﻿ KML Math Department

## Kettle Moraine Lutheran High School Mathematics Department

Instructors:

Mr. Tim Kuehl
(Department Chair)

Mr. Dar Schramm

Mr. James Ott

Mr. Joshua Schoeneck

MESA Exploratorium

## Courses Offered

Hover your mouse over a class to see the course description.

Click on "Video" next to the course for a video geared towards helping students make course selections.

Please note that some videos are not yet available.

Advanced Math Track - HA1 Start

Advanced Math Track - HA2 Start

Pre-Algebra Course Number: 40110
1 credit (2 semesters)
Required for students not ready for Algebra 1

Note: Pre-Algebra is not accepted by most colleges as a math credit.

This course is for those students who need to refine their mathematics skills before taking Algebra 1. Students review arithmetic skills and learn the basics of algebra and geometry to prepare them for these classes. Topics include: the use of formulas from algebra and geometry, simplifying expressions, graphing, solving one and two step equations, the basics of linear and quadratic equations, basic trigonometry, probability, statistics, symmetry, and geometric transformations.
Video

Algebra 1 Course Number: 40121
1 credit (2 semesters)
Required
Prerequisite: Pre-Algebra or freshman placement by math department

Algebra 1s a branch of mathematics that is an important stepping stone to higher mathematics and very useful in today's technological workplace. This course develops basic algebraic concepts in a problem solving and systematic way; turning arithmetic into algebra by using letters to represent unknown numbers, and continuing to find the unknown numbers through both algebraic and graphical means. Topics include: a review of algebraic concepts, solving one and two variable equations and inequalities, functions, finding and using linear equations and inequalities to solve problems, finding and using quadratic equations to solve problems, absolute value functions, graphs of equations, solving systems of equations and inequalities, rules of exponents, finding and using exponential equations to solve problems, matrices, one and two variable statistics, and probability. Algebra 1 is intended for those students with average math skills.
Video

Honors Algebra 1 Course Number: 40131
1 credit (2 semesters)
Elective
Prerequisite: Placement by math department

Note: This course is intended for students of above average math skills, as it goes into greater depth and at a faster pace than Algebra 1.

Algebra is a branch of mathematics that is an important stepping stone to higher mathematics and very useful in today's technological workplace. This course develops basic algebraic concepts in a problem solving and systematic way; turning arithmetic into Algebra by using letters to represent unknown numbers, and continuing to find the unknown numbers through algebraic and graphical means. Topics include: A review of algebraic concepts, solving one and two variable equations and inequalities, functions, finding and using linear equations and inequalities to solve problems, finding and using quadratic equations to solve problems, absolute value functions, graphs of equations, solving systems of equations and inequalities, rational and radical expressions and equations, rules of exponents, finding and using exponential equations to solve problems, an introduction to logarithms, studying quadratic, polynomial, and exponential equations and their graphs, matrices, one and two variable statistics and probability.
Video

Geometry Course Number: 40210
1 credit (2 semesters)
Elective
Prerequisite: Algebra 1 and recommendation of the math department

Where Algebra is the study of numerical patterns, geometry is the study of visual patterns. In this course, students study these patterns both geometrically and algebraically covering measurement, symmetry, transformations, congruence, correspondence, area, volume, and similarity. Students develop conjectures about the patterns they discover, and prove their theorems using logic with both informal and formal, deductive and inductive proof techniques. The course begins with the geometry of points, and flows naturally to the study of segments, rays, lines, polygons, polyhedrons, trigonometry, and circles. Geometry is intended for those students with average math skills.
Video

Honors Geometry Course Number: 40211
1 credit (2 semesters)
Elective
Prerequisite: Algebra 1 and recommendation of the math department

Note: This course is intended for students of above average math skills, as it goes into greater depth and at a faster pace than Geometry.
Note: This course may be taken concurrently with Honors Algebra 2 or Pre-Calculus.

Where Algebra is the study of numerical patterns, geometry is the study of visual patterns. In this course, students study these patterns both geometrically and algebraically covering measurement, symmetry, transformations, congruence, correspondence, area, volume, and similarity. Students develop conjectures about the patterns they discover and prove their theorems using logic with informal and formal, deductive and inductive proof techniques. The course begins with the geometry of points, and flows naturally to the study of segments, rays, lines, polygons, polyhedrons, trigonometry, and circles. In Honors Geometry fractal geometry and non-Euclidean geometry are also studied.
Video

Algebra 2 Course Number: 40222
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 1 and recommendation of the math department

Note: Algebra 2 may be taken concurrently with Geometry or Honors Geometry with the math department’s approval.

