MATHEMATICS

MATHEMATICS
The Mathematics Department seeks to serve students by assisting each student in developing the knowledge and skills he or she will find useful in further courses of study or in real life situations. Most freshman enter this progression at the Algebra I level.  
In order to meet the varying demands, needs and abilities of our students and to address all of the Performance Indicators in the Common Core, the Mathematics Department offers a wide range of courses. We strongly encourage students to take a math course in each of their four years in high school since the single greatest predictor of success in college or technical college courses is completion of four years of high school mathematics. 

MATH GRADUATION STANDARDS

The graduation standards for math are the Standards for Mathematical Practice from the Common Core. These mathematical practices represent what students are doing when engaging in mathematics and the complex reasoning we expect all of our students to demonstrate for College and Career Readiness. These Graduation Standards will be practiced and assessed over time via the points of intersection with specific content standards, also identified from the Common Core. 

To ensure the focus, rigor, and coherence of the Common Core, students must demonstrate proficiency on the content standards for Algebra I & Geometry. To earn a course credit, students must demonstrate that they are, at minimum, approaching all of the standards (no 1s) taught and assessed in that course. This is represented as a final grade score of 2.0 or higher. 

In order to move on to the next course in sequence (at the same level--CP, Honors, etc.), students must demonstrate proficiency on most but not all of the course standards.  This means that they may not have any “1s” and must achieve a final grade score of 2.75 (B-) or higher.  To remediate, students will be assigned either to Math Lab (no credit) or Individualized Math (credit option that remediates standards and includes additional math objectives identified by students’ needs).   

A final grade score below 2.0 is considered a failing grade and the student will be required to either repeat the course or take an equivalent course. 

Students must earn 3 credits of Math to graduate, reaching graduation standards at least through Geometry. Student placement for courses will be based on demonstrated readiness as evidenced by their performance of standards.
    

Math Graduation Standards

The Standards for Mathematical Practice:

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.


Algebra Content Standards:

Holt Chapter

Standard

1

Solving Equations

CCSS.MATH.CONTENT.HSA.REI.A.1

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (MP3)

2 Inequalities

CCSS.MATH.CONTENT.HSA.REI.B.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

3 Functions

CCSS.MATH.CONTENT.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

CCSS.MATH.CONTENT.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

4

Graph and Write Equations

CCSS.MATH.CONTENT.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.


CCSS.MATH.CONTENT.HSF.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

5 Systems

CCSS.MATH.CONTENT.HSA.REI.C.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

6 and 9

Exponents and Polynomials

CCSS.MATH.CONTENT.HSN.RN.A.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.


CCSS.MATH.CONTENT.HSF.LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).


CCSS.MATH.CONTENT.HSA.APR.A.1: Perform arithmetic operations on polynomials

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

7 Factoring

CCSS.MATH.CONTENT.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

8 Quadratics

CCSS.MATH.CONTENT.HSF.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*


CCSS.MATH.CONTENT.HSA.REI.B.4

Solve quadratic equations in one variable.


Geometry Content Standards:

Intro to Geometry

CCSS.MATH.CONTENT.HSG.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.


CCSS.MATH.CONTENT.HSG.GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

Proofs with Parallel and Perpendicular Lines

CCSS.MATH.CONTENT.HSG.CO.C.9

Prove theorems about lines and angles.Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Triangles

CCSS.MATH.CONTENT.HSG.CO.C.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point

Angles and Segments in Triangles

CCSS.MATH.CONTENT.HSG.GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Polygons

CCSS.MATH.CONTENT.HSG.CO.C.11

Prove theorems about parallelograms.

Similarity & Right Triangles

CCSS.MATH.CONTENT.HSG.SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.


CCSS.MATH.CONTENT.HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Circles

CCSS.MATH.CONTENT.HSG.C.A.2

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Geometric Solids

CCSS.MATH.CONTENT.HSG.GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.


Transformations and Tessellations

CCSS.MATH.CONTENT.HSG.CO.A.5

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.




MATHEMATICS COURSE PROGRESSIONS

NOTES:

Honors courses are available in Geometry, Algebra II, Pre-calculus and Calculus. AP classes are offered in Calculus and Statistics. Students wishing to take an honors math class must meet the prerequisite criteria for the desired class and complete a time management activity. To continue in honors math classes, students must meet all standards and work to exceed on some standards.

Entry into any course is dependent upon successful completion of the prerequisites listed for that course in the Program of Studies. When a student has not met the standards in a math course, that student is inadequately prepared for success in the next math course.

Students who are having difficulty succeeding in their math course may change from one course to another with the permission of the teachers involved in the change. This change must take place by the 5th week of the course. Any course changes after that time will be done only if initiated by the teacher of the course. No changes will be made without the permission of the parent.

Students are required to take at least three math classes, and should plan to leave MDIHS having met the geometry standards. This may mean that some students will take 4 or more math courses. Most 2- or 4-year colleges require Algebra II and many standardized tests (SAT, ACT) include Algebra II skills.


