Math Pathways for Instruction
Aligned with the Common Core
State Standards
LCHS 7/8 MATH NIGHT
APRIL 15, 2014
Agenda
Informational Power Point
7th Grade Teachers Mr. Kim & Mr. Savage
7th Grade Student Daniel Landesman
8th Grade Teachers Mrs. Dornian & Mrs. Wright
8th Grade Student Jeremy Herron
Q&A
Traditional vs. Integrated Approach
Traditional
• Uses a horizontal model with firstyear algebra, geometry and secondyear algebra taught in a linear
fashion.
• Lesson begins with the presentation
of a math concept and ends with
students attempt to apply the
concept.
• Students apply the model given to
solve the problem.
• Teacher provides direct instruction
and is primarily a lecturer.
• Traditional assessments tools are
used (formal tests, quizzes, etc.).
Integrated
• Uses a vertical model that interweaves
the three.
• Lesson begins with context-based
problem and concepts emerge as
students attempt to solve the problem.
• Students analyze data and make and test
conjectures about math models.
• Teacher is a facilitator who uses probing
questions to stimulate students and
interact with them.
• Uses a small group cooperative learning
model.
• Technology is used regularly to enhance
instruction
• A variety of assessment tools are used
(written journals, extended group
projects, etc.).
Courses in higher level mathematics: Precalculus,
Calculus, Advanced Statistics, Discrete Mathematics,
Advanced Quantitative Reasoning, etc.
Standards for Mathematical Practice
The Eight Standards for Mathematical
Practice place an emphasis on
student demonstrations of learning
that describe the thinking processes,
habits of mind, and dispositions that
students need to develop.
adapted from Briars & Mitchell (2010)
Getting Started with the Common Core State Standards
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. Reason abstractly and quantitatively
…make sense of quantities and their relationships to
problem situations
3. 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
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
The Key to Drive Successful
Implementation
Teacher
Professional
Development and
On-Going Support
Teacher Development Group-TDG
• Best practice seminars (4 days) focused on
Habits of Mind and Habits of Interaction
• 4 Studio Cycles to plan a lesson, observe it in
action and analyze instruction
• Resident Coaching (Individualized support) for
teachers
• Ongoing on line support and communication
with consultant and colleagues
• Leadership coaching for administration
Habits of Mind
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Generalize
Justify Why
Make Sense
Mathematical Representations
Metacognition Reflection
Regularity, Patterns, Structure
Connections
Mistakes & Stuck Points
Persevere & Seek More
Habit of Interaction
•
•
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Listen to Understand
Genuine Questions
Private Reasoning Time
Explore Multiple Pathways
Compare our Logic & Ideas
Critique & Debate
Math Reasoning is the Authority
Explain my Reasoning
Next steps
• Continued professional development to support
implementation of CCSS
• Strategic planning and alignment of master schedule
with teacher expertise to maximize student learning
• Designing Common Core aligned instructional pacing
guides, unit and lesson plans and assessments
• Rewriting course outlines to reflect the
implementation of CCSS in our curriculum and
submission for UC/CSU approval
Current 7/8 Math Offerings and Percent of
Students Currently Enrolled
7th Grade
Pre-Algebra (44.6%)
8th Grade
Algebra 1A (37.1%)
Adv. Pre-Algebra (46.7%) Algebra 1 (54.4%)
Algebra 1 (8.7%)*
Geometry (8.5%)
* It is anticipated that the number of 7th grade students
enrolled in Algebra 1 will drop significantly from its current
level since there are now two courses instead of one
between 6th grade CC math and Algebra 1 CC.
2014-15
th
7
Grade Math Offerings
1. 7th grade Common Core
2. 7th grade Advanced (CC + First ½ of 8th grade
Common Core)
3. Algebra 1 (Second ½ of 8th grade Common Core
and Algebra 1)
• Students will be placed in options 1 or 2 based upon
6th grade teacher recommendation (current practice)
• Students will be placed in option 3 only if they pass
the created Algebra 1 entrance test showing mastery
of 7th grade CC AND 8th grade CC standards
2014-15
th
8
Grade Math Offerings
1. 8th grade CC
2. 8th grade Advanced/Algebra 1 (Second half of 8th
grade CC + Algebra 1 CC)
3. Geometry CC or Honors Geometry
• Students will be placed in options 1 or 2 based upon
the 7th grade teacher’s recommendation
• Students will be placed in option 3 only if they
successfully passed Algebra 1 CC as a 7th grade
student
2014-15 Incoming
th
9
Grade Math Offerings
Incoming 2014 9th grade students (current 8th grade
students) will have the following offerings:
1. Algebra 1 CC (after completing 8th grade CC)
2. Geometry CC (after completing Algebra 1 CC)
3. Algebra 2 CC (after completing Geometry CC or
Honors Geometry)
Population Estimation with
the “Capture-Recapture”
Method
“Capture-Recapture” is a method
commonly used to estimate an animal
population’s size. The method is most useful
when it is not practical to count all the
animals in the population.
Students did the following:
Captured and tagged some beans. Set them free after
being tagged.
Recaptured a set of beans. Counted how many of those
were tagged.
Used the ratio of tagged beans in the set to generate a
proportion.
Used the proportion to estimate the total population of
beans.
N um ber of beans m arked in a sam ple
T otal num ber of beans in a sam ple

T otal num ber o f beans m arked
x (T otal population of beans )