Building upon basic concepts developed in Algebra 1 and Geometry, this course expands those concepts and develops additional ones for those students with average math ability. Engineers, chemists, physicists, persons in business and industry rely on advanced algebra to solve many problems. Linear, quadratic, polynomial, exponential, logarithmic, rational, and radical functions and their graphs, analytic geometry, matrices, probability, linear and non-linear regression, and one and two variable statistics are further developed in this class, while composition and inverse functions, variation, and the fundamental theorem of algebra are developed.
Video

Honors Algebra 2 Course Number: 40223
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 1 or Honors Algebra 1 and recommendation of the math department or freshman placement by math department.

Note: This course is intended for students of above average math skills, as it goes into greater depth and at a faster pace than Algebra 2.
Note: Students who plan to take Precalculus should take Honors Algebra 2 instead of Algebra 2.
Note: Honors Algebra 2 may be taken concurrently with Geometry or Honors Geometry with the math department’s approval.

Building upon basic concepts developed in Algebra 1 and Geometry, this course expands those concepts and develops additional ones for those students with above average math ability. Engineers, chemists, physicists, persons in business and industry rely on advanced algebra to solve many problems. Linear, quadratic, polynomial, exponential, logarithmic, rational, and radical functions and their graphs, analytic geometry, matrices, probability, linear and non-linear regression, and one and two variable statistics are further developed in this class, while composition and inverse functions, variation, and the fundamental theorem of algebra are developed. In Honors Algebra 2 series and sequences, conic sections, the binomial theorem, and recursion are also studied.
Video

Math Topics-Personal Finance Course Number: 40310
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 1

Note: This course may be taken concurrently with Geometry or any higher level math course.
Note: This course is not accepted by most colleges as a math credit.
Note: This course is offered on an alternate year basis. It will be offered in 2016-17.

Though open to all students, this course is designed particularly for students not intending to go to college to reinforce and develop the math skills they will need in daily life after high school. Topics will focus on the application of mathematics in life. Instruction will center on problem solving, and it will involve investigative and cooperative group work to learn and apply the concepts being studied. In addition to units involving basic arithmetic, algebra, geometry, and statistics, students will also study such topics as personal banking, taxes, credit cards, purchasing a car and house, and buying insurance.
Video

Math Topics-Technical Math Course Number: 40320
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 1.

Note: This course may be taken concurrently with Geometry or any higher level math course.
Note: This course is not accepted by most colleges as a math credit.
Note: This course is offered on an alternate year basis. It will be offered in 2017-18.

Though open to all students, this course is designed particularly for students not intending to go to college to reinforce and develop the math skills they will need in their work after high school. Topics will focus on the application of mathematics in life. Instruction will center on problem solving, and it will involve investigative and cooperative group work to learn and apply the concepts being studied. In addition to units involving basic arithmetic, algebra, geometry, statistics, probability, and trigonometry, students will also study such topics as business finances, mental math, measurement, and linear programming.
Video

Transition to College Mathematics Course Number: 40337
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 2 and recommendation of the math department

Note: Students who complete KML’s Algebra 1 - Geometry - Algebra 2 sequence plus this course will be well-prepared for two-year or four-year college programs that do not require calculus and also for training programs leading to career-level jobs.

This problem-based, inquiry-oriented, fourth-year high school mathematics course is intended for students who do not plan to major in the mathematical, physical, or biological sciences or engineering. It is intended to be a fourth year alternative to Precalculus, but may be taken anytime after taking Algebra 2. Topics include working with categorical data, counting methods, binomial distributions, statistical inference, function models, financial mathematics, informatics, spatial visualization and representations, decision-making, and trigonometry.
Video

Statistics Course Number: 40325
0.5 credits (1 semester)
Elective
Prerequisite: Credit in Algebra 2 and recommendation of the math department.

