2005 connecticut mathematics curriculum framework: building understanding across the grades november...
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2005 Connecticut 2005 Connecticut Mathematics Mathematics Curriculum Curriculum
FrameworkFramework: : Building Understanding Building Understanding
Across the GradesAcross the GradesNovember 9, 2005November 9, 2005
Your Presenters…Your Presenters…Roseanne Hornyak
ConsultantConnecticut Academy for Education
Marlene A. Megos 9 - 12Mathematics Consultant
Connecticut State Department of [email protected]
****Charlene Tate Nichols
PK – 8 Mathematics ConsultantConnecticut State Department of Education
By the end we hope you:By the end we hope you: become familiar with the 2005 become familiar with the 2005
Connecticut Mathematics Connecticut Mathematics Curriculum Framework;Curriculum Framework;
understand how certain concepts understand how certain concepts build across the grades; andbuild across the grades; and
learn how the framework can be learn how the framework can be implemented through effective implemented through effective instruction.instruction.
The The 2005 Connecticut 2005 Connecticut Mathematics Curriculum Mathematics Curriculum
FrameworkFrameworkA two-fold purpose…A two-fold purpose…
To articulate the mathematical To articulate the mathematical understandings that all understandings that all Connecticut students should have.Connecticut students should have.
To influence the way mathematics To influence the way mathematics is taught and assessed.is taught and assessed.
The The 2005 Connecticut 2005 Connecticut Mathematics Curriculum Mathematics Curriculum
FrameworkFrameworkSupporting DocumentsSupporting Documents
1998 Framework1998 Framework NCTM Principles and Standards for NCTM Principles and Standards for
School MathematicsSchool Mathematics CSDE Goals 2000 Curriculum CSDE Goals 2000 Curriculum
The The 2005 Connecticut 2005 Connecticut Mathematics Curriculum Mathematics Curriculum
FrameworkFrameworkSupporting DocumentsSupporting Documents
NAEP StandardsNAEP Standards Third International Mathematics and Third International Mathematics and
Science Study (TIMSS) – Science Study (TIMSS) – Mile wide/Inch DeepMile wide/Inch Deep Implementation of Rich ProblemsImplementation of Rich Problems
Program for International Student Program for International Student Assessment (PISA) Assessment (PISA)
Relevant resources related to contentRelevant resources related to content
What’s New?What’s New?
Grade by grade concept Grade by grade concept developmentdevelopment
Pre-Kindergarten – Grade 12Pre-Kindergarten – Grade 12
Core and extended high school Core and extended high school standardsstandards
1998/2005 Mathematics Frameworks Crosswalk (p. 4) 1998 2005
8: Patterns9: Algebra and Functions
1: Algebraic Reasoning: Patterns and Functions
1: Number Sense2: Operations3: Estimation and Approximation4: Ratio, Proportion and Percent
2: Numerical and Proportional Reasoning
5: Measurement6: Spatial Relationships and Geometry
3: Geometry and Measurement
7: Probability and Statistics10: Discrete Mathematics 4: Working with Data
Organization of FrameworkOrganization of FrameworkConsists of four Consists of four Content StandardsContent Standards with guiding questions: with guiding questions: (p. 5) (p. 5)
1.1. Algebraic Reasoning: Patterns and Functions –Algebraic Reasoning: Patterns and Functions –
Patterns and functional relationships can be represented Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and and analyzed using a variety of strategies, tools and technologies.technologies.
How do patterns and functions help us describe data and physical How do patterns and functions help us describe data and physical phenomena and solve a variety of problems?phenomena and solve a variety of problems?
2.2. Numerical and Proportional Reasoning –Numerical and Proportional Reasoning –
Quantitative relationships can be expressed numerically Quantitative relationships can be expressed numerically in multiple ways in order to make connections and in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools simplify calculations using a variety of strategies, tools and technologies.and technologies.
How are quantitative relationships represented by numbers?How are quantitative relationships represented by numbers?
