MATHEMATICS PREPARING FOR LAUNCH UNDERSTANDING …

CALIFORNIA COMMON CORE STATE STANDARDS

MATHEMATICS PREPARING FOR LAUNCH:

UNDERSTANDING THE CCSM GRADES K – 2 November 2, 2013

Presented by Christine Roberts

1

http://bit.ly/CCSSK-2

GOALS

¢ Key Instructional Shifts with CCSS Mathematics

¢ A Closer Look at the Standards

�  Standards for Mathematical Practice

�  Content Standards

¢ SBAC Assessment Consortium

¢ Resources

2

TIMED-ROUND-ROBIN

Have each person at your table share their response to the following questions. Be prepared to share with the whole group.

¢ What do I want to learn about the Common Core State Standards?

¢ What questions do I have about CCSS?

3

Kagan Cooperative Learning: It’s All About Engagement by Laurie Kagan, Dr. Spencer Kagan, and Miguel Kagan

COMMON CORE STANDARDS INITIATIVE - CALIFORNIA Adopted August 2010 ¢ Framework

�  Currently closed after 2nd round of public review from 8/30 – 10/30/13.

�  New math Framework scheduled to be adopted in November 2013.

¢ Materials �  New math materials will be adopted for K-8 by

January 2014. �  35 programs have been submitted and 30 were

recommended for approval.

¢ Assessment �  Field Testing SBAC 2014-15 (ELA or Math)

4

“Common Core State Standards Systems Implementation Plan for California,” California Department of Education

KEY SHIFTS FOR THE COMMON CORE STATE

STANDARDS FOR MATHEMATICS

5

What does it mean to have deep

understanding of mathematics?

A Mile Wide and an Inch

Deep

CCSS for Mathematics

6

Focus

Coherence

Rigor

Key Instructional Shifts of the Common Core State Standards for Mathematics

• Focus strongly where the Standards focus

• Think across grades and link to major topics within grades

•  In major topics, pursue with equal intensity: o  Conceptual understanding o  Procedural skill and fluency o  Application

Focus Strongly Where the Standards Focus

o  a rich classroom environment in which reasoning, sense-making, applications, and a range of mathematical practices all thrive.

The goal of focus is: o  greater depth of

understanding of mathematics

None of this is realistic in a

mile-wide, inch deep world.

K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, July 20, 2012, corestandards.org

8

Focus

K-5 Arithmetic with components of measurement that

support it.

“Teaching Less, Learning More”

Concepts underlying

arithmetic

Skills of arithmetic computation

Ability to apply arithmetic to

solve problems

9

Focus Focus Strongly Where the Standards Focus

FOCUS AREAS

10

Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K-2 Addition and Subtraction – Concepts, Skills, and Problem Solving

3-5 Multiplication and Division of Whole Numbers and Fractions – Concepts, Skills, and Problem Solving

6 Ratios and Proportional Relationships; Early Expressions and Equations

7 Ratios and Proportional Relationships; Arithmetic of Rational Numbers

8 Linear Algebra and Linear Functions

Tricks or Mnemonics

Think across grades and link to major topics within grades

Making Math Make Sense

Mathematics is an elegant subject in which powerful knowledge results from reasoning with a small number of principles such as place value and properties of operations.

11

Coherence

• The standards define progressions of learning that leverage the principles of mathematics as they build knowledge over the grades.

•  The standards emphasize connections between topics within the grade.

•  Do not treat standards as separate events.

12

Think across grades and link to major topics within grades

Coherence


The word “understand” is used in the Standards to set explicit expectations for conceptual understanding…

Grade 1 – Operations and Algebraic Thinking

•  Understand and apply properties of operations and the relationship between addition and subtraction. 4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Grade 2 – Numbers and Operations in Base Ten

•  Understand place value. 1. Understand that the three digits

of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics, July 20, 2012, corestandards.org

Rigor

13

•  Fluency is defined as accurate and reasonably fast.

•  Know single-digit products

and sums from memory.

