Download Making Sense of CCSS for HS Nov 21 SH

Making Sense of
The CT Mathematics Standards
(Common Core State Standards)
Grades 9-12
ATOMIC Conference
November 29, 2011
Shelbi Cole – CSDE
Sharon Heyman- UCONN
Peggy Neal-CREC
Goals
• Provide a brief tour of the Standards
– Standards for Mathematical Practice
– Mathematical Content Standards
– Critical Areas of Focus
– Layout
• Explain the CSDE Unit Template Development Process
• Review Sample Units
• Q&A
Mathematics Common Core Document
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Making Sense of the CT Mathematics
Standards
STANDARDS FOR MATHEMATICAL PRACTICE
Standards for Mathematical Practice
The standards for mathematical practices are located in the
front of the mathematics standards and within the “nature of
mathematics” section at each grade level.
The standards for mathematical practice illustrate the
connection between 21st century skills and mathematical
content and instruction.
The standards for mathematical practices should be
considered when creating curricula, assessments, and
professional development for teachers, and administrators.
Standards for Mathematical 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
SMP 1: Make sense of problems and persevere in solving them.
Mathematically Proficient Students:
 Explain the meaning of the problem to themselves
 Look for entry points
 Analyze givens, constraints, relationships, goals
 Make conjectures about the solution
 Plan a solution pathway
 Consider analogous problems
 Try special cases and similar forms
 Monitor and evaluate progress, and change course if necessary
 Check their answer to problems using a different method
 Continually ask themselves “Does this make sense?”
Gather
Information
Make a
plan
Anticipate
possible
solutions
Continuously
evaluate progress
Check
results
Question
sense of
solutions
SMP 2: Reason abstractly and quantitatively
Decontextualize
Represent as symbols, abstract the situation
5
½
Mathematical
Problem
P
x x x x
Contextualize
Pause as needed to refer back to situation
SMP 3: Construct viable arguments and critique the reasoning of
others
Make a conjecture
Build a logical progression of
statements to explore the
conjecture
Analyze situations by breaking
them into cases
Recognize and use counter
examples
SMP 4: Model with mathematics
Problems in
everyday life…
…reasoned using
mathematical methods
Mathematically proficient students
• make assumptions and approximations to simplify a situation,
realizing these may need revision later
• interpret mathematical results in the context of the situation
and reflect on whether they make sense
Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.com
SMP 5: Use appropriate tools strategically
Proficient students
•
are sufficiently familiar with
appropriate tools to decide
when each tool is helpful,
knowing both the benefit and
limitations
•
detect possible errors
•
identify relevant external
mathematical resources, and
use them to pose or solve
problems
SMP 6: Attend to precision
Mathematically proficient students
• communicate precisely to others
• use clear definitions
• state the meaning of the symbols they use
• specify units of measurement
• label the axes to clarify correspondence with problem
• calculate accurately and efficiently
• express numerical answers with an appropriate degree of
precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
SMP 7: Look for and make use of structure
Mathematically proficient students
•
•
•
look closely to discern a pattern or structure
step back for an overview and shift
perspective
see complicated things as single objects, or as
composed of several objects
SMP 8: Look for and express regularity in repeated reasoning
Mathematically proficient students
• notice if calculations are repeated
and look both for general
methods and for shortcuts
• maintain oversight of the process
while attending to the details, as
they work to solve a problem
• continually evaluate the
reasonableness of their
intermediate results
Making Sense of the CT Mathematics
Standards
MATHEMATICS CONTENT STANDARDS
Critical Areas of Focus
Each grade level
section of the
Common Core
contains
Critical Areas of
Focus
A description of the key
areas where instruction &
learning time should be
focused.
Mathematics | Kindergarten
In Kindergarten, instructional time should focus on two critical areas:
(1) representing, relating, and operating on whole numbers, initially
with sets of objects; (2) describing shapes and space. More learning
time in Kindergarten should be devoted to number than to other topics.
(1) Students use numbers, including written numerals, to represent
quantities and to solve quantitative problems, such as counting objects in
a set; counting out a given number of objects; comparing sets or numerals;
and modeling simple joining and separating situations with sets of objects,
or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten
students should see addition and subtraction equations, and student
writing of equations in kindergarten is encouraged, but it is not required.)
Students choose, combine, and apply effective strategies for answering
quantitative questions, including quickly recognizing the cardinalities of
small sets of objects, counting and producing sets of given sizes, counting
the number of objects in combined sets, or counting the number of objects
that remain in a set after some are taken away.
