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State Standards,National StandardsState Standards,National Standards

ICTM 2009

Jill Gardner – jgardner@jbgmath.comPJ Karafiol – pjkarafiol@gmail.com

Claran Einfeldt – claran@cmath2.com

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AGENDAAGENDAClaran – Welcome and OverviewPJ – Illinois Process and Draft DocumentJill – National Process and Draft DocumentJIGSAW ACTIVITY – State and National Comparison

• How are they alike/different?• What are your concerns about each?• What would you change in which document?

Claran – Groups Report Out

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The Road to Illinois’ New StandardsThe Road to Illinois’ New Standards

Fall 2008: Project Achieve! & ISBE team up to draft new standards.

January 2009: 34-member team selected, representing high schools, community colleges, 4-year colleges, universities

February-June 2009: Panel meets, drafts revised standards for review and comment.

May 2009: Illinois joins 43 other states in agreeing to create “common core” standards with Project Achieve!

Summer-Fall 2009: Draft IL standards circulated, presented at meetings

Fall 2009: Draft Common Core standards circulated, presented at meetings

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Standards Revision ProcessStandards Revision Process

Project Achieve: 44 ADP standards for HS graduates

Illinois: 100s of descriptors for grades 7-9 and 10-12

Side-by-side views assembled by Project Achieve compared each ADP standard with relevant IL descriptors

IL Panel used side-by-sides to decide on relevant categories and language

Drafts revised by subcommittee, Project Achieve, and then circulated for comment over the summer

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“Common Core” Agreement“Common Core” Agreement

Common core will form at least 85% of each state’s standards.

States are free to adopt additional standards (up to 15%).

IL’s draft standards can form the basis for our supplement to the common core.

6

Common Core State StandardsCommon Core State Standards

The K-12 standards work is expected to be completed in December 2009.

The two groups( Work group and Feedback group) also unveiled a new Web site at www.corestandards.org.

Forty-nine states and territories have joined the Common Core State Standards Initiative.

15 on the Work Group

7

Feedback GroupFeedback Group

Final decisions regarding the common core standards document will be made by the Standards Development Work Group. The Feedback Group will play an advisory role, not a decision-making role in the process.

19 people in the Feedback Group

8

The StandardsThe Standards

Mathematical Practice Number Quantity Expressions Equations Functions Modeling Shape Coordinates Probability Statistics

9

Mathematical PracticeMathematical Practice

Attend to precision.Construct viable arguments.Make sense of complex problems and persevere in solving them.Look for and make use of structure.Look for and express regularity in repeated reasoning.Make strategic decisions about the use of technological tools.

10

Number: Core ConceptsNumber: Core Concepts

Students understand that: The real numbers include the rational numbers and are in one-to-one correspondence with the points on the number line.Quantities can be compared using division, yielding rates and ratios.

A fraction can represent the result of dividing the numerator by the denominator; equivalent fractions have the same value.

Place value and the rules of arithmetic form the foundation for efficient algorithms.

11

Core Skills for NumberCore Skills for Number

Compare numbers and make sense of their magnitude.

Know when and how to use standard algorithms, and perform them flexibly, accurately and efficiently.

Use mental strategies and technology to formulate, represent and solve problems.

Solve multi-step problems involving fractions and percentages.

Use estimation and approximation to solve problems.

12

Quantity: Core ConceptQuantity: Core Concept

Students understand that: The value of a quantity is not specified unless the units are named or understood from the context.

Quantities can be added and subtracted only when they are of the same type (length, area, speed, etc.).

Quantities can be multiplied or divided to create new types of quantities, called derived quantities.

13

Expressions: Core ConceptsExpressions: Core Concepts

Expressions are constructions built up from numbers, variables, and operations, which have a numerical value when each variable is replaced with a number.

Complex expressions are made up of simpler expressions.

The rules of arithmetic can be applied to transform an expression without changing its value.

