Math Courses

Life Applications

Build confidence and ability in daily mathematical necessities.  Understand the tools for complex math problems.

Basic Math

Course Description

In‐depth treatment of solving equations with whole numbers, fractions, decimals, ratios; function properties and graphs; inverse functions; linear, quadratic, polynomial,  rational, exponential and logarithmic functions with applications; systems of equations.  

Topics

Time:  Understanding and calculations of analog and digital time and expressions.

Money:  Value and usage of US monetary system, with calculations for dollars and cents.  

Operations: Addition, subtraction, multiplication, and division of whole numbers.

Fractions:  Dissecting parts of the fraction and perform all basic fraction operations with whole numbers, fractions, and mixed numbers.

Decimals:  Place value and conversion between decimals, fractions, and whole numbers.

Metric:  Convert between US customary and metric systems.  Convert within metric units and values.

Graphs:  Read and create graphs that represent basic information.  Graph types and scaling.

Functions:  Simple and complex functions and equations.  

Expressions:  Powers, expressions, roots, and more are simplified and solved.

Systems:  Using sets and data to identify unknowns and create equations for simple and complex problems.

Learning Objectives

1. Demonstrate the ability to solve equations with whole numbers, fractions, decimals, and ratios.

2. Understand and apply function properties and graphing techniques.

3. Identify and solve linear, quadratic, polynomial, rational, exponential, and logarithmic functions with real-life applications.

4. Analyze and solve systems of equations.

5. Demonstrate proficiency in time and money calculations.

6. Apply basic mathematical operations (addition, subtraction, multiplication, and division) to whole numbers.

7. Dissect fractions and perform basic fraction operations with whole numbers, fractions, and mixed numbers.

8. Convert between decimals, fractions, and whole numbers and understand the place value of decimals.

9. Convert between US customary and metric systems and convert within metric units and values.

10. Read and create graphs that represent basic information and understand graph types and scaling.

11. Simplify and solve expressions involving powers, roots, and more.

12. Identify unknowns and create equations for simple and complex problems using sets and data.

13. Build confidence and ability in daily mathematical necessities and understand the tools for complex math problems.

Algebra

Course Description

This course is designed to provide students with a comprehensive foundation in the fundamental concepts of pre-algebra and algebra 1. 

In this course, students will review key mathematical concepts such as fractions, decimals, and percentages, and will also learn how to solve equations and inequalities. The course will then move on to more advanced topics, including functions, graphs, polynomials, and systems of equations. Students will also be introduced to real-world applications of algebraic concepts. 

Topics

1. Pre-Algebra Review

   • Basic arithmetic operations

   • Fractions and decimals

   • Exponents and radicals

   • Order of operations

2. Algebraic Expressions and Equations

   • Algebraic expressions and properties

   • Solving equations and inequalities

   • Word problems and applications

3. Graphing and Functions

   • Coordinate systems and graphing lines

   • Functions and their graphs

   • Transformations of graphs

4. Linear Equations and Inequalities

   • Solving linear equations and inequalities

   • Applications of linear equations and inequalities

   • Systems of linear equations

5. Quadratic Equations and Functions

   • Factoring quadratic expressions

   • Solving quadratic equations

   • Applications of quadratic functions

6. Rational Expressions and Equations

   • Simplifying rational expressions

   • Solving rational equations

   • Applications of rational expressions and equations

7. Exponential and Logarithmic Functions

   • Properties of exponential functions

   • Solving exponential equations

   • Properties of logarithmic functions

8. Sequences and Series

   • Arithmetic sequences and series

   • Geometric sequences and series

   • Applications of sequences and series

9. Conic Sections

   • Circles, parabolas, ellipses, and hyperbolas

   • Graphing conic sections

   • Applications of conic sections

Learning Objectives

1. Students will be able to perform basic arithmetic operations with integers, fractions, and decimals.

2. Students will be able to solve linear equations and inequalities in one variable and apply these skills to real-world problems.

3. Students will be able to simplify and factor algebraic expressions and apply these skills to solve quadratic equations.

4. Students will be able to graph linear equations and understand slope and intercepts.

5. Students will be able to use functions to model and solve real-world problems, including linear and quadratic functions.

6. Students will be able to solve systems of linear equations and inequalities.

7. Students will be able to apply algebraic concepts to geometry and measurement, including area, volume, and perimeter.

8. Students will be able to use logarithms and exponents to solve equations and real-world problems.

9. Students will be able to solve and graph exponential and logarithmic functions.

10. Students will be able to apply algebraic concepts to statistics and probability, including data analysis and basic probability calculations.

Geometry

Course Description

Students will learn about the properties and relationships of points, lines, angles, and shapes, as well as how to apply geometric principles to solve problems. The course will cover topics such as Euclidean geometry, coordinate geometry, transformations, and trigonometry. 

Topics

1. Points, Lines, and Planes: This topic introduces the basic concepts of geometry, including points, lines, and planes, and their relationships.

2. Angles and Measurement: This topic covers the measurement of angles, including degrees and radians, and different types of angles, such as acute, obtuse, and right angles.

