Transcript Stefanie Buckner - wcpssccmathtraining2013

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Core Plus
Mathematics
Stefanie Buckner
Buncombe County Schools
[email protected]
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Core Plus Mathematics Project
Essential Features
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Courses organized around interwoven mathematical strands
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Mathematical strands developed in coherent, focused units
connected by fundamental unifying idea
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Mathematics developed in context with an emphasis on
applications and mathematical modeling
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Student-centered investigations that promote active learning
through problem solving
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Full and appropriate use of technology tools
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Course One (“blue” book)
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Unit 1: Patterns of Change
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Unit 2: Patterns in Data
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Unit 3: Linear Functions
Unit 4: Vertex-Edge Graphs
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Unit 5: Exponential
Functions
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Unit 6: Patterns in Shape
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Unit 7: Quadratic Functions
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Unit 8: Patterns in Chance
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Common Core Math 1
How Buncombe County Does CCSS Math 1 using
Core Plus Materials (somewhat exclusively)
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Course Two (“green” book)
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Unit 1: Functions, Equations,
and Systems
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Unit 5: Nonlinear Functions
and Equations
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Unit 2: Matrix Methods
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Unit 3: Coordinate Methods
Unit 6: Regression and
Correlation
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Unit 7: Trigonometric
Methods
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Unit 8: Probability
Distributions
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Unit 4: Network
Optimization
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Common Core Math 21
How Buncombe County plans to do CCSS Math 2
using Core Plus Materials (somewhat exclusively)
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Course Three (“purple” book)
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Unit 1: Reasoning and Proof
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Unit 2: Inequalities and
Linear Programming
Unit 5: Polynomial and
Rational Functions
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Unit 3: Similarity and
Congruence
Unit 6: Circles and Circular
Functions
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Unit 4: Samples and
Variation
Unit 7: Recursion and
Iteration
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Unit 8: Inverse Functions
and Logarithms
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Course Four (“orange” book)
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Unit 5: Exponential Functions,
Logarithms, and Equations
Unit 2: Vectors and Motion
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Unit 3: Algebraic Functions
and Equations
Unit 6: Surfaces and Cross
Sections
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Unit 7: Rates of Change
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Unit 8: Counting Methods and
Induction
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Unit 9: Binomial Distributions and
Statistical Inference
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Unit 10: Mathematics of
Information Processing and the
Internet
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Unit 1: Families of Functions
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Unit 4: Trigonometric
Functions and Equations
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Instructional Support Materials
TeacherWorks CD
StudentWorks CD
ExamView Pro
Resource Masters
Teacher Editions (different approach)
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Core Plus
Instructional Model
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Launch – Think About the Situation (TATS)
 Full class discussion of a problem
situation and related questions to think
about; purpose is both affective and
cognitive.
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Explore – Investigation
 Group investigation of focused problems
and questions related to the launching
situation.
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Share and Summarize - Summarize the
Mathematics (STM)
 Class discussion of the mathematical
ideas, strategies and reasoning
developed in their groups leads to a
summary of important ideas.
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Apply (CYU)
 Tasks students complete individually to
check and reinforce their developing
understanding.
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Collaboration
Based
Student to student discourse
and student to teacher
discourse is at the heart of
CPMP investigations.
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Everyone has a job
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Collaborative Group Guidelines
Each member of the group:
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contributes to the group’s work;
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is responsible for listening carefully when another group
member is talking;
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has the responsibility and the right to ask questions;
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should help others in the group when asked;
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should be considerate and encouraging.
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All members should work together until everyone in the
group understands and can explain the group’s results.
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On Your
Owns
A new “twist” on practice
problems
Each LESSON is followed by an extensive set of
On Your Owns (OYOs)
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On Your Own Tasks
Applications
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Connections
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Provide opportunities for students to re-examine their thinking
about ideas in the lesson.
Extensions
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Help students to build links between mathematical topics in the
lesson and to connect those topics with other mathematics that
they know.
Reflections
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Provide opportunities for students to use and strengthen their
understanding of ideas they have learned in the lesson.
Provide opportunities for students to explore further or more
deeply the mathematics they are learning.
Review
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Provide opportunities for just-in-time review and distributed
practice of skills to maintain procedural fluency.
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Core Math
Tools
Mathematically proficient students consider the available tools when solving a
mathematical problem. These tools might include pencil and paper, concrete
models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra
system, a statistical package, or dynamic geometry software. Proficient
students are sufficiently familiar with tools appropriate for their grade or course
to make sound decisions about when each of these tools might be helpful. . . .
Common Core State Standards for Mathematics, 2010, p. 7
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Core Math Tools
aka CPMP tools
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Core Math Tools is freely available at:
www.nctm.org/coremathtools
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Core Math Tools is accompanied by user support and resources
at a CMT portal within the NCTM website.
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Core Math Tools is designed for use with any CCSSM‐ oriented
high school textbook series. BUT Core Plus Data sets are all
preloaded. The text often times references CPMP tools.
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Can be used online in mathematics classrooms, in school and
local libraries, or any other place offering Internet access.
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Can be freely downloaded to user’s class or home computer and
is self‐updating whenever connected to the Internet.
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General Purpose Tools
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Algebra Tools
Electronic spreadsheet, computer algebra
system (CAS) that produces tables and graphs,
manipulates algebraic expressions, and solves
equations inequalities. Also includes custom
apps supporting mathematical modeling.
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Geometry Tools
Interactive drawing tools for constructing,
measuring, manipulating, and transforming
geometric figures. Ability to turn off/on
coordinate plane. Includes simple
programming language for custom
applications. Custom apps specifics to
geometric properties.
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Statistics Tools
Tools for graphic display and analysis of both
univariate and bivariate data, simulation of
probabilistic situations and mathematical
modeling of quantitative relationships.
Spreadsheet capability has built in data sets
(correlate to CPMP text) and the ability to
enter your own data.
Customs apps are key in developing key
statistical ideas.
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Modeling with Core Math Tools
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Optimal Refinery Location:
Drilling teams from oil companies
search around the world for new
sites to place oil wells. Increasingly,
oil reserves are being discovered in
offshore waters. The Gulf Oil
Company has drilled two highcapacity wells in the Gulf of Mexico
about 5 km and 9 km from shore. The
company wants to build a refinery to
pipe oil from the two wells to a
single new refinery on shore.
Assume the 20 km of shoreline is
nearly straight.
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What are important considerations in
locating the refinery?
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What is your best estimate for the
location of the refinery? How did you
decide on that location?
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Interactive Geometry Approach
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Multiple Algebraic Approaches
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A Reflection Approach