(2) Students describe their physical world using geometric ideas (e.g.,
shape, orientation, spatial relations) and vocabulary. They identify, name,
and describe basic two-dimensional shapes, such as squares, triangles,
circles, rectangles, and hexagons, presented in a variety of ways (e.g., with
different sizes and orientations), as well as three-dimensional shapes such
as cubes, cones, cylinders, and spheres. They use basic shapes and spatial
reasoning to model objects in their environment and to construct more
complex shapes.
Mathematics Common Core Layout
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Mathematics Common Core Layout
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Mathematics Common Core Layout
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Mathematics Common Core Layout
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Common Core State Standards
K-12 Mathematics Learning Progressions
Kindergarten
1
2
3
4
5
6
7
8
Counting
and
Cardinality
HS
Number
and
Quantity
Number and Operations in Base Ten
Number and Operations:
Fractions
Operations and Algebraic Thinking
The Number System
Ratios and Proportional
Relationships (6 and 7)
Expressions and
Equations
Functions
Geometry
Measurement and Data
Algebra
Functions
Geometry
Geometry
Statistics and Probability
Statistics
And
Probability
http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=1704&ContentID=83475&Content=102764
Priorities in Mathematics
Grade
Priorities 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
Key Fluencies
Grade
Required Fluency
K
Add/subtract within 5
1
Add/subtract within 10
Add/subtract within 20
2
3
Add/subtract within 100 (pencil
and paper)
Multiply/divide within 100
Add/subtract within 1000
4
Add/subtract within 1,000,000
5
Multi-digit multiplication
6
Multi-digit division
Multi-digit decimal operations
7
Solve px + q = r, p(x + q) = r
8
Solve simple 22 systems by
inspection
http://commoncoretools.wordpress.com/
Organizational Notes for High School Standards
The high school standards specify the mathematics that
all students should learn in order to be college and career
ready.
The standards are not defined by grade levels, rather they
are defined by conceptual category.
The high school standards also describe
additional mathematics that students should learn in
order to take advanced courses such as calculus, advanced
statistics, or discrete mathematics.
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Appendix A in the Common Core shows two
paths in course design:
Traditional - Algebra, Geometry, Algebra II
Integrated - Math I, Math II, Math III
Making Sense of the CT Mathematics
Standards
THE DESIGN PROCESS
Team Structure
• Grade bands
•
•
•
•
K-2
3-5
6-8
HS
Rigorous Curriculum Design
Model
Providing a frame for district curriculum work
 Prioritized standards
 Curriculum Units of study
 With prioritized and supporting standards
 Pacing Calendar
 Unit Planning Organizer
Process
• Identified grade band standards as Priority or Supporting
– Based on critical areas of focus and overall continuum of learning
• Considered grade band progression of conceptual understanding and skill
acquisition
– ALL standards are important
– Example: CC.9-12.N.RN.2
CC.9-12.N.RN.1
• Aligned K-12 Standards
– All teams joined for the continuum gallery walk
– Consensus reached on status of standards (priority or supporting)
Geometry Units of Study Pacing
Unit Title
1. Transformations and the Coordinate
Plane
Pacing
4 weeks
Standards
G.CO.1, G.CO.4, G.GPE.5
G.CO.2, G.CO.3, G.CO.5
G.SRT.2, G.GPE.4, G.GPE.6, G.GPE.7
2. Congruence, Proof and Constructions
5 weeks
G.CO.7, G.CO.8, G.CO.9
G.CO.6, G.CO.12
3. Polygons
4 weeks
G.CO.10, G.CO.11
G.CO.13
4. Similarity, Proof and Trigonometry
5 weeks
5. Circles and other Conic Sections
4 weeks
6. Extend to Three Dimensions
4 weeks
7. Applications of Probability
3 weeks
G.SRT.5, G.SRT.8
G.MG.3, G.SRT.1, G.SRT.2
G.SRT.3, G.SRT.4, G.SRT.6, G.SRT.7
G.C.2, G.C.5, G.GPE.1
G.C.1, G.C.3, G.GPE.2,
G.GPE.4
G.GMD.3
G.GMD.1, G.GMD.4, G.MG.1, G.MG.2
S.CP.1, S.CP.3, S.CP.6
S.CP.2, S.CP.4, S.CP.5
S.CP.7
SDE Unit Planning Organizer
• C:\Documents and Settings\pneal\Desktop\ALG I -For Web
Posting\HS-ALGI-UNIT 1.doc
Transitioning to CCSS
• K-8 Transition Guide
• HS needs to fully implement in grade 9 during 2012-13
followed by grade 10
Web Links
• CCSS link
• State website
QUESTIONS