Organization of FrameworkOrganization of FrameworkConsists of four Consists of four Content StandardsContent Standards with guiding with guiding
questions: questions:
3. Geometry and Measurement –3. Geometry and Measurement – Shapes and structures can be analyzed, visualized, Shapes and structures can be analyzed, visualized, measured and transformed using a variety of measured and transformed using a variety of strategies, tools and technologies.strategies, tools and technologies.
How do geometric relationships and measurements help us to How do geometric relationships and measurements help us to solve problems and make sense of our world?solve problems and make sense of our world?
4. Working with Data: Probability and Statistics 4. Working with Data: Probability and Statistics –– Data can be analyzed to make informed decisions Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies. using a variety of strategies, tools and technologies.
How can collecting, organizing and displaying data help us How can collecting, organizing and displaying data help us analyze information and make reasonable and informed analyze information and make reasonable and informed decisions?decisions?
2005 Mathematics Framework - 2005 Mathematics Framework - MatrixMatrix
Students should… Pre-K Kindergarten Grade 1 Grade 2
1.1 Understand and describe patterns and functional relationships.
a. Sort and classify objects by an attribute.
b. Describe and extend patterns using the attributes of various objects.
a. Sort and classify objects using attributes.
b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence.
a. Examine attributes of objects and describe the relationships.
a. Describe and extend patterns.
b. Analyze change in terms of quantity and quality using patterns.
1.2 Represent and analyze quantitative relationships in a variety of ways.
a. Represent the result of counting, combining and separating sets of objects using number sentences.
a. Represent real-life situations using number sentences.
1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems.
a. Identify quantities as equivalent or non-equivalent.
a. Represent quantities that have the same value with an equal sign.
Framework Companion Framework Companion DocumentDocument
The The Content StandardsContent Standards provide the provide the foundation for all grades Pre-K to 12. foundation for all grades Pre-K to 12.
The The Performance StandardsPerformance Standards are are developmentally sequenced grade level developmentally sequenced grade level expectations.expectations.
TheThe Expected Performances Expected Performances define define
what students should be able to do what students should be able to do
related to the related to the Performance Performance
StandardsStandards & provide a basis & provide a basis
for CMT/CAPTfor CMT/CAPT
KindergartenALGEBRAIC REASONING: PATTERNS AND FUNCTIONS
Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.
How do patterns and functions help us describe data and physical phenomena and solve a variety of problems?
Students should…
Performance Standards Expected Performances
1.1 Understand and describe patterns and functional relationships.
a. Sort and classify objects using attributes.
(1) Sort and classify objects by size, shape, color, texture, use, position and orientation and describe the reason for the action.
b. Identify a pattern and describe the rule using the physical attributes or position of objects in a sequence.
(1) Recognize, copy and extend patterns of sounds, colors, shapes, textures and numbers in a variety of contexts and describe the rule of the pattern.(2) Make comparisons and describe qualitative and quantitative changes of a given pattern (more, less, bigger, smaller, longer, one more, one less).
(p. 10)
Framework Expected Performance Distribution
0
5
10
15
20
25
30
35
40
45
50
Pre
K K 1 2 3 4 5 6 7 8
Co
re
Ext
en
de
dLevel
Nu
mb
er
of
Ex
pe
cte
d
Pe
rfo
rma
nc
es
WORKING withDATA
GEOMETRY andMEASUREMENT
NUMERICALREASONING
ALGEBRAICREASONING
(p. 8)
Framework Coding Framework Coding A complete code for a performance expectation includes 5 characters.
2:1.3a (1) refers to: 2 - Grade 21.3 - Algebraic Reasoning content standard supportive concept 3a - performance standard a(1) – expected performance 1
1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.
a. Represent quantities that have the same value with an equal sign.
(1) Demonstrate understanding of the = sign as an equality symbol.
Coding (p. 7), Actual Standard (p. 12)
Using the 2005 Mathematics Using the 2005 Mathematics FrameworkFramework
Progressive development of essential Progressive development of essential concepts and skillsconcepts and skills
Deep conceptual understanding facilitated Deep conceptual understanding facilitated through emphasis on the through emphasis on the NCTM Process NCTM Process Standards:Standards: Problem solvingProblem solving Reasoning and proofReasoning and proof CommunicationCommunication ConnectionsConnections RepresentationRepresentation. .
