Description of Course Content

Math 4 is a new course designed to meet the needs of students in the 21st century.  The primary focus of this course is on functions and statistical thinking, continuing the study of algebra, functions, trigonometry and statistical concepts previously experienced in NC Math 1-3. The course is designed to be a capstone to introductory statistical concepts. Additionally, the course intentionally integrates concepts from algebra and functions to demonstrate the close relationship between algebraic reasoning as applied to the characteristics and behaviors of more complex functions. In many cases, undergraduate students majoring in nonSTEM fields will take an entry-level Algebra or Introductory Statistics course. Students will be prepared for college level algebra and statistics or as a bridge to prepare students for Precalculus or other advanced math courses.

Course Objectives

Math 4 Standards (2020)

N.1  Apply properties and operations with complex numbers

N.1.1  Execute procedures to add and subtract complex numbers.

N.1.2  Execute procedures to multiply complex numbers.

N.2  Apply properties and operations with matrices and vectors.

N.2.1  Execute procedures of addition, subtraction, multiplication, and scalar multiplication on matrices.

N.2.2  Execute procedures of addition, subtraction, and scalar multiplication on vectors.

AF.1 Apply properties of function composition to build new functions from existing functions.

AF.1.1 Execute algebraic procedures to compose two functions.

AF.1.2 Execute a procedure to determine the value of a composite function at a given value when the functions are in algebraic, graphical, or tabular representations.

AF.2 Apply properties of trigonometry to solve problems.

AF.2.1 Translate trigonometric expressions using the reciprocal and Pythagorean identities.

AF.2.2 Implement the Law of Sines and the Law of Cosines to solve problems.

AF.2.3 Interpret key features (amplitude, period, phase shift, vertical shifts, midline, domain, range) of models using sine and cosine functions in terms of a context.

AF.3 Apply the properties and key features of logarithmic functions.

AF.3.1 Execute properties of logarithms to simplify and solve equations algebraically.

AF.3.2 Implement properties of logarithms to solve equations in contextual situations.

AF.3.3 Interpret key features of a logarithmic function using multiple representations.

AF.4 Understand the properties and key features of piecewise functions.

AF.4.1 Translate between algebraic and graphical representations of piecewise functions (linear, exponential, quadratic, polynomial, square root).

AF.4.2 Construct piecewise functions to model a contextual situation.

AF.5 Understand how to model functions with regression.

AF.5.1 Construct regression models of linear, quadratic, exponential, logarithmic, & sinusoidal functions of bivariate data using technology to model data and solve problems.

AF.5.2 Compare residuals and residual plots of non-linear models to assess the goodness-of-fit of the model.

SP.1 Create statistical investigations to make sense of real world phenomenon.

SP.1.1 Construct statistical questions to guide explorations of data in context.

SP.1.2 Design sample surveys and comparative experiments using sampling methods to collect and analyze data to answer a statistical question.

SP 1.3 Organize large datasets of real world contexts (i.e. datasets that include 3 or more measures and have sample sizes >200) using technology (e.g. spreadsheets, dynamic data analysis tools) to determine: types of variables in the data set, possible outcomes for each variable, statistical questions that could be asked of the data, and types of numerical and graphical summaries could be used to make sense of the data.

SP.1.4 Interpret non-standard data visualizations from the media or scientific papers to make sense of real world phenomenon.

SP.2 Apply informal and formal statistical inference to make sense of, and make decisions in, meaningful real world contexts.

SP.2.1 Design a simulation to create a sampling distribution that can be used in making informal statistical inferences.

SP.2.2 Construct confidence intervals of population proportions in the context of the data.

SP.2.3 Implement a one proportion z-test to determine if an observed proportion is significantly different from a hypothesized proportion.

SP.3 Apply probability distributions in making decisions in uncertainty.

SP.3.1 Implement discrete probability distributions to model random phenomenon and make decisions (e.g., expected value of playing a game, etc.)

SP.3.2 Implement the binomial distribution to model situations and make decisions.

SP.3.3 Recognize from simulations of sampling distributions of sample means and proportions that a normal distribution can be used as an approximate model in certain situations.

SP.3.4 Implement the normal distribution as a probability distribution to determine the likelihood of events occurring.

Classroom expectations

What I expect of you will boil down to three things...

• CARE - Even if this is not your favorite subject, I expect you to care about doing a good job, care about learning something. 
• TRY - Come to class every day with a good attitude and make efforts to progress and improve.
• BE RESPECTFUL - Always keep in mind that you are not the only person in the class and that you are expected to behave in a manner that is professional and respectful of others and their learning (in person and remotely).

Class Meeting Times/Days

Mondays (last names A - D), Tuesdays (last names E - K), Wednesdays (last names L - Q), Thursdays (last names R - Z).

 

Grades

Students will be receiving participation grades for working through/practicing problems and completing activities.  Students who are absent and do not attend a live session will be responsible for completing these assignments on their own.  All graded assignments will be highlighted in the "To Do" list for each module.  These assignments will be due on Friday afternoons at 3:00 pm.  Students will also receive grades for assessments like quizzes, tests and projects.  Students will take a teacher-made Final Exam at the end of the course worth 25% of the final grade.  

Late work policy

Graded assignments will be due at 3:00 on Fridays.  I will accept late work, but get it to me as soon as possible.  Expect to have points deducted for assignments turned in past the due date.  The longer you wait to turn in the assignment, the more points will be deducted.  

Attendance/Signing on policy

Roughly the first half of each lesson given in class will be live-streamed.  To receive attendance for attending a class remotely, you will need to log in at the BEGINNING of the class period and participate in the assigned activities.

Cheating

I take academic dishonety very seriously.  Due to the nature of this learning situation, many things you do in class will be allowed to be collaborative.  However, there will be some assessments, assignments or projects that I expect you to complete individually.  I will do what I can to ensure that assessments meant to be completed individually and without aid from others will be done as such.  

Instagram

I will have an Instagram account for this class (katie_durham_math4).  This is not a personal account, but one meant for students to share and engage with the course material.  For an assignment, students will submit to me images or pictures that present/review the course content in a different and hopefully creative way.  I will post these images on the class account.  Students are encouraged to follow me to see each other's work (parents are welcome too).  I have never done this before and am pretty unfamiliar with Instagram, but I am going to give it a try. 

Supplies 

• Chromebook 
• Headphones/earbuds 
• Pencils 
• Colored Pencils/Markers
• Paper
• Folder for handouts

 

Contact Information

email:  katie.durham@ucps.k12.nc.us

phone:  704-296-6319