# 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

 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
 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)
(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

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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
5. Use appropriate tools strategically
Page 11

 Notice the continuum of development.

9

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

10
Standards for Mathematical Practice

Graphic
A

B

C

11
K-8 Standards for Mathematical Content
Turn to

 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
 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

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Examining a critical area further
For each of the critical areas

 more detailed information

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

 Remember the Glossary
Page 16

15

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)

• 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)

• 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)
• 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)
• 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
•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)

• 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

Domain – Number and
Operations in Base Ten

 Generalize place value . . .
 Use place value. . .

Standards listed under
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

 Increased attention to proportionality, probability and

 In depth study of linear algebra and introductions of

 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
prepare students to take courses such as calculus,  Geometry
discrete mathematics, or advanced statistics.       Statistics &
 * Standards indicate connection to Modeling          Probability

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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
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

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

38

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