## Mathematics

The Mathematics department at Madison Park Technical Vocational High School is committed to the academic success of all students. The Math faculty is committed to helping students develop critical thinking and analytical skills. A strong math foundation is essential to student success in all industries.

#### Math Sequence

Students that pass Algebra 1 in 8th grade or do accelerated Math work in summers or during the school year will have an opportunity to follow an advanced sequence and have the opportunity to enroll in Calculus in the Senior year. Calculus is the capstone course in the Math curriculum.

Beginning in the 2017-2018 school year, the Boston Public Schools moved to integrated math program which includes Algebra, Geometry and Advanced Algebra standards into each sequential math course. Please see the diagram below.

#### Standardized Testing

The Math faculty at Madison Park prepare students for the standardized entrance or placement exams at post-secondary institutions. Community colleges require the Accuplacer test to place students in college courses or remedial courses if necessary. Four year colleges often require students to take the SAT or ACT test for admission, with different cutoff scores at each institution.

**GRADE 9**

**Integrated Math I**

#### Course Overview

Integrated Math I is the first course in an integrated high school mathematics pathway consisting of Math I, 2, and 3 replacing the traditional pathway consisting of Algebra I, Geometry, and Algebra II. The fundamental purpose of the Integrated Math I course is to formalize and extend the mathematics that students learned in the middle grades.

In this course, students use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas and through this collaboration achieve fluency with the mathematical content.

#### Course Objectives

By the end of the course students will be able to:

- extend their understanding of numerical manipulation to algebraic manipulation
- synthesize their understanding of function;
- deepen and extend their understanding of linear relationships
- apply linear models to data that exhibit a linear trend
- establish criteria for congruence based on rigid motions
- apply the Pythagorean Theorem to the coordinate plane

#### Course Assessments

- Integrated Math 1 will follow the district assessments as part of the district Scope and Sequence

### RoxxMapp Accelerated Math 1

#### Course Overview

Accelerated Math is an advanced Grade 9 offering for students who have mastered most Algebra 1 concepts. Selection for this course is based on a placement test given in the first week of school. This course will cover all Algebra and Geometry concepts and prepare students for Advanced Algebra in their sophomore year. The curriculum of this course is aligned to Bunker Hill Community College’s MATH 097.

#### Course Objectives

By the end of the year, students will master the objectives of Algebra 1 and Geometry

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

**GRADE 10**

**Geometry**

*to be replaced by Integrated Math 2 during the 2018-2019 school year*

#### Course Overview

The fundamental purpose of the high school Geometry course is to formalize and extend students’ geometric experiences from the middle grades. In this course, students explore more complex geometric situations and deepen their explanations of geometric relationships, presenting and hearing formal mathematical arguments. Note that important differences exist between this course, where transformations are emphasized, and the historical approach taken in geometry classes.

#### Course Objectives

By the end of the year students will be able to:

- Establish criteria for congruence of triangles based on rigid motions
- Establish criteria for similarity of triangles based on dilations and proportional reasoning
- Develop explanations of circumference, area, and volume formulas
- Apply the Pythagorean Theorem to the coordinate plane
- Prove basic geometric theorems
- Extend work with probability

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

### Roxx Mapp Accelerated Math 2

Advanced Algebra is an accelerated Grade 10 offering for students who excelled in Algebra 1. This course will cover Geometry and Advanced Algebra concepts and prepare students for Precalculus in the junior year. This course is aligned to Bunker Hill Community College’s MATH-99.

**GRADE 11**

**Advanced Algebra**

*to be replaced by Integrated Math 3 during the 2019-2020 school year.*

#### Course Overview

This high school Algebra II course builds on work with linear, quadratic, and exponential functions, with students extending their repertoire of functions to include logarithmic, polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, are facile with algebraic manipulations of expressions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.

#### Course Objectives

By the end of the course students will be able to:

- relate arithmetic of rational expressions to arithmetic of rational numbers
- expand understandings of functions and graphing to include trigonometric functions
- synthesize and generalize functions and extending understanding of exponential functions to logarithmic functions
- relate data display and summary statistics to probability and explore a variety of data collection methods.