K.OA.5 – Fluently add and subtract within 5. 5.NBT.5 - Fluently multiply multi-digit whole numbers using the standard algorithm.

•  Methods and algorithms are general and

based on principles of mathematics, not mnemonics or tricks.

14


Rigor

Key Instruction Shifts of the Common Core State Standards for Mathematics, achievethecore.org

15

Grade Standard Required Fluency

K K.OA.5 Add/Subtract within 5

1 1.OA.6 Add/Subtract within 10

2 2.OA.2, 2.NBT.5 Add/Subtract within 20 Add/Subtract within 100

3 3.OA.7, 3.NBT.2 Multiply/Divide within 100 Add/Subtract within 1000

4 4.NBT.4 Add/Subtract within 1,000,000

5 5.NBT.5 Multi-digit Multiplication

6 6.NS.2, 3 Multi-digit Division Multi-digit decimal operations


Rigor

The phrase “real-world problems” and the star symbol (⋆) is used to set expectations and flag opportunities for applications and modeling. •  Ample single-step and multi-step contextual problems

•  Modeling real-world problems builds slowly across K-8.

It is a conceptual category in high school.

Problem Solving Individually and Collaboratively


Rigor

DISCUSS

¢ Share one key shift for CCSS mathematics that stands out in your mind and describe why you chose it.

17

CRITERIA FOR DEVELOPMENT OF CCSS

¢ Aligned with college and work expectations: ¢ Include rigorous content and application of

knowledge through high-order skills; ¢ Build upon strengths and lessons of current state

standards; ¢ Informed by top-performing countries, so that all

students are prepared to succeed in our global economy and society; and,

¢ Evidence and/or research-based 18

HOW DO YOU CREATE BETTER STANDARDS IN MATH?

19

Phil Daro - Chair, Mathematics College and Career Readiness Standards Work Group; Writing Team, Mathematics K-12 Common Core Standards Committee; Senior Fellow, America's Choice, currently Director at the San Francisco field site for SERP Institute.

HOW DO YOU CREATE BETTER STANDARDS IN MATH?

20

ANSWER GETTING VS. LEARNING MATHEMATICS

¢ USA: How can I teach my kids to get the answer to this

problem? Use mathematics they already know. Easy, reliable, works

with bottom half, good for classroom management.

¢  Japan: How can I use this problem to teach the

mathematics of this unit?

21

commoncoretools.wordpress.com

CCSS STRUCTURE- DOMAINS K-8

K 1 2 3 4 5 6 7 8

Counting and Cardinality

Ratios and Proportional Relationships

Operations and Algebraic Thinking Expressions and Equations

Number & Operations in Base Ten The Number System

Fractions

Measurement and Data Functions

Geometry

Statistics and Probability

23

Tulare County Office of Education

!

!California!Department!of!Education! i!|!March!2013!

!

Common Core State Standards for Mathematics

for California Public Schools Kindergarten Through Grade Twelve

Adopted'by'the!California!!State!Board!of!Education!!August!2010!Updated!January!2013!Prepublication!Version!

June 2010

August 2010

CA Revised Jan 2013

Prepublication Version

April 2013

CA CCSS MATH STANDARDS

¢ Mathematical Practice (recurring throughout the grades)

¢ Mathematical Content (different at each grade level or course)

24

COMMON CORE STANDARDS FOR MATHEMATICS: TWO TYPES

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

25

MATHEMATICAL PRACTICES

26

commoncoretools.wordpress.com

K-8: CA ADDITIONS Grade Previous Number of CA

Additions Current Number of CA

Additions K 1 0 1 3 0 2 7 3 3 4 0 4 4 2 5 4 1 6 3 (from grade 7) 0 7 5 (from Grade 8)

1 other addition 0

8 0 0

27

¢ Critical areas �  Describe the mathematical concepts that should be the focus

of instructional time

¢ Overview page �  Lists domains, clusters and mathematical practices

¢ 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

STRUCTURE OF THE STANDARDS: K-8

28

K CRITICAL AREAS

29

30

1ST GRADE OVERVIEW PAGE

31

2ND GRADE EXAMPLE

GLOSSARY

32

Contains Glossary and 5

tables referenced in the

standards.

