Mathematics

• California Department of Education Mathematics Framework
• Common Core States Standards

Standard Pathway

Middle School

Grade 6	Grade 7	Grade 8
Foundational Math The content of this course is a combination of California’s Common Core State Standards from Grade 6, Grade 7, and Algebra. The areas of content focus are: number system, expressions and equations, ratios and proportions, two-dimensional geometry, and data analysis and statistics.	Concepts in Math The content of this course is a combination of California’s Common Core State Standards from Grade 6, Grade 7 and Math 8.The areas of content focus are: number system, expressions and equations, ratios and proportions, three-dimensional geometry, and probability and bivariate data.	Algebra 1 The content of this course encompasses the California’s Common Core State Standards for Algebra 1. The first part of the course is focused on linear functions. The second part of the course is focused on nonlinear functions.

• Middle school follows compacted program (4 years of math in 3 years)
• Algebra 1 leads to Geometry or Geometry H in 9th grade.

High School

Grade 9	Grade 10	Grade 11	Grade 12
Geometry H Geometry Algebra 1	Algebra 2/Trig H Algebra 2/Trig A Algebra 2 Geometry Statistics Applications	Analysis H Intro to Analysis & Calculus (IAC) Precalculus Algebra 2 AP Stats Intro to Data Science Statistics Applications Applied Math H	AP Calculus BC AP Calculus AB Calculus Precalculus AP Stats Intro to Data Science Statistics Applications Applied Math H

 

Acceleration Pathway

Middle School

Grade 6	Grade 7	Grade 8
Validation tests passed in May of 5th grade:
Concepts in Math	Algebra 1	Geometry H
Validation tests passed in May of 6th grade:
Foundational Math	Algebra 1	Geometry H
Validation tests passed in May of 7th grade:
Foundational Math	Concepts in Math	Geometry H

High School

Grade 9	Grade 10	Grade 11	Grade 12
Algebra 2/Trig H Algebra 2/Trig A	Analysis H Intro to Analysis & Calculus (IAC)	AP Calculus BC AP Calculus AB AP Stats Intro to Data Science Applied Math H	AP Stats Intro to Data Science Applied Math H Community college courses

Students who wish to accelerate beyond the already compacted middle school math program may take part in the Math Validation Process and, in effect, cover 5 years of math in 3 years. Students successful in the Math Validation Process may only accelerate one additional year in the PAUSD middle school pathway. Students may participate more than once if they do not pass the assessments in a previous validation process.

The math validation process consists of two parts:

• Part 1 assesses readiness for the basic math course the student would like to enter. Students who meet the critical levels in all strands on MDTP Readiness assessment are eligible to take Part 2 of the Math Validation Process.
• Part 2 assesses students' knowledge of the topics and skills covered in the course the student would like to accelerate through. This placement assessment is aligned to the state-adopted mathematics content standards covered in that course.

For students new to PAUSD enrolling for the 2023-24 school year, the math validation process will take place in August after school starts.

Changing Math Placement

Students who feel they are not appropriately placed should meet with their teacher and counselor to determine if a schedule correction is needed (BP 6152.1). Within 10 school days of an initial placement decision or placement decision upon reevaluation, a student and their parent/guardian may appeal the decision to the Superintendent or designee.

Challenge by Examination

PAUSD Board Policy allows high school students to challenge courses by examination (BP 6155). This examination is aligned to state-adopted content standards in mathematics taught in the course being challenged. If a student successfully challenges a course, a grade based on their results and units will be added to their transcript with a note indicating that the requirement was met by examination.

Students wishing to take off-campus courses (non-PAUSD) must have prior approval. Please see the Gunn and Paly websites for more detailed information regarding off-campus courses.

Elementary School

Bridges in Mathematics, 2nd edition, published by the Math Learning Center

Middle School

• Foundational Math (select the green book).
• Concepts in Mathematics (select the red book).
• Algebra 1 (select the blue and gold book).

