Overview 1 © 2011 California County Superintendents Educational Services Association Mathematics...

California Common Core Standards for Mathematics

Overview

1© 2011 California County Superintendents Educational Services Association • Mathematics General Overview

General Content Overview

◦ Focus and Coherence

◦ Similarities

◦ Shifts

◦ Structure/Organization

◦ Activity

Objectives

2

Mathematical Practices Overview

◦ Purpose

◦Structure

◦8 Practices

◦Standards Alignment

◦Activity

Common Core Standards Overview:Toward Greater Focus and Coherence

3

Avoid the problem of “mile wide and an inch deep”

Recognize that “fewer standards” are no substitute for focused standards

Aim for clarity and specificity

© 2011 California County Superintendents Educational Services Association • Mathematics General Overview

Topics and performances are logical over time

Based on learning progressions research on how students learn

Reflect hierarchical nature of the content

Evolve from particulars to deeper structures

Coherence Design


Define what students should understand and be able to do in their study of mathematics

◦ Is the ability to justify appropriate to student’s math maturity

◦ Understanding and procedural skill are equally important and can be assessed using tasks of sufficient richness

Are internationally benchmarked

◦ Reflect rigor, focus and coherence of standards in top-performing countries

Common Core Standards


Do:

◦Set grade-level standards K-8

◦Identify standards for Algebra 1

◦Provide conceptual cluster standards in high school

◦Provide clear signposts along the way toward the goal of college and career readiness for all students



Do not:

◦Define intervention methods or materials

◦Define the full range of supports for English learners, students with special needs and students who are well above or below grade level expectations

◦Dictate curriculum or teaching methods



Common Core Standards for Mathematics: Two Types

Mathematical Content (different at each grade level)

Mathematical Practice (recurring throughout the grades)


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Mathematical Content

Common Core State Standards for CA DOMAINS

California Standards • Grades K-7 STRANDS

K-5•Counting and Cardinality (K only)•Operations and Algebraic Thinking•Number and Operations in Base 10•Number and Operations-Fractions•Measurement and Data

6-8•Ratio and Proportional Relationships (grade 6-7)•The Number System•Expressions and Equations•Functions (Grade 8)•Geometry•Statistics and probability

• Number Sense

• Algebra and Functions

• Measurement and Geometry

• Statistics, Data Analysis and Probability

• Mathematical Reasoning

Mathematical Content Comparison


Comparison Example


Domains K-8

12© 2013 Actions Learning Systems, Inc.

K 1 2 3 4 5 6 7 8

Counting & Cardinality x

Operations & Algebraic Thinking

x x x x x X

Number & Base Ten x x x x X x

Numbers & Operations-Fractions

x x X

Ratios & Proportional Relationships

x x

The Number system x x x

Expressions & Equation x x X

Functions x

Geometry x x x x x x x x X

Measurement & Data x x x x x X

Statistics & Probability x x x


Grade Shifts: Examples

Developed by SCFIRD

Concept 1997 Standards CCCS

Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle)

Grade2

K

Introduction to ProbabilityGrade

3Grade

7

Introduction of fractions as numbers

Grade2

Grade3

Add and subtract simple fractions

Grade3

Grade4

Introduction of integers Grade 4

Grade6


© 2011 California County Superintendents Educational Services Association • Mathematics General Overview 15

Teaching Algebra and Functions

https://www.teachingchannel.org/videos/algebra-lesson-planning

Example of Common Core Math in an Intermediate Classroom



Overview page◦ Lists domains, clusters and mathematical practices

Domains◦ Larger groups of related standards. Standards from

different domains may be closely related.

Standards-by grade level◦ Defines what students should understand and be able to do

Clusters◦ Groups of related standards. Standards from different

clusters may be closely related

Mathematical ContentGrade K-8 Standards


Overview Page

17

Reading the Standards

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Standards-by grade level: Defines what students should understand and be able to do

Clusters: Groups of related standards. Standards from different clusters may be closely related

Domains: Larger groups of related standards. Standards from different domains may be closely related.

Domain

StandardCLUSTER

Operations and Algebraic Thinking 5.OA

Write and interpret numerical expressions.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.Analyze patterns and relationships.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.Number and Operations in Base Ten 5.

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Label the Domain, Standards, and Clusters for Grade 5 Common Core Mathematics.

Circle, underline or highlight key academic vocabulary within the standards and compare to DOK chart.

Go to U Drive, Curriculum, Common Core State Standards, Common Core Unpacked Math, k-12_math_crosswalk pgs. 77-96.

Using the CCSS Math and the crosswalk, choose a standard and compare similarities and differences.

Be prepared to discuss.

Mathematical Content Activity

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Mathematical Practice

Common Core Standards: Mathematical Proficiency

Standards for Mathematical Practice

◦Describe habits of mind of a mathematically expert student

◦Relate to mathematical proficiency as defined by the California Framework

◦Consistent throughout grade levels


Problem Solving

Computational & Procedural

Skills

DOING MATH

Conceptual Understanding

“WHERE” THE MATHEMATICSWORK

“HOW” THE

MATHEMATICSWORK

“WHY” THE

MATHEMATICSWORK

Mathematical Proficiency as defined by the California Framework


Standards for Mathematical Practice…

“ …describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high schools years.”


Structuring the Standards for Mathematical Practice

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1. Make sense of problems and persevere in solving them.

6. Attend to precision

2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of other

Reasoning and explaining

4. Model with mathematics

5. Use appropriate tools strategies

Modeling and using tools

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Seeing structure and generalizing

Standards for Mathematical Practice

Mathematically Proficient Students:

1. Make sense of problems and

persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and

critique the reasoning

4. Model with mathematics

25

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5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for an express regularity in repeated

reasoning

Standards for Mathematical PracticeMathematically proficient students:


Example of Mathematical Practices in the 5th Grade Classroom: Proportions and Ratios

http://www.insidemathematics.org/index.php/exemplary-lessons-integrating-practice-standards

Inside Mathematics Video




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Activity #1◦ Label the Mathematical Practices that align with

specific standards.◦ Choose a standard and its Mathematical

Practice(s)◦ Go to U Drive, Curriculum, Common Core State

Standards, Common Core Unpacked Math, Find your grade level

◦ Brain storm how you can integrate the Mathematical Practice with the Common Core Standard you chose.

◦ Be prepared to share.

Mathematical Practices Aligned to Common Core Standards


Activity #2◦ Choose a standard and its Mathematical

Practice(s)◦ Go to U Drive, Curriculum, Common Core State

Standards, Common Core Unpacked Math, Find CCSSMathTasks_Grade5

◦ Review a performance task and brainstorm how you might be able to integrate one into a lesson.

◦ Be prepared to share.

Mathematical Practices Aligned to Common Core Standards

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SBAC Math Testhttp://www.smarterbalanced.org/practice-test/

SCROLL DOWN AND CLICK ON PRACTICE TEST

http://www.smarterbalanced.org/practice-test/

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