Parents’
Secondary Math
Information
AGENDA:
 Common Core California State
Standards (Slide 3)
 6th Grade Math (Slide 6)
 Laning description (Slide 10)
 6th to 7th Grade Placement
Process (Slide 17)
 MS Math Pathways (Slide 28)

Grade level and accelerated courses
 HS Math Pathways (Slide 31)


Grade level, Advanced and Honors courses
Math electives & AP Courses (Slide 42)
Common Core
California State
Standards
Common Core California State
Standards in Math
(CCSS-Math)
•
Adopted by 45 states including California
•
Smarter Balanced Tests, aligned to these
standards, are in the Spring
•
2 Types of Standards:
•
Mathematical Practices (next slide)
•
Content by Grade Level (PDF:
http://www.cde.ca.gov/be/st/ss/documen
ts/ccssmathstandardaug2013.pdf )
Eight Common Core Mathematical Practices
Grades K-12
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.
Sixth Grade math
Math 6
 Students follow the 6th grade Common Core
State Standards. (CCSS Math 6)
 The content includes Ratios & Proportional
Relationships, the Number System (Rational
numbers), Expressions & Equations,
Geometry, and Statistics & Probability.
 Students are heterogeneously grouped
in 6th grade and work both
independently and in cooperative
group situations with instruction that is
differentiated to appropriately
challenge all students.
 Extension and enrichment opportunities are
available to all students.
th
6
Grade Differentiation
 For those that need extra challenge
 Einstein Problems, Extensions, or Test-Outs
of classroom problems and investigations
 Join Math Club
 For those that need additional
help
 Math workshop
 Any student, regardless of needs
 May work with their teacher or another
math teacher outside of class
As students leave the 6th grade
program, teachers suggest placement
in one of two courses, Math 7 and
Math 7A, according to:
Student interest in math,
Student response to challenge (readiness for
acceleration), and
Student demonstrated performance with the
CCSS-Math 6 curriculum.
Laning Description
LANING VS. TRACKING
LANING = flexible
TRACKING = rigid
With planning and “signaling,” the laning system
allows students to move among levels of a
course
at the end of a year (or sometimes the
semester)
as their interest and success in a course shifts.
GOALS of Laning:
 To find the best fit in math for each student in terms
of challenge and success for each school year
 To provide a variety of pacing and support for our
variety of students
 In middle schools, to maintain grade-level
standards as the baseline for the course offerings
(grade-level courses, Math 7 & Math8)
and to provide an opportunity for acceleration in
order to help students compress two years of
grade-level math and one year of advanced level
Algebra into two middle school years (accelerated
courses, Math 7A & Alg 8).
 In high schools, to maintain grade-level standards
as the baseline for the course offerings (grade-level
courses)
and to provide additional depth in the baseline
topics as well as additional topics (advanced- and
honors-level courses) to interested and prepared
students.
PAUSD’s Laning Attitudes
 The variety of lanes are available to meet the interests
and needs of all of our college-bound students.
 Every secondary course is a college-prep course.
 The Grade-level courses are challenging and
respectable. They are the proper fit (pace, challenge &
success) for many students to learn math.
Students can move among lanes:
 “Laning down” is not a source of shame; it is the
appropriate response for students finding themselves
over-extended. When “laning down” students will find
themselves in a course that will continue to challenge
them, but in which they should find more success.
 Students also “lane up” at the end of a semester or year,
sometimes requiring summer work. “Laning up” is not a
source of pride; it is the appropriate response for students
finding themselves under-challenged and interested in
extensions.
Laning begins as students move
from Grade 6 to Grade 7
So, what are the differences
between
Math7 & Math7A*?
