Mathematics

 MATHEMATICS

Melrose High School Mathematics curriculum is aligned to the Massachusetts Curriculum Frameworks, adopted in 2011. The frameworks are composed of content standards that span over six conceptual categories: Number and Quantity, Algebra, Functions, Geometry, Modeling, and Statistics and Probability, and eight practice standards outlined below. All of the standards are aligned with college and career expectations and prepare all students with the skills and knowledge needed for post-graduation success. The new frameworks provide our students with the opportunity to experience a more focused, coherent, and rigorous curriculum. The key elements to achieve mathematical proficiency include conceptual understanding, procedural skill and fluency, application, and use of mathematical practices. Students are expected to gain a deep understanding of mathematical concepts, carry out procedures accurately and efficiently, apply concepts and skills to new situations, and use the habits of mind called for in the practices effectively and efficiently. Students are expected to develop a deep understanding of mathematical concepts through complex problem solving and writing and speaking about their understanding.

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics
5. Use appropriate tools strategically.
6. Attend to Precision.
7. Look for and make use of structure.
8. Look for an express regularity in repeated reasoning.

The following are sample course sequences within the mathematics program. Alternate sequences may be created to meet the needs of individual students. Students can move in and out of sequences based on criteria.

9th 10th 11th 12th
Integrated Integrated Integrated Integrated
Mathematics 1A Mathematics 1B Mathematics 2 Mathematics 3

Geometry CP Intermediate Algebra Algebra 2 CP Advanced Algebra/Trig;
or Algebra 1 Pre-Calculus CP; AMDM;
Statistics CP

Geometry CP Algebra 2 CP Pre-Calculus CP Applied Calculus; AP or CP Statistics; AMDM
Advanced Algebra/Trig

Geometry H Algebra 2 H Pre-Calculus H; Calculus H;
and AP Statistics AP Calculus AB or BC;
and/or AP Statistics

Geometry H Accelerated Algebra 2/ AP Calculus AB; AP Calculus BC;
Pre-Calculus H and/or AP Statistics and/or AP Statistics
222 Geometry Level:  CP       1 Math Credit
Prerequisite: Successful completion of 8th grade Math                                                                                                                                                                                                                                             Grade 9, 10
Expectations: Students are expected to use their mathematical knowledge to reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, use appropriate tools strategically, attend to precision, and look for and make use of structure. Students are expected to build fluency with triangle congruence and similarity throughout their investigations of triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. Students are expected to use coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool. Students are expected to use construct tools, physical and computational, to model geometric phenomenon allowing students to lead to conjectures and proofs. Students are expected to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open response and 4 core assignments. The Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading, and projects. Scientific calculators are used in this course.

216 Geometry Level: H          1 Math Credit
Grade 9, 10
Prerequisite: 4 of the following 5: Average grade of B+ in Honors Algebra 1 or an average grade of A in Algebra; 85% on Midyear Exam; 80% on placement test; Advanced score on MCAS; Teacher recommendation (effort, homework completion, participation, study habits).

Prerequisite Skills: Students are expected to have a high level of conceptual understanding and procedural fluency in the prerequisite course as well as proficiency with the mathematical practice standards. In this course, students are working to achieve mastery of the content. Mastery is defined by the “Placement Criteria for Honors Level.” Advanced topics can include applying trigonometry to general triangle and constructing a tangent line from a point outside a given circle.

Expectations: Students are expected to use their mathematical knowledge to reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, use appropriate tools strategically, attend to precision, and look for and make use of structure. Students are expected to build fluency with triangle congruence and similarity throughout their investigation of triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. Students are expected to use coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool. Students will use construction tools, physical and computational, to model appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open response and 4 core assignments. The curriculum for this course requires 3-5 hours a week of independent practice such as homework, reading and projects. Scientific calculators are used in this course.

210 Algebra 1 Level CP                                      1 Math Credit
Prerequisite: Successful completion of 8th grade Math                                                                                                                                                                                                                                          Grades 9, 10

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, reason abstractly and quantitatively, use appropriate tools strategically, attend to precision, look for and make use of structure, look for and express regularity in repeated reasoning. Students are expected to build fluency with solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given a point and a slope. Students are expected to become fluent in adding, subtracting, and multiplying polynomials, and in transforming expressions. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

221 Intermediate Algebra Level: CP               1 Math Credit
Prerequisite: Successful completion of 8th grade Math                                                                                                                                                                                                                                            Grades 9, 10

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, reason abstractly and quantitatively, use appropriate tools strategically, attend to precision, look for and make use of structure, and look for and express regularity in repeated reasoning. Students are expected to build fluency with solving with solving characteristic problems involving the analytic geometry of lines, such as writing down the equation of a line given point and slope. Students are expected to become fluent in adding, subtracting, and multiplying polynomials, and in transforming expressions. Students are expected to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Scientific and graphing calculators are used in this class.
Note: This course is structured to give students the opportunity to strengthen their algebraic skills before enrolling in Algebra 2.

