Download Algebra - Walnut Creek School District

Parent Information Meeting
ACCELERATED PATHWAYS IN MATH
WALNUT CREEK SCHOOL DISTRICT
MARCH 4, 2015
Information
 Overview of Common Core State Standards for Math
(CCSSM)
 Course Sequences for CCSSM
 Course Content for CCSSM and Accelerated Pathway
 Criteria for Accelerated Pathway
Instructional Shifts
 Focus: Place a strong emphasis on the grade-level
and course-level standards
 Coherence: Think across grades and link major
topics in each grade
 Rigor: Pursue with equal intensity
Conceptual understanding
 Procedural skills and fluency
 Applications
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Why Students Need Common Core Math
 Math as a learning subject not a performance subject.
 Classrooms need to teach multi-dimensional
mathematics.
 All students should be encouraged to take work to the
highest level possible.
 Classrooms should encourage more depth, less speed.
Jo Boaler – Stanford University
Video: http://youcubed.stanford.edu/why-we-needcommon-core-math/
CCSS Aligned Math Courses
CCSS Math 6
CCSS Math 7
CCSS Math 8
 More rigorous
 Increased depth and complexity
 Increased problem solving and application of
conceptual and procedural understanding
True/False
 A number of CCSSM topics at the middle school level
are repeated over various grade levels.
 False: The CCSSM greatly reduce the topic
repetition in mathematics curriculum for grades 5-8.
Each grade level has its own significant topics that
are not repeated.
CCSSM Math 6
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by
fractions.
Compute fluently with multi-digit numbers and find common factors and multiples.
Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one-variable equations and inequalities.
Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
Develop understanding of statistical variability.
Summarize and describe distributions.
CCSSM Math 7
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Ratios and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide
rational numbers.
Know that there are numbers that are not rational and approximate them by rational numbers.
Expressions and Equations
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry
Draw, construct and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Solve real-life and mathematical problems involving volume of cylinders, cones, and spheres.
Statistics and Probability
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
True/False
 The California Standards adopted in 1997 had grade-
level specific standards for grade eight.
 False: Prior to adoption of the rigorous California
CCSSM grade eight standards, there were not gradelevel specific standards for grade eight.
CA Mathematics Framework 2013
True/False
 The 1997 California Standards Algebra I course is a less
rigorous course than the CCSSM for Grade 8 course.
 True: Prior to the adoption of the CCSSM - Algebra I was
the course name for increasing numbers of students in
eighth grade. Algebra I is the course name in ninth grade
for most students who moving forward will complete the
CA CCSSM for grade eight – a course that is more
rigorous and more demanding than earlier versions of
“Algebra I.”
CA Mathematics Framework 2013
CCSSM Math 8
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The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
Work with radicals and integer exponents.
Understand the connection between proportional relationships, lines, and linear equations.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions
Define, evaluate, and compare functions.
Use functions to model relationships between quantities.
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry
software.
 Understand and apply the Pythagorean Theorem.
 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
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Statistics and Probability
Investigate patterns of association in bivariate data.
CCSSM Grade 8 – More Rigorous
 CCSSM Math 8 addresses the foundations of algebra:
 In-depth study of linear relationships and equations
 More formal treatment of functions
 Exploration of Irrational Numbers
 Geometry
 Transformations and triangle proofs
 Relate graphing to algebra
 Statistics
 Connect linear relationships with the representation of
bivariate data
Mastery of K-8 Math
“Mastery of the algebra content, including attention
to the Standards for Mathematical Practice, is
fundamental for success in further mathematics and
on college entrance examinations. Skipping over
material to get students to a particular point in the
curriculum will create gaps in students’
mathematical background.”
CA Mathematical Framework, 2013
CCSS Accelerated Path
Math 6
Pre-Algebra – Compacted CCSSM 7/8
Algebra I (Math 8)
 Compacted content
 Accelerated pace
 Upon successful completion students enroll in
Geometry
What is Compacting?
To compress the content - three years of math content
into two years:
 All content standards must be fully addressed
 All practice standards are fully addressed
 Requires a faster pace to complete the course
It does not mean skipping content or opportunities for
problem solving and application of conceptual and
procedural understanding.
Pre-Algebra /Compacted Math 7 & 8
 Rational Numbers and Exponents
 Proportionality and Linear Relationships
 Introduction to Sampling Inference
 Creating, Comparing and Analyzing Geometric
Figures
Nearly all of the CCSSM for Grade 7 & 8 are included
in this course with the exception of three standard
sets.
