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 this already compacted program may take part in the Math Validation Process and, in effect, cover five years of math in three 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.

For Spring 2025, rising sixth, seventh, and eighth-grade students who wish to accelerate beyond the already compacted middle school math program may participate in the Math Validation Process. 

The Math Validation Process consists of one paper-and-pencil assessment. This assessment will evaluate the readiness of the grade-level math course the student would like to challenge, in addition to the student's knowledge of the topics and skills covered in the course. In early February, registration information will be provided to parents of current grade 5, 6, and 7th-grade students via Parent Square.

These assessments are aligned to the state-adopted mathematics content standards. They consist of multiple-choice (MC) and free-response questions (FRQ). The assessments were developed in partnership with WestEd, a national research, development, and service leader, alongside PAUSD Math Instructional Leaders. 

• Interested students may opt in to take the test.
• The test will be administered in March. 
• The test will cover the grade-specific standards and concepts for mastery. 

Grade 6 Validation Process

Grade 5 students who attempt but do not pass the validation test will be enrolled in  Grade 6 Foundational Math as described in the sequence. Students who pass the test will be enrolled in 7th-grade Math Concepts.

Grade 7 Validation Process

Grade 6 students who attempt but do not pass the validation test will be enrolled in Grade 7 Math Concepts as described in the sequence. Concepts in Math is the appropriate math placement for most students for their 7th-grade year. Students who pass the test will be enrolled in 8th grade Algebra 1 (with 8th grade students).

Grade 8 Validation Process

Grade 7 students who attempt but do not pass the validation test will be enrolled in Algebra 1. Algebra 1 is the appropriate math placement for most students for their 8th-grade year. Students who pass the test will be enrolled in Geometry Honors.

• Q: Is my child required to take the math validation test?
  A: No, this test is optional.  In late January, registration information (with specific testing dates) will be provided to parents of current grade 5, 6, and 7th-grade students via Parent Square. Students must register to participate.
   
• Q: What are the dates for the validation test?
  A: In late January, registration information (with specific testing dates) will be provided to parents of current grade 5, 6, and 7th-grade students via Parent Square. Students must register to participate.
   
• Q: Where will the validation test be held?
  A: Validation tests will be administered (after school hours) at JLS. 
   
• Q: How long does the test take?
  A: Test time will be approximately 1.5 – 2 hours.
   
• Q: Are there study materials for the test?
  A: No. Only the information on the standards of the course being challenged will be available.
   
• Q: Is there just one test, or a separate test for each challenged course?
  A: There will be only one test for each challenged course. (i.e., one for each grade level: 6, 7, and 8).
   
• Q: Who is scoring the paper-and-pencil test?
  A: PAUSD math teachers will score the test.
   
• Q: Will my child’s results be shared with me after they are scored?
  A: Yes.
   
• Q: What happens if my child doesn’t pass the validation test?
  A: Students who do not pass the validation test will be placed in a math course based on their current grade-level sequence.
   
• Q: Are retakes allowed?
  A: No. Retakes will not be allowed.
   
• Q: May I accompany my child during the test?
  A: No. All students must complete the test in a standardized testing environment without parent accompaniment.
   
• Q: May a parent review the test if they believe there was an error in scoring?
  A: No, as these are secure tests.