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Overview of Alaska’s Proposed Mathematics Standards.pptx

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					     Overview of Alaska’s Proposed
           Mathematics Standards
Alaska Department of Education & Early Development
Topics for the Webinar

 Encourage Changes to Practice

 Understand Alaska’s Mathematics Standards Organization

 Knowledge of the Standards for Mathematical Practice

 Examine the Standards for Mathematical Content

                                 Standards can be downloaded from
 Next Steps                  http://www.eed.state.ak.us/standfaqs.html



 2
Encourage Changes to Practice

 The proposed mathematics standards support
  improved curriculum and instruction due to increased:

      FOCUS, via critical areas at each grade level

      COHERENCE, through carefully developed
       progression of topics within and across grades

      RIGOR, including a focus on College and Career Readiness
       and Standards for Mathematical Practice throughout K-12



 3
Mathematics Standards Organization
 Introduction/Description

 Standards for Mathematical Practice
      Taught in all grade levels


 Standards for Mathematical Content
      Grade Level K-8 Standards organized in grade spans
      High school standards are in domains


 Glossary for the Alaska Mathematics Standards


 4
Standards for Mathematical Practice

Both a goal and a vehicle -

The goal is to move students along a continuum –
 always deepening their use of the mathematical practices.

They are a vehicle for learning the content standards.




 5
Background Information
                    The National Research
                   National Council of
                    Council’s Report
                    Teachers of Mathematics
                    Principal and (2001)
                    Adding It Up Standards
                    (2000)

                       Problem Solving
                       Reasoning and Proof
                       Connections
                       Communication
                       Representation



6
Standards for Mathematical Practice

    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
                                                         Turn to
                                                         Page 4

7
Mathematical Practice Descriptions
                                                          Turn to
                                                          Page 11




 Read the paragraph description for Practice #5.

 Notice the verbs used to describe actions students will take.


 8
Grade-Span Proficiency Descriptors
5. Use appropriate tools strategically
                                                          Page 11




 Read the proficiency descriptors for TWO grade spans.
 Notice the continuum of development.

 9
Mathematical Practice Task

     In October, John’s PFD check for $1100
     arrives. His parents give him 2 choices so the
     rest can be saved for post-secondary options.

        •   Choice 1: Spend 1/5 of the PFD
        •   Choice 2: Spent 15% of the PFD

     Which would give him the most spending
     money? Justify your answer


10
Standards for Mathematical Practice

Graphic
                               A




                               B




                                   C




11
K-8 Standards for Mathematical Content
                                                         Turn to
  Grade Span                                            Page 15

      Instructional   Domains
       Focus            Counting, Cardinality and Ordinality
      Standards for    Operations and Algebraic Thinking
       Mathematical     Number and Operations in Base Ten
       Content          Measurement and Data
                        Number and Operations – Fractions
  Grade Level          Geometry
                        Ratios and Proportional Relationships
    Domains            The Number System
      Clusters         Expressions and Equations
                        Functions
       Standards       Statistics and Probability


12
Focus – Critical Areas
                                                         Turn to
                                                         Page 16




      For each grade level, there are typically two
       to four critical areas for instructional focus.

      Let’s look at Kindergarten Instructional Focus

13
Kindergarten Instructional Focus

     Instructional time should focus on two critical areas:


       (1) representing, relating, and operating on
         whole numbers, initially with sets of objects;

       (2) describing shapes and space.


       More learning time in Kindergarten should be
       devoted to number than to other topics.
                                                              Page 16


14
Examining a critical area further
               For each of the critical areas
                 for K-8 grade levels:

                more detailed information

                Kindergarten students should
                 see addition and subtraction
                 equations and writing is
                 encouraged but not required.

                Remember the Glossary
                                                Page 16



15
Critical Areas by Grade Levels

     Grade

             Addition and subtraction,
     K–2
             measurement using whole number quantities
             Multiplication and division of whole numbers
     3–5
             and fractions
             Ratios and proportional reasoning;
      6
             early expressions and equations
             Ratios and proportional reasoning;
      7
             arithmetic of rational numbers
      8      Linear algebra

16
Coherence - Domains
                                    Mathematics - Domain Progression Overview by Grade
     K                1             2         3              4               5        6                7           8          HS
Counting, Cardinality and
Ordinality
                                                                                 Ratios and Proportional                  Number &
                                                                                 Relationships                            Quantity
Number and Operations in Base Ten

                                         Number and Operations - Fractions       Number System

                                                                                 Expressions and Equations                Algebra
Operations and Algebraic Thinking                                                                             Functions   Functions

Geometry                                                                                                                  Geometry
                                                                                                                          Statistics
                                                                                                                          and
Measurement and Data                                                             Statistics and Probability
                                                                                                                          Probability




  Domains – large groups of related standards.
  They may begin and end in different grades.

