Walter Lewiswlewis@icoe.org760.312.6176

Welcome /Outcomes /Agenda Overview-What is the direction of Math

Education? Math CCSS

Standards for Mathematical Practice Content Standards

Assessment/Consideration/Reflection

Max bought 2 items in a sale.

One item was 10% off.One item was 20% off.

Max says he saved 15% altogether. Is he right?

Explain.

Max bought 2 items in a sale.

One item was 10% off.One item was 20% off.

Max says he saved 15% altogether. Is he right?

Explain.

Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide.

Will one toilet roll be enough to wrap a person?

Describe your reasoning as fully as possible.(You will need to estimate the average size of an adult person)

Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide.

Will one toilet roll be enough to wrap a person?

Describe your reasoning as fully as possible.

(You will need to estimate the average size of an adult person)

The Perils and Promises of Discovery Learning

Quality instruction

Checking for Understanding

California Common Core State Standards

TECHNOLOGy

Quality MjResearch Mj

Based MjInstruction Mj

Access Prior MjKnowledge Mj

Skill MjDevelopment Mj

Concept MjDevelopment Mj

Standards MjBased Mj

Learning MjObjective Mj

Guided MjInstruction Mj

Application, MjInnovation, Mj

and MjExtension Mj

Guided MjPractice Mj

Project MjBased Mj

Learning Mj

Skill Practice Mj

Homework Mj

21 st

CENTURY

LEARNINGg

What I already know about the Common Core State Standards.

What I would like to learn about the Common Core State Standards.

What I learned today about the Common Core State Standards.

Common Core State Standards

Ensure that our students are… meeting college and career expectations with

text complexity increased K-12; provided a vision of what it means to be an

academically literate person in the twenty-first century;

prepared to succeed in our global economy and society; and

provided with rigorous content and applications of higher knowledge through higher order thinking skills.

Internationally benchmarked Evidence and research-based Expectations clear to students, parents, teachers, and the general public

Costs to the state reduced Consistent expectations for all—not dependent on a zip code

Math

Standards for Mathematical

Practice

ELA

College and Career

Readiness Standards

Standards for Mathematical Practice AND Content Standards

Professor Jason PhilWilliam Zimba DaroMcCallum Ph.D.

National Council of Teachers of Mathematics

5 Process Standards• Problem Solving• Reasoning and Proof• Communication• Connections• Representations NCTM (2000). Principles and

Standards for School Mathematics. Reston, VA: Author.

1. Make sense of problems and persevere in solving them…start by explaining the meaning of a problem and looking for entry points to its solution

2. Reason abstractly and quantitatively…make sense of quantities and their relationships to problem situations

3. Construct viable arguments and critique the reasoning of others…understand and use stated assumptions, definitions, and previously established results in constructing arguments

4. Model with mathematics…can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace

5. Use appropriate tools strategically…consider the available tools when solving a mathematical problem

6. Attend to precision…communicate precisely using clear definitions and calculate accurately and efficiently

7. Look for and make use of structure…look closely to discern a pattern or structure

8. Look for and express regularity in repeated reasoning…notice if calculations are repeated, and look for both general methods and for shortcuts

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.

4. Model with mathematics.5. Use appropriate tools strategically.

7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

Common Core State StandardsMathematical Practices

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

Mathematically Proficient Students… Briars, Diane. “Getting Started with the Common Core State Standards.”

Power Point Presentation. NCSM Winter Conference, 2011.

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…Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

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

that describe the thinking processes, habits of mind, and dispositions that students need to develop.that describe mathematical content students need to learn.

Adapted from Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

K 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base TenRatios and Proportional

RelationshipsNumber & Quantity

Number and Operations – Fractions

The Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability

Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

Domain K 1 2 3 4 5

Counting and Cardinality (CC)

Operations and Algebraic Thinking (OA)

Number and Operations in Base Ten (NBT)

Measurement and Data (MD)

Geometry (G) Number and Operations – Fractions (NF)

Domain 6 7 8

Ratios and Proportional Relationships (RP)

The Number System (NS)

Expressions and Equations (EE)

Geometry (G)

Statistics and Probability (SP)

Functions (F)

Concept1997

Standards CCSS

Dividing fractions by fractionsGrade

5

Grade

6

Concepts of mean and median to

summarize data sets Grade

5

Grade

6

Operations with numbers in scientific notation

Grade

7

Grade

8

Pythagorean TheoremGrade

7

Grade

8

The Goal for 8th grade students is Algebra 1.

