Mathematics

FOUNDATIONAL MATHEMATICS is the first year in a three-year accelerated math course sequence preparing students for high school Algebra in 8th grade. It extends student understanding and skill to compute with rational numbers (decimals, fractions, integers) and introduces algebraic and proportional reasoning. Many of the concepts and skills will have further reinforcement in a context requiring statistical and geometric (2D) reasoning. 

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. Instruction is guided by The 8 Mathematical Practice Standards: make sense of problems and persevere in solving them; reason abstractly and quantitatively; model with mathematics; attend to precision; use appropriate tools strategically; look for and make use of structure; and look for and express regularity in repeated reasoning. 

In 6th grade, students are heterogeneously grouped. Extension and enrichment opportunities are available to all students. Information about the math pathways can be found at the district website.

CONCEPTS IN MATHEMATICS is the second year in a three-year accelerated math course sequence preparing students for high school Algebra in 8th grade. 

It extends student understanding and skill to compute with rational numbers to irrational numbers and extends algebraic and proportional reasoning. Students solve real world problems with 3-dimensional figures (surface area, volume); draw, construct, and describe 2D and 3D figures, understand congruence and similarity of figures using models and other mathematical tools, and solve real-life and mathematical problems involving angle measures. Students move from plotting discrete points to graphing and manipulating linear equations in a variety of forms and investigating patterns associated with bivariate data. This Grade 7 course provides initial exposure to investigating chance processes where students develop, use, and evaluate probability models. 

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. Instruction is guided by The 8 Mathematical Practice Standards: make sense of problems and persevere in solving them; reason abstractly and quantitatively; model with mathematics; attend to precision; use appropriate tools strategically; look for and make use of structure; and look for and express regularity in repeated reasoning. 

In 7th grade, students are heterogeneously grouped. Extension and enrichment opportunities are available to all students. Information about the math pathways can be found at the district website.

The fundamental objectives of this Common Core-aligned course are to formalize and extend the mathematics students learned in their previous two courses in middle school. The course includes the study of both linear and non-linear functions. Topics covered include introduction to the concept of a function, solving algebraic equations, solving and graphing linear inequalities, graphing linear equations, writing linear equations for a variety of contexts, and solving systems of linear equations as well as simplifying exponential expressions, graphing exponential functions, factoring quadratics, solving and graphing quadratic functions, applications of quadratic and exponential functions and simplifying irrational and exponential expressions. The course will prepare students for one of the Geometry courses offered to entering high school students.

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.

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