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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