High School

• Algebra 1 (Prentice Hall); Charles, Hall, Kennedy, et al (Pearson Ed)
• Algebra 1 Common Core; Randall Charles, et. al.; Pearson
• Algebra 2 (Prentice Hall); Charles, Hall, Kennedy, et al (Pearson Ed)
• Algebra and Trigonometry Graphs & Models, Third Edition; Bittinger, Beecher, Ellenbogen and Penna (Pearson Ed)
• Algebra and Trigonometry: Graphs & Models 4th ed
• Calculus, Concepts and Applications Second Edition; Paul A Foerster (Key Curriculum Press)
• Calculus, Early Transcendentals, 8th Edition
• The Practice of Statistics by Starnes et al; published by BFW; 5th ed
• Geometry (Prentice Hall) Foundation Series; Charles, Hall, Kennedy, et al (Pearson Ed)
• Geometry Common Core by Charles, Hall, Kennedy, Bass, Johnson, Murphy, and Wiggins
• Geometry by Jurgenson Brown Jurgenson Published by Houghton Mifflin
• Precalculus Graphical, Numerical, Algebraic Seventh Ed; Demana, Waits, Foley, & Kennedy (Addison Wesley)
• Precalculus, A Graphing Approach; Holt, Rinehart, and Winston (Harcourt Classroom Edu Co) *reference*

Elementary School

• Bridges Family Support Resources.
• Bridges in Mathematics is a research based program.
• What you need to know about Bridges.
• Parent Handout - English | Spanish.

Middle School

• Foundational Math (select the green book).
• Concepts in Mathematics (select the red book).
• Algebra 1 (select the blue and gold book).

In accordance with Senate Bill 359, annually, the Board and the Superintendent or designee shall review student data related to placement and advancement in the mathematics courses offered at District high schools to ensure that ninth-grade students who are qualified to progress in mathematics courses based on their performance on objective academic measures are not held back in a disproportionate manner on the basis of their race, ethnicity, gender, or socioeconomic background.

This report provides the Board with information about 2022-23 current ninth-grade enrollment, class size, and associated trends in mathematics courses. This report is based on data from two weeks after the end of the first quarter. In the future, the math placement data will be collected two weeks after the end of the first quarter, and will be presented to the Board thereafter.

What is the course sequence for middle school? How does that compare to Common Core State Standards for Mathematics (CCSS)?

• The traditional course sequence for most students will cover 4 years of Common Core Math standards in 3 years (Common Core 6, 7, 8, and Algebra)
  • 6th Grade: Foundational Math
  • 7th Grade: Concepts in Math
  • 8th Grade: Algebra 1
• The course sequence for students who pass the validation tests before entering 6th grade will cover 4 (different) years of Common Core math standards in 3 years (Common Core 7, 8, Algebra, and Geometry).
  • 6th grade: Concepts in Math
  • 7th Grade: Algebra 1
  • 8th Grade: Geometry H
• The course sequence for students who pass the validation tests before entering 7th grade, will cover 3 (different) years of Common Core math standards in their remaining 2 years.
  • 7th Grade - Algebra 1
  • 8th Grade - Geometry H

In which grades are validation tests offered?

• Students entering 6th grade may choose to take validation tests in the Spring of their 5th grade year.
• Students entering 7th grade may choose to take validation tests in the Spring of their 6th grade year.
• Students entering 8th grade may choose to take validation tests in the Spring of their 7th grade year.

Can a 6th grade student take 7th grade math?

• Yes. The only way for a 6th grade student to be placed into 7th grade math is to pass the validation tests.

Can a 7th grade student take 8th grade math?

• Yes. 7th grade students who passed the validation tests will be enrolled in Algebra 1 which is an 8th grade course.

Can an 8th grade student take Geometry?

• Yes. 8th grade students who passed validation tests at the end of 5th, 6th or 7th will be placed in Geometry.

How many years of math can a middle school student accelerate through with the validation process?

