Transcript Rowland CC - Rowland Blogs

California Common
Core State Standards
Mathematics
Rowland Unified School District
Geometry
October 1, 2014
Le Anderson & Gus Lopez
Day 1 Agenda
Overview of the CCSS in Mathematics
 Math Content and Structure
 Mathematical Practices
 Instruction
 Assessment
 Next Steps

Let’s do Math…….
Mc Donald’s Claim:
Wikipedia reports that 8% of all Americans eat
at Mc Donald’s. In the US there are
approximately 310 million Americans and
12,800 Mc Donald restaurants.
Do you believe the Wikipedia report to be
true? Create a mathematical argument to
justify your position.
Be prepared to present your argument.
States that Adopted
© Copyright 2010. National Governors Association Center for Best
Practices and Council of Chief State School Officers. All rights reserved
 Why?
To ensure that our students are…
 meeting college and career expectations
(Text Complexity needs to be 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.
2011 © CA County Superintendents Educational Services Association
 So What is Different?





Focus on College & Career Pathways
Emphasis on Mathematical Modeling
Standards of Mathematical Practice
Multiple Formats for Testing
Alignment with current and future
business and professional needs
We are here
Significantly Higher Rigor

97 Algebra 1 ≠ CCSSM Algebra I

97 Geometry ≠ CCSSM Geometry

97 Algebra 2 ≠ CCSSM Algebra II
 What’s new in curriculum?
“The CCSS for Mathematics move
instruction and assessment beyond
the notion of answer getting driven by
procedurally-based questions to one
that focuses attention on students’
mathematical sense making and
understanding.”
Understanding Language
“Teacher Development to Support English Language Learners
Standards”
in the Context Of Common Core State
Stanford University, 2012
 Algebra Topics Moved to 8th
Grade Common Core Math
Properties
 Liner equations with one variable
 Graphing of linear equations
 Systems of equations and two variables
using graphing
 Radicals and integer exponents

 Geometry Topics Moved to
8th Grade Math
Parallel lines with transversal
 Supplementary and complementary
angles
 Pythagorean Theorem and right triangles
 Properties of rotations, reflections
translations
 Congruence and similarity
 Volumes of cylinders, cones and spheres

 What’s left?
 Focus in Algebra is on
 functions of linear equations & inequalities,
 function of exponential equations, and
 function of quadratic equations.

Focus in Geometry is on

Volume
 3-Dimemsion
 Transformations
 Proofs
PreCalculus
Statistics &
Probability
Algebra II
Math III
Geometry
Geometry
Math II
Algebra
Algebra II
Math I
Algebra I
N-RN 1-3
A-SSE 2-3
A-APR 1
A-REI 4, 7
F-IF 8
F-BF 4
F-LE 6
Math I
N-Q 1-3
A-SSE 1
A-CED 1-4
A-REI 1, 3, 3.1, 5, 6,
10, 11, 12
F-IF 1-7, 9
F-BF 1-3
F-LE 1-3, 5
S-ID 1-3, 5-9
G-CO 1-8,
12-13
G-GPE 4, 5, 7
Underlined standard is California revised addition
Geometry
G-CO 1-8,
12-13
G-SRT 9-11
GPE 5-7
G-GMD 4
G-MG 1-3
Math II
G-CO 9-11
G-STR 1-8, 8.1
G-C 1-5
G-GPE 1-2, 4
G-GMD 1, 3, 5, 6
S-CP 1-9
S-MD 6-7
N-RN 1-3
N-CN 1-2, 7-9
A-SSE 1, 2, 3
A-APR 1
A-CED 1, 2, 4
A-REI 4, 7
F-IF 4-7, 8, 9
F-BF 1, 3, 4
F-LE 3, 6
F-TF 8
Underlined standards are California revised addition.
Standards in blue are also in Math I.
Algebra II
N-CN 1-2, 7
A-REI 3.1
F-TF 8
Underlined standards
are California revised.
Standards in purple are also in
Math I, II and Algebra 1.
Math III
N-CN 8-9
A-SSE 1, 2, 4
A-APR 1, 2-7
A-CED 1-4
A-REI 2, 11
F-IF 4-9
F-BF 1, 3, 4
F-LE 4, 4.1, 4.2, 4.3
F-TF 1, 2, 2.1, 5
G-GPE 3.1
S-ID 4
S-IC 1-6
S-MD 6-7
G-SRT 9-11
G-GMD 4
G-MG 1-3
 CCSSM 8th Grade Are
HS Standards
67%
 Algebra/
Functons
20%  Geometry
(Transformations &
Triangle Proofs)
10%  Bivariate Data
3%
 Cross Concept
Project
Suggested Scope & Sequence from .SVMI & Pearson
 Conceptual Categories






