Common Core State Standards Math Workgroup Training

Includes information from OSPI, ESDs, NCTM, Ohio Department of Education and other sources

MathCommon Core State Standards

Dr. Marci ShepardOrting School District

CCSS Math Workgroup April 2012

Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

Did you miss previous sessions?

http://www.orting.wednet.edu/education/components/layout/default.php?sectionid=374&Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

Office of Superintendent of Public InstructionRandy I. Dorn, State Superintendent

Common Core State Standards The Big Ideas in MATH

CCSS Webinar Series Part 2: Mathematics

4

Focusing on the Foundation…Washington’s Implementation Timeline & Activities

2010-11 2011-12 2012-13 2013-14 2014-15

Phase 1: CCSS Exploration

Phase 2: Build Awareness & Begin Building Statewide Capacity

Phase 3: Build Statewide Capacity and Classroom Transitions

Phase 4: Statewide Application and Assessment

Ongoing: Statewide Coordination and Collaboration to Support Implementation

January 2012

http://www.youtube.com/watch?v=dnjbwJdcPjE&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=5&feature=plcp

Orting School District * Teaching, Learning and Assessment * 2012

CCSS Webinar Series Part 2: Mathematics

6

Content Progressions and Major Shifts

January 2012

Major ShiftsFocus• Fewer big ideas ---

learn more • Learning of concepts

is emphasized

Coherence• Articulated progressions of topics

and performances that are developmental and connected to other progressions

Application• Being able to apply

concepts and skills to new situations

Structural Comparison:WA Standards vs. CCSS Mathematics

WA Mathematics Standards Common Core State Standards

Presentation of Standards

Grade K-8, high school standards presented in traditional and integrated pathways.

Grades K-8, high school standards presented through six mathematical domains including specially noted STEM standards - denoted by (+)

symbols.

Organization Grade-level standards are broken into core content areas, additional key content, and

mathematical processes.

Grade-level standards are broken into clusters of learning under several

domains and all have Standards for Mathematical Practice.

Examples Standards are accompanied by explanatory comments and examples.

Standards have occasional examples in italics.

Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8Transition for Algebra I | Transition for Geometry | Integrated Math I | Integrated Math II

http://www.k12.wa.us/CoreStandards/pubdocs/TransitionKindergarten.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition1st.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition2nd.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition3rd.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition4th.pdf





http://www.k12.wa.us/CoreStandards/pubdocs/TransitionforAlgebraI.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/TransitionforGeometry.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/IntegratedMathI.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/IntegratedMathII.pdf

Reading Literacy StandardsGrades 6-8


What does literacy look like in the mathematics classroom?

• Learning to read mathematical text• Communicating using correct mathematical terminology• Reading, discussing and applying the mathematics found in

literature• Researching mathematics topics or related problems• Reading appropriate text providing explanations for

mathematical concepts, reasoning or procedures• Applying readings as citing for mathematical reasoning• Listening and critiquing peer explanations• Justifying orally and in writing mathematical reasoning• Representing and interpreting data


Organization of the Standards


CCSS Design and Organization


Format of K-8 Standards Grade Level

Domain

Standard

Cluster


Grade Level Introduction

Critical Area of Focus

Cross-cutting themes


Grade Level OverviewGrade 4 OverviewOperations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.Gain familiarity with factors and multiples.Generate and analyze patterns.

Number and Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.Use place value understanding and properties of operations to perform

multi-digit arithmetic.

Number and Operations—FractionsExtend understanding of fraction equivalence and ordering.Build fractions from unit fractions by applying and extending previous

understandings of operations on whole numbers.Understand decimal notation for fractions, and compare decimal

fractions.

Measurement and DataSolve problems involving measurement and conversion of measurements

from a larger unit to a smaller unit.Represent and interpret data.Geometric measurement: understand concepts of angle and measure

angles.

GeometryDraw and identify lines and angles, and classify shapes by properties of

their lines and angles.

Mathematical Practices1. Make sense of problems and

persevere in solving them2. Reason abstractly and

quantitatively3. Construct viable arguments and

critique the reasoning of others4. Model with mathematics5. Use appropriate tools

strategically6. Attend to precision7. Look for and make use of

structure8. Look for and express regularity

in repeated reasoning


CCSS for High School Mathematics

• Organized in “Conceptual Categories”– Number and Quantity– Algebra– Functions– Modeling– Geometry– Statistics and Probability

• Conceptual categories are not courses • Additional mathematics for advanced courses

indicated by (+)• Standards with connections to modeling

indicated by (★)


Format of High School StandardsDomain

Cluster

Standard

Advanced


Format of Standards


Conceptual Category Introduction


Conceptual Category Overview

Domain

Cluster


High School Mathematical Pathways

• Two main pathways:– Traditional: Two algebra courses and a geometry course, with

statistics and probability in each– Integrated: Three courses, each of which includes algebra,

geometry, statistics, and probability

• Both pathways: – Complete the Common Core in the third year– Include the same “critical areas”– Require rethinking high school mathematics– Prepare students for a menu of fourth-year courses

Typical in U.S.

