COMMON CORE STANDARDSCOLLEGE- AND CAREER-READINESS
STANDARDS
North East Florida Educational Consortium
Fall 2011
FLORIDA’S PLAN FOR IMPLEMENTATION
Learning Goals
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Teachers will know the design and organization of the Mathematics Common Core Standards.
Teachers will understand that the Mathematical Practices and Mathematic Content Standards describe varieties of expertise that mathematics educators should seek to develop in their students.
Teachers will be able to integrate the Mathematical Practices and Mathematic Content Standards when developing student learning goals.
Your Personal Goal
Essential Question: How can you develop learning goals for your students using the Common Core Mathematic Standards?
Mathematic Standards
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Mathematical Practices
The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students.
These practices are similar to NCTM’s Mathematical Processes from the Principles and Standards for School Mathematics.
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Mathematical Practices: Focus on “Processes and Proficiencies”
problem solving,
reasoning and proof,
communication,
representation, and
connections
adaptive reasoning,
strategic competence,
conceptual understanding,
procedural fluency, and
productive disposition
Process standards Proficiency standards
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Mathematics/Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
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Small Group Activity – UnpackingWhat students should know and be able to do.
1.Read the Mathematical Practice (pgs. 6-8)
2.Highlight: Know what? / Demonstrate how?
3.Reflect on how the practices will: help in teacher role in the classroom? impact instruction? appear in the classroom? help inform professional development
needs?Prepare to share out
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Group Sorting Activity
Activity: Connect Practice Standards to Fraction Lesson
Materials: Mathematical Practices Sorting Mat Teacher Action sorting cards
Match the learning activity to the best Mathematical Practice that will be demonstrated by students
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Mathematics FormatDomains• Larger groups of related standards.
• Standards from different domains may sometimes be closely related.
• Look for the name with the code number on it for a Domain.
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Mathematics FormatClusters • Groups of related standards.
• Standards from different clusters may sometimes be closely related, because mathematics is a connected subject.
• Clusters appear inside domains.
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Mathematics FormatStandards• Define what students should be able to
understand and be able to do.
• Standards are part of a cluster.
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Common Core Format
K-8High
SchoolConceptual Category
DomainCluster
Standards
Grade Domain
Cluster Standards
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K-8 Grade Level Overview
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Grade Page
K 9
1 13
2 17
3 21
4 27
5 33
6 39
7 46
8 52
Common Core – Domain
Domains are overarching big ideas that connect topics across the grades
Descriptions of the mathematical content to be learned elaborated through clusters and standards
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Common Core – Clusters
May appear in multiple grade levels in the K-8 Common Core. There is increasing development as the grade levels progress
What students should know and be able to do at each grade level
Reflect both mathematical understandings and skills, which are equally important
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Common Core – Standards
Standards are content statements. An example content statement is: “Use properties of operations to generate equivalent expressions.”
Progressions of increasing complexity from grade to grade
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Format of High School
Conceptual
Page Category
58 Number & Quantity
62 Algebra
67 Functions
72 Modeling
74 Geometry
79 Statistics &
Probability
Format of High School Standards
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Domains K-8 / HS Conceptual Categories
Coding Key for Math Standards
Grades K-5 KeyCCMA.K.CC.# = Counting and
Cardinality
CCMA.K.OA.# = Operations and Algebraic
Thinking
CCMA.K.NBT.# = Number and Operations on
Base Ten
CCMA.K.NF.# = Number and Operations – Fractions
CCMA.K.MD.# = Measurement and Data
CCMA.K.G.# = Geometry
Grades 6-8 KeyCCMA.6.RP.# = Ratios and
Proportional Relationships
CCMA.6.NS.# = The Number System
CCMA.6.EE.# = Expressions and Equations
CCMA.6.F.# = Functions
CCMA.6.G.# = Geometry
CCMA.6.SP.# = Statistics and Probability
CCMA.K12.MP.# = Mathematical Practice
Conceptual Categories
Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability
CCMA.K12.MP.# = Mathematical PracticeCCMA.(CC).(D).#
Select a domain
for your grade
level.
