# Mathematics

• Math Core 6
COURSE DESCRIPTION/OVERVIEW: Math Core 6 represents the middle school math course for students entering sixth grade. Math Core 6 denotes the Grade 6 Common Core math standards. This course is one full year.

COURSE OBJECTIVES / GOALS: Students will develop an understanding of connecting ration and rate to whole number multiplication and division, and using concepts of ration and rate to solve problems; completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; writing interpreting, and using expressions and equations and developing understanding of statistical thinking. These are the four critical areas of instructional time focus within the Grade 6 common core standards.

Ratios and Proportional Relationships: understand ratio concepts and use ratio reasoning to solve problems.

Number System: Apply and extend previous understanding of multiplication and division to divide fraction by fractions; compute fluently with mjulti-di9git numbers and find common factors and multiples; apply and extend previous understandings of numbers to the system of rational numbers.

Expression and Equations: Apply and extend previous understandings of arithmetic to algebraic expressions; reason about and solve one-variable equations and inequalities; represent and analyze quantitative relationships between dependent and independent variables.

Geometry: Solve real world and mathematical problems involving area, surface area, and volume.

Statistics and Probability: Develop understanding of statistical variability; and summarize and describe distributions.

Instruction will utilize core textbooks, supplemental readings. Evaluation of students’ mastery levels will be assessed through a variety of means including individual and group problem and project based learning components.

Instruction will utilize core textbooks, supplemental readings. Evaluation of students’ mastery levels will be assessed through a variety of means including individual and group problem and project based learning components.

Math Core 7
COURSE DESCRIPTION/OVERVIEW: Math Core 7 represents the middle school math course for students entering seventh grade. Math Core 7 denotes the Grade 7 Common Core math standards. This course is one full year.

COURSE OBJECTIVES / GOALS: Students will develop an understanding of and applying proportional relationships; develop an understanding of operations with rational numbers and working with expressions and linear equations; solving problems involving scale drawing and informal geometric constructions, and working with two and three dimensional shapes to solve problems involving area, surface area, and volume; and drawing inferences about populations based on samples. These are the four critical areas of instructional time and focus within the Grade 7 Common Core standards.

Ratios and Proportional Relationships: Analyze proportional relationships and use them to solve real world and mathematical problems.

Number System: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

Expression and Equations: Use properties of operations to generate equivalent expressions; solve real life and mathematical problems using numerical and algebraic expressions and equations.

Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them; solve real life and mathematical problems involving angle, measure, area, surface, and volume.

Statistics and Probability: Use random sampling to draw inferences about a population; draw informal comparative inferences about two populations; investigate chance processes and develop, use, and evaluate probability models.

Instruction will utilize core textbooks, supplemental readings. Evaluation of students’ mastery levels will be assessed through a variety of means including individual and group problem and project based learning components.

Math Core 7/8
COURSE DESCRIPTION/OVERVIEW: Math Core 7/8 is an accelerated one year math course for students entering seventh grade which combines the Grade 7 common core math standards, typically taught in one complete school year as well as the Grade 8 common core math standards, typically taught in one complete school year to students entering eighth grade.

COURSE OBJECTIVES / GOALS: There are four critical areas of instructional time focus within the Grade 7 Common Core math standards: Students will develop an understanding of and applying proportional relationships; develop an understanding of operations with rational numbers and working with expressions and linear equations; solving problems involving scale drawing and informal geometric constructions, and working with two-and three-dimensional shapes to solve problems involving area, surface area, and volume; and drawing inferences about populations based on samples. Furthermore, there are three critical areas of instructional time focus within the Grade 8 common core math standards including: Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; grasping two and three dimensional space and figures using distance, angle similarity and congruence and understanding and applying the Pythagorean Theorem.

Ratios and Proportional Relationships: Analyze proportional relationships and use them to solve real world and mathematical problems. (7)

Number System: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers (7); Know that there are numbers that are not rational, and approximate them by rational numbers (8).

Expression and Equations: Use properties of operations to generate equivalent expressions; solve real life and mathematical problems using numerical and algebraic expressions and equations (7); Work with radicals and integer exponents; understand the connection between proportional relationships, lines, and linear equations (8).

Functions: Define, evaluate, and compare functions; use functions to model relationships between quantities (8).

Geometry: Draw, construct, and describe geometrical figures and describe the relationships between them; solve real life and mathematical problems involving angle, measure, area, surface, and volume. (7); Understand congruence and similarity using physical models, transparencies, or geometry software; understand and apply the Pythagorean Theorem; solve real world and mathematical problems involving volume of cylinders, cones, and spheres (8).

Statistics and Probability: Use random sampling to draw inferences about a population; draw informal comparative inferences about two populations; investigate chance processes and develop, use, and evaluate probability models. (7); Investigate patterns of association in bivariate data (8).

Instruction will utilize core textbooks, supplemental readings and laboratory experiences. Evaluation of students’ mastery levels will be assessed through a variety of means including individual and group problem and project based learning components.

Math Core 8
COURSE DESCRIPTION/OVERVIEW: Math Core 8 represents the middle school math course for students entering eighth grade. Math Core 8 denotes the Grade 8 Common Core math standards. This course is one full year.

COURSE OBJECTIVES / GOALS: (1) Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping two and three dimensional space and figures using distance, angle similarity and congruence; and (3) understanding and applying the Pythagorean Theorem.

Number System: Know that there are numbers that are not rational, and approximate them by rational numbers (8).

Expression and Equations: Work with radicals and integer exponents; understand the connection between proportional relationships, lines, and linear equations (8).

Functions: Define, evaluate, and compare functions; use functions to model relationships between quantities (8).

Geometry: Understand congruence and similarity using physical models, transparencies, or geometry software; understand and apply the Pythagorean Theorem; solve real world and mathematical problems involving volume of cylinders, cones, and spheres (8).

Statistics and Probability: Investigate patterns of association in bivariate data (8).Instruction will utilize core textbooks, supplemental readings and laboratory experiences.

Evaluation of students’ mastery levels will be assessed through a variety of means including individual and group problem and project based learning components.

Algebra
Algebra 1 uses a variety of representations to develop the comprehensive understanding of algebra topics. Topics include linear and quadratic functions, systems of equations, inequalities, polynomials and rational and radical expressions. Students learn the relationships between equations, graphs and solutions to equations. Students solve problems by employing algebraic techniques such as factoring and applying the quadratic formula. They extend their mathematical reasoning by justifying steps in an algebraic procedure and checking algebraic arguments for validity.

Algebra 1 HP
Algebra 1 HP uses a variety of representations to develop the comprehensive understanding of algebra topics. Topics include linear and quadratic functions, systems of equations, inequalities, polynomials and rational and radical expressions. Students learn the relationships between equations, graphs and solutions to equations. Students solve problems by employing algebraic techniques such as factoring and applying the quadratic formula. They extend their mathematical reasoning by justifying steps in an algebraic procedure and checking algebraic arguments for validity. In Algebra 1 HP concepts are studied in depth through more challenging problems and critical thinking. Requirement: Math 6 HP (or equivalent) and a recommendation from Math 6 HP teacher.

Geometry
Topics of study include patterns, geometric constructions, properties of lines, angles, polygons, triangles, circles, and polyhedrons, congruence and similarity, the Pythagorean Theorem and trigonometry of right angles. Technology programs are integrated throughout the course. The concepts taught in Geometry HP are studied in-depth through problems that are more challenging and critical thinking. Requirement: Algebra 1 HP (or equivalent) and a recommendation from Algebra 1 HP teacher.