*PAUSD Savvy: “A”
means “Accelerated”
in middle school, and
“Advanced” in high
school
Math 7
 CCSS: Math 7, only
 Ratios & Proportional
Relationships
 Proportions
 The Number System
 Fractions
 Expressions & Equations
 Order of Operations
 Applications
 Geometry
 Draw & construct figures
 Angles, area, volume
 Statistics & Probability
 Random sampling &
inferences
Math 7A (Accelerated)
 CCSS: Math 7 (see first column)
 Ratios & Proportional Relationships
 The Number System
 Expressions & Equations
 Geometry
 Statistics & Probability
 + CCSS: Math 8
 The Number System
 Irrationals & their approximations
 Expressions & Equations
 Radicals and exponents
 Linear equations
 Functions
 Compare populations
 Definition, evaluation & comparison
 Use probability models
 Modeling relationships b’t’n quantities
Math 7 = one year of CCSS math
Math 7A = 1.5+ years of CCSS math
The Two Math Lanes in Middle School
Grade-Level
7th Grade
8th Grade
Lane
Course
Content
Course
Content
PAUSD’s
Math 7
Course
CCSS
Math 7
CCSS Math 7
PAUSD’s
Math 8
Course
Pacing
description
CCSS
Math 8
Advanced
Algebra
Two Years of
CCSS Math
in Two Years
Three Years
of CCSS Math
(CCSS Math 7,
8, & Algebra 1)
plus Algebra 1
Extensions in
Two Years
Acceleration
Lane
PAUSD’s
Math 7A
Course
PAUSD’s
Alg 8
Course
Sixth to Seventh Grade
Laning Process
Multiple Indicators help teachers
determine a rubric score and course
placement suggestion…
The teacher’s criteria for
suggested course placement
includes student…
achievement on classroom tests
homework completion and turn-in
rate
work and interest in extension and
challenge opportunities
work on math applications
opportunities
achievement on end-of-year exams
The Course Placement
Suggestion
From the teacher’s criteria-based input
sheet (9 boxes on the input sheet)
Generally:
Suggested Placement:
Most Xs in Math 7 column
……….. Math 7
Most Xs in Math 7A column
……….Math 7A
Math 7 or Math 7A?
Some students are not ready for
course acceleration in 7th grade.
There are summer school options
for those students should they be
interested in accelerating at a
later date.
These options are available at
the end of 7th, 9th ,10th and 11th
grades.
Note: Students who earn 4
or 5 Xs in each column
The student is in a grey area.
The student may be more
successful in Math 7… or…
The student may enroll in Math
7A, but may need some
additional support (extra HW
time, time with teacher, etc.)
If a student earned Xs in
the Math 7 column only…
…the student may need
additional support in the Math 7
course,
such as extra HW time, additional
teacher time, or enrollment in
Math 7 Workshop.
If a student earned Xs in the
Math 7A column only…
The student will be invited to take the
Math 7A Mastery Test* (for placement
directly into Algebra). Please note that
students are not required to accept the
invitation. *Topics posted online on each middle
school’s website.
There are NO opportunities to take the
Math 7A Mastery Test without all Xs in
the Math 7A column.
There are other opportunities for
acceleration—wait for the right
time:
 Although acceleration is not appropriate for
every student, as students grow and change,
new capabilities may appear and, in math,
students may grow to
Show interest
Embrace challenge
Demonstrate mastery of grade-level
standards
Increase the rate at which new ideas,
concepts, and skills can be acquired
For example:
Bridging to Algebra 8 After Math 7
Students must:
Earn solid As on tests in both semesters in Math 7
Take advantage of extension opportunities
Demonstrate ease with computation
Participate in summer bridge* course (4 weeks; 4
hrs/day) & earn a B- or better
*An independent study option is available for
students who cannot attend the summer bridge
course.
Acceleration opportunities:
 Between 7th & 8th Grade, after Math 7
 Summer School: 4-week Alg 8 Summer Bridge
course
 Between 9th & 10th Grade, after Alg 1 or Alg 1A
 Summer School: 6-week intense Geometry A
course
 Between 10th & 11th Grade, after Geo or Geo A
 Summer School: 4-week Algebra 2 course
 Between 11th & 12th Grade, after Pre-Calc or IAC
 Summer School: 3-week Intro to Calc course
Middle School Math
Pathways
Students enrolled in
Students enrolled in
Math 7
Math 7A
Student consistently
earned less than an Aon classroom tests
Student consistently
earned an A- or better
on classroom tests
Math 8
Is the student
interested in
acceleration?
No: The current lane is
the correct level of
challenge & success:
Math 8
Yes: Bridge to Algebra 8
4-Week Summer
Course
Student consistently
earned less than a Bon classroom tests
Student consistently
earned an B- or better
on classroom tests
Is the student
interested in
continued
acceleration?