Rewriting expressions in equivalent forms serves a purpose in solving problems.

14

Equations: Core ConceptsEquations: Core Concepts

An equation is a statement that two expressions are equal.

The solutions of an equation are the values of the variables that make the resulting numerical statement true.

The steps in solving an equation are guided by understanding and justified by logical reasoning.

Equations not solvable in one number system may have solutions in a larger number system.

15

Functions: Core ConceptsFunctions: Core Concepts

A function is a rule, often defined by an expression, that assigns a unique output for every input.

The graph of a function f is a set of ordered pairs (x, f(x)) in the coordinate plane.

Functions model situations where one quantity determines another.

Common functions occur in families where each member describes a similar type of dependence.

16

Modeling: Core ConceptsModeling: Core Concepts

Mathematical models involve choices and assumptions that abstract key features from situations to help us solve problems.

Even very simple models can be useful.

17

Shape: Core ConceptsShape: Core Concepts

Shapes and their parts, attributes, and measurements can be analyzed deductively.

Congruence, similarity, and symmetry can be analyzed using transformations.

Mathematical shapes model the physical world, resulting in practical applications of geometry.

Right triangles and the Pythagorean theorem are central to geometry and its applications, including trigonometry

18

Coordinates: Core ConceptsCoordinates: Core Concepts

Locations in the plane or in space can be specified by pairs or triples of numbers called coordinates.

Coordinates link algebra with geometry and allow methods in one domain to solve problems in the other.

The set of solutions to an equation in two variables forms a curve in the coordinate plane—such as a line, parabola, circle—and the solutions to systems of equations correspond to intersections of these curves.

19

Probability: Core ConceptsProbability: Core Concepts

Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of uncertainty in terms of relative frequency of occurrence.

The law of large numbers provides the basis for estimating certain probabilities by use of empirical relative frequencies.

The laws of probability govern the calculation of probabilities of combined events.

Interpreting probabilities contextually is essential to rational decision-making in situations involving randomness

20

Statistics: Core ConceptsStatistics: Core Concepts

Statistical methods take variability into account to support making informed decisions based on quantitative studies designed to answer specific questions.

Visual displays and summary statistics condense the information in data sets into usable knowledge.

Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic.

The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions.

21

Validation CommitteeValidation Committee

National and international experts will be appointed to the committee.

They will review the process and substance of the common core state standards to ensure they are research and evidence-based and will validate state adoption on the common core standards.

Members of the committee will be selected by governors and chiefs of the participating states.

22

Common Core State StandardsCommon Core State Standards

The K-12 standards work is expected to be completed in December 2009.

The two groups( Work group and Feedback group) also unveiled a new Web site at www.corestandards.org.

Forty-nine states and territories have joined the Common Core State Standards Initiative.

15 on the Work Group

23

Feedback GroupFeedback Group

Final decisions regarding the common core standards document will be made by the Standards Development Work Group. The Feedback Group will play an advisory role, not a decision-making role in the process.

19 people in the Feedback Group

24

The StandardsThe Standards

Mathematical Practice Number Quantity Expressions Equations Functions Modeling Shape Coordinates Probability Statistics

25

Mathematical PracticeMathematical Practice

Attend to precision.Construct viable arguments.Make sense of complex problems and persevere in solving them.Look for and make use of structure.Look for and express regularity in repeated reasoning.Make strategic decisions about the use of technological tools.

26

Number: Core ConceptsNumber: Core Concepts

Students understand that: The real numbers include the rational numbers and are in one-to-one correspondence with the points on the number line.Quantities can be compared using division, yielding rates and ratios.

A fraction can represent the result of dividing the numerator by the denominator; equivalent fractions have the same value.

Place value and the rules of arithmetic form the foundation for efficient algorithms.

27

Core Skills for NumberCore Skills for Number

Compare numbers and make sense of their magnitude.

Know when and how to use standard algorithms, and perform them flexibly, accurately and efficiently.