• Students may accelerate through a total of 1 year of math while in middle school. This will in effect put them 2 years ahead in math.

What does the validation process look like?

• When choosing to partake in the validation process, students will participate in a two part process.
• Students will take Part 1 of the validation process. Contingent on their results on this first part, students will get notified of whether they qualify to continue onto Part 2.

When will the validation tests take place? (how long is the test, where is the test, etc)

• Grade 6 validation tests will be held during the week of May 8, 2023 on the student's current elementary school site (Part 1) and on May 15, 2023 at JLS (Part 2).
• Grade 7 validation tests will be held on May 17, 2023 at the student's current middle school site (Part 1) and on May 22, 2023 at JLS (Part 2).
• Grade 8 validation tests will be held on May 17, 2023 at the student's current middle school site (Part 1) and on May 22, 2023, at JLS (Part 2).
• For Spring 2023, the validation tests will be in-person.

How do I register for the test to skip 6th grade mathematics?

• No registration needed in 2023.

How do I register for the assessment to skip 7th grade mathematics?

• Register your student for the assessment by Monday, April 10, 2023 at 5pm using the form in the letter you received through ParentSquare.

How do I register for the assessment to skip Algebra 1?

• Register your students for the assessment by Monday, April 10, 2023 at 5pm using the form in the letter you received through ParentSquare.

Is there a list of topics covered on the validation tests?

• Yes, the list of topics for the Grade 6 validation tests include:
  • 6th grade:
  • Numerical Expressions and Factors
  • Integers
  • Fractions and Decimals
  • Algebraic Expressions and Properties
  • Equations and Inequalities
  • Ratios and Rates
  • Data and Statistics
  • Area of 2-D Shapes
• Yes, the list of topics for the Grade 7 validation tests include:
  • Operations with Integers, Decimals and Fractions
  • Expressions, Equations and Inequalities
  • Proportional Relationships
  • Bivariate Data
  • 2-D Geometry (angles)
  • Pythagorean Theorem
  • 3-D Geometry
  • Exponents
  • Transformations
  • Probability
• Yes, the list of topics for the Algebra 1 validation test include
  • Functions
  • Equations and Inequalities
  • Linear Functions
  • Systems of Linear Equations
  • Exponential Expressions and Functions
  • Quadratics

Is there a deadline for registration for the tests?

• The deadline for registration for the 7th and 8th grade tests is Monday, April 10, 2023 at 5pm. There is no late registration. The form is included in the notice you received from ParentSquare.

What is the expected level of understanding that a student must demonstrate to pass the test?

• Students are expected to show mastery of the content and the practice standards. This will require fluency in problem solving and in math procedures paired with clear communication in the documentation of their work.
• This test is not a test of potential. Students may be terrific mathematicians but not yet have been exposed to material. This test looks for mastery of the material that is covered within the year-long course.

If my student doesn't pass the validation process before 6th grade, is there another opportunity to accelerate?

• If your student does not pass the test, they will take the 6th grade Foundational Math class. Students have two more opportunities to accelerate; at the end of 6th grade and again at the end of 7th grade. Please note that students may accelerate only once during middle school.

Will we receive a score for the mastery test?

• Yes. A score for the test will be digitally provided and reported to parents/guardians.

What happens if my student is sick on the day of the test?

• If your student is sick on the day of the test, please email msmathil@pausd.org.

If my student has a 504 or IEP will they receive accommodations for the validation tests?

• Yes. Please make sure to note on the form if your student has a 504 or IEP with approved testing accommodations.
• Rising 6th grade students, we will work with your elementary principal regarding needed accommodations.

Does my student need to bring anything on the day of the test? Can my student use a calculator on the test?

• The test is in-person; students should bring a district-issued device, a pencil and an eraser.
• Students should not bring a calculator, smartphone or smart watch with a calculator.

If my student passes the test, will they be in a class with older students?