Using the Mathematics Framework in Your District…
CSDE CMT/CAPTAssessment of selected concepts and skills in Grades 3-8 and 10.
DISTRICTCurriculum, Instruction and
Assessment Guidelines
STUDENT LEARNING
CSDE FRAMEWORKGuide for mathematics
content and instruction in grades PreK-12.
DISTRICTCurriculum,
Instruction and Assessment Guidelines
STUDENT LEARNING
CSDE FRAMEWORK
CSDE CMT/CAPT
Connecting the Framework to Connecting the Framework to the CMT AND CAPTthe CMT AND CAPT
The Framework outlines:The Framework outlines:
what concepts and skills should be what concepts and skills should be taughttaught
how and to what extent the concepts how and to what extent the concepts and skills should be taught at the and skills should be taught at the grade level indicatedgrade level indicated
Connecting the Framework to Connecting the Framework to the CMT and CAPT the CMT and CAPT
The CMT and CAPT assess selected The CMT and CAPT assess selected skills and concepts at the grade skills and concepts at the grade levels indicatedlevels indicated
The mathematics concepts and skills The mathematics concepts and skills assessed on the CMT and CAPT assessed on the CMT and CAPT reflect what students have learned-reflect what students have learned-not just at the grade levels when the not just at the grade levels when the tests are administeredtests are administered
CMT Changes Generation 4
Testing for each grade, 3-8. Spring testing beginning 2006. There are no separate answer booklets. Students can underline and highlight in booklets. There are no grid-in items for Grades 3 and 4. Grade-appropriate rulers are provided. A formula sheet is provided for Grade 8, other grades
should know formulae and conversions. Number of multiple-choice items decreases while
constructed-response items increases as the grade level increases.
There will be 2 strand 25 questions at each grade level. There will be 2 strand 25 questions at each grade level. Both questions will be on the same session. Care has Both questions will be on the same session. Care has been taken to balance the work required on that been taken to balance the work required on that session.session.
Reporting Format
25 content strands organized by the four standards: numerical and proportional reasoning; geometry and measurement; working with data: probability and statistics;
and algebraic reasoning: patterns and functions.
The CMT scores will continue to be reported by strand.
CMT Handbook (p. 1)
Handbook
Available on the CSDE website, on CD and in limited quantity in hard copy.
Will be periodically updated. Information is organized by grade
level. Vocabulary lists are cumulative. New vocabulary at a grade level is in
bold print.CMT Handbook (p. 1)
Rulers For Use During The Connecticut Mastery Test
CMT Handbook (p. 2)
Rulers for Grades 3 & 4
Ruler for Grades 5, 6, 7 & 8
ConnectinConnecting CMT g CMT
and CAPT and CAPT
Grade 8 Grade 8 Formula Formula SheetSheet
CMT Handbook CMT Handbook (p. 3)(p. 3)
Preparing students for the Connecticut Mastery Test (CMT) should be an ongoing process.
A sound K-8 mathematics program embeds these strategies into all instructional planning.
Strategy 1: Asking “Why?”
Strategy 2: Embed In Context, Present As A Problem
CMT Handbook (p. 10)CMT Handbook (p. 10)
Sample Lessons and Activities by
Standard and Grade Level (p. 15)
NUMERICAL and PROPORTIONAL REASONINGPreK-2 PageLet's Count to 10 17Do It with Dominoes 17How Many More Fish? 17Grades 3-5Estimation 17Fun With Estimation 17Parking at the Mall 17Grades 6-8A Conceptual Model for Solving Percent Problems (5-8)
17Shops at the Mall 17Developing Number Sense 18
Sample Lesson and Activity Descriptions
NUMERICAL AND PROPORTIONAL REASONING
Let's Count to 10 – Grades PreK-2 – http://illuminations.nctm.org/index_o.aspx?id=147
Do It with Dominoes – Grades PreK-2 – http://illuminations.nctm.org/index_o.aspx?id=47
CMT Handbook p. 17
Mathematics
Grade 3 Vocabular
y List
CMT Handbook
(p. 40)This list, while not exhaustive, includes vocabulary with which all teachers and students should be familiar.
