# mathematics

##### Perhaps more than any other subject, mathematics is sequential; students layer new concepts onto previous knowledge. The pace of moving forward with curriculum, therefore, is less important than students’ genuine mastery of foundational material. Teachers design learning experiences that make math intriguing, not fearsome, and provide students with the increasing opportunity to synthesize their learning. At Ursuline, students develop a robust problem-solving ability, with the emphasis on showing their thinking pattern rather than merely arriving at answers. In this rigorous curriculum, students progress from arithmetic to working with abstract number concepts in courses that challenge and encourage them to take risks while yielding the satisfaction that comes from successful engagement. Working with data in real-world applications, students become proficient at adapting multiple approaches to solutions.

## Mathematics Classes

- Pre-Algebra AB
- Pre-Algebra A
- Pre-Algebra B
- Algebra I
- Geometry
- Geometry Honors
- Algebra II
- Algebra II Honors
- Pre-Calculus
- Pre-Calculus Honors
- Calculus
- AP Calculus
- Statistics

## Pre-Algebra AB

Intended for 7th grade students with a strong preparatory background in arithmetic and problem solving, this one-year pre-algebra course includes all standard topics of middle school mathematics and introduces students to operations with rational and irrational numbers. It includes evaluating expressions, solving equations and inequalities, writing equations and inequalities to solve problems, measurement and conversions, linear graphs, surface area and volume, and data analysis and probability. Teachers emphasize developing excellent mathematical habits, such as reading mathematics, writing about solutions, and doing neat, complete work. (Grade 7)

## Pre-Algebra A

## Pre-Algebra B

## Algebra I

Students enrolled in Algebra 1 acquire facility in applying algebraic concepts and skills to operations with polynomials, fractions, and exponents, and learn to solve equations and inequalities. Teachers introduce graphing solution sets of open sentences in two variables, particularly linear equations and inequalities, exponents, exponential, quadratic, rational equations and functions. As with all courses, student rely on problem solving techniques and critical thinking in this fast- paced course. (Grade 8 or 9)

## Geometry

In this course students master the basic structure of plane and coordinate Geometry. Teachers develop students’ deductive reasoning powers as students visualize relationships among geometric elements. Students must use their algebraic skills throughout the course and see that the two areas of math are complementary. The course aims to help students acquire precision in their use of mathematical language and increase their critical, creative problem-solving. (Grade 9 or 10)

## Geometry Honors

Students in Geometry Honors reason using postulates and theorems in paragraph, indirect, and formal proofs. Students interact in groups discussing, writing, and communicating ideas towards solution of real-world problems. They look for patterns and write mathematical models. Throughout the course, the teacher presents coordinate geometry, with an emphasis on algebraic concepts. The course contributes to the development of the student’s habits of detail, precise mathematical language and logic. (Grade 9 or 10)

## Algebra II

Algebra II students study functions, their graphs, their inverse functions, operations domain and range of functions. Types of functions studied include quadratic, exponential, logarithmic, higher order polynomial, radical, and rational functions. Students also benefit from an introduction to trigonometric ratios, trig functions, and data analysis. (Grade 10 or 11)

## Algebra II Honors

Algebra II Honors is primarily a fast-paced study of functions; defining functions and inverse functions, operations with functions and domain and range of functions. Students learn about quadratic, exponential, logarithmic, higher order polynomial, radical, rational and trigonometric functions and also work on other topics including data analysis and probability and conic sections. (Grade 10 or 11)

## Pre-Calculus

Prerequisite: Algebra II; teacher recommendation required

Through Pre-Calculus, students prepare for their continued study of mathematics in either high school or college, beginning with a thorough review of Algebra through the study of linear and quadratic functions, exponential and logarithmic functions, trigonometric functions and their applications. Students also encounter polar coordinates and vectors and study number theory, probability and related topics. Students learn to integrate a A TI-83 or TI-84 calculator in their problem-solving. (Grade 11 or 12)

## Pre-Calculus Honors

Prerequisite: Algebra II; teacher recommendation required

Through Pre-Calculus, students prepare for their continued study of mathematics in either high school or college. It includes a thorough review of Algebra through the study of linear and quadratic functions, exponential and logarithmic functions, trigonometric functions and their applications. Students also encounter polar coordinates and vectors and study number theory, probability and related topics and conclude the year by learning about limits. Students rely on their problem-solving skills to engage real-world situations with the utilization of technology. Students learn to integrate a TI-83 or TI-84 calculator in their problem-solving. (Grade 11 or 12)

## Calculus

Prerequisite: Pre-calculus

Students begin this course by studying limits and continuity and progress through derivatives, derivative rules and applications of the derivative, including optimization, curve sketching and related rates. Students study Riemann sums and integrals and use the graphing calculator to explore concepts and verify and facilitate solutions. Students regularly communicate mathematics orally and in sentence format to explain problem solutions. (Grade 12)

## AP Calculus

Prerequisite: Precalculus

This college-level course follows the program required for Calculus AB in the Advanced Placement course description including limits, differentiation and integration. Students work rigorously to achieve a high level of understanding of underlying concepts of calculus, concepts which are not necessarily developed explicitly in class. Students use the graphing calculator extensively to explore concepts, verify calculations, and support many problems with visual representation. (Grade 12)

## Statistics

This course, offered to juniors and seniors, may be taken concurrently with AP Calculus, Calculus or Pre-Calculus. Through real-world case analysis, students explore and develop their statistical thinking and understanding of data concepts such as frequency distribution and graphs, measures of central tendency, variation and position, counting techniques, probability, normal distribution, confidence intervals and hypothesis testing. (Grade 11 or 12)