228 Algebra 2 Level: CP                                      1 Math Credit
Prerequisite: Successful completion of Algebra 1 and Geometry, or Integrated 1A and 1B                                                                                                                                                                              Grade 10, 11

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, and look for and express regularity in repeated reasoning. Students are expected to build fluency with dividing polynomials with remainder by inspection in simple cases by restructuring rational expressions. Students will see structure in expressions and use this structure to rewrite expressions in everything from advanced factoring (e.g. grouping) to summing series to the rewriting of rational expressions to examine the end behavior of corresponding rational function. Students are expected to build fluency in translating between recursive definitions and closed forms when dealing with many problems involving sequences and series and with applications ranging from filling functions to tables to problems in finance. Students are expected to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

215 Algebra 2 Level: H                                       1 Math Credit
Grades 10, 11

Prerequisite: Successful completion of Algebra 1 and 4 of the following 5: 80% or better on Algebra skills assessments; Average grade of B- in Honors level course or an average grade of A in a CP level course; 80% on Honors Midyear Exam or 90% on CP Midyear exam; Average grade of 80% on Open response/Core Assignments; Teacher recommendation (effort, homework completion, participation, study habits).
Prerequisite Skills: Students are expected to have a high level of conceptual understanding and procedural fluency in the prerequisite course as well as proficiency with the mathematical practice standards. Curriculum for this course requires students to achieve mastery of the content. Mastery is defined by the “Placement Criteria for Honors Level.” Advanced topics can include representing and modeling with vector quantities, performing operations on matrices and using matrices in applications, and using probability to evaluate outcomes of decisions.

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, and look for and express regularity in repeated reasoning. Students are expected to build fluency with dividing polynomials with remainder by restructuring rational expressions. Students are expected to recognize structure in expressions and use this structure to rewrite expressions in everything from advanced factory (e.g. grouping) to summing series to the rewriting of rational expressions to examine the end behavior of corresponding rational function. Students will build fluency in translating between recursive definitions and closed forms when dealing with many problems involving sequences and series and with applications ranging from filling functions to tables to problems in finance. Students are expected to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. This course requires 3-5 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

233 Integrated Math 1A Level: CP                      1 Math Credit
Prerequisite: Successful completion of 8th grade Math                                                                                                                                                                                                                                                Grade 9
Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, use appropriate tools strategically, attend to precision, look for and make use of structure, and look and express regularity in repeated reasoning. Students are expected to build fluency with solving characteristic problems involving the analytic geometry of lines such as writing down the equation of a line given a point and slope. Students are expected to build fluency with triangle congruence throughout their investigations of triangles, quadrilaterals, circles, and parallelism. Students are expected to use construction tools, physical and computational, to model geometric phenomenon allowing students to lead to conjectures and proofs. Students will learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Scientific calculators are used in this class.

235 Integrated Math1B Level: CP                 1 Math Credit
Prerequisite: Successful completion of Integrated 1A                                                                                                                                                                                                                                                       Grade 10

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, use appropriate tools strategically, attend to precision, look for and make use of structure, and look and express regularity in repeated reasoning. Students are expected to become fluent in adding, subtracting, and multiplying polynomials, and in transforming expressions. Students are expected to build fluency with triangle similarity throughout their investigations of triangles, quadrilaterals, circles, and parallelism, and trigonometric ratios. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Scientific calculators are used in this class.
237 Integrated Math 2 Level: CP               1 Math Credit
Prerequisite: Successful completion of Integrated 1B                                                                                                                                                                                                                                               Grade 11

Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, and look and express regularity in repeated reasoning. Students are expected to see structure in expressions and use their structure to rewrite expressions. Students will learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to be expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are used in this class.

238 Integrated Math 3 Level: CP          1 Math Credit
Prerequisite: Successful completion of Integrated 2                                                                                                                                                                                                                                             Grade 12
Expectations: Students are expected to use their mathematical knowledge to make sense of problems and persevere in solving them, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, and look and express regularity in repeated reasoning. Students are expected to build fluency in translating in between recursive definitions and closed forms when dealing with many problems involving sequences and series and with applications ranging from fitting functions to tables to problems in finance. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are used in this class.