Problem Types

Properties

Glossary

32

GRADE SHIFT EXAMPLES: K-2

Concept 1997 Standards CCSS

Count from 30 to 100 Grade

1 K

Skip count by 2s, 5s, and 10s to 100 Grade

1 Grade

2 Know from memory the multiplication tables for 2s and 5s *CCSS 3.OA.7-Know from memory all products of two one-digit numbers

Grade 2

Grade 3*

Introduction to fractions as numbers Grade

2 Grade

3

33 Adapted from the California Department of Education

UNDERSTANDING THE STANDARDS

Standards

Progressions

Illustrative Tasks from illustrativemathematics.org

34

¢  K-5, Number and Operations in Base Ten

¢  K, Counting and Cardinality; K-5, Operations and Algebraic Thinking

¢  K-3, Categorical Data; Grades 2-5, Measurement Data

¢  K-5, Geometric Measurement

¢  K-6, Geometry

¢  3-5, Number and Operations – Fractions

DRAFT PROGRESSIONS

35

www.commoncoretools.wordpress.com

A CLOSER LOOK AT SBAC ASSESSMENT

36

ASSESSMENT 37

�  One of two Assessment Consortiums �  California is one of 22 governing states �  www.smarterbalanced.org

37

38 SBAC DESIGN

38

SMARTER BALANCED ASSESSMENT CONSORTIUM

¢ Test will be for grades 3-8 and grade 11. ¢ Administered via computer.

�  Paper-and-pencil will be offered for three years for those that lack sufficient technology.

¢ Assess full range of CCSS in English language arts and mathematics.

¢  Includes Summative Assessment and Optional Interim Assessments.

¢ Results of Summative are expected within two weeks. �  Show current achievement and growth across time. �  Comparable from state-to-state.

39

SUMMATIVE ASSESSMENT FOR ACCOUNTABILITY Final 12 weeks of school year ¢ Performance Tasks

�  1 reading/writing and 1 math �  Delivered via computer �  Time – 1 to 1.5 hours

¢ Computer Adaptive Assessments �  30-45 Items types

¢  Selected-response ¢  Constructed response ¢  Technology-enhanced items

�  Time – 1.5 to 2 hours �  Retake option

¢ Each student may complete one retake ¢ No cost 40

Grades 3-8 1 hour

Grade 11 1.5 hours

Grades 3-5 1.5 hours

Grade 6-8, 11 2 hours

OVERVIEW OF SBAC CLAIMS ¢  Claim 1 – Concepts and Procedures

�  Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

¢  Claim 2 – Problem Solving

�  Students can solve a range of complex, well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

¢  Claim 3 – Communicating Reasoning

�  Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

¢  Claim 4 – Modeling and Data Analysis

�  Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

41

http://www.smarterbalanced.org

SBAC ITEM TYPES Computer Adaptive

¢ Selected Response

¢ Constructed Response

¢ Technology Enhanced

Performance Task

¢ Extended Response

¢ Performance Task 42

SBAC: Mathematics Item Specifications Grades 3-5, developed by Measured Progress/ETS Collaborative, April 16, 2012, http://www.smarterbalanced.org/smarter-balanced-assessments/#item

SELECTED RESPONSE – YES/NO

� Research based � More complex

than traditional multiple choice

� Worth multiple points

43

SBAC Zip Files: Grades 3-5, http://www.smarterbalanced.org/smarter-balanced-assessments/#item

Grade&3&Mathematics&Sample&SR&Item&C1&T1! !!