MATH LAB

Open to: 9-12


Math Lab is a supported study hall for any student enrolled in a math class or needing to reinforce math skills from previous grade level math work. Students will receive support for their math class, including review of prerequisite skills, reteaching new concepts, assistance on homework and meeting standards in current or prior math classes. Students enrolled in the Math Lab are expected to use the time to complete their math homework and have the Math Lab supervisor check their work before moving on to homework for other courses. In addition, students may use the Math Lab to practice for the PSAT, SAT, or the Accuplacer Exam. Students successfully attending Math Lab receive 0.5 elective credits for a semester, 0.25 for a quarter. Successfully attending means being present in the Math Lab, working constructively on either math class work or assigned prerequisite review work, or steadily practicing for future exams or courses.



PRE-ALGEBRA

Open to: 9, 10

Credit: 1

Prerequisite: A RIT score of less than 225 on the NWEA Math 6+ exam or recommendation by the 8th grade teacher.


In this course, students will focus on the essential skills needed to be successful in future math classes. The course will begin by building students’ number sense and computation skills, setting the foundation for higher level algebra concepts. Students will also be introduced to solving equations, inequalities, and graphing. After successful completion of this course, students will be prepared to enroll in Algebra I - Part 1.



ALGEBRA I – PART 1

Credit: 1

Open to: 9, 10, 11

Prerequisite: 225 or greater on the NWEA Math 6+ Exam


In Algebra I - Part 1 and Part 2, students will study Algebra I concepts over two consecutive semesters so that students have more time to process and practice the Algebra I standards.  Thirteen Common Core Standards will be assessed over the course of the two semesters.  In Part 1, students will focus on solving equations and inequalities, domain and range, function notation, linear functions, and solving systems of equations. After successful completion of this course, students should take Algebra I Part 2.



ALGEBRA I - PART 2

Credit: 1

Open to: 9, 10, 11

Prerequisite: Successful completion of Algebra I - Part 1.


Students in Algebra I-Part 2 will continue the study of Algebra I standards that they started in Algebra I-Part 1. Major concepts in this course include exponent properties, polynomials and factoring, and exponential and quadratic functions. After successful completion of Algebra I-Part 2, students will be prepared to take Algebraic Geometry or Geometry.



ALGEBRA I

Credit: 1

Open to: 9, 10

Prerequisite: 245 or greater on the NWEA 6+ exam


Algebra I is a one semester, one credit course. Students will study equations and inequalities, domain and range, function notation, systems of equations, exponent properties, polynomials and factoring, and numerous types of functions (linear, absolute value, exponential, quadratic).  Thirteen Common Core Standards will be assessed in this course.  Students successfully  meeting the Algebra I standards will be academically prepared to take Geometry.  


ALGEBRAIC GEOMETRY

Credit: 2

Open to: 9, 10

Prerequisite: Algebra I or Algebra I-Parts 1 and 2


In Algebraic Geometry, students will study geometry concepts over two consecutive semesters so that students have more time to process and practice the standards. In addition, students in this class will be introduced to some of the fundamental standards of Algebra ll. Algebraic Geometry Students will be assessed on eleven Common Core Standards including topics such as geometry definitions, line and angle relationships, how to prove theorems and use them to solve problems, coordinate geometry, perimeter, area, volume, transformations, congruence, similarity and trigonometric relationships. Students who successfully complete this course will be prepared for Algebra II.


GEOMETRY

Credit: 1

Open to: 10, 11, 12

Prerequisite: Algebra I or Algebra I-Parts 1 and 2.


Geometry is a one semester, one credit course. Students will learn basic geometry definitions, line and angle relationships, how to prove theorems and use them to solve problems, coordinate geometry, perimeter, area, volume, transformations, congruence, similarity and trigonometric relationships.  Eleven Common Core Standards will be assessed. Students successfully completing this course should plan to take Algebra 2.



HONORS GEOMETRY

Credit: 1

Open to: 9, 10

Prerequisite: Algebra I with a 3.25 or higher, and NWEA End-of-Subject Algebra I score of 260 or higher


In this course, students will study eleven Common-Core standards in geometry with a focus on logical rigor and formal proof. Topics include inductive and deductive reasoning about angles, triangles, quadrilaterals, circles, coordinate geometry, perimeter, area, volume, transformations, congruence, similarity and trigonometric relationships. This course is designed for students who are excited about math, are seeking a challenge, and are willing to work independently to achieve mastery. Students successfully completing this course will be prepared for Honors Algebra II.



ALGEBRA II

Credit: 1

Open to: 10, 11, 12

Prerequisite: Successful completion of Algebra I and Geometry standards


In Algebra II, students will review linear equations, systems of equations, and linear functions. Topics include quadratic, polynomial, radical, rational, exponential, logarithmic and trigonometric functions. Students successfully completing this course will be prepared for Precalculus or Probability and Statistics.



HONORS ALGEBRA II

Credit: 1

Open to: 10, 11

Prerequisite: Successful completion of Honors Geometry and a score of 265 or better on the NWEA Geometry and Algebra 1 Subject Tests


In Honors Algebra II, students will immediately begin working on the chosen Common Core standards, and students will be expected to review any Algebra I concepts on their own.  Topics include quadratic, polynomial, radical, rational, exponential, logarithmic and trigonometric functions.  This course exposes students to higher level applications. Students successfully completing this course will be prepared for Honors Precalculus or AP Statistics.