Number and Quantities (N)
Algebra (A)
Geometry (G)
Function (F)
Statistics and Probability (S)
Modeling (*)
High School
Mathematics Standards
Conceptual Categories Modeling:
 Number & Quantity
 Algebra
 Functions
 Modeling
 Geometry
 Statistics & Probability
21
Links classroom mathematics
and statistics to everyday life,
work, and decision-making
Is the process of choosing and
using appropriate mathematics
and statistics
Uses technology to explore
consequences
and compare predictions with
data
 Acceleration
Districts
are encouraged
to work the
“When students
have mastered
with
theirdescribed
mathematics
content
in theleadership,
Common
teachers,
andfor
curriculum
Core Stateparents,
Standards
coordinators
design
pathways that
Mathematics to
with
California
best
meet for
thekindergarten
needs of theirthrough
Additions
students.
grade eight, they will be ready to
complete Common Core Algebra I or
Common Core Mathematics I. ”
2013 CA Mathematics Framework- Instructional Materials to Support the California Common Core State Standards for Mathematics - pg 6 (200-202)
 Acceleration Suggestions from the
2013 CA Mathematics Framework
Compacting in Middle School
Part of
Grade 7
Grade 6
Grade 8 +
+ Part of
Algebra I or
Grade 8
Integrated I
Geometry
or
Integrated
II
Algebra II or
Integrated
III
Precalc
Calculus
Acceleration Decision Point
Doubling Up in High School
Grade 6
Grade 7
Grade 8
Algebra I
Geometry
Acceleration Decision Point
2013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 18
Algebra II
Precalc
Calculus
Accelerated Integrated Pathway
Grade 6
Grade 7
Grade 8
Part of
Integrated I
and Integrated
II
Part of
Integrated II
and Integrated
III
Precalc
Calculus
Enhanced
Algebra
I/Integrated I
Enhanced
Geometry/Int
egrated II
Enhanced
Algebra
II/Integrated
III
Calculus
Acceleration Decision Point
Enhanced Pathway
Grade 6
Grade 7
Grade 8
Acceleration Decision
Point
2013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 19, & 20
 21st Century Thinking
Critical Thinking and Problem Solving
 Communication
 Collaboration
 Creativity and Innovation
 Construction of Knowledge

Part 1: Standards for
Mathematical Practice
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.
3.
Reason abstractly and quantitatively
…make sense of quantities and their relationships to
problem situations
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
2011 © CA County Superintendents Educational Services Association
Part 2: Standards for
Mathematical Practice
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
2011 © CA County Superintendents Educational Services Association
 Dan Meyer

Math Class Needs a Makeover
http://www.ted.com/talks/view/lang/en//id/855
 Task: “Over the Hill”
A cell phone tower will be built on the west side
of a hill (see handout). How far up the hill must
the tower be placed to provide a signal to
anyone on the east side of the lake?
From NCTM Secondary Institute - June 2012
29
Activit
y
A Model
Approach to Problem Solving
Maintain the level of difficulty.
 Require problem solving with peers.
 Encourage a variety of media.
 Ask students to generate solutions that
can be shared and generalized.
 Assess how students’ assumptions and
approaches change.