Algebra 8
No: Math 8
Did the student
consistently earn a Bor better on classroom
tests?
No: Math 8
Yes: Algebra 8
Yes: Bridge to Algebra 8
4-Week Summer Course
Did the student
consistently earn a Bor better on classroom
tests?
No: Math 8
Yes: Algebra 8
Another view of MS Math
Pathways
Math 6
Math 7
Math 7A
Bridge
to Alg 8
Mastered
Math 7A
Material?
Alg 8
Mastered Alg
8 Materials?
Math 8
Alg 8
HS Course:
Geo H
High School Math
Pathways
The Three Lanes in PAUSD
High Schools
 The graduation required mathematics curriculum of
(Algebra, Geometry and Algebra 2) is mostly offered
at three levels, with the base level set at the
Common Core California State Standards.
 Note that Alg 8, the 8th grade Algebra and Math 8
course is considered a blend of Accelerated and
Advanced work.
 Grade level courses are Algebra 1, Geometry, and
Algebra 2.
 Advanced courses are Algebra 1A, Geometry A, and
Algebra 2/Trig A.
 Honors courses are Geometry H and Algebra 2/Trig H
What are the differences among
the grade-level, advanced, and
honors lanes?
Grade-level courses meet the
Common Core California State
Requirements, as described in the
January 2013 document at CDE.org.
What are the differences
among the grade-level,
advanced, and honors lanes?
Advanced courses exceed the
CCSS-M requirements, and extend
the included topics or include
topics and levels of problem
solving not required by CCSS-M.
(HW expectations for time and
complexity of problem sets are
higher than grade-level courses.)
What are the differences
among the grade-level,
advanced, and honors
lanes?
Honors courses exceed the CCSS-M
requirements, explore the depth of the
concepts, and preview topics beyond
the scope of the course. Honors courses
demand rigorous reasoning and
communication. (HW expectations for
time and complexity of problem sets
are higher than advanced courses.)
What’s the student personality
type for each lane?
 Generally, the more the student enjoys mathematics,
the more complex math course the student takes.
 Students also reduce the consideration of complexity
of a math course when they reflect on their other
activities, such as sports, theater, music, or a total
academic course load.
 Thus the enjoyment of math is only one factor for
choice of more complex math courses.
 Truly, there are students who love math in each lane.
The best way to engender math appreciation is to
help the student choose the most appropriate course
for both challenge and success.
After 8th grade, there are
choices and opportunities
for a good fit.
Math 8
Algebra
(Gunn)
Alg 1.1
Alg 1
Alg 8
Repeat
Algebra (see
first column)
Geo A
Alg 1A
(Paly)
Geo H
Let’s walk through some typical samples,
beginning with 8th grade’s Math 8: Grade
Level and Advanced courses
Grade
9th
Struggling
Struggling
in
Math 8
in
Math 8
Bs or Cs
in
Math 8
Bs or Cs
in
Math 8
As or Bs
in
Math 8
As or Bs
in
Math 8
Algebra Algebra Algebra Algebra Algebra Algebra
(Gunn) or
(Gunn) or
(Gunn) or
(Gunn) or
(Gunn) or
(Gunn) or
Alg 1.1
Alg 1.1
Alg 1
Alg 1
Alg 1A
Alg 1A
(Paly)
(Paly)
(Paly)
(Paly)
(Paly)
Alg 1
summer
(Paly)
Geo A
10th
Alg 1.2
Geo
Geo
Geo A
Geo A
Alg
2/Trig A
11th
Geo
Alg 2
Alg 2
Alg 2/
Trig A
Alg 2/
Trig A
IAC
12th
Alg 2
PrePreIAC or
IAC
AP Calc
Calc or Calc or AP Stats and/or AB
AP Stats AP Stats
AP Stats
Sample Advanced and
Honors courses
Grad
e
As or Bs
in
Math 8
As or Bs
in
Math 8
9th
Alg 1A
Alg 1A
summer
Bs or Cs
in
Alg 8
As or Bs
in
Alg 8
Alg 1A
Geo A
Geo A
Bs
in 8th
grade
As
in 8th
grade
HS’ Geo H
HS’ Geo H
Geo H
Geo H
Alg 2/
Trig H
Alg 2/
Trig A
Alg 2/
Trig H
Alg 2/
Trig H
Analysis H
Geo A
summer
10th
Cs
in
Alg 8
Geo A
Alg 2/
Trig A
Alg 2
Alg 2
11th
IAC
IAC
IAC
IAC
Analysis H Analysis H AP Calc
12th
AP Calc
AB
AP Calc
AB
AP Calc
AB
AP Calc
AB
AP Calc
BC
BC
AP Calc
BC
AP Stats
District Flowchart
Four years of high
school math are a
good predictor of
success in college.