PRECALCULUS

Credit: 1

Open to: 11, 12

Prerequisite: Algebra II


Students in this course will explore topics in Advanced Algebra and Trigonometry. Topics will include linear and quadratic functions, polynomial functions, trigonometry of triangles, graphs of trigonometric functions, trigonometric identities, exponents and logarithms. This course is designed for students who are interested in continuing their study of algebra-based mathematics beyond Algebra II. Students who successfully complete this course will be prepared for entry-level mathematics courses at most colleges. Students may take this course concurrently with Probability and Statistics (CP), if scheduling allows.



HONORS PRECALCULUS

Credit: 1

Open to: 11, 12

Prerequisite: Successful completion of Honors Algebra II, including a recommended 270 on the Algebra II NWEA


Honors Precalculus is an honors level course where students study and apply linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions with greater complexity and rigor. These functions will be presented in a variety of ways: verbally, geometrically, numerically, and analytically. Additionally, as time allows, students will be introduced to matrices, parametric equations, conic sections, sequences and series, and limits. Students successfully completing this course will be prepared to take Honors Calculus.




PROBABILITY AND STATISTICS

Credit: 1

Open to: 11, 12

Prerequisite: Algebra II


The growing consensus is that students who want an edge in the competition for top jobs need a foundation in statistics. In a world where we are bombarded by statistics on a daily basis, it is essential that we can determine the validity of the information we see and ponder its implications.


Probability and Statistics is an introductory course offered to juniors and seniors who have met algebra and geometry graduation standards. Students study four broad conceptual themes including: exploring data, planning experiments and studies, using probability and simulation, and statistical inference.


This course is intended for college-bound students who are interested in taking a mathematics elective and in becoming well prepared for a college-level statistics course. Although students will use some math skills from previous classes, this course will be more interdisciplinary and will strongly emphasize critical thinking skills.


TOPICS IN MATHEMATICS

Credit: ½

Prerequisite: Honors Geometry or College Prep Algebra II with 3.0 or better

This is a math elective offered only in Quarter 4, for students who like math and want to take an additional course outside the usual curriculum. The subject will differ from year to year and will be offered pass/fail.

Possible Topics:

  • Matrices and Linear Algebra (solving systems of equations, rotating coordinate systems)

  • 3-D Geometry

  • Modular Math

  • Sequences and Series

  • Polar Coordinates and parametric equations

  • Chaos and fractals

The course will be problem-based and will be differentiated to challenge everyone.




ADVANCED PLACEMENT STATISTICS

Credit: 1

Open to: 11, 12

Prerequisite: Algebra II


Statistics is one of the most useful and interesting courses a high school student can take, and it has become more and more applicable in recent years. In this course, students will explore advanced topics in statistics, with emphasis on the study and collection of data and the inferences one can make from such data. Concepts include: observing patterns in data, planning experiments and studies, using probability and simulation, and inferring information about the real world from smaller samples.


This course is intended for college-bound students who wish to satisfy a college requirement with the AP exam. This class is fast-paced to cover all of the content tested by the AP examination and to allow time for practice for this exam. This course will be offered in the fall semester, with optional continuation in the quarter-long Advanced Topics in Statistics course.


ADVANCED TOPICS IN STATISTICS

Credit: ½

Open to: 11, 12

Prerequisite: AP Statistics


This one-quarter class continues advanced topics introduced in the AP Statistics course.  Students will complete a major statistics project and continue practicing for the Advanced Placement test. Topics of particular focus include multivariable inference using chi-squared methods and regression inference.


HONORS CALCULUS

Credit: 1

Open to: 11, 12

Prerequisite: Successful completion of Honors Precalculus


Students taking Calculus will continue to look at functions and how they change, from a variety of perspectives: geometrically, verbally, numerically, and analytically. This course will cover the four basic tenets of calculus; limits, derivatives, definite integrals and indefinite integrals. “Real life” applications of calculus will be studied throughout the course. This one semester, college level calculus class will cover the content of the AP curriculum. Students who are successful in this course will be encouraged to take Advanced Placement Calculus where the emphasis will be on learning some additional calculus topics and preparing for the AP exam in May.



ADVANCED PLACEMENT CALCULUS

Credit: 1

Open to: 11, 12

Prerequisite: Honors Calculus


Students who have successfully completed Honors Calculus will have the option of continuing their study of calculus and preparing to take the AP exam in May. It is important for students to realize that after completing first semester calculus, they will have already learned the required material for the AP Calculus AB exam. This Advanced Placement course will have three main focuses: a continuation of advanced calculus topics (some BC topics), preparation for the AP exam and a project of the student’s own choosing. Completion of this course along with Honors Calculus will provide students with the equivalent of a college course in calculus. Students who wish for an extension of the AP Calculus AB curriculum (and who need less practice for that exam) will be offered the option of independently learning the remaining material covered on the BC exam and taking that exam in May.