods and for shortcuts
·  Maintain oversight of the process during problems solving while attending to the details
·  Continually evaluate the reasonableness of their intermediate results
Primary interdisciplinary connections:
Technology, Language Arts, Science, Social Studies
21st century themes:
Problem solving, reasoning and proof, communication, representation, connections, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Learning Targets
GMP 8 / Can the student:
8.1 Use patterns and structures to create and explain rules and shortcuts
8.2 Use properties, rules, and shortcuts to solve problems
8.3 Reflect on your thinking before, during, and after you solve a problem