Mathematics

This course is designed for those students who have completed the Middle School Extended Mathematics curriculum prior to 8th grade or completed 8th grade Pre-Algebra with a "B" or better. Advanced Algebra 1 students are expected to master all the Algebra 1 objectives as well as some of the Algebra 2 objectives. Students taking this course are expected to continue their studies with an Advanced Geometry course followed by Advanced Algebra 2.

The successful mastery of Algebra 1 is widely considered to be the gatekeeper to success in the study of upper-level mathematics. The study of algebraic thinking begins in kindergarten and is progressively formalized prior to the study of the algebraic content found in the Algebra 1 Standards of Learning. Included in the progression of algebraic content is patterning, generalization of arithmetic concepts, proportional reasoning, and representing mathematical relationships using tables, symbols, and graphs. All students are expected to achieve the Algebra 1 standards. The study of Algebra 1 assists students in generalizing patterns or modeling relevant, practical situations with algebraic models. In order for students to develop meaning and connect algebraic concepts to geometry and statistics, consideration should be given to the sequential development of concepts and skills by using concrete materials to assist students in making the transition from the numeric to the symbolic. Connections between Algebra 1 and other subject areas through practical applications may assist in helping students attach meaning to the abstract concepts of algebra. These standards require students to use algebra as a tool for representing and solving a variety of practical problems. Tables and graphs will be used to interpret algebraic expressions, equations, and inequalities and to analyze behaviors of functions.

These standards include a transformational approach to graphing functions and writing equations when given the graph of the equation. Transformational graphing builds a strong connection between algebraic and graphic representations of functions. Graphing utilities (calculators, computers, and other technology tools) will be used to assist in teaching and learning. Graphing utilities facilitate visualizing, analyzing, and understanding algebraic and statistical behaviors and provide a powerful tool for solving and verifying solutions.

Students in this course will complete the Algebra 1 Standards of Learning (SOL) test.

This course includes emphasis on two- and three-dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. In addition, students begin the study of the Unit Circle. Students will use a variety of applications and problem-solving techniques including Algebraic skills. The intent of this course is to provide students with many opportunities to explore, conjecture, reason logically, formulate and solve problems, and communicate mathematically. Graphing utilities, computers, dynamic geometry software, and other appropriate technology tools will be used to assist in teaching and learning. Students taking this course are expected to continue their studies with an Advanced Algebra II course. This course has an associated Standards of Learning (SOL) test. 

The standards for Math 6 Extended provide a transition from the emphasis placed on whole number arithmetic in the elementary grades to an emphasis on the foundations of algebra. The standards include a focus on rational numbers and operations involving rational numbers. Students will engage with the data cycle to formulate questions, collect and acquire data, organize and represent data, and analyze and communicate their results. Students will use ratios to compare data sets; recognize decimals, fractions, and percents as ratios; solve single-step and multistep problems using rational numbers; and gain a foundation in the understanding of and operations with integers. Students will solve problems involving area and perimeter, relationships among the properties of quadrilaterals, and graph in a coordinate plane. In addition, students will build on the concept of graphical representation of data developed in the elementary grades and develop concepts regarding measures of center. Students will solve linear equations and inequalities in one variable and use algebraic terminology. Students will represent proportional relationships using two variables and discern between proportional and non-proportional relationships and begin to develop a concept of slope as rate of change. Students continue to develop their understanding of solving linear equations and inequalities in one variable by applying the properties of real numbers.

The use of appropriate technology and the interpretation of the results from applying technology tools must be an integral part of teaching, learning, and assessment. While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies to facilitate problem solving. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative and algebraic concepts or for proficiency in basic computations.

The acquisition of specialized mathematical vocabulary and language is crucial to a student’s understanding and appreciation of the subject and fosters confidence in mathematics communication and problem solving.

Problem solving is integrated throughout the content strands. The development of problem-solving skills is a major goal of the mathematics program at every grade level. The development of skills and problem-solving strategies must be integrated early and continuously into each student’s mathematics education.

Standards taught in PWCS Math 6 Extended include all of Math 6 and 7.NS.1, 7.NS.2, 7.NS.3, 7.CE.2, 7.MG.2, 7.MG.3, 7.MG.4, 7.PFA.1, 7.PFA.3.

Students in this course will complete the Grade Six Mathematics Standards of Learning (SOL) test.

The standards for Math 7 Extended continue to emphasize the foundations of algebra and build on the concepts needed for success in high school level algebra, geometry, and statistics. Students will engage with the data cycle to formulate questions, collect and acquire data, organize and represent data, and analyze and communicate their results. Students will explore real numbers and the subsets of the real number system. Proportional reasoning is expounded upon as students solve a variety of problems including similarity of geometric figures. Students find the volume and surface area of more complex three-dimensional figures and apply transformations to geometric shapes in the coordinate plane. Students will verify and apply the Pythagorean Theorem creating a foundation for further study of triangular relationships in geometry. Students will represent data, both univariate and bivariate data, and make predictions by observing data patterns. Students focus on algebraic concepts which include simplifying algebraic expressions, solving multistep equations and inequalities, and graphing linear functions. These standards are vital to providing a solid foundation in Algebra I for students in middle school mathematics.

The use of appropriate technology and the interpretation of the results from applying technology tools must be an integral part of teaching, learning, and assessment. While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies to facilitate problem solving. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative and algebraic concepts or for proficiency in basic computations.

The acquisition of specialized mathematical vocabulary and language is crucial to a student’s understanding and appreciation of the subject and fosters confidence in mathematics communication and problem solving.

Problem solving is integrated throughout the content strands. The development of problem-solving skills is a major goal of the mathematics program at every grade level. The development of skills and problem-solving strategies must be integrated early and continuously into each student’s mathematics education.

Standards taught in PWCS Math 7 Extended include 7.PS.2, 7.PFA.2, 7.CE.1, 7.MG.1, 7.PFA.4, 7.PS.1, and all of Grade 8 Mathematics.

Students in this course will complete the Grade Eight Mathematics Standards of Learning (SOL) test.

The eighth-grade standards continue to build on the concepts needed for success in high school level algebra, geometry, and statistics. Students will engage with the data cycle to formulate questions, collect and acquire data, organize and represent data, and analyze and communicate their results. Students will explore real numbers and the subsets of the real number system. Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three-dimensional figures and apply transformations to geometric shapes in the coordinate plane. Students will verify and apply the Pythagorean Theorem creating a foundation for further study of triangular relationships in geometry. Students will represent data, both univariate and bivariate data, and make predictions by observing data patterns. Students build upon the algebraic concepts developed in the standards for grades six and seven mathematics, which include simplifying algebraic expressions, solving multistep equations and inequalities, and graphing linear functions. The grade eight standards are vital to providing a solid foundation in Algebra 1, Geometry, and Statistics for students in middle school mathematics.

The use of appropriate technology and the interpretation of the results from applying technology tools must be an integral part of teaching, learning, and assessment. While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies to facilitate problem solving. However, facility in the use of technology shall not be regarded as a substitute for a student’s understanding of quantitative and algebraic concepts or for proficiency in basic computations.

The acquisition of specialized mathematical vocabulary and language is crucial to a student’s understanding and appreciation of the subject and fosters confidence in mathematics communication and problem solving.

Problem solving is integrated throughout the content strands. The development of problem-solving skills is a major goal of the mathematics program at every grade level. The development of skills and problem-solving strategies must be integrated early and continuously into each student’s mathematics education.

Students in this course will complete the Grade Eight Mathematics Standards of Learning (SOL) test.