Mathematics

Accelerated Math 6 Plus (AMP 6+)

Illustrative Mathematics 6–8 Math Accelerated provides an alternate pathway to Algebra 1 by the 8th grade addressing access, opportunity, and equity for students mathematically by allowing them to complete a graduation requirement in middle school and enroll in more advanced-level math courses in high school to prepare them for college and career-readiness. Current Grade 5 students enrolled in the Math 5 course will be able to take the Accelerated Grade 6+ course in Grade 6, the Accelerated Grade 7+ course in Grade 7, and Algebra 1 in Grade 8. The Illustrative Mathematics 6–8 Math Accelerated course is a comprehensive, standards-aligned, two-course curriculum designed to provide an effective accelerated pathway to Algebra 1. It includes all of the standards in Illustrative Mathematics Grades 6–8 Math and compacts them into a two-year curriculum meant to be covered during the 6th and 7th grades. The pace is faster than Illustrative Mathematics Grades 6–8 Math, but no crucial mathematical concepts are missed.

The Accelerated Math 6 Plus (AMP 6+) course begins with a study of area and surface area concepts. This work sets the tone for later units that use area models for arithmetic using rational numbers. Next, students begin study of ratios, rates, and percentages with an introduction using representations such as number line diagrams, tape diagrams, and tables. Student understanding of these concepts expands by exploring fraction and decimal representations of rational numbers. They explore sums, differences, products, and quotients using intuitive methods and efficient algorithms. Next, students are introduced to equations and expressions including finding solutions for linear equations in one variable and basic equations involving exponents. Student understanding of ratios and rates combined with a basic understanding of equations leads students to study proportional relationships with special emphasis on circumference and area of a circle as an example and nonexample of proportional relationships. This is followed by looking at percentage concepts and applications such as sales tax, tipping, and markup. They learn about rational numbers less than zero expanding their understanding of arithmetic to negative numbers. A brief study of data and statistics concludes the new concepts in the course. The last unit offers students an optional opportunity to synthesize their learning from the year using a number of different applications.

Investigations into Mathematics (IM)

Applied Investigations into Mathematics (AIM)

Course Description:

Investigations into Mathematics (IM) extends students’ understanding of mathematical concepts developed in Mathematics 6 and accelerates the pace of instruction to prepare for Algebra 1. This course compacts all of the Grade 7 Common Core State Standards and much of the Grade 8 Common Core State Standards into a single year. Students who successfully complete IM are prepared for Algebra 1 in Grade 8. The remaining Grade 8 CCSS are compacted into the Algebra 1 course. Instruction for IM will focus on four critical areas: (1) developing a unified understanding of number, recognizing fractions, decimals (including both those that have a finite or a repeating decimal representation), and percents as different representations of rational numbers; (2) using linear equations and systems of linear equations to represent, analyze, and solve a variety of problems; (3) comparing two data distributions and reasoning about differences between populations; (4) analyzing geometric relationships in order to solve real-world mathematical problems.

Content Emphasis:

IM focuses on the Standards for Mathematical Practice to build a climate that engages students in the exploration of mathematics. The Standards for Mathematical Practice are habits of mind applied throughout the course so that students see mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Through this course, students will . . .

  • Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide positive and negative rational numbers.

  • Create and interpret numerical and algebraic expressions and equations in one variable.

  • Develop understanding of proportionality through the use of linear equations and systems of equations to solve and graph single- and multi-step real world and mathematical problems.

  • Reason about geometric relationships among two-dimensional and three-dimensional figures.

  • Compare two data distributions and generate data sets by random sampling.

  • Investigate chance processes and develop, use, and evaluate probability models.

  • Use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems including the association between two quantities in bivariate data.

  • Solve and analyze situations using systems of two linear equations in two variables and relate the systems to pairs of lines in the plane.

  • Understand that functions describe situations where one quantity determines another.

  • Use ideas about distance and angles to describe and analyze two-dimensional figures.

  • Understand and apply the Pythagorean Theorem to find distances between points on a coordinate plane, to find lengths, and to analyze polygons.

  • Complete their work on volume by solving problems involving cones, cylinders, and spheres

Topics of Study:

Rational Numbers and Exponents

  • Apply and extend previous understandings of operations with fractions to rational numbers.

  • Develop understanding of irrational numbers by using rational approximations. Develop understanding of radicals and integer exponents.

Proportionality and Linear Relationships

  • Analyze proportional relationships and use them to solve problems.

  • Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations.

Statistics and Probability

  • Use random sampling to draw inferences about a population and compare two populations. Develop understanding of probability models.

Creating, Comparing, and Analyzing Geometric Figures

  • Construct and describe geometric figures through understanding of congruence and similarity. Investigate angle measures, area, surface area, and volume of geometric figures.