Typical outside

U.S.


Two Main Pathways


Pathway Overview


Course Overview: Critical Areas (units)


Course Detail by Unit (critical area)


QUESTIONS 1-4Understanding the Math Common Core State Standards


Content


GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2 Addition and subtraction, measurement using whole number quantities

3–5 Multiplication and division of whole numbers and fractions

6 Ratios and proportional reasoning; early expressions and equations

7 Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

Critical Areas in Mathematics


Activity 2:K-8 Critical Areas of Focus

HS Critical Areas• Read a K-8 grade level’s Critical

Areas of Focus or HS Critical Area– What are the concepts?– What are the skills and

procedures?– What relationships are students

to make?Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

Concepts, Skills and ProceduresConcepts• Big ideas • Understandings or meanings • Strategies • RelationshipsUnderstanding concepts underlies the development and usage of

skills and procedures and leads to connections and transfer.

Skills and Procedures• Rules• Routines• AlgorithmsSkills and procedures evolve from the understanding and usage of

concepts. Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

Concepts, Skills and ProceduresGrade 4 Number and Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.

• Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

• Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

• Use place value understanding to round multi-digit whole numbers to any place.


Activity 2Critical Areas

• Read the grade level Critical Areas of Focus or HS Critical AreasWhat are the concepts? What are the procedures and skills?What relationships are students to make?

• Look at the domains, clusters and standards for the same grade(s) or High School Course

How do the Critical Areas inform their instruction?


Critical Areas of Focus


Digging into the Standards….Focusing on the Domain

• Read using a highlighter to identify language someone might have difficulty with

• Develop parent friendly language and/or examples for 2nd column of template


QUESTION 5Understanding the Math Common Core State Standards


Progressions


Progressions

• Progressions– Describe a sequence of increasing

sophistication in understanding and skill within an area of study

• Three types of progressions– Learning progressions– Standards progressions– Task progressions


Learning Progression for Single-Digit Addition

From Adding It Up: Helping Children Learn Mathematics, NRC, 2001.


Learning Progressions Document for CCSSM

http://ime.math.arizona.edu/progressions/ • Narratives • Typical learning progression of a topic• Children's cognitive development • The logical structure of mathematics• Math Common Core Writing Team with

Bill McCallum as Creator/Lead Author


http://ime.math.arizona.edu/progressions/

Standards Progressions


CCSS Domain ProgressionK 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base TenRatios and Proportional

Relationships Number & QuantityNumber and Operations –

FractionsThe Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability


Standards Progression: Number and Operations in Base Ten


Use Place Value UnderstandingGrade 1 Grade 2 Grade 3Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 9. Explain why addition and subtraction strategies work, using place value and the properties of operations.

Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

High School Pathways• The CCSSM Model Pathways

– Two models that organize the CCSSM into coherent, rigorous courses

– NOT required. The two sequences are examples, not mandates

• Pathway A: Consists of two algebra courses and a geometry course, with some data, probability and statistics infused throughout each (traditional)

• Pathway B: Typically seen internationally that consists of a sequence of 3 courses each of which treats aspects of algebra, geometry and data, probability, and statistics.


Flows Leading to Algebra


TASK PROGRESSION(later in presentation)


QUESTIONS 6-14Understanding the Math Common Core State Standards


Practices


8 CCSSM Mathematical Practices

– Make sense of problems and persevere in solving them– Reason abstractly and quantitatively– Construct viable arguments and critique the reasoning of

others– Model with mathematics– Use appropriate tools strategically– Attend to precision– Look for and make use of structure– Look for and express regularity in repeated reasoning

Standards for Mathematical Practice


Standards for Mathematical Practices

Graphic




Take a moment to examine the first three words of each of the 8 mathematical practices… what do you notice?

Mathematically Proficient Students…



• Consider the verbs that illustrate the student actions each practice.

• For example, examine Practice #3: Construct viable arguments and critique the reasoning of others.

Highlight the verbs.Discuss with a partner: What jumps out at you?



Mathematical Practice #3: Construct viablearguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.


