Overview

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• Ma

the

ma

tics G

en

era

l Ove

rview

1

BEYOND RIGHT ANSWERS: MATH AND THE CCSS

Teaching Channel video www.teachingchannel.org/videos/teaching-math-

ccss

2

3

© 2

01

1 C

alio

rnia

Co

un

ty S

up

erin

ten

de

nts E

du

catio

na

l S

ervice

s Asso

ciatio

n •

Ma

the

ma

tics Ge

ne

ral O

vervie

w

Topics and performances are logical over time

Based on learning progression research on how students learn

Reflect hierarchical nature of the content

Evolve from particulars to deeper structures

4

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

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 5

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

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

6

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

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 7

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

Mathematical Practice (recurring throughout the grades)

Mathematical Content (different at each grade level)

8

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

9

© 2

01

3 A

ction

s Le

arn

ing

Syste

ms, In

c.

K 1 2 3 4 5 6 7 8Counting & Cardinality xOperations & Algebraic Thinking

x x x x x x

Number & Base Ten x x x x x xNumbers & Operations-Fractions

x x x

Ratios & Proportional Relationships

x x

The Number system x x xExpressions & Equation x x xFunctions xGeometry x x x x x x x x xMeasurement & Data x x x x x xStatistics & Probability x x x

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

10

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

Additional standard language or whole standards

Bolded and underlined Added to maintain rigor of California expectations

11

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

12

Grade 3 Overview

Operations and Algebraic Thinking• Represent and solve problems involving multiplication and division.•Understand properties of multiplication and the relationship betweenmultiplication and division.•Multiply and divide within 100.•Solve problems involving the four operations, and identify andExplain patterns in arithmetic.Number and Operations in Base Ten•Use place value understanding and properties of operations toperform multi-digit arithmetic.Number and Operations - Fractions•Develop understanding of fractions as numbers.Measurement and Data•Solve problems involving measurement and estimation ofIntervals of time, liquid volumes, and masses of objects.Geometry•Reason with shapes and their attributes.

Mathematical Practices1. 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.

READING THE STANDARDSREADING THE STANDARDS

13

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

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.

Ratios and Proportional Relationships 3.RP

Domain

Understand ratio concepts and use ratio reasoning to solve problems.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1

Standard CLUSTER

GRADE SHIFTS: GRADE SHIFTS: EXAMPLESEXAMPLES

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

14

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

Developed by SCFIRD

MATHEMATICAL CONTENT ACTIVITY

Discuss the standards which have been added or deleted from the 3rd grade. Discuss the implications for teaching mathematics.

Using the key vocabulary page, look through the standards and highlight where the key terms are found.

15

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

16

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

Problem Solving

Computational & Procedural

Skills

DOING MATH

Conceptual Understanding

“WHERE” THE MATHEMATICSWORK

“HOW” THE

MATHEMATICSWORK

“WHY” THE

MATHEMATICSWORK 17

© 2

01

1 C

alifo

rnia

Co

un

ty S

up

erin

ten

de

nts

Ed

uca

tion

al S

ervice

s A

ssocia

tion

• Ma

the

ma

tics G

en

era

l Ove

rview

“ …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.”

18

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

STRUCTURING THE STANDARDS FOR STRUCTURING THE STANDARDS FOR MATMATHEMATICAL PRACTICEHEMATICAL PRACTICE

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

19

20

11

Ca

liforn

ia C

ou

nty S

up

erin

ten

de

nts

Ed

uca

tion

al S

ervice

s Asso

ciatio

n •

Ma

the

ma

tics Ge

ne

ral O

vervie

w

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

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

20

© 2

01

1 C

alifo

rnia

Co

un

ty Su

pe

rinte

nd

en

ts E

du

catio

na

l Se

rvices A

ssocia

tion

• M

ath

em

atics G

en

era

l Ove

rview

MATHEMATICAL PRACTICES ALIGNED TO COMMON CORE STANDARDS

Activity Look at the articulation of mathematical

practices of grades below and above. How do the practices progress? What are the implications for teaching?

21

RESOURCES Tulare County Office of Education – Common Core State

Standards (mathematics – resources)www.tcoe.org/ERS/CCSS/index.shtm

Common Core Support Tools – Public Schools of North Carolina (unpacking standards)

www.ncpublicachools.org/acre/standards/common-core-tools/

Arizona’s Common Core State Standards for Mathematics

www.azed.gov/azccrs/teachers/

www.Learnzillion.com/common_core/math/3

Illinois State Board of Educationwww.isbe.net/common_core/htmls/math-model-units.htm

22

CLASSROOM LESSON VIDEOS

23