Version&1.0&

MAT.03.SR.1.000OA.A.220&C1&T1!Sample&Item&ID:& MAT.03.SR.1.000OA.A.220&

Grade:& 03&Claim(s):& Claim&1:&Concepts&and&Procedures&&

Students&can&explain&and&apply&mathematical&concepts&and&carry&out&mathematical&procedures&with&precision&and&fluency.&

Assessment&Target(s):& 1&A:&Represent&and&solve&problems&involving&multiplication&and&division.&&

Content&Domain:& Operations&and&Algebraic&Thinking&Standard(s):& 3.OA.3&

Mathematical&Practice(s):& 1,&4&DOK:& 2&

Item&Type:& SR&Score&Points:& 1&Difficulty:& M&

Key:& NYYN&Stimulus/Source:& &

TargetSspecific&attributes&(e.g.,&accessibility&

issues):&

&

Notes:& MultiSpart&item&!Marcus&has&36&marbles.&He&is&putting&an&equal&number&of&marbles&into&4&bags.&&&For&1a–1d,&choose&Yes&or&No&to&indicate&whether&each&number&sentence&could&be&used&to&find&the&number&of&marbles&Marcus&puts&in&each&bag.&&&

1a.&&&&36 4 &&&� � &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Yes&&&&&&&&&&&&&&No&

1b.&&&&36 4 &&&� � &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Yes&&&&&&&&&&&&&&No&

1c.&&&&4 &&& 36� � &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Yes&&&&&&&&&&&&&&No&

1d.&&&&4 &&& 36� � &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Yes&&&&&&&&&&&&&&No&

!

3.OA.3

44


SELECTED RESPONSE

Grade&3&Mathematics&Sample&SR&Item&C1&T1! !!

Version&1.0&

MAT.03.SR.1.00NBT.A.217&C1&T1!Sample&Item&ID:& MAT.03.SR.1.00NBT.A.217&

Grade:& 03&Claim(s):& Claim&1:&Concepts&and&Procedures&&


Assessment&Target(s):& 1&E:&Use&placeMvalue&understanding&and&properties&of&operations&to&perform&multiMdigit&arithmetic.&&

Content&Domain:& Number&and&Operations&in&Base&Ten&Standard(s):& 3.NBT.2&

Mathematical&Practice(s):& 2,&4,&6&DOK:& 1&

Item&Type:& SR&Score&Points:& 1&Difficulty:& L&

Key:& 9&from&tens&and&2&from&ones&&OR&8&from&tens&and&12&from&ones&

Stimulus/Source:& &TargetMspecific&attributes&(e.g.,&accessibility&issues):&

Add&and&subtract&within&1000.&

Notes:& &!The&number&sentence&below&can&be&solved&using&tens&and&ones.&&&&&&&&&&&&&&67&+&25&=&__?__&tens&and&__?__

&&

&ones.&&Select&one&number&from&each&column&to&make&the&number&sentence&true.&&

!

3.NBT.2

45

CONSTRUCTED RESPONSE


Grade&3&Mathematics&Sample&CR&Item&C1&T1&! !!

Version&1.0&

MAT.03.CR.1.000OA.A.230&C1&T1!Sample&Item&ID:& MAT.03.CR.1.000OA.A.230&

Grade:& 03&Claim(s):& Claim&1:&Concepts&and&Procedures&


Assessment&Target(s):& 1&A:&Represent&and&solve&problems&involving&multiplication&and&division.&&&1&E:&Use&place&value&understanding&and&properties&of&arithmetic&to&perform&multiMdigit&arithmetic.&

Content&Domain:& Operations&and&Algebraic&Thinking&Standard(s):& 3.OA.2,&3.OA.7,&3.NBT.3&

Mathematical&Practice(s):& 1&DOK:& 1&

Item&Type:& CR&Score&Points:& 1&Difficulty:& L&

Key:& 6&Stimulus/Source:& &

TargetMSpecific&Attributes&(e.g.,&Accessibility&Issues):&

&

Notes:& The&response&box&will&only&accept&up&to&3&digits.&

!!Cali&had&60&pounds&of&sand.&The&sand&was&measured&equally&into&bags.&Each&bag&held&10&pounds&of&sand.&How&many&bags&of&sand&did&Cali&have?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Bags&!!!!&

!3.OA.2, 3.OA.

7, 3.NBT.3

Grade&3&Mathematics&Sample&CR&Item&C1&T1&! !!

Version!1.0!!