3. Triangles: This topic covers the different types of triangles, including equilateral, isosceles, and scalene triangles, and the properties of triangles, such as the Pythagorean theorem and the triangle inequality theorem.

4. Quadrilaterals: This topic covers the properties of quadrilaterals, including parallelograms, rectangles, squares, rhombuses, and trapezoids.

5. Circles: This topic covers the properties of circles, including chords, tangents, and secants, and the relationships between angles and arcs in circles.

6. Three-Dimensional Figures: This topic covers the properties of three-dimensional figures, including cubes, prisms, pyramids, spheres, and cones.

7. Geometric Transformations: This topic covers the different types of geometric transformations, including translations, reflections, rotations, and dilations, and their effects on shapes and figures.

8. Similarity and Congruence: This topic covers the concepts of similarity and congruence in geometry, including the corresponding parts of congruent figures and the properties of similar triangles.

9. Geometric Proofs: This topic covers the different types of geometric proofs, including direct proofs, indirect proofs, and proofs by contradiction, and how to use these techniques to prove geometric statements.

10. Coordinate Geometry: This topic covers the use of coordinates in geometry, including plotting points in the Cartesian plane, finding distances and midpoints, and graphing equations of lines and circles.

Learning Objectives

1. Identify and apply the fundamental concepts of Euclidean geometry, including points, lines, angles, and polygons.

2. Use geometric principles and formulas to solve problems involving area, perimeter, volume, and surface area.

3. Understand and apply the properties of circles, including chords, tangents, and arcs.

4. Identify and apply the different types of transformations, including reflections, translations, and rotations.

5. Use coordinate geometry to solve problems involving lines, circles, and other shapes on a coordinate plane.

6. Apply trigonometric functions to solve problems involving right triangles and other geometric shapes.

7. Use logical reasoning and deductive proofs to demonstrate geometric concepts and theorems.

8. Analyze and interpret geometric diagrams and graphs to solve problems and make conjectures.

9. Apply geometric concepts to real-world situations, including architecture, engineering, and design.

10. Develop critical thinking skills by solving challenging geometric problems and exploring geometric puzzles.

Statistics

Course Description

Students will learn the basics of descriptive and inferential statistics, probability theory, hypothesis testing, and regression analysis.

Throughout the course, students will gain a deep understanding of statistical concepts and the ability to apply statistical methods to real-world problems. The course will also emphasize the use of statistical software, such as R or Python, to perform data analysis and visualization.

Topics

1. Introduction to Statistics: This includes the history and uses of statistics, the types of data, and the role of statistics in decision making.

2. Descriptive Statistics: This involves summarizing data using measures of central tendency and measures of variability. It also includes graphical representations of data.

3. Probability: This covers the basic concepts of probability, including probability rules, conditional probability, independence, and Bayes' theorem.

4. Probability Distributions: This involves the different types of probability distributions, including discrete distributions (such as the binomial and Poisson distributions) and continuous distributions (such as the normal and exponential distributions).

5. Sampling Distributions: This covers the concept of sampling distributions, the central limit theorem, and the sampling distribution of the sample mean.

6. Confidence Intervals: This includes the concept of confidence intervals and how to construct them for means and proportions.

7. Hypothesis Testing: This involves the process of hypothesis testing, including the null and alternative hypotheses, type I and type II errors, and the significance level.

8. Inference for Means: This covers the different methods for performing hypothesis tests and constructing confidence intervals for means.

9. Inference for Proportions: This includes the different methods for performing hypothesis tests and constructing confidence intervals for proportions.

10. Simple Linear Regression: This covers the basics of simple linear regression, including the relationship between two variables, the least squares regression line, and the coefficient of determination.

11. Multiple Regression: This involves extending the concept of simple linear regression to multiple regression, including the multiple regression model, model selection, and interpreting the regression coefficients.

12. Analysis of Variance: This covers the basic concepts of analysis of variance, including the F-test, the ANOVA table, and the assumptions of the ANOVA model.

13. Nonparametric Methods: This includes nonparametric methods for hypothesis testing and confidence intervals, such as the Wilcoxon rank-sum test and the Kruskal-Wallis test.

14. Quality Control: This involves statistical process control and quality control methods, including control charts and process capability analysis.

15. Time Series Analysis: This covers the basics of time series analysis, including trend analysis, seasonal analysis, and forecasting.

Learning Objectives

1. Develop a foundational understanding of statistical concepts, including measures of central tendency, variability, and correlation.

2. Analyze data using graphical and numerical methods, such as histograms, box plots, scatterplots, and summary statistics.

3. Apply probability concepts, including random variables and probability distributions, to statistical problems.

4. Use statistical inference to make conclusions about population parameters based on sample data, including hypothesis testing and confidence intervals.

5. Understand the principles and techniques of regression analysis, including simple and multiple linear regression and logistic regression.

6. Interpret and communicate statistical results, including presenting findings in written and visual form.

7. Use statistical software and technology, such as R or Python, to analyze and visualize data.

8. Understand ethical and practical considerations in statistical analysis, including data privacy, bias, and the reproducibility of results.

9. Apply statistical methods to real-world problems and research questions, including designing and conducting experiments and surveys.

10. Develop critical thinking skills through problem-solving and analysis of real-world data sets.