• Yes. For students entering 6th grade and who pass the Grade 6 tests are placed into math classes with 7th grade students. There is no guarantee that they will have any other 6th grade students in their class.
• Yes. For students entering 7th grade and who pass the Grade 7 test will likely be placed into math classes with 8th grade students. There is no guarantee that they will have any other 7th grade students in their class.

How do I know if my student is ready to skip a grade of math?

• First and foremost, students should be performing strongly in their current grade level course. Students should also have a deep understanding of the material from the course they wish to skip (which is listed above). Additionally, students who are ready to skip a year of math also have solid organization skills, a genuine interest in math, the ability to learn material on their own (without the help of outside tutors), are comfortable asking questions when they are not sure of an answer, are able to work independently, and often look for extensions to the work they are doing in class.

Does PAUSD provide preparation materials for the validation process?

• No. Students who are opting to participate in the validation process must prepare on their own, outside of their current course. Teachers are responsible for providing material relevant to the current course only.

Can my student test out of Geometry?

• Most students will be enrolled in a Geometry course in 9th grade which leads to a calculus course in 12th grade.
• Once students enter high school, they are allowed to challenge courses by examination (BP 6155). If they pass the examination, they will receive a grade and units on their high school transcript with a note that the course requirement was met by examination.

What are the freshman math course offerings for high school?

• Students who successfully complete Algebra in 8th grade will take a Geometry course in 9th grade (Geometry or Geometry H). Students who successfully complete Geometry H in 8th grade will take Algebra 2, Algebra 2/Trig A or Algebra 2/Trig H in 9th grade. Please refer to the district website for more information.

If there are further questions, contact the guidance office of your neighborhood middle school.

• Fletcher Guidance Office
• JLS Guidance Office
• Greene Guidance Office

This FAQ applies to both Multivariable Calculus and Linear Algebra courses.
Students who have taken Multivariable Calculus may choose to move on to Linear Algebra.

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What type of course is Multivariable Calculus (MVC) in PAUSD?

MVC is categorized under the concurrent (not dual) enrollment category. Foothill College has been offering MVC as an online course outside of the regular bell schedule since the 2019-20 school year. The Foothill instructor does not hold a high school teaching credential. Scroll down for definitions of Concurrent and Dual Enrollment.

How many sections of the course have traditionally been taught?

One (1) section for approximately 30 students from both high schools in PAUSD.

What is the history of advanced math courses from community college at PAUSD high schools?

2012-2015
A PAUSD teacher, who was also employed by Cañada College as an instructor, taught the classes through Cañada College. The course was offered outside of school hours. Students from both Paly and Gunn could participate and had to travel to the high school campus where the course was offered, if it was not at their campus of enrollment.

2016-2018
The advanced math courses were taught by other Cañada College instructors; offered mid-way through 7th period plus after school hours, to accommodate the course being a college course and students traveling to either Gunn or Palo Alto High School.

2019-2023
Beginning in 2020, the course moved to an online platform taught by a Foothill College instructor outside of school hours.

The California Department of Education (CDE) updated the dual enrollment parameters in the 2020-21 school year, categorizing these courses as concurrent enrollment.

What is concurrent enrollment?

Concurrent enrollment refers to students taking community college courses that have not undergone curricular alignment or articulation with high school courses. Students in concurrent enrollment courses may transfer credit based on the credit acceptance policy, and these courses are generally scheduled outside of regular bell schedules. The instructors teaching concurrent enrollment courses at the college level do not need high school teaching credentials.

What is dual enrollment?

Dual enrollment is a type of concurrent enrollment guided by the College and Career Access Pathways Act-CCAP (AB 288).

Dual enrollment students take courses, during the regular bell schedule, from PAUSD teachers who hold a high school teaching credential. The California Community College system requires that these instructors meet the minimum qualifications to issue college credit. These courses have gone through a curricular alignment process with Foothill-De Anza Community College District. In addition, PAUSD staff are authorized by the Foothill-De Anza Community College District to teach specific dual enrollment courses through College and Career Access Pathways (CCAP).