Mathematics Grade 3 Content
CMT Handbook (p. 31)
CAPT Mathematics CAPT Mathematics Generation 3Generation 3
Direct alignment between Direct alignment between Framework Expected Performances Framework Expected Performances and CAPT Itemsand CAPT Items
Solving Problems in ContextSolving Problems in Context Reported by the 4 Content Standards Reported by the 4 Content Standards Categorized by the Components of Categorized by the Components of
the Standard { 1.1, 1.2, 1.3, 2.1, 2.2,the Standard { 1.1, 1.2, 1.3, 2.1, 2.2,…}…}
CAPT Mathematics CAPT Mathematics Generation 3Generation 3
Formula Sheet Formula Sheet Handbook out “early” next yearHandbook out “early” next year 12 points per content standard12 points per content standard
2 open ended2 open ended 6 grid ins6 grid ins
Scavenger HuntScavenger Hunt
Work with a Work with a partner with partner with expertise at expertise at a different a different grade level grade level
to “hunt” for to “hunt” for the answers. the answers.
Algebraic Reasoning:Algebraic Reasoning:Patterns and FunctionsPatterns and Functions
Following the Developmental PathFollowing the Developmental Path
JigsawJigsawMove to one grade level table to do the given Move to one grade level table to do the given
activity:activity:
Grade 1 – Grade 1 – Follow the Number RoadsFollow the Number Roads
Grade 3 – Grade 3 – The Ups and Downs of PatternsThe Ups and Downs of Patterns
Grade 5 – Grade 5 – What’s the Best DealWhat’s the Best Deal
Grade 7 – Grade 7 – Bouncing Tennis BallsBouncing Tennis Balls
Grade 9 – Grade 9 – Modeling Orbital Debris, Activity Modeling Orbital Debris, Activity 22
Source: Navigating through Algebra & Illuminations, NCTMSource: Navigating through Algebra & Illuminations, NCTM
Algebraic Reasoning:Algebraic Reasoning:Patterns and FunctionsPatterns and Functions
Decide what students have to Decide what students have to know & do to have success know & do to have success with the given activitywith the given activity
Pick out expected Pick out expected performances In Algebraic performances In Algebraic Reasoning that apply from the Reasoning that apply from the given grade level– chart your given grade level– chart your 3 main EP’s3 main EP’s
Next …
JigsawJigsawMove to mixed groups to:Move to mixed groups to: share your activityshare your activity share your 3 main Expected share your 3 main Expected
Performances; and Performances; and answer the focus question.answer the focus question.
How does the development of How does the development of Algebraic concepts build through Algebraic concepts build through the grades?the grades?
Integrating the StandardsIntegrating the StandardsWork with a team with varied grade level experiences.Work with a team with varied grade level experiences.
Activities:Activities:Grade 1- Find the PictureGrade 1- Find the PictureGrade 7 – Land Use ProjectGrade 7 – Land Use Project
What instruction would one have to do in What instruction would one have to do in order to lead up to these activities?order to lead up to these activities?
What strategies would you use?What strategies would you use?What expected performances are What expected performances are
assessed through the use of the assessed through the use of the performance tasks?performance tasks?
Using the Mathematics Framework in Your District…
What will YOU do?
Moving On From Here…Moving On From Here…
Ideas, Ideas, questions, questions,
comments?comments?
For more information…For more information… CSDE Mathematics Page - CSDE Mathematics Page -
http://www.state.ct.us/sde/dtl/curriculum/chttp://www.state.ct.us/sde/dtl/curriculum/currmath.htmurrmath.htm
Implementing the Standards - Implementing the Standards - http://http://illuminations.nctm.org/index.aspilluminations.nctm.org/index.asp
Project Interactive - Project Interactive - http://http://www.shodor.org/interactivate/index.htmlwww.shodor.org/interactivate/index.html
Performance Assessments – Performance Assessments – http://http://ctcurriculum.orgctcurriculum.org//
Thanks and have a great Thanks and have a great day!day!
Roseanne [email protected]
****Marlene A. Megos
Charlene Tate [email protected]