DeMatteo (2010)
Informing Practice
30
A National Consortium of States



28 states
representing
44% of K-12
students
21 governing,
7 advisory
states
Washington
state is fiscal
agent
 What is Depth of
Knowledge (DOK)?
 A scale of cognitive demand (thinking) to
align standards with assessments
 Based on the research of Norman Webb,
University of Wisconsin Center for
Education Research and the National
Institute for Science Education.
 Karen Hess on
Depth of Knowledge
http://youtu.be/Cu8SfdLfbm8
http://vimeo.com/20998609
 Depth Of Knowledge in the
Common Core Assessments
Current
Assessments
New SBAC
Assessments
Mathematics
ELA/Literacy
DOK3 DOK4
DOK3
DOK4
<2%
0%
20%
2%
49%
21%
43%
25%
What are the implications for the
classroom?
Yuan & Le (2012); Herman & Linn (2013) from Linda Darling-‐Hammond, Assembly Hearing,3.6.13
 Some general rules of thumb...
 If there is only one correct answer, it is probably
level DOK 1 or DOK 2:
• DOK 1: you either know or you don’t.
• DOK 2: (conceptual): apply one concept, then make a decision before
going on to apply a second concept.
 If more than one solution/approach, requiring
evidence, it is DOK 3 or 4
• DOK 3: Must provide supporting evidence and reasoning (not just HOW
it was solved, but WHY – explain reasoning).
• DOK 4: all of “3”+ use of multiple sources or texts.
Karin Hess January 2012
 Assessment Claims
1.
Concepts and Procedures: Students can explain
and apply mathematical problems with precision and
fluency.
2.
Problem Solving: Students can frame and solve a
range of complex problems in pure and applied
mathematics.
3.
Communicating Reasoning: Students can clarify
and precisely conduct viable arguments to support their
reasoning and to critique the reasoning of others.
4.
Modeling and Data Analysis: Students can
analyze complex, real-world scenarios and can use
mathematical models to interpret and solve problems.
 Test Questions
Types and Designs

Items and the collection of items MUST
measure deeper understanding and
application of concepts.

Therefore, a variety of item types are
necessary.
 Item Types

Selected-response


Multiple choice items designed to determine
student’s understanding while eliminating
obtaining the correct answer through “testtaking” skills
Constructed-response

Complex thinking skills, comparison and contrast,
cause and effect, patterns, conflicting points of
view, categorizing, summarizing, interpreting
information

Extended constructed-response


Performance Tasks


Assess knowledge and skills not easily accessed
with selected response or constructed response
(e.g., oral presentations, exhibitions, product
Integrate knowledge and skills across
multiple standards
Technology-enhanced

Requires productive use of technology
 Performance Task Items
Collections of questions and real-world tasks connected to
a single theme or scenario:
 A student may be presented with reading material on
a given topic, and asked questions about the reading
 That may be followed by reading on the same topic,
but from a different perspective, with questions on
that reading, plus some compare/contrast questions
 Finally, the student may be provided additional
readings on the same, or an associated topic, and
asked to take a position or provide an argument
 Each performance task could take place across more
than one sitting of 45-60 minutes each
 Explore the SBAC website




Go to: http://www.smarterbalanced.org/sampleitems-and-performance-tasks/
direct link to sbac assessment files by grade
level:http://www.dese.mo.gov/divimprove/assess/sbac
.html#sbacsample
Try some technology-enhanced items.
Look at other items, including those with DOK 3
and 4.
 Next Steps





Start now with new instructional techniques
and real-world problems
Have students explain verbally how they
worked the problem, then begin to have
them write the explanation.
Focus on conceptual understanding
Review your pacing plans to reflect the
CCSS curriculum
Implement the new 8th grade math class for
8th grades and HS Algebra Readiness
(transition).