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:

 

 

 

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

 

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 a faster pace 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. The use of graphing calculators will be introduced in this course: A TI-83 or TI-84 graphing calculator is recommended. Upon completion of the course students should be able to solve a variety of algebraic problems individually and collaboratively.

Course Sequence: Completion of Algebra 1 Honors or Algebra 1 Additional Topics. 
Students need to achieve a final grade of 80 or above in Algebra 1 Honors  and receive a teacher recommendation for courses 431. 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 back 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-83 or TI-84 graphing calculator is recommended. 

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

 

Course Sequence: Completion of Algebra 2 (parts 1 & 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. Students are required to take the AP Exam in the spring.

 

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.

 

Course Sequence: Completion of Precalculus

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. Students need to achieve a final grade of 80 or above in Precalculus, and receive a teacher recommendation for this course. This course prepares students to take the AP Calculus AB exam.  There is the potential to earn college credit for this course. Students are required to participate in the alternating day second semester portion of the course and to take the AP Exam.