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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