Note: May be taken concurrently with Algebra 2 or a higher level math course with approval of the math department.
Note: College-bound students are advised to contact their potential college to confirm acceptance of this course as a college prep math course.
Note: This class is the same as the first semester of CAPP/AP Statistics. Students who sign up only for Statistics may make a schedule change during the year and continue with the second semester of CAPP/AP Statistics, and take the AP test, but they will not be eligible for the CAPP college credit.

Statistics surround us in modern education, business, and life. The need for people to become statistically literate is imperative for them to be able to fully comprehend information that will continually bombard them in life. In this class, students go beyond the basic statistics they have learned to explore the statistics of both categorical and quantitative data, constructing and interpreting graphical displays of distributions of univariate and bivariate data (dotplot, stemplot, histogram, cumulative frequency plot, scatterplots, two-way tables), summarizing distributions of univariate data, comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots), exploring bivariate data, transformations to achieve linearity, methods of data collection, planning and conducting surveys, sampling, planning and conducting experiments, discussing results and types of conclusions that can be drawn from observational studies, experiments, and surveys, the normal distribution, and properties of the normal distribution.
Video

CAPP/AP Statistics Course Number: 40327
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 2 and recommendation of the math department.

Note: Sophomores may only take AP Statistics as the CAPP program is not available to sophomores.
Note: Students enrolling in the CAPP dual-credit option will be required to meet the prerequisites established by UW-Oshkosh and to pay an additional fee.
Note: Students enrolled in the CAPP course will receive 3 college credits for Elementary Statistics (MAT109) from UW-Oshkosh upon successful completion of the course.
Note: Students opting to take the AP test should contact their intended college for information on AP scores and transferability.

Statistics surround us in modern education, business, and life. The need for people to become statistically literate is imperative for them to be able to fully comprehend information that will continually bombard them in life. In this class, students go beyond the basic statistics they have learned to explore the statistics of both categorical and quantitative data, constructing and interpreting graphical displays of distributions of univariate and bivariate data (dotplot, stemplot, histogram, cumulative frequency plot, scatter plots, two-way tables), summarizing distributrions of univariate data, comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots), exploring bivariate data, transformations to achieve linearity, logarithmic and power transformations, methods of data collection, planning and conducting experiments, discussing results and types of conclusions that can be drawn from observational studies, experiments, and surveys, probability, combining independent random variables, the normal distribution, properties of the normal distribution, sampling distributions, statistical inference, point estimators and confidence intervals, and tests of significance.
Video

Pre-Calculus Course Number: 40342
1 credit (2 semesters)
Elective
Prerequisite: Credit in Algebra 2 and recommendation of the math department

Note: Pre-Calculus may be taken concurrently with Honors Geometry, Statistics or CAPP/AP Statistics.
Note: Students who plan to take Calculus I should take Precalculus.

Students who have found an aptitude and interest in mathematics and whose career choices require a strong math background will benefit from this course. The course includes an in-depth study of trigonometry. Students also study the linear, quadratic, polynomial, rational, radical, exponential, and logarithmic functions to a greater depth and techniques used to fit equations to variable data. Also included is a study of matrices, parametric equations, conic sections, the binomial theorem, mathematical induction, limits, series and sequences, permutations, and combinations. An introduction to calculus is embedded in the course work and will serve as a lead-in to higher-level math courses.
Video

CAPP/AP Calculus I Course Number: 40422
0.5 credits (1 semester)
Elective
Prerequisite: Credit in Precalculus and recommendation of the math department

Note: Students that have shown a strong ability in mathematics and need to study calculus for their future career are encouraged to take this course.
Note: Students enrolling in the CAPP dual-credit option will be required to meet the prerequisite established by UW-Oshkosh and to pay an additional fee.
Note: Students enrolled in the CAPP course will receive 4 college credits for Calculus I (MAT171) from UW-Oshkosh upon successful completion of the course.
Note: Students opting to take the AP test should contact their intended college for information on AP scores and transferability. Students opting for the AP test will also need to take Calculus II in order to cover the topics on the AP test.

This course is based on the study of real valued functions of a single variable. The course topics include derivatives, anti-derivatives, and, if time permits, definite integrals. Applications of differentiation, such as related rates, optimization, and curve-sketching, are also covered.
Video

CAPP/AP Calculus II Course Number: 40423
0.5 credits (1 semester)
Elective
Prerequisite: Credit in Calculus I and recommendation of the math department.