!Ms.&Clancy&uses&a&backpack&on&a&hiking&trip.&She&took&about&2&kg&of&food&out&of&her&backpack&to&make&it&lighter.&The&scale&below&shows&how&much&the&backpack&weighed&after&she&took&out&the&food.&&&

&&

How&much&did&the&backpack&weigh,&in&kg,&before&she&took&the&food&out?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&kg&&!

3.MD.2

TECHNOLOGY ENHANCED MATH – GRADE 3

46

http://www.smarterbalanced.org

3.G.1

EXTENDED CONSTRUCTED RESPONSE

3.NF.3, 3.G.2

Grade&3&Mathematics&Sample&ER&Item&Claim&2&! !!

Version&1.0&

Jasper&used&the&expression& � �� 5 10 3 &to&find&the&area&of&a&rectangular&closet&floor,&in&square&feet.&&On&the&grid,&draw&a&rectangle&that&Jasper&could&have&measured.&&

&&What&is&the&area&of&the&closet&floor?&&&&&&&&_______&square&feet&&&Jasper&has&200&square&feet&of&tile.&He&will&use&some&of&the&tile&to&cover&the&closet&floor.&He&will&only&use&whole&tiles.&&How&many&square&feet&of&tile&will&Jasper&have&left&after&covering&the&closet&floor&with&tile?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&_______&square&feet&

48

EXTENDED RESPONSE

3.MD.7, 3.OA.8


Grade&3&Mathematics&Sample&ER&Item&Claim&2&! !!

Version&1.0&

Jasper&wants&to&use&some&of&the&remaining&tile&to&cover&the&floor&of&a&kitchen.&The&kitchen&is&12&feet&long&and&12&feet&wide.&&Does&Jasper&have&enough&tiles&to&cover&the&kitchen&floor?&Circle&your&answer.&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Yes&&&&&&&&&&&No&&Show&how&you&got&your&answer.&You&may&use&drawings,&mathematical&expressions/equations,&and&words.&&&&&&&&&!!Sample!Top*Score!Response:&&Draws&a&5x13&rectangle&65&135&11&No&He&only&has&135&square&feet&of&tile.&12&x&12&=&144,&this&is&more&than&135.&!Scoring!Rubric:&&Responses&to&this&item&will&receive&0–4&points,&based&on&the&following:&&4"points:&The&student&shows&thorough&understanding&of&solving&word&problems&involving&the&concepts&of&area&by&doing&the&following:&

�! Draws&a&5x13&rectangle&�! Writes&65&�! Writes&135&�! Writes&11&�! Circles&”No”&&(or&if&not&responding&here,&states&no&in&the&work&that&follows)&�! Shows&work&that&leads&to&the&answer&that&Jasper&does&not&have&enough&tile&(or&that&he&needs&more)&&

PERFORMANCE TASK

49


3.OA.8, 3.NBT.3, 3.MD.3

SAMPLE ASSESSMENT ITEMS

Discuss: ¢ What specific impact will this type of assessment

system have on classroom instruction?

50

¢ What are your first steps as you begin the transition to Common Core Standards?

51

THINKING ABOUT TRANSITION

commoncore.tcoe.org

52

TCOE EDMODO GROUPS Edmodo.com ¢ Go to edmodo.com ¢ Register as a user ¢ Join one of our groups:

�  CCSS TCOE Math TK-2: 2speyj

�  CCSS TCOE Math 3-5: x5535h

�  CCSS TCOE Math 6-8: iym9mw

�  CCSS TCOE Math 9-12: vmcqe6

�  CCSS TCOE Math: svheaq 53

RESOURCES ¢ TCOE CCSS Mathematics Bitly

�  http://bit.ly/CCSSK-2

¢ TCOE Website �  www.tcoe.org/commoncore

¢ TCOE Common Core Website �  http://commoncore.tcoe.org

¢ E-mail

�  Christine Roberts – [email protected]

54

MATHEMATICS PREPARING FOR LAUNCH UNDERSTANDING …

Documents

Transcript of MATHEMATICS PREPARING FOR LAUNCH UNDERSTANDING …