Math 6
Math 7
Math 7A
Math 8
Algebra 8
Algebra 1/1A
(Gunn)
Algebra 1/1A
(Gunn)
Algebra 1 (Paly)
Algebra 1A (Paly)
Geometry
Geometry
Algebra 2
Algebra 1.1
(Paly)
Algebra 1.2
(Paly)
The lanes shown are
typical routes taken
6th by
students. Movement
between lanes isGrade
possible based on
student performance,
7th
teacher suggestion,
and
Grade
potential summer
coursework.
8th
Grade
9th
Grade
Geo A
Geo H
Geo A
Algebra 2 & Trig A
Algebra 2 & Trig H
10th
Grade
Algebra 2
Algebra 2 & Trig A
Introduction to
Analysis &
Calculus
Analysis H
11th
Grade
Pre-Calculus
Introduction to
Analysis &
Calculus
AP Calculus AB
AP Calculus BC
12th
Grade
PAUSD Math Flowchart showing the flexibility
Math 6
Math 7
Math 7A
summer
school
Math 8
Algebra 1/1A
(Gunn)
Algebra 1.1
(Paly)
Algebra 8
summer
school
Algebra 1.2
(Paly)
Algebra 1/1A
(Gunn)
Algebra 1 (Paly)
Algebra 1A (Paly)
Geometry
Geo A
summer
school
Geometry
Algebra 2
Algebra 2
Pre-Calculus
Or
AP Stats
Geo A
Geo H
Algebra 2 & Trig
A
Algebra 2 & Trig H
summer
school
summer
school
Algebra 2 & Trig
A
Introduction to
Analysis &
And/or
Calculus
AP Stats
Introduction to
Analysis &
Calculus
AP Calculus AB
And
AP Stats
And/or
AP Stats
Analysis H
AP Calculus BC
…and the Math Electives
 MS Applied Math Elective: Money Matters,
 HS Math Electives that may be taken in addition to the
graduation requirements of Algebra 1, Algebra 2 and
Geometry:
 Advanced Problem Solving in Mathematics 1 & 2, Advanced Problem
Solving in Mathematics 3 & 4,
 Geometry & Algebra Support (Paly),
 Algebra 1 & 2 Support (Gunn),
 Business, Entrepreneurship and Math(BEAM) (Gunn),
 Topics in Applied Math (Gunn),
 Stats Applications (Paly),
 and HS Computer Science Courses (either CTE or Math
Elective Credit):
 Functional Programming, Object-Oriented Programming, AP Computer
Science, Introduction to Computer Science Principles (Gunn),
Programming for Mobile Devices (Gunn), CS Capstone Project (Paly)
Considerations
 It is important that a student chooses or is placed
appropriately for both challenge and success in
math courses throughout secondary education,
which they can largely meet on their own.
 Building success is a journey, not a race. Student
success is not only the mastery of content and
skills, but includes enthusiasm for math along with
a healthy, balanced, and happy life.
 The UC Requirements for Admission (and PAUSD
Graduation Requirements) in mathematics is the
successful completion of an Algebra 2 Course.
The Math Electives and AP Courses
(page 1 of 8)
Electives: By definition, any course that is not required
for graduation is an elective. (Alg 2 is the last
requirement for graduation)
 Electives that help our students prepare for calculus are
Pre-Calculus, IAC, and Analysis H
Other Electives:
 Advanced Problem Solving 1, 2, 3 & 4 (Paly & Gunn)
 These semester courses foster excellence in problem
solving. Students engage in non-routine problem solving,
participate in math contests, and investigate mathematics
not often found in classrooms. A variety of students enroll
in this course because of their interest in math. (No
prerequisites required.)
