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Mathematics

It is the core mission of Ashburnham-Westminster Regional School District for every student to approach mathematics with confidence, be empowered to think quantitatively, and to be a creative problem solver.  To this end, we are committed to a program built on teaching and learning that actively engages students in experiences that stimulate curiosity, inquiry, joy, and a deep understanding. We recognize the need to move students beyond the memorization of procedural components in order to communicate mathematically through sound reasoning and conceptual understanding. 

 

We will consistently and expertly:

  • Maintain high expectations
  • Foster student engagement through a growth mindset
  • Differentiate instruction through small groups, centers, and tiered activities
  • Develop meaningful, stimulating, rich tasks 
  • Elicit and celebrate different approaches to problem solving
  • Promote discourse to encourage discovery and convey understanding

 

We believe mathematics surpasses content and skills and serves as a conduit for the development of lifelong, logical thinking pathways.

  • MAT 0452  Algebra 1  (Grade 9) Everyday Full Semester 1.00 Credit

    MAT 0450  Algebra 1 Additional Topics (Grade 10)  Everyday other day Full Semester 0.50 Credit

    MAT 0456  Algebra 1 Honors (Grade 9) Everyday Full Semester 1.00 Credit 

    Course Sequence: Completion of Algebra 1 for Algebra 1 Additional Topics. Students need to receive a teacher recommendation for honors.

    Courses Algebra 1 (417) and Algebra 1 Additional Topics are designed to develop mastery of Algebra 1 mathematical concepts over a longer period of time, whereas the honors version of Algebra 1, course 416, will introduce concepts at an accelerated rate and explore topics at a deeper level.

    These courses will focus on four critical areas:

    (1) deepen and extend understanding of linear and exponential relationships;

    (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions;

    (3) extend the laws of exponents to square and cube roots; and

    (4) apply linear models to data that exhibit a linear trend.

     

    Along with the four critical areas, the course will also incorporate the use of critical thinking, including repeated reasoning, and precise written and oral communication.

    At a minimum, a scientific calculator, such as a TI-30XIIS, is strongly encouraged for the course. As the use of graphing calculators will be introduced in this course, a TI-84 graphing calculator is recommended instead. Upon completion of the course, students should be able to solve a variety of algebraic problems individually and collaboratively.

     

  • MAT 0440 Geometry (Grades 10-11) Everyday Full Semester 1.00 Credit 

    MAT 0446 Geometry Honors (Grades 9-10) Everyday Full Semester 1.00 Credit 

    Course Sequence: Students must achieve a final grade of 80 or above in Algebra 1 and receive a teacher recommendation for Geometry Honors, course 0446.

    The fundamental purpose of the Geometry course is to formalize and extend students’ geometric experiences with emphasis on precise communication and logical repeated reasoning while working independently and collaboratively. Students will practice perseverance in solving problems while looking to discern patterns and derive general methods and shortcuts. Concepts covered in this course include congruence, similarity, right triangles, trigonometry, circles, measurement, probability, and statistics.

    The course will focus on six critical areas:

    (1) establish criteria for congruence of triangles based on rigid motions;

    (2) establish criteria for similarity of triangles based on dilations and proportional reasoning;

    (3) informally develop explanations of circumference, area, and volume formulas;

    (4) apply the Pythagorean Theorem to the coordinate plane;

    (5) prove basic geometric theorems; and

    (6) extend work with probability.

    At the honors level, this course will introduce concepts at an accelerated pace and explore topics in greater depth than those covered in course 427.

    A scientific calculator capable of evaluating trigonometric functions, such as a TI-30XIIS, is strongly recommended for this course.  

  • Quantitative Reasoning (Grade12) Everyday Full Semester 1.00 Credit

    Course Sequence: Completion of Algebra 2.  

    QR is an engaging and rigorous course for students of all levels/or with a variety of mathematical backgrounds that prepares students for a range of future options in non-mathematics-intensive college majors or for entering workforce training programs. This integrated course emphasizes statistics, financial literacy, and the application of previously learned skills to new real-life situations.  The course prepares students to use algebra, geometry, trigonometry, and discrete mathematics to model a range of situations and solve problems. QR builds on, reinforces, and extends what students have learned and covers a wide range of mathematics topics in an effort to help students understand mathematics more deeply. The course offers student activities in a range of applied contexts and helps students develop college and career readiness skills.

  • MAT 0460 Algebra 2 Essentials(Grade 12) Everyday Full Semester 1.00 Credit

    MAT 0462 Algebra 2 (Grades 10-11) Everyday Full Semester 1.00 Credit 

    MAT 0463 Algebra 2 Honors (Grade 10-11) Everyday Full Semester 1.00 Credit 

    Course Sequence: Completion of Algebra 1 Honors or Algebra 1 Additional Topics. Students must achieve a final grade of 80 or above in Algebra 1 Honors and receive a teacher recommendation for courses 0463. Students need to successfully complete the Geometry course prior to entering any level Algebra 2 course.

    Building on their work with linear, quadratic, and exponential functions from Algebra 1, students will extend their repertoire of functions to include logarithmic, polynomial, rational, trigonometric, and radical functions in the Algebra 2 course. Concepts covered in this course also include the complex number system, polynomials, rational expressions and equations, inequalities, and probability and statistics.