239 Advanced Algebra/Trigonometry Level: CP     1 Math Credit
Prerequisite: Successful completion of Algebra 2                                                                                                                                                                                                                                                Grades 11, 12
Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. Students will strengthen and extend their understanding of the concepts covered in Algebra 2. Applications of functions will be emphasized including linear programming. Students are expected to build fluency working with trigonometric functions. Students are expected to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

224 Pre-Calculus Level: CP                                         1 Math Credit
Prerequisite: B- or better in Algebra 2 CP or successful completion of Algebra 2 H                                                                                                                                                                                  Grades 11, 12
Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. Students are expected to build fluency with graphical and algebraic representation of functions and their inverses, transformation of functions, analytic geometry (conic sections), and trigonometry. Curriculum for this course is designed to prepare students for enrollment in Calculus, either in high school or college. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

217 Pre-Calculus Level: H                                          1 Math Credit
Grade 11, 12
Prerequisite: 3 of the following 4: Average grade of B- in Honors level course or an average grade of A in a CP level course; 80% on Honors Midyear Exam or 90% on CP Midyear exam; Average grade of 80% on Open response/Core Assignments; Teacher recommendation (effort, homework completion, participation, study habits).

Prerequisite skills: Students are expected to have a high level of conceptual understanding and procedural fluency in the prerequisite course as well as proficiency with the mathematical practice standards. Curriculum for this course requires students to achieve mastery of the content. Mastery is defined by the “Placement Criteria for Honors Level.” Advanced topics can include sequences and series and the fundamentals of differential calculus including limits and derivatives.

Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. Students are expected to build fluency with graphical and algebraic representation of functions and their inverses, transformation of functions, analytic geometry (conic sections), and trigonometry. Curriculum for this course is designed to prepare students for enrollment in Calculus, either in high school or college. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 3-5 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

219 Accelerated Algebra 2/Pre-Calculus Level: H  1 Math Credit
Grade 10
Prerequisite: Algebra 1 H & Geometry H; Average grade of A- in Honors level course; 90% on Honors Midyear exam; Average grade of 90% on Open response/Core Assignments; a score indicating readiness on placement test; Teacher recommendation (effort, homework completion, participation, study habits).

Prerequisite skills: Students are expected to have a high level of conceptual understanding and procedural fluency in the prerequisite course as well as proficiency with the mathematical practice standards. Students are expected to have a strong foundation of Algebra 1 and have the ability to learn mathematical concepts at an accelerated pace. Curriculum for this course will cover all the topics of Algebra 2 and Pre-Calculus curriculum in one year. Curriculum for this course requires students to achieve mastery of the content. Mastery is defined by the “Placement Criteria for Honors Level.”

Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. Students will build fluency with graphical and algebraic representation of functions and their inverses, transformation of functions, analytic geometry (conic sections), and trigonometry. Students are expected to divide polynomial with remainder by restructuring rational expressions. Students are expected to divide polynomials with remainder b restructuring rational expressions. Students will see structure in expressions and use this structure to rewrite expressions in everything from advanced factory (e.g. grouping) to summing series to the rewriting of rational expressions to examine the end behavior of corresponding rational function. Students are expected to build fluency in translating between recursive definitions and closed forms involving sequences and series and with applications ranging from fitting functions to tables to problems in finance. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 4-6 hours a week of independent practice such as homework, reading, and projects. Graphing calculators are required. Students who successfully complete this course will be able to take AP AB Calculus the following year.

265 Applied Calculus Level: CP                                 1 Math Credit
Prerequisite: Successful completion of Pre-Calculus                                                                                                                                                                                                                                              Grade 12

Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. This course strengthens students’ understanding of functions in preparation for the process of differentiation and integration. Calculus concepts explored include limits and continuity, derivatives, definite integrals, exponential and logarithmic functions, trigonometric functions, and techniques of integration. Emphasis is placed on the exploration of real-world calculus applications. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 2-3 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

214 Calculus Level: H                                                    1 Math Credit
Grades 11, 12
Prerequisite: Successful completion of Pre-Calculus; 3 of the following 4: Average grade of B- in Honors level course or an average grade of A in a CP level course; 80% on Honors Midyear Exam or 90% on CP Midyear exam; Average grade of 80% on Open response/Core Assignments; Teacher recommendation (effort, homework completion, participation, study habits).

Prerequisite skills: Prerequisite Skills: Students are expected to have a high level of conceptual understanding and procedural fluency in the prerequisite course as well as proficiency with the mathematical practice standards. Curriculum for this course requires students to achieve mastery of the content. Mastery is defined by the “Placement Criteria for Honors Level.” Advanced topics can include parametric equations, infinite integral, work, and power off functions.

Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. Topics include limits and continuity, derivatives, definite integrals, and techniques of integration. Students are expected to learn to choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 3-5 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.
204 Advanced Placement Calculus AB Level: AP   1 Math Credit
Grades 11, 12

Prerequisite: Successful completion of Pre-Calculus Honors or Accelerated Algebra 2/Pre-Calculus H and teacher recommendation

Expectations: Students are expected to use their mathematical knowledge and practices to solve problems. This course covers the syllabus for the Advanced Placement Calculus AB Examination of the College Board. Curriculum topics include the review of functions and their representations, limits and continuity, derivatives and its applications, the definite integral, techniques and applications of integration and the Fundamental Theorem of the Calculus. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 5-8 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required. Students enrolled in this course are required to take the AP Calculus AB exam.

205 Advanced Placement Calculus BC Level: AP   1 Math Credit
Grades 11, 12
Prerequisite: Successful completion of Pre-Calculus Honors or Accelerated Algebra 2/Pre-Calculus H and teacher recommendation
Expectations: Curriculum for this course includes the syllabus for the Advanced Placement Calculus BC Examination of the College Board. All of the topics from AP Calculus AB are covered with the following additional topics: advanced techniques of integration, calculus of parametric functions, velocity and acceleration vectors representing two-dimensional motion, sequences and series, and the epsilon/delta definition of limits. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 5-8 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required. Students enrolled in this course are required to take the AP Calculus BC exam.

207 Statistics Level: CP                                                 1 Math Credit
Prerequisite: Successful completion of Algebra 2.                                                                                                                                                                                                                                                      Grades 11, 12
Expectations: Curriculum for this course covers the basic concepts of Statistics and Probability. The purpose of this course is to introduce students to the major concepts and tools of Statistics that can be applied to multiple disciplines. The topics include exploring data by describing patterns and departures from patterns, sampling and experimentation which include planning and conducting a study, anticipating and analyzing patterns by exploring random phenomena using probability and simulation, and drawing conclusions using statistical inference to estimate population parameters and test hypotheses. A graphing calculator and some computer software programs are used as tools to enhance data exploration. Curriculum for this course requires strong analytical reading skills; clear and concise writing skills will benefit students in the course. Students will be expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 3-5 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required.

206 Advanced Placement Statistics Level: AP      1 Math Credit
Prerequisite: Successful completion of Algebra 2 and teacher recommendation.                                                                                                                                                                                            Grades 11, 12
Expectations: Curriculum for this course covers the syllabus of the Advanced Placement Statistics Examination of the College Board. The purpose of this course is to introduce students to the major concepts and tools of Statistics that can be applied to multiple disciplines. The topics include exploring data by describing patterns and departures from patterns, sampling and experimentation which include planning and conducting a study, anticipating and analyzing patterns by exploring random phenomena using probability and simulation, and drawing conclusions using statistical inference to estimate population parameters and test hypotheses. A graphing calculator and some computer software programs are used as tools to enhance data exploration. Curriculum for this course requires strong analytical reading skills as well as clear and concise writing skills. Students will be expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 5-8 hours a week of independent practice such as homework, reading and projects. Graphing calculators are required. Students enrolled in this course are required to take the AP Statistics exam.

240 Advanced Mathematical Decision Making Level: CP 1 Math Credit
Prerequisite: Successful completion of Algebra 2                                                                                                                                                                                                                                                      Grade 12
Expectations: Curriculum for this course is divided into two semester-long units, probability and statistics, and consumer math and business finance. The first semester includes the study of probability and statistics. Students will concentrate on exploring data, planning and conducting a survey, and discovering patterns using probability. Units include the construction and comparison of graphical representations, measures of center and spread (mean, median, mode, rang), characteristics of surveys, bias, combinatorics, and making predictions. The second semester prepares students to apply computing skills to solve every day personal finances. Units include banking, checking accounts, credit cards, budgeting, job related finances, taxes, housing installment buying, household bills, insurance, financing a car, investing, and retirement. Students are expected to complete 4 open responses and 4 core assignments. Curriculum for this course requires 1-3 hours a week of independent practice such as homework, reading and projects. A graphing calculator is used in this course.

270 Algebra Lab Level: CP                                                       0.5 Credit
Prerequisite: 8th Grade Math                                                                                                                                                                                                                                                                                        Grade 10

Expectations: Curriculum for this course is designed to support students who have demonstrated a need for additional instructions and practice in Algebra. Curriculum for this course will supplement the instruction in the student’s current math class. Students will attend this course every other day for the entire year. Students will be recommended for this course based on their needs.

280 Geometry Lab Level: CP                                                    0.5 Credit
Prerequisite: 8th Grade Math                                                                                                                                                                                                                                                                                         Grade 9

Expectations: Curriculum for this course is designed to support students who have demonstrated a need for additional instruction and practice in Geometry. Curriculum for this course will supplement the instruction in the student’s current math class. Students will attend this course every other day for the entire year. Students will be recommended for this course based on their needs.