The Math Electives and AP Courses
(page 2 of 8)
 Advanced Placement Statistics, AP Stats (Gunn & Paly)
 One semester of college Statistics. Course content includes
examination of exploratory data analysis, experimental and
survey design, the study of random variables (including
some probability theory), and inferential statistics for one
and two variables. Graphing calculators and computers will
be used extensively as an aide to statistical analysis.
Students are expected to take the Statistics Advanced
Placement Exam, with the goal of earning advanced
placement in college and/or college credit.
 Pre-Requisite: Alg 2, Alg 2/Trig A or Alg 2/Trig H
 This course may be taken concurrently with other math
courses.
The Math Electives and AP Courses
(page 3 of 8)
 Statistics’ Applications (Stats Apps) (Paly)
 This course is designed to be a project-based
introduction to applied Statistics. Topics include:
looking at data (descriptive statistics), probability
and simulation, normal, linear regression, survey
design and basic inference. A final project is
required for this course.
 Pre-requisite: Alg 2, Alg 2/Trig A or Alg 2/Trig H
 One-semester course
 This course may be taken currently with other math
courses.
The Math Electives and AP Courses
(page 4 of 8)
 Geometry and Algebra 2 Support (Paly)
 This course provides additional instruction and extra
support for students who are not mastering essential
learning objectives in either Geometry or Algebra 2.
In addition to mini-lessons that support the
instruction in the regular Geometry and Algebra 2
classroom, students are given time to work on
homework assignments. The class size is limited to
ensure individual support for each student.
 Pre-requisite: concurrent enrollment in grade-level
Geometry or Algebra 2 courses.
The Math Electives and AP Courses
(page 5 of 8)
 AP Calculus AB & BC (Gunn & Paly)
 AB is an intensive study of functional relationships and
analytic Geometry and cover the first two quarters of
college calculus (derivatives and integration).
 BC provides students with the equivalent of the first year
of college mathematics. In addition to all topics
covered in AP Calculus AB, this course explores infinite
series, simple differential equations, area and conic
sections in polar coordinates, vectors and an
introduction to the calculus of vector-valued functions.
 Students are expected to take the Calculus AB or BC
Advanced Placement Exam, with the goal of earning
advanced placement in college and/or college credit.
The Math Electives and AP Courses
(page 6 of 8)
 BEAM BUSINESS, ENTREPRENEURSHIP, & MATH (Gunn)
 Students will study business and entrepreneurship, finance,
and quantitative marketing modules developed in
collaboration with Ernst and Young and Pricewaterhouse
Coopers. During second semester, students connect with
the innovation community of Palo Alto and gain hands-on
experience through their volunteer work for local small
businesses and nonprofit organizations. Students give back
to the community by creating a public-private partnership
between Henry M. Gunn High School and local businesses.
Students also receive mentorship and start-up networking
support from private sector firms. The course is run as an
organization, where students have executive and nonexecutive roles.
 Prerequisite: Algebra 1
The Math Electives and AP Courses
(page 7 of 8)
 Algebra 1 & 2 Support (Gunn)
 This course provides additional instruction and
extra support for students who are not mastering
essential learning objectives in either Algebra 1 or
Algebra 2. In addition to mini-lessons that support
the instruction in the regular Algebra classroom,
students are given time to work on homework
assignments. The class size is limited to ensure
individual support for each student
 Prerequisite: Students must be concurrently
enrolled in Algebra or Algebra 2.
The Math Electives and AP Courses
(page 8 of 8)
Computer Science:
Gunn
 Introduction to
Computer Science
Principles
 Functional and ObjectOriented Programming
 AP Computer Science A
 Programming for Mobile
Devices
Paly
 Computer Science
Principles
 Functional programming
 Object-Oriented
Programming
 AP Computer Science A
 Computer Science
Capstone Project
 Animation and Game
Creation
Making a good decision…
What is good for your student?
Does the student enjoy math?
Is this course what the student wants?
Weigh the time that must be spent
with the student’s interest in the
course.
Consider the pacing of the course.
Know what to expect in the event of a
lane change.
Students and their math
education are at the center
of our work.
 Any questions?
 Contact us so we can work
together.
1. Your student’s math teacher
2. Your school’s Math Instructional
Supervisor (IS)
3. PAUSD’s Secondary CCSS Math
TOSA
4. PAUSD’s Chief Academic Officer
for Secondary Education