Webb Bridge Middle School
Common Core Georgia Performance Standards
Accelerated Coordinate Algebra
2012 - 2013
Exemplifying Excellence Every Day!
Robert A. Swanson
Textbooks: Georgia High School Mathematics 1; McDougal Littell; 2008
Replacement cost: current price
Georgia High School Mathematics 2; McDougal Littell; 2008
Replacement cost: current price
Course Description / Objectives:
Common Core Georgia Performance Standards Accelerated Coordinate Algebra consists of nine units.
1. Relationships between quantities
By the end of eighth grade students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. The first unit of Coordinate Algebra involves relationships between quantities. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students will be provided with examples of real-world problems that can be modeled by writing an equation or inequality. Students will develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They will also master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations (limited to integer exponents). Skills from this unit will also be embedded in other units in this course.
2. Reasoning with equations and inequalities
By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation and to justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students explore systems of equations and inequalities, and they find and interpret their solutions. All of this work is grounded on understanding quantities and on relationships between them.
3. Linear and exponential functions
In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
4. Describing Data
In high school, students build on knowledge and experience described in the 6-8 Statistics and Probability Progression. They develop a more formal and precise understanding of statistical inference, which requires a deeper understanding of probability. Students learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random, and these procedures may not be informative when analyzing nonrandomized studies, often called observational studies. For example, a random selection of 100 students from your school will allow you to draw some conclusion about all the students in the school, whereas taking your class as a sample will not allow that generalization.
5. Transformations in the coordinate plane
A main feature of the CCGPS is the seamless transition from eighth grade transformations to transformations in the coordinate plane in high school. In broad terms, the key ideas about transformations (basic rigid motions and dilations) are gently introduced in grade eight through hands-on activities; the high school course then begins the normal mathematical study of the plane by building on students' prior empirical experience with these transformations. In lieu of the usual axioms, the high school course makes use of the assumptions about basic rigid motions. In this unit, students will use the geometry software and other tools to explore reflections, transformations and rotation. They will also learn the vocabulary associated with transformations as they communicate their understandings of transformations to one another. Since students should be somewhat familiar with transformations from eighth grade, making the algebraic connection between transformations and the coordinate plane should be a seamless one.
6. Connecting algebra and geometry through coordinates
Analytic geometry connects algebra and geometry, resulting in powerful methods of analysis and problem solving. Just as the number line associates numbers with locations in one dimension, a pair of perpendicular axes associates pairs of numbers with locations in two dimensions. This correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. The solution set of an equation becomes a geometric curve, making visualization a tool for doing and understanding algebra. Geometric shapes can be described by equations, making algebraic manipulation into a tool for geometric understanding, modeling, and proof. Geometric transformations of the graphs of equations correspond to algebraic changes in their equations. Dynamic geometry environments provide students with experimental and modeling tools that allow them to investigate geometric phenomena in much the same way as computer algebra systems allow them to experiment with algebraic phenomena.
7. Similarity, congruence and proofs
Students apply their earlier experience with transformations and proportional reasoning to build a formal understanding of similarity and congruence. They identify criteria for similarity and congruence of triangles and use them to solve problems. It is in this unit that students develop facility with geometric proof. They use what they know about congruence and similarity to prove theorems involving lines, angles, triangles, and other polygons. They explore a variety of formats for writing proofs.
8. Right triangle trigonometry
Students apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem.
9. Circles and volume
In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. Students develop informal arguments justifying common formulas for circumference, area, and volume of geometric objects, especially those related to circles.
Course Outline
First Semester / Second Semester1. Relationships between quantities / 6. Connecting algebra and geometry
through coordinates
2. Reasoning with equations and inequalities / 7. Similarity, congruence, and proofs
3. Linear and exponential functions / 8. Right triangle trigonometry
4. Describing data / 9. Circles and volumes
5. Transformations in the coordinate plane
Teacher / Parent Communication:
Email - is the most efficient way to contact teachers
Conferences – may be scheduled based on each student’s needs
Interim Report Cards – come home every 4 ½ weeks
Home Access Center – please check frequently for your child’s progress and always
provide us with your current email address
My email is and I update my web site daily to inform
students and parents of upcoming work and due dates.
Please ensure you are also registered for the Home Access Center (HAC) so you can
View your child’s grades. Teachers will post grades in TAC within 2 weeks of test dates
or project / assignment due dates
Grading Weights:
Summative: Tests and Projects – 55%
Formative: Quizzes, Class Work, and Home Work – 45%
Note: An End Of Course Test (EOCT) will be administered in the spring which will be
weighted as 20% of a student’s second semester grade.
WBMS Re-Assessment Procedure: Grades reflect what students know and have learned. If a student is failing, they are not learning. All students will be able to participate in a re-assessment of summative assignments in an effort to make sure all students are learning. Students need to participate in a re-teaching activity along with a re-learning activity to make sure the student understands the material. Teachers will offer re-teaching during advisement or help sessions. Teachers will document the re-teaching and re-learning activity along with the new summative grade. General education students scoring below 73 (Advanced and TAG 79 and below) are required to take a re-assessment. General education students scoring 74 and above (Advanced and TAG 80 and above) have the option to take a re-assessment for a better grade. The re-learning activity and re-teaching activity must take place prior to the summativere-assessment.
Help Sessions:
Extra Assistance is available before school on Tuesday morning from 8:00 AM until dismissal to class with 24 hours advance notice.
Absence Make-Up Procedure:
Upon returning to school following an absence, it is the student’s responsibility to contact the teacher to request make-up work. Make-up work must be completed by the student within the time specified by the teacher. At WBMS, students will be given the same amount of time to make-up the work as the student was absent unless other arrangements are mutually agreed upon. The student will receive the actual grade on the make-up work if the absence was “excused”.
Academic Dishonesty:
Cheating or plagiarism in any form is not accepted. An office referral will be made for this type of behavior.
Probation for Gifted Services:
Students failing to meet the Continuation Criteria are automatically placed on probation. Probation may last as little as one grading period, but nor more than one school year. Parents must be notified in writing when a student is placed on probation. A written plan explaining how a student can be removed from probationary status must be included in the notification to the parent and student. In placing a student on probation, it should be considered that unsatisfactory performance in a content area of service would be documented with a grade of < 80%.
Classroom Procedures and Expectations:
1. Show respect for himself/herself, others, and property
2. Follow school rules and guidelines
3. Be on time and be prepared for class everyday
4. Keep classroom neat
5. Accept responsibility for his/her actions