Whom may I contact for questions regarding dual enrollment guidelines?

For questions or additional information: Click Here.

What is the difference between College and Career Access Pathways (CCAP) courses and non-CCAP courses?

Dual enrollment courses refer to high school courses that have gone through curricular alignment with a community college. Dual enrollment students are enrolled in two institutions concurrently, therefore earning high school credits and college credits simultaneously. There are two categories: College and Career Access Pathways (CCAP) and non-CCAP.

1. CCAP authorizes California Community College districts to enter into formal partnership agreements with local school districts to expand access to concurrent enrollment opportunities for high school students (AB 288) opportunities for students who may not already be college bound or who are underrepresented in higher education. These courses are taught during the school day by Palo Alto Unified School District (PAUSD) teachers, who are authorized by the Foothill-De Anza Community College District to teach specific dual enrollment courses. Grading for CCAP dual enrollment courses is as follows:
   1. Students in dual enrollment courses receive regular credit per course. For example, if a high school level course earns five credits, the dual enrollment version of that course also earns five credits.
   2. Grades, upon completion of the course, will be weighted similarly to Advanced Placement (AP) or Honors (H) classes in weighted Grade Point Average (GPA) calculations, as they are rigorous courses that have gone through an alignment process with the community college.
2. All other community college courses are non-CCAP courses. Non-CCAP courses are taught by community college instructors during after-school hours.
   1. Prior approval is needed to enroll, and the official community college transcript is provided to the high school so that the course may be added to the high school transcript.
   2. Non-CCAP courses receive double credit; e.g., a five-unit class receives 10 units of credit.
   3. Courses taken off-campus with prior approval will be listed as Credit or No Credit on the PAUSD transcript and will not be included in the GPA.
   4. Students are expected to include their official community college transcript/s as part of their college applications, in addition to the PAUSD transcript. (PAUSD Administrative Regulation AR 6146.11 - Alternative Credits Toward Graduation)

What resources are available for students taking Multivariable Calculus?

Students should contact their counselors with specific questions regarding transcript and graduation requirements, or visit the high school's Off-Campus Courses Frequently Asked Questions (FAQ) page (Palo Alto High or Gunn High).

Is there a cost for classes?

Foothill and De Anza Colleges offer multiple sections of MVC at no cost. High school students are eligible to enroll in any community college in the state without charge as long as they are enrolled in courses that earn them less than the number of units determined by the college. Please refer to the Foothill and De Anza websites for specific information.

How are these math courses identified at Foothill and De Anza colleges?

Foothill course codes are:

• Multivariable Calculus: MATH 1C and 1D
• Linear Algebra: MATH 2B

Can students take Multivariable Calculus at a college or university other than Foothill or De Anza?

Yes, students can take courses from colleges other than Foothill or De Anza and may transfer credit based on the credit acceptance policy, which includes pre-approval. There may be a cost at other colleges.

What is the teaching credential requirement for dual enrollment?

With a recent update from CDE, community college instructors need a high school teaching credential to issue high school credit in dual enrollment (More information at this link for the CDE's Frequently Asked Questions page - question 1). In order to teach a dual enrollment course, PAUSD teachers need to be authorized by the community college to issue college credit.

What is the difference between Single Credit (Concurrent) versus Dual Credit (Dual Enrollment) course?

What are the requirements to teach at a public high school in California?

Teachers must meet the proper credentialing requirements of the state of California. Information can be found at: www.ctc.ca.gov

How can a student sign up for the advanced math course at Foothill?

Foothill offers advanced math courses in various modalities, including asynchronous sections for students with specific schedule needs. In partnership with PAUSD, Foothill screens students to ensure that they meet the prerequisites for the course and makes an effort to accommodate students who wish to be in the same section as their peers. Please contact Foothill Coordinator, Alejandro Favela, for questions regarding the prerequisite screening or enrollment process.

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