Highlight the verbs
within the cluster
content statements &
standards
Progression of SkillsHighlight your grade level & the one directly below & above.
What do you notice about the progression?
Small Group Activity – Unpacking
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Find your Grade Level in the CCSS Document
Look through the Domains & Standards
Complete the Unpacking handout; identify concepts that are:o Newo The Sameo Not Includedo Located in another grade
level
Article Reading
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Read the article and highlight two sentences and two words that you think is particularly important.
First Round: (1 minute each person)Each person shares one sentence and why significant.Identify location with group – page/paragraph – read sentence out loud; share reason selected
Second Round: (1 minute each person)Each person shares the word and why significant.
Third Round: (10 minutes total)Group discussion about what they heard.
Connecting Mathematical Practices w/ Content Standards
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Small Group Activity pg. 1 Find the first page for your grade level,
locate the instructional focus “critical areas”, and list the key concepts for each area.
Follow the next set of directions Small Group Activity pg. 2
Follow directions for the activity. You find a different standard for each
mathematical practice
Rubric
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RubricEvaluation
Level 4.0
In addition to score 3.0, teacher can explain how the Mathematics Practices and Mathematics Content Standards interconnect with each other and why both are necessary for Mathematics instruction.
Level 3.0Target
The teacher can explain the design and organization of the MCCS and can integrate the Mathematics Practices and Content Standards when developing unit goals.
Level 2.0
Teacher can explain the how the MCCS is organized but needs assistance in integrating the Mathematical Practices and Concept Standards when developing unit goals.
Level 1.0
With help, teacher can explain the design of the MCCS and can integrate the Mathematical Practices and Concept Standards when developing unit learning goals.
Level 0.0
Even with help, no understanding of the Mathematics CCS or the Mathematical Practices and Mathematic Content Standards is demonstrated.
Rubric /Lesson Plan
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Course Name Mathematics / Grade 1Standard(s):MACC.1.OA.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Note: See Table 1
Learning Goal(s)/Objective(s)
The student will understand and/or be able to solve addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations.
Essential Question(s)
How can you solve addition and subtraction problems that involve comparing with unknowns in all positions?
Rubric/Evaluation
Level 4.0
In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught the student is able to:Create and solve their own original addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations.
Level 3.0Target
The student understands and is able to:Solve addition and subtraction problems within 20 that involve comparing, with unknowns in all positions, using models, explanation, and equations.The student exhibits no major errors or omissions
Level 2.0
With help, a partial understanding of some of the simpler details and processes as the student is able to:Solve addition and subtraction problems within 20 that involve comparing, with unknowns in two of three positions, using two or three strategies included in the Score 3.0 target.However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Level 1.0
With help, a partial understanding of some of the simpler details and processes as the student is able to:Solve addition and subtraction problems within 20 that involve comparing, with unknowns in one of three positions, using models.
Level 0.0
Even with help, no understanding or skill demonstration
Regularly encourage students to demonstrate and deepen their understanding of numbers and operations by solving interesting, contextualized problems and by discussing the representations and strategies they use.
Regularly encourage students to demonstrate and deepen their understanding of numbers and operations by solving interesting, contextualized problems and by discussing the representations and strategies they use.
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Key Advances
Focus and coherence Focus on key topics at each grade level. Coherent progressions across grade levels.
Balance of concepts and skills Content standards require both conceptual
understanding and procedural fluency.Mathematical practices
Foster reasoning and sense-making in mathematics.
College and career readiness Level is ambitious but achievable.
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Problem Solving
Computational & Procedural
SkillsDOING MATH
Conceptual Understanding
“WHERE” THE MATHEMATICSWORK
“HOW” THE
MATHEMATICSWORK
“WHY” THE
MATHEMATICSWORK
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