17
Coherence - Clusters




 Clusters – groups of closely related standards
  inside domains, subsets of domains.
 Let’s look at the grades 3-5 clusters.        Turn to
                                                  Page 30



18
Operations and Algebraic Thinking (3-5)

 Grade 3                        Grade 4                     Grade 5
 • Represent and solve          • Use the four operations   • Write and interpret
 problems involving             with whole numbers to       numerical expressions.
 multiplication and division.   solve problems.
 • Understand properties of                                 • Analyze patterns and
 multiplication and the         • Gain familiarity with     relationships.
 relationship between           factors and multiples.
 multiplication and division.
 • Multiply and divide within   • Generate and analyze
 100.                           patterns.
 • Solve problems involving
 the four operations, and
 identify and explain
 patterns in arithmetic.

                                                                       Pages 30-31

19
Number and Operations in Base Ten (3-5)

 Grade 3                    Grade 4                    Grade 5
 • Use place value          • Generalize place value   • Understand the place
 understanding and          understanding for multi-   value system.
 properties of operations   digit whole numbers.
 to perform multi-digit                                • Perform operations with
 arithmetic.                • Use place value          multi-digit whole numbers
                            understanding and          and with decimals to
                            properties of operations   hundredths.
                            to perform multi-digit
                            arithmetic.




                                                                     Pages 33-34

20
Number and Operations—Fractions (3-5)
 Grade 3                    Grade 4                       Grade 5
 • Develop understanding    • Extend understanding of     • Use equivalent fractions
 of fractions as numbers.   fraction equivalence and      as a strategy to add and
                            ordering.                     subtract fractions.

                            • Build fractions from unit   • Apply and extend
                            fractions by applying and     previous understandings
                            extending previous            of multiplication and
                            understandings of             division to multiply and
                            operations on whole           divide fractions.
                            numbers.

                            • Understand decimal
                            notation for fractions, and
                            compare decimal fractions.

                                                                        Pages 35-37

21
Measurement and Data (3-5)
 Grade 3                              Grade 4                    Grade 5
 • Solve problems involving           • Solve problems           • Convert like
 measurement and estimation of        involving measurement      measurement units
 intervals of time, liquid volumes,   and conversion of          within a given
 and masses of objects.               measurements from a        measurement system.
 • Represent and interpret data.      larger unit to a smaller   • Represent and
 • Geometric measurement:             unit.                      interpret data.
      •understand concepts of         • Represent and            • Geometric
      area and relate area to         interpret data.            measurement:
      multiplication and to           • Geometric                understand concepts of
      addition.                       measurement:               volume and relate
      •recognize perimeter as         understand concepts of     volume to multiplication
      an attribute of plane           angle and measure          and to addition.
      figures and distinguish         angles.
      between linear and area
      measures.
                                                                             Pages 39-43

22
Geometry (3-5)

 Grade 3                    Grade 4                     Grade 5
 • Reason with shapes and   • Draw and identify lines   • Graph points on the
 their attributes.          and angles, and classify    coordinate plane to solve
                            shapes by properties of     real-world and
                            their lines and angles.     mathematical problems.

                                                        • Classify two-dimensional
                                                        figures into categories
                                                        based on their properties.




                                                                       Pages 43-44

23
Examining a cluster
                 Grade 4 Standards

                 Domain – Number and
                  Operations in Base Ten

                  Cluster Headings –
                   Generalize place value . . .
                   Use place value. . .

