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Quantitative Reasoning With Advanced Math Topics (QRAT)


This course is intended for students who are not ready for or interested in the Pre-calculus/Calculus pathway their senior year but still want to continue developing their mathematical knowledge and challenge their math skills while preparing for attendance at a CSU or UC. These students may be interested in math-intensive majors such as science, technology, engineering, and/or math (STEM), but this is not a requirement to participate in this course.

QRAT At-A-Glance

The units of study build from previous math concepts such as linear, quadratic, and exponential functions, to provide opportunities for students to develop a greater perspective of the underlying structures of mathematics and how to connect mathematical topics. This enables students to continue to persevere through problem-solving and to develop quantitative reasoning skills necessary for success in college-level courses. Polynomial and rational functions, as well as basic calculus concepts, advance the student's mathematical content knowledge through a quantitative reasoning lens. The course culminates with an in-depth unit about the mathematics of finance. The national Common Core Standards for Mathematical Practice are an integral part of each lesson and specific highschool Common Core State Standards are the focus of the mathematical content. Through a facilitative teaching approach, the lessons and tasks provide students with opportunities to solve challenging problems in which they gather, analyze, and evaluate information, work effectively in groups to make decisions using critical reasoning skills, as well as opportunities to communicate concisely through written and oral language.

  • UNIT 1 | Team Building & Problem Solving
  • UNIT 2 | Linear Functions
  • UNIT 3 | Quadratic Functions
  • UNIT 4 | Exponential Functions
  • UNIT 5 | Logarithmic Functions
  • UNIT 6 | Systems of Equations & Inequalities
  • UNIT 7 | Absolute Value & Piecewise Functions
  • UNIT 8 | Financial Mathematics

A passing grade in Integrated Math III or Intermediate Algebra II

Intended for high school seniors who place into:

  • Level 3 “Standard Met” on CAASPP
  • Level 2 “Standard Nearly Met” on CAASPP (students who placed into Level 2 “Standard Nearly Met” may participate in the course with a counselor/math teacher recommendation)

Students who typically enroll in this course:

  • Are not ready to take an AP level math/QR course.
  • May have originally been placed into pre-Calculus.
  • Could move beyond a “just-got-by” status from IM III or Intermediate Algebra II and improve their preparation to succeed in college-level mathematics
  • Would prefer to take a course that looks and feels different and gives them credit, rather than retaking a course for no additional credit.
  • May not have planned on taking a senior year math course.

  • Students are immediately engaged in a Daily 2 and a Number Sense activity developed specifically for 4th-year math students.
  • A task is launched using a variety of strategies, such as real-world context, video, or group activity. Students proceed in groups to complete the task while the teacher facilitates the learning by providing questions, giving structure to think time and group collaboration, selecting and sequencing student work to be presented during the whole class discussion.
  • Each task is debriefed by the entire class through various methods. Some examples include students presenting their work, making comparisons and connections with the work of others or questions from the teacher that ensure complete understanding.
  • Students write and reflect about their reasoning and work, as well as the work of their peers, through exit slips or journal entries.

Why Our Courses?

ravinccr.jpgFor over a decade, Sac States’ Center for College & Career Readiness has leveraged the expertise of 4-year institutions, feeder high school districts, community colleges, and county offices of education to better prepare college and career-bound high school seniors with the 21st Century skills necessary to meet the mathematical thinking and problem-solving expectations of higher education courses and workplace requirements.

The success of our courses stems from the fact that it is not only a living curriculum and pedagogy that is designed to meet the immediate needs of high school seniors, but it also embodies the structural flexibility to continually be informed by our vibrant intersegmental partnerships. All educational segments collaborate to define the challenges around preparation in mathematics while providing the foundation to forge better-aligned instructional practices across schools, colleges, and universities for the success of our students.

Our courses were created to serve the students we have traditionally given up on mathematically.

Ravin Pan, Assoc. Professor, Sac State Teaching Credentials Program

QRAT & TQR Professional Learning Program

thumbnail_qrat_cover.pngThe professional learning program offers background and instruction in using facilitation as the classroom approach to helping seniors in high school think more critically, solve problems in different ways, and be able to apply their learning to real-world contexts. Teachers who attend will read about growth mindset and apply this notion in the classroom. Similarly, teachers will examine authentic student work, using formative assessment to guide their instruction and understand how to differentiate their instruction to meet the needs of all learners.

Learning Outcomes for Teachers

  • Demonstrate their new understanding of what comprises good teaching: moving teachers from lecture and direct instruction to a facilitative approach.
  • Use a variety of formative assessment tools and practices to plan and evaluate their instruction better to meet the needs of all learners in the classroom. Teachers will guide and support students to use standards for mathematical practice, such as the ability to make sense of problems and persevere in solving them; reason abstractly and quantitatively; construct viable arguments and critique the reasoning of others; model with mathematics; use appropriate tools strategically; attend to precision; look for and make use of structure; look for and express regularity in repeated reasoning.
  • Use a variety of facilitative teaching and questioning strategies to provide opportunities for students to access, investigate, and reason through the mathematical content of the TQR/QRAT courses.
  • Learn the value of engaging with teachers in the professional learning program and in their own schools to discuss and practice a growth mindset.
  • Demonstrate the ability to gather, evaluate, and apply important and valuable contextual qualitative and quantitative data to understand the student’s academic abilities in math with a greater foundation of conceptual understanding. Hence, students taught by teachers in this professional learning program will be able to solve conceptual and pragmatic mathematics questions in the 12th-grade course.

To accommodate teachers' busy schedules, the Professional Learning Program is offered twice a year: once in the summer, over the course of a week, and once in the winter, over the course of several months.

Continuing Education Units (CEUs)

Continuing Education Units are available to teachers upon successful completion of the TQR/QRAT Professional Learning Program. Registration and payment must be received no later than two weeks following the last class meeting.

Complete this Registration Agreement and follow the instructions listed.

The cost is $65.00 for 2 units.

For more information, contact:
Liz Arellanes
Sacramento State College of Continuing Education
(916) 278-6249

Other CSU Mathematics Bridge Courses

In addition to Quantitative Reasoning with Advanced Math Topics (QRAT), there are other mathematics courses and projects within the CSU that focus on supporting mathematics and quantitative reasoning readiness among K-12, CSU, and community college educators.

The Projects in the CSU Focus On:

  • Principles in preparing teachers for 12th-grade mathematics and/or quantitative reasoning
  • Content and pedagogical practices
  • Topics in mathematics and quantitative reasoning that develop and address K-12, community college, and CSU requirements
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