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

**GRADE 12**

**Pre-Calculus**

#### Course Overview

Precalculus is a course designed to prepare students for topics covered in an introductory Calculus course at the college level. This course focuses on mastery of critical skills and exposure to new skills necessary for success in subsequent math classes. It begins with a comprehensive study of functions and moves into an analysis of fundamental calculus concepts such as the difference quotient and the notion of “taking a limit.” In addition to introducing students to terminology and concepts essential to the study of Calculus, this course should also help students develop reasoning and analytical skills which may be applied to problems outside the typical realm of mathematics.

*Pre-requisite*: Advanced Algebra and Geometry

#### Course Objectives

At the end of the course students should be able to:

- Graph linear, polynomial, trigonometric, exponential, and logarithmic equations
- Identify and describe transformations for given graphs with different parameters
- Invert, compose, multiply and divide functions
- Represent and solve real-world problems requiring optimization of trigonometric functions (mostly sine and cosine functions)
- Use the unit circle to determine the values of trigonometric functions
- Define, state and apply trigonometric identities
- Represent and solve real world problems involving trigonometric functions
- Define and evaluate the six trigonometric ratios
- Solve triangles using trigonometric ratios

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

**Calculus**

#### Course Overview

Differentiation of algebraic and transcendental functions, applications of the derivative, differentials, indefinite integrals, definite integrals. Partially fulfills Core Mathematics requirement.

The goal here is developing the student’s geometric insight into the concepts of differentiation and integration, and applying these concepts to problem-solving and “real world application.” Knowledge and the ability to work these ideas is necessary for further studies of mathematical subjects.

Students will become proficient in techniques of differentiation, understand the concept of rate of change and how to use it to solve real world problems, the concept of definite and indefinite integral and their relations to area and rate of change. In particular, the students will be able to explain the concept of continuous functions, compute instantaneous rate of change, compute derivatives of polynomial and transcendental functions, differentiation to solve related rate and optimization problems, compute definite and indefinite integrals

*Pre-requisite*: Pre-Calculus or Pre-Calc Summer Bridge Program at Northeastern University

#### Course Objectives

By the end of the course students will be able to:

- Use both the limit definition and rules of differentiation to differentiate functions.
- Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
- Learn to work with exponential, logarithmic and trigonometric functions and their applications in applied problems.
- Calculate derivate for various type of functions using definition and rules.
- Apply differentiation to solve applied max/min problems.
- Apply differentiation to solve related rates problems.
- Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
- Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
- Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions, and integration by parts.
- Use L’Hospital’s rule to evaluate certain indefinite forms.
- Learn about anti-derivative and the Fundamental Theorem of Calculus and its application.
- Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
- Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

**Statistics**

#### Course Overview

This senior-year course is designed to examine the concepts of Center, Spread, and Shape of one-variable data. The course will also focus on two-variable data sets as well as designing observational and experimental experiments. The importance of the Central Limit Theorem and Sample size will be covered as well as how to make an inference about data in order to help in decision making. At BCLA, Statistics is also designed to complement the Senior Civics course in designing and analyzing data around their chosen Civics issue. Students will work toward completing an Exhibition toward their Civics project that will include: Data Collection and making inferences about the data from the study. *Pre-Requisite*: Advanced Algebra

Course Objectives

By the end of the course, students will be able to:

- Examine distributions of data and detect important characteristics, such as shape, location, variability and unusual features

- Observe patterns in data and generate conjectures about relationships among variables
- Connect the notion of how one variable may be associated with another permeates almost all of statistics by making simple comparisons of proportions through linear regression
- Understand the difference between association and causation
- Understand that if data is to be collected to provide an answer to a question of interest, a careful plan must be developed
- Collect data in a reasonable way, through either sampling or experimentation
- Analyze data and draw conclusions from data in an appropriate way that depends on how the data was collected
- Understand that random phenomena are not haphazard; they display an order that emerges only in the long run and is described by a distribution
- Understand that the mathematical description of variation is central to statistics
- Use models to draw conclusions from data, while the data is allowed to criticize and even falsify the model through inferential and diagnostic methods
- Select a reasonable model, including a statement in probability language, when making an inference from data

#### Course Assessments

- September pre-assessment
- December and March- formative assessments
- June summative assessment

**Questions and Concerns?** Please reach out to your son or daughter’s Math teacher or guidance counselor.