                      Standards listed under
                      cluster heading are even
                      more closely related.
                                                   Page 33



24
    Mathematics K-8 Standards Guide
K-8 Math Domains:
•   Counting, Cardinality, and Ordinality – CC
•   Operations and Algebraic Thinking – OA
•   Number and Operations in Base Ten – NBT
•   Measurement and Data - MD
•   Number and Operations—Fractions - NF
•   Geometry - G
•   Ratios and Proportional Relationships – RP
•   The Number System - NS
•   Expressions and Equations - EE
•   Functions - F
•   Statistics and Probability - SP




                          Page 48


       25
Closer Look at Standards (6-8)
                                 Domain

Example




                                  Clusters


Subparts




           Page 54



  26
A Strong Foundation for Algebra

     Through the K-8 Standards Progression

      Focus on number, operations, and fractions in early
       grades

      Increased attention to proportionality, probability and
       statistics in middle grades

      In depth study of linear algebra and introductions of
       functions in Grade 8

      Provide good preparation for high school mathematics

27
High School Standards for Math Content
                                                                  Turn to
                                                                  Page 66
 Organized in six Domains
   Crosses course boundaries                          Domains
   Span high school years 9-12                         Number &
   Highlights key points in the narratives              Quantity
                                                        Algebra
 Standards                                             Functions
   Majority are core for all students                  Modeling
   + Additional standards for advanced courses to
    prepare students to take courses such as calculus,  Geometry
    discrete mathematics, or advanced statistics.       Statistics &
   * Standards indicate connection to Modeling          Probability
      threaded throughout the other domains.


 28
Focus - Modeling




      Narrative is provided for each domain
      Highlights key points of focus          Turn to
                                               Page 84



29
9-12 Domains and Subdomains
     Number and           Algebra                Functions
     Quantity
     The Real Number      Seeing Structure in    Interpreting Functions
     System               Expressions
                                                 Building Functions
     Quantities           Arithmetic with         
                          Polynomials and        Linear, Quadratic, and
     The Complex Number   Rational Expressions   Exponential Models*
     System                                       
                          Creating Equations*    Trigonometric Functions
     Vector and Matrix
     Quantities           Reasoning with
                          Equations and
                          Inequalities

           Pages 67-71           Pages 72-77           Pages 78-83

30
9-12 Domains and Subdomains
Geometry                               Statistics and Probability*
Congruence                             Interpreting Categorical and
                                       Quantitative Data




                                                                          tin the other five domains
                                                                           Modeling (*) – integrated
Similarity, Right Triangles, and        
Trigonometry                           Making Inferences and Justifying
                                       Conclusions
Circles                                 
                                       Conditional Probability and the
Expressing Geometric Properties with   Rules of Probability
Equations                               
                                       Using Probability to Make
Geometric Measurement and              Decisions
Dimension
 
Modeling with Geometry
              Pages 86-92                         Pages 93-97

31
    Mathematics 9-12 Standards Guide
9-12 Math Domains:
•   Number and Quantity - N
•   Algebra - A
•   Functions - F
•   Modeling - M
•   Geometry - G
•   Statistics and Probability - P




     32
Closer Look at Standards (9-12)
                                  Domain - Geometry    Turn to
                                                       Page 92




                                                      Subdomains




                                                         Clusters




                      Standards

     (+) Additional      Core          Modeling (*)

33
Rigor and Relevance – Modeling

      Links classroom mathematics and statistics to
       everyday life, work and decision-making.

      In Grades K-8, modeling skills are developed as
       one of the Standards for Mathematical Practice.

      Modeling is both a High School Domain
       and a Standards for Mathematical Practice
        Domains, Strands, Clusters or Individual Standards
         have been identified by *


34
Encourage Changes to Practice

 The proposed mathematics standards support
  improved curriculum and instruction due to increased:

   FOCUS, via critical areas at each grade level

   COHERENCE, through carefully developed progression of
    topics (domains, strands and clusters) within and across grades

   RIGOR, including a focus on College and Career Readiness
    and Standards for Mathematical Practice throughout K-12



 35
Timeline



     January – May 12, 2012    Public comment period

     February– April 2012      Webinars and presentations about the new
                               standards scheduled

     June 2012                 New standards potentially adopted

     Fall 2012 – Spring 2015   Transition from GLEs to new standards

     Spring 2016               New assessments potentially administered




36
Support for Districts
 EED Website provides information and updated weekly
  http://www.eed.state.ak.us/tls/assessment/GLEHome.html
 Frequently asked questions have been created for
  distribution http://www.eed.state.ak.us/standfaqs.html
 Webinars have been scheduled for an in-depth review of
  the proposed standards (dates are posted on the
  website)
 Publications for parents, teachers, and the community will
  be available.
 Curriculum and Alignment Institute will support districts
  with the transition of curriculum.
 37
Thank You

 Your time is much appreciated!

 Public comment can be made at
   http://eed.state.ak.us/regs


 Questions about the math standards
   Cecilia Miller, Math Content Specialist
   cecilia.miller@alaska.gov



 38

				
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