The Number System

  • Know that there are numbers that are not rational, and approximate them by rational numbers.

Expressions and Equations

  • Work with radicals and integer exponents.

  • Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations.

Functions

  • Define, evaluate, and compare functions and use functions to model relationships.

Geometry

  • Understand congruence and similarity using physical models Understand and apply the Pythagorean Theorem.

  • Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

Statistics and Probability

  • Investigate patterns of association in bivariate data.

* The topics of study listed above may not necessarily be taught in the order listed.

Algebra 1

Course Description:

Algebra 1 is designed to analyze and model real-world phenomena.

Exploration of linear, exponential, and quadratic functions forms the foundation of the course. Key characteristics and representations of functions – graphic, numeric, symbolic, and verbal – are analyzed and compared. Students develop fluency in solving equations and inequalities. One- and two-variable data sets are interpreted using mathematical models.

Content Emphasis:

Algebra 1 focuses on the Standards for Mathematical Practice to build a climate that engages students in the exploration of mathematics. The Standards of Mathematical Practice are habits of mind applied throughout the course so that students see mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Through this course, students will . . .

  • Develop fluency and master writing, interpreting, and translating between various forms of linear equations and inequalities in one variable, and using them to solve problems

  • Solve simple exponential equations that rely only on the application of the laws of exponents

  • Interpret functions (graphically, numerically, symbolically, verbally), translate between representations, and understand the limitations of various representations

  • Use regression techniques to describe approximately linear relationships between quantities and look at residuals to analyze the goodness of fit and use more formal means of assessing how a model fits data

  • Compare the key characteristics of quadratic functions to those of linear and exponential functions and select from among these functions to model phenomena

  • Explore more specialized functions—absolute value, step, and those that are piece wise defined and select from among these models to model phenomena and solve problems

Topics of Study:

Relationships between Quantities and Reasoning with Equations

  • Linear Equations in One Variable

  • Linear Inequalities in One Variable

  • Exponential Equations in One Variable

Linear and Exponential Relationships

  • Characteristics of Functions

  • Constructing and Comparing Linear and Exponential Functions

  • Solving Systems of Equations and Inequalities in Two Variables

Descriptive Statistics

  • Analyzing Data Representations

Quadratic Relationships

  • Quadratic Functions

  • Equations in Two Variables

  • Solving Quadratic Equations

Generalizing Function Properties

  • Function Families

* The topics of study listed above may not necessarily be taught in the order listed.

Honors Geometry

Course Description:

Honors Geometry formalizes and extends students’ geometric experiences from the elementary and middle school grades. Students explore more complex geometric situations and deepen their understanding of geometric relationships, progressing towards formal mathematical arguments. Instruction at this level will focus on the understanding and application of congruence as a basis for developing formal proofs; the relationship among similarity, trigonometry, and triangles; the relationship between two- and three-dimensional objects and their measurements; exploration of geometric descriptions and equations for conic sections; and application of geometric concepts in modeling situations.

Content Emphasis:

Honors Geometry focuses on the Standards for Mathematical Practice to build a climate that engages students in the exploration of mathematics. The Standards of Mathematical Practice are habits of mind applied throughout the course so that students see mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Through this course, the student will . . .

  • Prove theorems and solve problems about triangles, quadrilaterals, and other polygons.

  • Apply understanding of similarity and right triangle trigonometry to find missing measures of triangles.

  • Utilize the rectangular coordinate system to verify geometric relationships.

  • Apply understanding of circles to derive equations and solve problems.

  • Measure two and three-dimensional objects.

Topics of Study: *

Congruence

  • Experiment with transformations in the plane

  • Understand congruence in terms of rigid motions

  • Prove geometric theorems

  • Make geometric constructions

Similarity, Right Triangles, and Trigonometry

  • Understand similarity in terms of similarity transformations

  • Prove theorems involving similarity

  • Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles

Circles

  • Understand and apply theorems about circles

  • Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations

  • Translate between the geometric description and the equation for a conic section Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimension

  • Explain volume formulas and use them to solve problems

  • Visualize relationships between two-dimensional and three-dimensional objects

Modeling with Geometry

  • Apply geometric concepts in modeling situations

* The topics of study listed above may not necessarily be taught in the order listed.

Mathematics Intervention

Math 180 Course Overview:

Math 180 is a comprehensive system of instruction, assessment, and professional development designed to help older, struggling students thrive in algebra. The program directly addresses individual needs through adaptive and instructional software, high-interest materials, and direct instruction in mathematical calculation and application skills. Students rotate among a small group, teacher-directed lessons, a computer station for reinforcement and practice, and an independent brain arcade where students complete math problems at their instructional level. Built with the student in mind, the learning experience is a uniquely motivating and fun way to accelerate to grade-level ability.