    The course will focus on four critical areas:

    (1) relate arithmetic of rational expressions to arithmetic of rational numbers;

    (2) expand understandings of functions and graphing to include trigonometric functions;

    (3) synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions; and

    (4) express patterns as sequences and series and relate to linear and exponential equations. 

    Along with the four critical areas, the course will also incorporate the use of critical thinking, including repeated reasoning, and precise written and oral communication.

    Upon completion of the course, students should be able to solve a variety of algebraic problems individually and collaboratively. The use of technology will be an integral part of this course, and graphing calculators will be used frequently: A TI-84 graphing calculator is strongly recommended. 

     

    The sequence of Algebra 2 courses is offered at three different levels. The Algebra 2 Essentials sequence is designed for students who would like to take a concept-building approach to the introduction and mastery of mathematical concepts typically covered in an Algebra 2 course. The honors-level courses will introduce concepts at an accelerated pace and explore topics at a deeper level than typically covered in an Algebra 2 course.  

     

  • Pre-Calculus (Grades 11-12) Everyday Full Semester 1.00 Credit 

    Course Sequence: Completion of Algebra 2

    This course is required for all students intending to study calculus in the future and is a good choice for any student who plans to continue their education in an engineering, business, or science-related field.

    The course will focus on 4 critical areas:

    (1) extend work with complex numbers;

    (2) expand understanding of logarithmic, exponential, and trigonometric functions;

    (3) use characteristics of polynomial and rational functions to sketch graphs of those functions; and

    (4) introduce the graphical and algebraic concept of limits.

    Graphing calculators are an integral part of the course and, therefore, will be required for all students. (A TI-84 graphing calculator is a strongly recommended model) Emphasis is placed on active participation through modeling, technology, critical thinking, group activities, and precise communication in mathematics

     

     

     

  • MAT 0482 Probability and Statistics (Grades 11-12) Everyday Full Semester 1.00 Credit 

    MAT 0484 AP Probability and Statistics (Grade 12) Everyday Full Semester 1.00 Credit 

    Course Sequence: Completion of Algebra 2

    This course is an elective for those students wishing to continue their study in mathematics.  Many academic programs at the college level include Statistics as a requirement, and some knowledge of statistics is necessary to be an informed citizen.   Students will be given the opportunity to explore major statistical and probabilistic concepts in order to make decisions and conclusions. Such topics include describing variation in data and investigating probability distributions, understanding patterns and uncertainty, and developing data-based predictions, decisions, and conclusions. Students will explore the major concepts of statistics through investigations, problem solving, use of technology, and writing.

    The use of technology will be an integral part of this course; graphing calculators and computational programs will be used frequently. Students should have achieved a final grade of 75 or better in Algebra 2 and/or a teacher recommendation to be prepared for this course.

    Summer work may be required. Enrollment in the AP course requires students to take the AP Exam in May.

     

  • MAT 0492 Calculus Honors (Grade 12) Everyday Full Semester 1.00 Credit

    Course Sequence: Completion of Precalculus

    Calculus is the mathematics of change and motion. This course will review key concepts learned in the Precalculus course and apply these concepts to the study of limits, derivatives, integration, and their applications. Emphasis will be placed on active participation through modeling, critical thinking, group learning activities, and precise communications in mathematics.  Students will use graphing calculators as a tool to support problem solving. As an honors course, this course will address topics at a quicker pace and explore concepts at a deeper level. Students need to achieve a final grade of 80 or above in Precalculus, and receive a teacher recommendation for this course.

     

  • MAT 0494 Advanced Placement Calculus AB (Grade 12) Everyday Full Semester 1.00 Credit

    MAT 0495 AP Calculus AB Part 2 (Grade 12) Every other day Full Semester 0.50 Credit

     

    Course Sequence: Students need to achieve a final grade of 80 or above in Precalculus, and receive a teacher recommendation for this course. 

    This course follows the AP Calculus outline as presented by the College Board. Topics covered are functions and graphs, limits and continuity, differential calculus, integral calculus and the application of these concepts to real world problems. Emphasis will be placed on active participation through modeling, critical thinking, group learning activities, and precise communications in mathematics.  Students will use graphing calculators as a tool to support problem solving and communications. Summer work may be required. This course prepares students to take the AP Calculus AB exam. Enrollment in this course requires students to take the AP Exam in May.

     

     

  • AP Pre-Calculus  (Grades 11-12) Everyday Full Semester 1.00 Credit 

    Course Sequence: Completion of Algebra 2

    This course is required for all students intending to study Advanced Placement (AP) Calculus in the future and is strongly recommended for any student who plans to continue their education in an engineering, business, or a science related field. The course is designed to be the equivalent of a first-semester college precalculus course. AP Precalculus provides students with an understanding of the concepts of college algebra, trigonometry, and additional topics that prepare students for further college-level mathematics courses.

    This course explores a variety of function types and their applications—polynomial, rational, exponential, logarithmic, trigonometric, polar, parametric, vector-valued, implicitly defined, and linear transformation functions using matrices.  Graphing calculators are an integral part of the course and, therefore, will be required for all students. (A TI-84 graphing calculator is a strongly recommended model)

    Emphasis is placed on active participation through modeling, technology, critical thinking, group activities, and precise communication in mathematics. Students are strongly encouraged to take the AP Exam in May.