mathematics preparing for launch understanding …
TRANSCRIPT
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CALIFORNIA COMMON CORE STATE STANDARDS
MATHEMATICS PREPARING FOR LAUNCH:
UNDERSTANDING THE CCSM GRADES K – 2 November 2, 2013
Presented by Christine Roberts
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http://bit.ly/CCSSK-2
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GOALS
¢ Key Instructional Shifts with CCSS Mathematics
¢ A Closer Look at the Standards
� Standards for Mathematical Practice
� Content Standards
¢ SBAC Assessment Consortium
¢ Resources
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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?
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Kagan Cooperative Learning: It’s All About Engagement by Laurie Kagan, Dr. Spencer Kagan, and Miguel Kagan
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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)
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“Common Core State Standards Systems Implementation Plan for California,” California Department of Education
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KEY SHIFTS FOR THE COMMON CORE STATE
STANDARDS FOR MATHEMATICS
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What does it mean to have deep
understanding of mathematics?
A Mile Wide and an Inch
Deep
CCSS for Mathematics
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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
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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
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Focus
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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
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Focus Focus Strongly Where the Standards Focus
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FOCUS AREAS
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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
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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.
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Coherence
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• 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.
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Think across grades and link to major topics within grades
Coherence
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• In major topics, pursue with equal intensity: o Conceptual understanding o Procedural skill and fluency o Application
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
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• 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.
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• In major topics, pursue with equal intensity: o Conceptual understanding o Procedural skill and fluency o Application
Rigor
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Key Instruction Shifts of the Common Core State Standards for Mathematics, achievethecore.org
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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
• In major topics, pursue with equal intensity: o Conceptual understanding o Procedural skill and fluency o Application
Rigor
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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
• In major topics, pursue with equal intensity: o Conceptual understanding o Procedural skill and fluency o Application
Rigor
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DISCUSS
¢ Share one key shift for CCSS mathematics that stands out in your mind and describe why you chose it.
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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
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HOW DO YOU CREATE BETTER STANDARDS IN MATH?
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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.
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HOW DO YOU CREATE BETTER STANDARDS IN MATH?
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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?
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commoncoretools.wordpress.com
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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
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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
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¢ Mathematical Practice (recurring throughout the grades)
¢ Mathematical Content (different at each grade level or course)
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COMMON CORE STANDARDS FOR MATHEMATICS: TWO TYPES
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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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MATHEMATICAL PRACTICES
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commoncoretools.wordpress.com
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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
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¢ 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
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K CRITICAL AREAS
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1ST GRADE OVERVIEW PAGE
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2ND GRADE EXAMPLE
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GLOSSARY
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Contains Glossary and 5
tables referenced in the
standards.
Problem Types
Properties
Glossary
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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
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UNDERSTANDING THE STANDARDS
Standards
Progressions
Illustrative Tasks from illustrativemathematics.org
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¢ 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
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www.commoncoretools.wordpress.com
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A CLOSER LOOK AT SBAC ASSESSMENT
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ASSESSMENT 37
� One of two Assessment Consortiums � California is one of 22 governing states � www.smarterbalanced.org
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38 SBAC DESIGN
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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.
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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
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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.
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http://www.smarterbalanced.org
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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
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SELECTED RESPONSE – YES/NO
� Research based � More complex
than traditional multiple choice
� Worth multiple points
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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
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SBAC Zip Files: Grades 3-5, http://www.smarterbalanced.org/smarter-balanced-assessments/#item
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&&
Students&can&explain&and&apply&mathematical&concepts&and&carry&out&mathematical&procedures&with&precision&and&fluency.&
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
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CONSTRUCTED RESPONSE
SBAC Zip Files: Grades 3-5, http://www.smarterbalanced.org/smarter-balanced-assessments/#item
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&
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.&&&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£s&of&sand.&The&sand&was&measured&equally&into&bags.&Each&bag&held&10£s&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
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TECHNOLOGY ENHANCED MATH – GRADE 3
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http://www.smarterbalanced.org
3.G.1
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EXTENDED CONSTRUCTED RESPONSE
3.NF.3, 3.G.2
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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&
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EXTENDED RESPONSE
3.MD.7, 3.OA.8
SBAC Zip Files: Grades 3-5, http://www.smarterbalanced.org/smarter-balanced-assessments/#item
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¬&responding&here,&states&no&in&the&work&that&follows)&�! Shows&work&that&leads&to&the&answer&that&Jasper&does¬&have&enough&tile&(or&that&he&needs&more)&&
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PERFORMANCE TASK
49
SBAC Zip Files: Grades 3-5, http://www.smarterbalanced.org/smarter-balanced-assessments/#item
3.OA.8, 3.NBT.3, 3.MD.3
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SAMPLE ASSESSMENT ITEMS
Discuss: ¢ What specific impact will this type of assessment
system have on classroom instruction?
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¢ What are your first steps as you begin the transition to Common Core Standards?
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THINKING ABOUT TRANSITION
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commoncore.tcoe.org
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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
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RESOURCES ¢ TCOE CCSS Mathematics Bitly
� http://bit.ly/CCSSK-2
¢ TCOE Website � www.tcoe.org/commoncore
¢ TCOE Common Core Website � http://commoncore.tcoe.org
� Christine Roberts – [email protected]
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