Mathematical Practice #3: Construct viablearguments and critique the reasoning of others

Mathematically proficient students:• understand and use stated assumptions, definitions, and previously established results inconstructing arguments.• make conjectures and build a logical progression of statements to explore the truth of theirconjectures.• analyze situations by breaking them into cases, and can recognize and use counterexamples.• justify their conclusions, communicate them to others, and respond to the arguments of others.• reason inductively about data, making plausible arguments that take into account the contextfrom which the data arose.• compare the effectiveness of two plausible arguments, distinguish correct logic or reasoningfrom that which is flawed, and-if there is a flaw in an argument-explain what it is.• construct arguments using concrete referents such as objects, drawings, diagrams, and actions.Such arguments can make sense and be correct, even though they are not generalized or madeformal until later grades.• determine domains to which an argument applies.• listen or read the arguments of others, decide whether they make sense, and ask usefulquestions to clarify or improve the arguments.


Mathematical Practice #3: Construct viablearguments and critique the reasoning of othersMathematically proficient students:• understand and use stated assumptions, definitions, and previously established results in

constructing arguments.

• make conjectures and build a logical progression of statements to explore the truth of their

conjectures.

• analyze situations by breaking them into cases, and can recognize and use counterexamples.

• justify their conclusions, communicate them to others, and respond to the arguments of others.

• reason inductively about data, making plausible arguments that take into account the context

from which the data arose.

• compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning

from that which is flawed, and-if there is a flaw in an argument-explain what it is.

• construct arguments using concrete referents such as objects, drawings, diagrams, and actions.

Such arguments can make sense and be correct, even though they are not generalized or made

formal until later grades.

• determine domains to which an argument applies.

• listen or read the arguments of others, decide whether they make sense, and ask useful

questions to clarify or improve the arguments.


Observations

• What do you notice?

• What will students be doing differently?

• What will teachers be doing differently?


The Standards for [Student]Mathematical Practice

On a scale of 1 (low) to 6 (high),to what extent is your school/our district

promoting students’ proficiency in Practice 3?Evidence for your rating?


The Standards for [Student]Mathematical Practice

• SMP1: Explain and make conjectures…• SMP2: Make sense of…• SMP3: Understand and use…• SMP4: Apply and interpret…• SMP5: Consider and detect…• SMP6: Communicate precisely to others…• SMP7: Discern and recognize…• SMP8: Notice and pay attention to…



…describe the thinking processes, habits of mind and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end

SP1. Make sense of problems“….they [students] analyze givens, constraints, relationships and goals. ….they monitor and evaluatetheir progress and change course if necessary. …. andthey continually ask themselves “Does this make sense?”



AND…. describe mathematical content students need to learn

SP1. Make sense of problems“……. students can explain correspondences betweenequations, verbal descriptions, tables, and graphs ordraw diagrams of important features andrelationships, graph data, and search for regularity ortrends.”


Buttons TaskGita plays with her grandmother’s collection of black & white buttons.

She arranges them in patterns. Her first 3 patterns are shown below.

Pattern #1 Pattern #2 Pattern #3 Pattern #4

1. Draw pattern 4 next to pattern 3.

2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out.

3. How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out.

4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct? How many buttons does she need to make Pattern 24?Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

Buttons Task1. Individually complete parts 1 - 3.2. Then work with a partner to compare yourwork and complete part 4. (Look for as manyways to solve parts 3 and 4 as possible.)


Buttons TaskGita plays with her grandmother’s collection of black & white buttons.

She arranges them in patterns. Her first 3 patterns are shown below.

Pattern #1 Pattern #2 Pattern #3 Pattern #4

1. Draw pattern 4 next to pattern 3.

2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out.

3. How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out.

4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct?

How many buttons does she need to make Pattern 24?

15 buttons and 18 buttons

34 buttons

73 buttons


Buttons Task


Buttons TaskWhich mathematical practices are needed completethe task?Indicate the primary 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.


Standards for [Student] Mathematical Practice

“Not all tasks are created equal, and different

tasks will provoke different levels and kinds

of student thinking.”Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in which

students engage determines what they

will learn.”Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997


The Nature of Tasks Used in theClassroom …

…Will Impact Student Learning!


But, WHAT TEACHERS DOwith the tasks matters too!

The Mathematical Tasks Framework

Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)


http://www.insidemathematics.org/index.php/classroom-videovisits/public-lessons-numerical-patterning/218-numerical-patterninglesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-LXtX3WJ4e8


Learner A


Learner B


Buttons Task Revisited

What might a teacher get out of using the same math task two days in a row, rather than switching to a different task(s)?

– Address common misconceptions– Support students in moving from less to more sophisticated solutions


Buttons Task RevisitedWhich of the Standards of Mathematical Practice did the students engage in when they revisited the task?

Indicate the primary 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.Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

But, WHAT TEACHERS DOwith the tasks matters too!

The Mathematical Tasks Framework

Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)


The 8 Standards for Mathematical Practice –place an emphasis on student demonstrationsof learning…

Equity begins with an understanding of howthe selection of tasks, the assessment of tasks,the student learning environment creates great

inequity in our schools…



To what extent do all students in yourclass, school or our district have theopportunity to engage in tasks that

promote attainment of the mathematicalpractices on a regular basis?