Note: Students that have shown a strong ability in mathematics and need to study calculus for their future career are encouraged to take this course.
Note: Students enrolling in the CAPP dual-credit option will be required to meet the prerequisite established by UW-Oshkosh and to pay an additional fee.
Note: Students enrolled in the CAPP course will receive 4 college credits for Calculus II (MAT172) from UW-Oshkosh upon successful completion of the course.
Note: Students opting to take the AP test should contact their intended college for information on AP scores and transferability. Students will be prepared to take either the Calculus AB or the Calculus BC AP test.

This course covers definite integration and applications, several techniques of integration, approximation, and improper integrals. Numerical differential equations, slope fields, Euler's method, and mathematical modeling. Taylor and Fourier Series are also covered.
Video

CAPP Calculus III Course Number: 40424
0.5 credits (1 semester)
Elective
Prerequisite: Credit in Calculus II and recommendation of the math department

Note: Students that have shown a strong ability in mathematics and need to study calculus for their future career are encouraged to take this course.
Note: Students enrolling in the CAPP dual-credit option will be required to meet the prerequisite established by UW-Oshkosh and to pay an additional fee.
Note: Students enrolled in the CAPP course will receive 4 college credits for Calculus III (MAT273) from UW-Oshkosh upon successful completion of the course.

This course covers vectors in two and three dimensions and vector functions. Multivariate differential and integral calculus, partial derivatives and multiple integrals. Line and surface integrals.
Video

Differential Equations Course Number: Independent Study
0.5 credit (1 semester)
Elective
Prerequisite: Credit in Calculus II and recommendation of the math department

Note: This class is offerred through UW-Online second semester. Upon successful completion, students will earn 3 college credits for MAT 271 from UW-Online in addition to 0.5 credits from KML.

Ordinary differential equations of the first and second order, series solutions, higher order linear equations, the Wronskian, Laplace transform and applications, numerical methods and boundary value problems
Video

Additional Independent Study Math Courses Course Number: Independent Study
0.5 credits (1 semester)
Elective
Prerequisite: Varies by course.

Students with stong math abilities are welcome to further their studies in mathematics through various college and online options. These can include classes from college prep programs offered at numerous universities during the summer and/or online classes from universities, high schools, and course providers. Students desiring to take a class through one of these programs and also have it count for KML credit need to complete the Outside Study form available from Student Services. Students may also opt to take these courses separately from KML credit.

A list of known and recommended courses is provided below.
Video

Known and recommended programs:

MAT 210 Topics in Finite Mathematics from UW-Online
Prerequisite: Algebra 2 Offerred second semester

MAT 113 Trigonometry from UW-Online
Prerequisite: Algebra 2 Offerred in the summer and first and second semester

Northwestern University College Preparation Program
Summer Calculus and Linear Algebra courses

Stanford University College Preparation Program
Summer Calculus and Linear Algebra courses

## Department Outcomes

The goal of the KMLHS Mathematics Department is to train children of God to appreciate God’s order of creation in the logical structure of math.

Graduates of the KMLHS Mathematics Department will be:

1. Children of God who

1.1 appraise their current math skills and, building on their previous knowledge of mathematics, develop their math skills in light of new developments in their lives and in society.
1.2 evaluate data to guide their lives of Christian stewardship.
1.3 utilize their God-given abilities in mathematics to serve Him.

2. Self-directed learners who

2.1. integrate the rules of mathematics to solve problems.
2.2. incorporate the use of numbers and variables effectively.
2.3. integrate mathematical reasoning to produce a solution.
2.4. evaluate a problem solving situation and choose an appropriate problem solving strategy.
2.5. solve problems using various appropriate strategies.
2.6. justify solutions to their work.

3. Problem solvers who

3.1. organize a plan to complete a project.
3.2. recognize and analyze patterns and incorporate them into problem solving situations.
3.3. decide upon an appropriate tool for solving a problem.

4. Cooperative learners who

4.1. contribute in solving group projects.
4.2. communicate effectively to
4.2.1. relate their understanding of mathematics.
4.2.2. provide sound explanations of their reasoning in problem-solving situations.
4.3. develop and complete tasks assigned to them.

5. Informed citizens who

5.1. analyze data in their lives.
5.2. incorporate their mathematical knowledge and skills as a productive member of society.