Mathematics

The Johnson High School Mathematics Department offers a variety of courses to  introduce students to the most powerful tool mankind has developed for investigating  the world. Heavy emphasis on the standards for passing the Minnesota Comprehensive  Assessment (MCA) in mathematics will be covered in Integrated Math I, Integrated  Math II, and Integrated Math III.  

Mathematics Course Sequence 

Regular mathematics pathway 

9th grade Integrated Math I  

10th grade Integrated Math II 

                                                                                                                                                    Integrated Math II & III

                                         Integrated Math III

11th grade Algebra II or Algebra II Accelerated (Honors) 

12th grade Electives 

    Analysis 

Pre-Calculus (Honors) 

AP Probability and Statistics 

Advanced mathematics pathway 

9th grade Integrated Math II 

10th grade Integrated Math II and III 

11th grade Pre-Calculus 

Electives 

AP Probability and Statistics  

12th grade Calculus 

Electives 

SPC: College Algebra  

AP Probability and Statistics  

Integrated Math 1 

Course Number(s): M404601 

Length: 2 Semesters (4 Credits) 

Prerequisites: Must have passed basic math. Students  must be able to add, subtract, multiply, and divide. Grade: 9 

Integrated Math I is the first required course of a 3-year  integrated mathematics progression. Students enrolled  in this course will make connections between algebraic,  

geometric, and statistical concepts, while developing  problem solving skills involving the use of inquiry,  discourse, collaborative work, logical progression, and  deductive reasoning. Students will explore the  interconnectedness of topics involving linear systems as  they relate to parallel lines, perpendicular lines,  foundational topics of geometry, triangles and  congruence, then apply their algebraic understanding to  exponents, exponential functions, and statistics. The  

ability to solve linear equations is foundational to this  course. 

Integrated Math II 

Course Number(s): M404111 

Length: 2 Semesters (4 Credits) 

Prerequisites: Integrated Math I 

Grade: 9-12 

Integrated Math II is the second required course of a  three year mathematics progression. Students enrolled  in this course will continue to make connections  between algebraic, geometric and statistical concepts,  while further developing problem solving skills  involving the use of inquiry, discourse, collaborative  work, logical progression and deductive reasoning.  They will also further explore concepts involving  exponents, roots and polynomials, then connect their  understanding to quadratic equations and functions.  They will explore complex geometric concepts involving triangle relationships, quadrilaterals,  similarity, and probability. 

Integrated Math II & III 

Course Number(s): M402221(sem 1), M402231 (sem 2) Length: 2 Semesters (4 Credits each semester) Prerequisites: Integrated Math I 

Grade: 10 

Integrated Math II & III satisfies the second and third  required courses of a three-year mathematics  progression. The purpose of this double credit course  that meets daily is to provide a pathway to advanced  mathematics for students who enrolled in Integrated  Math I as a ninth grader. Students enrolled in this  course strengthen connections between algebraic,  geometric, and statistical concepts. There will be  continued development using inquiry, discourse,  collaboration, logic, and deductive reasoning. Topics  covered in this combined course include: exponents and  roots, polynomials and factoring, quadratics and  complex numbers, triangle relationships and similarity,  quadrilaterals and other polygons, probability,  polynomial functions, rational functions, radical  functions, rational exponents, data analysis and  statistics, circles, and two- and three- dimensional  models. Students who successfully complete this course  have a variety of options to further their study in  advanced mathematics. (M402221 & M402231, 8 credits) 

Integrated Math III 

Course Number(s): M402231 

Length: 2 Semesters (4 Credits each semester) Prerequisites: Integrated Math I & II

Grade: 11

 Integrated Math III is the third required course of a three-year mathematics progression. Different disciplines of math are intertwined to make meaningful connections for students. This course moves towards more complex functions and advanced applications of geometry and statistics. This progression allows for a strong development of the algebra strand in a consistent instructional arc. Upon completion of this course, students will be eligible to enroll in various advanced mathematics courses.

Analysis  

Course number(s): M407501 

Length: 2 Semesters (4 Credits) 

Prerequisites: In order to enroll in this course, all  students must have taken and passed Integrated Math I, II, & III 

Grade: 10-12 

This course is designed to help students who want to go  beyond the traditional Algebra 1, Geometry, and Algebra  2, but do not want to pursue the rigor of Pre-Calculus.  This course is designed to prepare students for further  study of mathematics at the college level. Students will  revisit and explore concepts and skills related to linear,  quadratic, exponential, logarithmic, polynomial,  rational, and trigonometric functions. This course will  also include topics and applications in the areas of  sequences and series, probability and statistics, matrices,  and data analysis. Technology will be utilized to graph  and analyze data in a variety of mathematical and real  world contexts. Content and methods of the course will  be personalized to meet the needs of a broad range of  learners.

Pre-Calculus (Honors) 

Course Number(s): M437051 

Length: 2 Semesters (4 Credits) 

Prerequisites: B or higher in Algebra II Accelerated; A in Algebra II; B or higher in the Integrated Math II & III course 

Grade: 10-12 

Students planning on taking Calculus must take this  course. The focus of this course is to prepare students  for AP Calculus. It involves an in depth study of  algebraic topics not previously covered and  concentrates on the use of graphing  to solve  difficult real world problems. This course is for the  highly motivated mathematics student who wishes to  develop mature study habits necessary for college work. 

The function concept provides the basis for most of the  course’s study. Polynomial functions receive thorough treatment; logarithms and exponents are taught with  primary emphasis given to solution of logarithmic and  exponential equations. Matrix algebra is studied, as are  series, sequences and probability. The slope of a curve  and tangent line to a curve are discussed in connection  with polynomial and exponential functions. Right  triangle and Unit Circle trigonometry are covered, along  with a study of the graphs of the trigonometric  functions. Time is also spent solving trigonometric  equations. Series, sequence and probability are also  covered.

SPC: College Algebra  

Course Number(s): M491201 

Length: 2 Semesters (4 Credits) 

Prerequisites: A or B in Analysis, B or C in Pre-Calculus Grade: 11-12 

This course covers algebraic functions and their  applications. Topics include linear and quadratic  functions, functions and graphs, polynomial and  rational functions, exponential and logarithmic  functions, systems of equations and inequalities, matrix  algebra, discrete algebra, the binomial theorem and  probability. Graphing calculators are used to further the  student’s understanding of essential mathematical  concepts. Note: This course is a Saint Paul College course which is  taught in high school. Upon successful completion of  

this course, students receive three semester credits from  Saint Paul College 

AP Statistics (Honors) 

Course Number(s): M456111 

Length: 2 Semesters (4 Credits) 

Prerequisites: C or better in Intermediate Math III

Grade: 11-12 

Statistical data, summaries and inferences appear more  frequently in the work and everyday lives of people  than any other form of mathematical analysis. Students  in this course will learn to collect, organize and analyze  data and then draw reasonable, usable conclusions.  They will study applications in business, physical and  social science, economics, and engineering.  Students  will be prepared to take the advanced placement exam  in Statistics in the spring. This is a wonderful way to  earn college credit while in high school!  

AP Calculus AB (Honors)  

Course number(s): M457101 

Length: 2 Semesters (4 Credits) 

Prerequisites: B or higher in Pre-Calculus 

Grade: 11-12 

This course in differential and integral calculus is  equivalent to the freshman calculus course offered in  most colleges and universities. The course is demanding  and requires mature study habits.