## Middle School

Course Offerings

**Grade 6 Math**

The focus is on five critical areas:

- Connecting concepts of ratio, rate, and proportion to solve problems
- Extending the number system to rational numbers and integers
- Writing, interpreting, and applying expressions and equations
- Developing understanding of probability and statistical thinking
- Reasoning about geometric shapes and their measurements

**Foundations of Algebra**

The focus is on four critical areas:

- Develop understanding of and applying proportional relationships
- Develop understanding of operations with rational numbers and work with variable expressions and linear equations
- Solving problems involving scale and geometric constructions and investigating two- and three- dimensional shape
- Drawing inferences about populations based on samples

**Algebra 1**

The focus is on four critical areas:

- Formulating and reasoning about expressions and linear equations in both one and two variables
- Solving and applying linear equations and systems of linear equations
- Investigating functions and their applications
- Analyzing two- and three-dimensional space and figures using geometric concepts and Pythagorean Theorem

## Upper School

**Integrated Math Sequence:** Drawing on the Massachusetts Mathematics Curriculum Framework: Model Integrated Pathway, this three-year integrated math sequence looks deeply at mathematical reasoning as a framework for discovery, exploration, and understanding. The courses build innovators’ competence in mathematical reasoning: asking probing questions, generalizing patterns, building strong arguments, finding multiple approaches to solving problems, reflecting on the problem-solving process, and communicating clear results.

**Upper School Course Offerings**

Innovators will explore mathematics as a cycle: we take problems (sometimes from the real world), abstract them, perform mathematical processes and then apply and communicate our understanding. Each course spirals through the threads of number and quantity, statistics and probability, algebra, geometry, trigonometry, and functions, going deeper and integrating these content domains to help innovators develop various tools, representations, and ways of thinking mathematically.

**Math electives:** After completing the integrated math sequence, innovators may select from a series of electives that may include statistics, calculus, and multi-variable calculus.

**Integrated Math I** — Prerequisite: Algebra I or by placement

- Extend understanding of numerical manipulation to algebraic
- Synthesize understanding of function
- Deepen and extend understanding of linear, exponential, and quadratic expressions and functions
- Linear modeling
- Congruence and right triangle geometry
- Apply geometry to the coordinate plane

**Integrated Math II** — Prerequisite: Algebra I or by placement

- Parent functions and their transformations
- Polynomial, rational, and logarithmic functions
- Conic sections and circles
- Combinations and probability
- Right triangle trigonometry and establish criteria for similarity of triangles based on dilations and proportional reasoning
- Apply geometry proof

**Integrated Math III** — Prerequisite: Integrated Math II or by placement

- Apply methods from probability and statistics to draw inferences and conclusions from data
- Trigonometric functions and their graphs
- Trigonometric identities and proof
- Vectors, polar coordinates, and parametric equations
- Difference quotient and introduction to limits

**Calculus** — Prerequisite: Integrated Math III or by placement

- Parent functions and their transformations
- Polynomial, rational, and logarithmic functions
- Conic sections and circles
- Combinations and probability
- Right triangle trigonometry and establish criteria for similarity of triangles based on dilations and proportional reasoning
- Apply geometry proof

**Calculus** — Prerequisite: Integrated Math III or by placement

This is a full-year course designed to show how Calculus can be used to solve real-world problems and to prepare students to find success in a first-year college Calculus course. Students begin the year by reviewing functions and are introduced to limits, differentiation and its applications, and integration and its applications as the year progresses. Applications play an important role in this course and are drawn from business, social and behavioral sciences, life sciences, and physicals sciences. Since technology is widely incorporated into the course, students are required to use the TI-Nspire CX CAS graphing calculator.

**Statistics** — Prerequisite: Integrated Math III or by placement

Statistics includes the topics of sampling strategies and experimental design, numerical and graphical methods of describing data, probability distributions (both discrete and continuous), sampling distributions, confidence intervals, hypothesis testing, and simple linear regression. Emphasis will be on data visualization and analysis using spreadsheets and graphing calculators.