Math 6
The 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. Students will be introduced to discrete diagrams and double-number line diagrams to support representational thinking about equivalent ratios before moving into tables of equivalent ratios. Next, they expand their fractional reasoning with the ability to describe and represent situations involving rate, ratio, and rates per 1. Drawing on their multiplicative reasoning, students consider how the relative sizes of the numerator and denominator affect the size of their quotient, moving into computing quotients of fractions, interpretations of division in situations that involve fractions, and efficient algorithms. They work with linear equations that have single occurrences of one variable, building towards writing expressions with whole-number exponents and whole-number fractions to representing collections of equivalent ratios as equations. They learn signed numbers and plot points in all four quadrants of the coordinate plane, including the representation of situations that involve inequalities, symbolically and with the number line. A brief data and statistics study concludes the course's new concepts. The last unit offers students an optional opportunity to synthesize their learning from the year using a number of different applications.
Accelerated Math 6
Placement is based on an appropriate body of evidence that supports the student’s capacity to master both procedural and conceptual math concepts at an accelerated pace.
The 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 the 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 a 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 rational numbers less than zero, expanding their understanding of arithmetic to negative numbers. A brief data and statistics study concludes the course's new concepts. The last unit offers students an optional opportunity to synthesize their learning from the year using several different applications.
Math 7
As in grade 6, students start grade 7 by studying scale drawings, an engaging geometric topic that supports the subsequent work on proportional relationships in the second and fourth units. It also uses grade 6 arithmetic understanding and skill, without arithmetic becoming the primary focus of attention. Geometry and proportional relationships are also interwoven in the third unit on circles, where the proportional relationship between a circle's circumference and diameter is studied. By the time students reach the fifth unit on operations with rational numbers, both positive and negative, students have had time to brush up on and solidify their understanding and skill in grade 6 arithmetic. The work on operations using rational numbers, emphasizing the role of the properties of operations in determining the rules for operating with negative numbers, is a natural lead-in to the work on expressions and equations in the next unit. Students then put their arithmetical and algebraic skills to work in the last two units on angles, triangles, prisms, probability, and sampling.
Accelerated Math 7
Placement is based on Mastery of Accelerated Math 6 content and an appropriate body of evidence that supports the student’s capacity to master both procedural and conceptual math concepts at an accelerated pace.
Students begin the course with transformational geometry. They study rigid transformations and congruence, then scale drawings, dilations, and similarity (this provides background for understanding the slope of a line in the coordinate plane). Next, they expand their ability to work with linear equations in one and two variables and deepen their understanding of equivalent expressions. They then build on their understanding of proportional relationships from the previous course to study linear relationships. They express linear relationships using equations, tables, and graphs and make connections across these representations. Building on their understanding of a solution to an equation in one or two variables, they understand what is meant by a solution to a system of equations in two variables. They apply their understanding of linear relationships to contexts involving data with variability. They learn that linear relationships are an example of a special relationship called a function. They extend the definition of exponents to include all integers and, in the process, codify the properties of exponents. They learn about orders of magnitude and scientific notation to represent and compute with very large and very small quantities. They encounter irrational numbers for the first time and informally extend the rational number system to the real number system, motivated by their work with the Pythagorean Theorem. The last unit offers students an optional opportunity to synthesize their learning from the year using several different applications.
Math 8
Students begin grade 8 with transformational geometry. They study rigid transformations and congruence, then dilations and similarity (this provides background for understanding the slope of a line in the coordinate plane). Next, they build on their understanding of proportional relationships from grade 7 to study linear relationships. They express linear relationships using equations, tables, and graphs and make connections across these representations. They expand their ability to work with linear equations in one and two variables. Building on their understanding of a solution to an equation in one or two variables, they understand what is meant by a solution of a system of equations in two variables. They learn that linear relationships are an example of function to contexts involving data with variability. They extend the definition of linear relationships to include all integers and, in the process, codify the properties of exponents. They learn about orders of magnitude and scientific notation to represent and compute with very large and very small quantities. They encounter irrational numbers for the first time and informally extend the rational number system to the real number system, motivated by their work with the Pythagorean Theorem.
Algebra 1
Prerequisite: Mastery of Math 6, Math 7, and Math 8 content and an appropriate body of evidence that supports the student’s capacity to master both procedural and conceptual math concepts at an accelerated pace.
* A TI 84+ or TI 84 CE is strongly recommended for this course. It is a required purchase for high school, so your student will get more use in the coming years of mathematics instruction.
Students in Algebra 1 will solidify and extend their understanding of functions, solving equations, and data analysis. The first three units of the course focus on functions and how they are used to model relationships between two quantities. Unit 4 expands students’ algebraic skills, focusing on solving equations and inequalities. In this course, students will build on their previous knowledge of solving equations to be able to solve multistep and literal equations. This course adds to students’ prior understanding as they learn to solve systems using various methods. Following their work with systems, students will work with quadratic functions. Students consider similarities and differences between quadratic functions and the linear and exponential functions they focused on during the first part of this course. In the course's final unit, students focus on data and create different representations as models to assist with interpreting the data. These lessons provide students with real-world data-modeling opportunities. The work in this course establishes a base of reasoning and understanding about relationships that help students be sensible in decision-making and predicting outcomes. Additionally, students connect with rates of change and develop both a conceptual understanding and procedural fluency for linear, exponential, and quadratic functions. The work with functions in this course is foundational for future math courses up through calculus and beyond.
Geometry
Prerequisite: Mastery of Colorado Academic Standards-based Algebra 1 and an appropriate body of evidence that supports the student’s capacity to master both procedural and conceptual math concepts at an accelerated pace.
* A TI 84+ or TI 84 CE is strongly recommended for this course. It is a required purchase for high school, so your student will get more use in the coming years of mathematics instruction.
Geometry covers a wide range of topics that demand advanced algebraic skills previously mastered for geometric problem-solving and proof. The course is structured to integrate the practice of proving geometric theorems and statements across all units. Beginning with an initial focus on logical reasoning and problem-solving, students will investigate congruence criteria and applications related to congruent triangles. Throughout the course, there is an exploration of geometric transformations, translations, reflections, rotations, and dilations to deepen the understanding of congruence and similarity principles. Students will then examine lines, angles, and the properties of parallel and perpendicular lines, including transversals and related angle theorems. This is followed by examining the properties of parallel lines and quadrilaterals. As the curriculum progresses, students will extend their understanding of geometric concepts into three-dimensional space. They will also study relationships among chords, arcs, and angles within circles, along with exploring the properties and theorems associated with circles. Geometry also introduces the unique properties of special right triangles and applies trigonometric functions to solve non-right triangles, thereby establishing the groundwork for Algebra 2/Trigonometry. The curriculum encompasses fundamental and advanced geometric principles, providing students with a comprehensive understanding of geometry and its practical applications.