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State Standards,
National Standards
ICTM 2009
Jill Gardner – [email protected]
PJ Karafiol – [email protected]
Claran Einfeldt – [email protected]
All Rights Reserved | © 2007 JBG Mathematics
AGENDA
Claran – Welcome and Overview
PJ – Illinois Process and Draft Document
Jill – National Process and Draft Document
JIGSAW 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
2
The 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
3
Standards 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
4
“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.
5
Common 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
6
Feedback 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
7
The Standards
Mathematical Practice
Number
Quantity
Expressions
Equations
Functions
Modeling
Shape
Coordinates
Probability
Statistics
8
Mathematical 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.
9
Number: 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.
10
Core 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.
11
Quantity: 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.
12
Expressions: 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.
13
Equations: 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.
14
Functions: 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.
15
Modeling: 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.
16
Shape: 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
17
Coordinates: 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.
18
Probability: 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
19
Statistics: 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.
20
Validation Committee
National and international experts will be
appointed to the committee.
Members of the committee will be selected
by governors and chiefs of the
participating states.
They will review the process and substance
of the common core state standards to
ensure they are research and evidencebased and will validate state adoption on
the common core standards.
21
Common 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
22
Feedback 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
23
The Standards
Mathematical Practice
Number
Quantity
Expressions
Equations
Functions
Modeling
Shape
Coordinates
Probability
Statistics
24
Mathematical 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.
25
Number: 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.
26
Core 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.
27
Quantity: 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.
28
Expressions: 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.
29
Equations: Core Concepts
An equation is a statement that two expressions are
equal.
see examples
The solutions of an equation are the values of the
variables that make the resulting numerical statement
true.
see examples
The steps in solving an equation are guided by
understanding and justified by logical reasoning.
see examples
Equations not solvable in one number system may
have solutions in a larger number system.
see examples
30
Functions: 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.
31
Modeling: 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.
32
Shape: 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
33
Coordinates: 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.
34
Probability: 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
35
Statistics: 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.
36
Validation Committee
National and international experts will be
appointed to the committee.
Members of the committee will be selected by
governors and chiefs of the participating
states.
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.
37
JIGSAW 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 Standard
Group Reflections
• How are they alike/different?
• What are your concerns about each?
• What would you change in which document?
One minute report out
38
Group Number/Core Standard
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Mathematical Practice
Number
Quantity
Expressions
Equations
Functions
Modeling
Shape
Coordinates
Probability
Statistics
39
STAY TUNED
www.cmath2.com
www.corestandards.org
www.isbe.net
40