Please rate on a scale of1 (low) to 6 (high).




Content and Practices


Cognitive Complexity


Depth of Knowledge Levels


Sorting Activity

• Categorize tasks into level 1, 2, 3, or 4 using Cognitive Complexity Levels. Record your responses on the provided worksheet.

• Share results and come to consensus at your table. One person will record results on the “master” copy.

• Share results and review criteria groups used for low and high levels.


Sorting questions to ponder…

• How did you determine between levels 2 & 3?• Does a task presented as a word problem

always have a high level of cognitive complexity?

• If a task requires an explanation, does it have a high level of cognitive complexity?


Changing the Cognitive Complexity Level

• Pick out a task that was placed in level 1 or 2. Determine how you would modify your task to be a level 3 task.

• Share task out with whole group.


Cognitive Complexity and Mathematical Practices

Which levels of cognitive complexity allow students to develop the mathematical practices?


Task Progression

• A rich mathematical task can be reframed or resized to serve different mathematical goals


Are there various levels of Cognitive Complexity in your instructional materials?

• Review several types of problems/tasks found in your instructional materials.

• What level of cognitive complexity are these tasks?– Level 1 (recall)– Level 2 (skill/concept)– Level 3 (strategic thinking)– Level 4 (extended thinking)


Are there various levels of Cognitive Complexity in your instructional materials?

Share the types of problems/tasks you found.• What are the prevalent levels of complexity in

your instructional materials?• How will this impact meeting the standards for

mathematical practice?


Gas Mileage Problem

• With scaffolding• Without scaffolding


Who’s Doing the Work?

TEDtalk: Dan Meyer Video

http://www.youtube.com/watch?v=BlvKWEvKSi8Dr. Marci Shepard Orting School District Teaching, Learning & Assessment 2012

http://www.youtube.com/watch?v=BlvKWEvKSi8

Video Debrief

• How much is too much support; how much is too little?

• How does scaffolding interfere/promote standards for mathematical practice?

• Compare/contrast Gas Mileage activities


Appendix A

Questions 15-22Understanding the Math Common Core State Standards


Tables

Understanding the Math Common Core State Standards

Question 23


Transition Plans


Three-Year Transition Plan for Common Core State Standards for Mathematics by Grade Level



State Resources for Transition

Grade-level transition documents describe:

– What standards to continue– What standards to remove– What standards to move to


OSD RESOURCESMATH COMMON CORE STATE STANDARDS


OSD Teaching, Learning and Assessment Website: Common Core State Standards: http://www.orting.wednet.edu/education/components/scrapbook/default.php?sectiondetailid=3910&

Common Core State Standards for Math: http://www.k12.wa.us/CoreStandards/Mathematics/pubdocs/CCSSI_MathStandards.pdf Designing High School Mathematics Courses (Appendix A): http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

Illustrative Math: http://illustrativemathematics.org/


http://www.orting.wednet.edu/education/components/scrapbook/default.php?sectiondetailid=3910&

http://www.k12.wa.us/CoreStandards/Mathematics/pubdocs/CCSSI_MathStandards.pdf

http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://illustrativemathematics.org/

Mathematical Practices by Grade Level: http://www.azed.gov/standards-practices/files/2011/10/2010mathglossary.pdf

3-Year Transition Plan: http://www.k12.wa.us/CoreStandards/pubdocs/Three-YearDomainImplementation.pdf


http://www.azed.gov/standards-practices/files/2011/10/2010mathglossary.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Three-YearDomainImplementation.pdf

Transition Plans by Grade Level:Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Grade 7 | Grade 8Transition for Algebra I | Transition for Geometry | Integrated Math I | Integrated Math II

Progressions Documents: http://ime.math.arizona.edu/progressions/

Videos on CCSS-M: http://www.youtube.com/playlist?list=PLD7F4C7DE7CB3D2E6&feature=plcp


http://www.k12.wa.us/CoreStandards/pubdocs/TransitionKindergarten.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition1st.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition2nd.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/Transition3rd.pdf






http://www.k12.wa.us/CoreStandards/pubdocs/TransitionforAlgebraI.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/TransitionforGeometry.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/IntegratedMathI.pdf

http://www.k12.wa.us/CoreStandards/pubdocs/IntegratedMathII.pdf

http://ime.math.arizona.edu/progressions/

http://www.youtube.com/playlist?list=PLD7F4C7DE7CB3D2E6&feature=plcp

It is time to recognize that standards are not just promises to our children, but promises we intend to keep.”1 Students need to meet the standards, and in order to do that, what they must learn is not standards but mathematics.2

1 CCSS, 2010, p. 5 2 PARCC – Draft Content Framework - 2011