Algebra I Compacted
 CCSSM Grade 8
 Algebra and Functions: Systems of equations
 Geometry: Congruence and similarity, triangle proofs
 Statistics: Statistical inferences
 Algebra I
 Number and Quantity
 Algebra
 Functions
 Statistics and Probability
Algebra I
Number and Quantity
Exponents to rational exponents
Properties of rational and irrational numbers.
Reason quantitatively and use units to solve problems.
Algebra
Interpret the structure of expressions.
Write expressions in equivalent forms to solve problems.
Perform arithmetic operations on polynomials.
Create equations that describe numbers or relationships.
Understand solving equations as a process of reasoning and explain the reasoning.
Solve equations and inequalities in one variable.
Solve systems of equations.
Represent and solve equations and inequalities graphically.
Algebra I (continued)
Functions
Understand the concept of a function
Use function notation.
Interpret functions.
Analyze functions using different representations.
Build a function that models a relationship between two quantities.
Build new functions from existing functions.
Construct and compare linear, quadratic, and exponential models and solve problems.
Interpret expressions for functions
Statistics and Probability
Summarize, represent, and interpret data on a single count or measurement variable.
Summarize, represent, and interpret data on two categorical and quantitative
variables.
Interpret linear models.
Algebra I
This course whether taken in Middle School or High
School builds on the CCSSM for grade 8 and is
correspondingly more advanced than previous
algebra courses.
True/False
 The University of California’s A-G requirements
include passing calculus in high school.
 False: A-G recommends a 4th year of mathematics –
it is not required.
Middle to High School Course Sequence
CCSS Aligned Math
Courses – Path 1
CCSS Aligned Math
Courses – Path 2
 Math 6
 Math 6
 Math 7
 Math 7
 Math 8
 Math 8
 Algebra I
 Algebra I
 Geometry
 Geometry/Honors
 Algebra II
 Algebra II/Trig
 Pre- Calculus
 Calculus AB
Middle to High School Course Sequence
CCSS Accelerated Path 1
CCSS Accelerated Path 2
 Math 6
 Math 6
 Pre-Algebra
 Pre-Algebra
 Algebra I
 Algebra I
 Geometry
 Geometry
 Algebra II
 Pre-Calculus
 Calculus AB
 Algebra II/Trig
 Calculus AB
 Calculus BC/AP
Statistics
Considerations for Accelerated Placement
 To ensure that students are developmentally ready
for accelerated content it is not recommended to
compact before grade seven.
 Solid evidence of student’s conceptual
understanding, knowledge of procedural skills, and
ability to apply mathematics before moving into an
accelerated pathway.
CA Mathematics Framework, 2013
WCSD Criteria
 Grades
 Tests
 Mathematics Diagnostic Testing Project – CA State
University/University of CA
 MARS exam
 Teacher Input
Teacher Input
 Completes homework
 Understands complex concepts and relationships;
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undertakes sophisticated problem solving
Is a quick learner; keenly observant, responds
rapidly
Perseveres in problem solving
Advocates for self and asks for help
Collaborates well with peers
Student demonstrates motivation for learning
Pre-Algebra – CCSSM 7/8 Compacted
 Eligible students must meet the following matrix
criteria:
3
2
1
0
Grade
Average
Q1-Q3
95% and
above
93-94.9%
92.9-90%
89.9%
and below
Test
Average
Q1-Q3
93% and
above
90-92.9%
87-89.9%
86.9%
and below
MDTP
35-40
34
33
0-32
MARS
32-40
26-31
22-25
0-21
Algebra I
 Eligible students must meet the following matrix
criteria:
3
2
1
0
Grade
95% and
Average Q1- above
Q3
93-94.9%
92.9-90%
89.9% and
below
Test
93% and
Average Q1- above
Q3
90-92.9%
87-89.9%
86.9% and
below
District
Assessment
80% and
above
75-79.9%
73-74.9%
72% and
below
MARS
14-16
12-13
10-11
0-9
Eligibility Criteria
Case 1
 Matrix Score 10-12
 No zeros
Case 2
 Matrix Score 8-9
 Teacher Input Score
28-35
 No zeros
Parents may appeal for students who do not
meet the above criteria.
Timeline 2014-2015
Sixth Grade
 MDTP – Week of March 9
 MARS Exam – Last two weeks of April
Seventh Grade
 Placement Exams – Week of May 4
Notification of eligibility by letter at the end of June