Use mental strategies and technology to formulate, represent and solve problems.

Solve multi-step problems involving fractions and percentages.

Use estimation and approximation to solve problems.

28

Quantity: Core ConceptQuantity: Core Concept

Students understand that: The value of a quantity is not specified unless the units are named or understood from the context.

Quantities can be added and subtracted only when they are of the same type (length, area, speed, etc.).

Quantities can be multiplied or divided to create new types of quantities, called derived quantities.

29

Expressions: Core ConceptsExpressions: Core Concepts

Expressions are constructions built up from numbers, variables, and operations, which have a numerical value when each variable is replaced with a number.

Complex expressions are made up of simpler expressions.

The rules of arithmetic can be applied to transform an expression without changing its value.

Rewriting expressions in equivalent forms serves a purpose in solving problems.

30

Equations: Core ConceptsEquations: Core Concepts

An equation is a statement that two expressions are equal.see examplesThe solutions of an equation are the values of the variables that make the resulting numerical statement true.see examplesThe steps in solving an equation are guided by understanding and justified by logical reasoning.see examplesEquations not solvable in one number system may have solutions in a larger number system.see examples

31

Functions: Core ConceptsFunctions: Core Concepts

A function is a rule, often defined by an expression, that assigns a unique output for every input.

The graph of a function f is a set of ordered pairs (x, f(x)) in the coordinate plane.

Functions model situations where one quantity determines another.

Common functions occur in families where each member describes a similar type of dependence.

32

Modeling: Core ConceptsModeling: Core Concepts

Mathematical models involve choices and assumptions that abstract key features from situations to help us solve problems.

Even very simple models can be useful.

33

Shape: Core ConceptsShape: Core Concepts

Shapes and their parts, attributes, and measurements can be analyzed deductively.

Congruence, similarity, and symmetry can be analyzed using transformations.

Mathematical shapes model the physical world, resulting in practical applications of geometry.

Right triangles and the Pythagorean theorem are central to geometry and its applications, including trigonometry

34

Coordinates: Core ConceptsCoordinates: Core Concepts

Locations in the plane or in space can be specified by pairs or triples of numbers called coordinates.

Coordinates link algebra with geometry and allow methods in one domain to solve problems in the other.

The set of solutions to an equation in two variables forms a curve in the coordinate plane—such as a line, parabola, circle—and the solutions to systems of equations correspond to intersections of these curves.

35

Probability: Core ConceptsProbability: Core Concepts

Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of uncertainty in terms of relative frequency of occurrence.

The law of large numbers provides the basis for estimating certain probabilities by use of empirical relative frequencies.

The laws of probability govern the calculation of probabilities of combined events.

Interpreting probabilities contextually is essential to rational decision-making in situations involving randomness

36

Statistics: Core ConceptsStatistics: Core Concepts

Statistical methods take variability into account to support making informed decisions based on quantitative studies designed to answer specific questions.

Visual displays and summary statistics condense the information in data sets into usable knowledge.

Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic.

The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions.

37

Validation CommitteeValidation Committee

National and international experts will be appointed to the committee.

They will review the process and substance of the common core state standards to ensure they are research and evidence-based and will validate state adoption on the common core standards.

Members of the committee will be selected by governors and chiefs of the participating states.

38

JIGSAW ACTIVITYJIGSAW ACTIVITY

Form 11 groups (one for each core standard)Each group has one copy of the Illinois Draft and 5 copies of the assigned Core StandardGroup Reflections

• How are they alike/different?• What are your concerns about each?• What would you change in which document?

One minute report out

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Group Number/Core StandardGroup Number/Core Standard

1. Mathematical Practice 2. Number 3. Quantity 4. Expressions 5. Equations 6. Functions 7. Modeling 8. Shape 9. Coordinates 10. Probability 11. Statistics

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STAY TUNEDSTAY TUNEDwww.cmath2.comwww.corestandards.orgwww.isbe.net