However, there are two sets of standards for grade 8Standards for Algebra 1-Taken from 8th

grade Common Core, high school Algebra content cluster and CA Algebra standards

8th grade Common Core-Finalize preparation for students in high school.

The CCSS high school standards are organized in 6 conceptual categories: Number and Quantity Algebra Functions Modeling (*) Geometry Statistics and Probability

California additions: Advanced Placement Probability and Statistics Calculus

Modeling standards are indicated by a (*) symbol.Standards necessary to prepare for advanced courses in mathematics are indicated by a (+) symbol.

Two Regular Sequences:

Traditional Pathway2 Algebra courses,1 Geometry course, with Probability and Statistics interwoven

Integrated Pathway3 courses that attend to Algebra, Geometry, and Probability and Statistics each year

Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career technical programs of study.

Algebra II

Geometry

High School Algebra I

Mathematics III

Mathematics I

Mathematics II

Traditional Pathway Typical in U.S.

Integrated PathwayTypical outside of U.S.

Two Mathematics Pathways

Accelerated PathwayTwo additional pathways (one traditional and one integrated) that compact the curriculum and require a faster pace

The traditional compacted pathway has students completing the content of 7th grade, 8th grade, and High School Algebra I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I), enabling students to finish Algebra II by the end of the sophomore year.The integrated compacted pathway has students completing the content of 7th grade, 8th grade, and Mathematics I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Mathematics I), enabling them to complete Math III by the end of the sophomore year.Both prepare students for Precalculus in their junior year and Calculus in their senior year

Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011

How to Read the Standards

Geometry Conceptual Category Example

Assessments will begin in 2014California has recently signed on with

SMARTER Balanced Assessment ConsortiumAssessments will include:

Computer Adaptive Assessments (interim & summative)Performance Assessments (interim & summative)

Selected ResponseConstructed ResponseBoth Two-hour and Extended Performance Assessments

3 Assessments Each Year Reading Writing, Listening and Speaking, Language Math

Optional Interim Assessments in ELA and Math

Computer-adaptive 2 ELA and 2 Math “performance

events” for Grades 3-8 Up to six math and ELA “events” for

Grade 11 Grades 9 & 10 Optional Combination of computer and human

scoring

Computer-adaptive To be implemented based on state and

district policy Teacher-administered “performance-events” Combination of human and computer scoring

within 2 weeks Items will be non-secure for teacher and

principal analysis

Writing Prompts Constructed Responses Technology-Enhanced Items Standardized Performance Events Single Session; administered within 12

weeks of end of the school year

 

The K‐5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals‐‐which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.

In kindergarten, the standards follow successful international models and recommendations from the National Research Council’s Early Math Panel report, by focusing kindergarten work on the number core: learning how numbers correspond to quantities, and learning how to put numbers together and take them apart (the beginnings of addition and subtraction).

The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels ‐ rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year.

Having built a strong foundation K‐5, students can do hands on learning in geometry, algebra and probability and statistics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be well‐ prepared for algebra in grade 8.

The K‐5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.

The middle school standards are robust and provide a coherent and rich preparation for high school mathematics.

The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically.

The high school standards set a rigorous definition of college and career readiness, by helping students develop a depth of understanding and ability to apply mathematics to novel situations, as college students and employees regularly do.

The high school standards emphasize mathematical modeling, the use of mathematics and statistics to analyze empirical situations, understand them better, and improve decisions. For example, the draft standards state: “Modeling links classroom mathematics and statistics to everyday life, work, and decision‐making. It is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data

COMMON CORE RESOURCES

California Department of Education ResourcesHunt Institute CCSS Video LibrarySMARTER BALANCED ASSESSMENT CONSORTIUMICOE Math BoE Pagewlewis@icoe.org