# Math Class Descriptions

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### Algebra I

Quarter 1, 2, 3, 4: Starts on September 7, 2018

Class Time: 2:00 pm Duration: 55 min

Instructor: Katherine Hoeck

Grade Range: 7th-10th

Prerequisites:

**This is a year-long class that is in-progress. Mid-term enrollment may be possible by contacting Compass to discuss placement. **

This is a complete course in Algebra I which will cover fundamental concepts in algebra and provide a solid foundation of mathematical literacy, problem solving, and critical thinking skills that are necessary for the exploration of more advanced and rigorous topics in mathematics. This course is designed to emphasize the study of algebraic problem-solving with the incorporation of mathematical reasoning, analysis, communication skills, and real world applications. Students will build on prior knowledge by exploring and understanding our number system, linear systems, rational numbers and proportional relationships, complex numbers, exponents, quadratics, polynomials, factoring, data analysis and probability, and solving, graphing, and writing linear equations and inequalities. Students will discover these topics through hands-on activities, class discussions, and open-ended problem solving. Each assignment will be categorized as either cooperative group investigations, partner collaboration, or individual work. Individual work will consist of periodic checks for understanding and independent-study activities that students are expected to complete outside of class.

Students should have a solid foundation in pre-algebra topics in order to take this class. Students should expect to spend 3 hours on independent study activities for each hour spent in class, or about 6 hours per week.

The required textbook for this class is The Art of Problem Solving: Introduction to Algebra (ISBN# 978-1-934124-14-7) and the corresponding and solutions manual (ISBN# 978-1-934124-15-4). These can be purchased from https://artofproblemsolving.com/store/item/intro-algebra. A calculator is not necessary for this course. Homeschool families may wish to count this course as a complete credit in Algebra for purposes of a high school transcript.

### Geometry

Quarter 1, 2, 3, 4: Starts on September 7, 2018

Class Time: 1:00 pm Duration: 55 min

Instructor: Katherine Hoeck

Grade Range: 9th-12th

Prerequisites:

**This is a year-long class that is in-progress. Mid-term enrollment may be possible by contacting Compass to discuss placement. **

This is a complete course in high school Geometry which will cover the fundamental concepts of Euclidean geometry and focus on developing critical thinking skills as they relate to logical reasoning and argument. This course is designed to emphasize analytical thinking and will include an in-depth analysis of plane, solid, and coordinate geometry through abstract mathematical ideas as well as real world problem solutions. Students will connect concepts from Algebra I to geometric phenomena with the analysis of parallel lines and polygons, perimeter and area, volume and surface area, similarity and congruence, and introductory trigonometry. Students will develop an understanding of these concepts through the study of geometric definitions, theorems, axioms, and postulates by writing reasoned, logical explanations that arrive at the conclusion about the geometric statement. A key focus will be on the development and history of the concepts being studied. Students can expect to spend time in class learning how to articulate the logical progression of concepts in addition to a thorough analysis of the topics. Independent study will involve reading assignments on concepts *before* they are presented in class as well as various problems to support what is covered in class.

Students should have a solid foundation in Algebra I in order to take this class. Students should expect to spend 3 hours on independent study activities for each hour spent in class, or about 6 hours per week.

The required textbook for this class is The Art of Problem Solving: Introduction to Geometry text (ISBN: 978-1-934124-08-6) and corresponding solutions manual (ISBN #978-1-934124-09-3). These can be purchased from https://artofproblemsolving.com/store/item/intro-algebra. Additional resources for the development of geometric proofs will be pulled from Euclidean and Non-Euclidean Geometries: Development and History. Students will be provided with the material used from this book. A calculator is not necessary for this course. Homeschool families may wish to count this course as a complete credit in Geometry for purposes of a high school transcript.

### Pre-Algebra

Quarter 1, 2, 3, 4: Starts on September 7, 2018

Class Time: 10:00 am Duration: 55 min

Instructor: Natalie Di Vietri

Grade Range: 7th-9th

Prerequisites:

**This is a year-long class that is in-progress. Mid-term enrollment may be possible by contacting Compass to discuss placement. **

This is a full year course in Pre-Algebra with an emphasis on problem solving skills and computations of math facts. The major topics covered in this course are variables, expressions, integers, order of operations, solving equations, and multi-step equations. The course will also cover inequalities, factors, fractions, exponents, and rational numbers. Additional Pre-Algebra concepts that will be taught include ratios, proportion, probability, percentages, linear functions, real numbers, right triangles, measurement, area, volume, and data analysis. Students will learn to use formulas to solve a variety of math problems encompassing geometry, probability, and statistics. Students will also be applying their learning to real life scenarios to solve problems.

For this course, students should be capable of basic computation, math facts, and an ability to work with fractions and decimals at the 6th/7th grade level. For anyone who is unsure if their child is ready for pre-algebra, the instructor can recommend one or more assessments or pretests to confirm placement. Students should expect to spend 3-4 hours per week outside of class to complete practice problems, homework, and assessments. Please note, all assessments will be taken outside of class with the parental oversight to maximize in-class instructional time.

For this class, students will need a regular notebook and paper and graph paper or graphing notebook. Students will be required to rent or purchase the class textbook, McDougall Littell s Pre-Algebra (ISBM #978-0618250035), purchase the practice workbook (ISBN # 978-0618257522), and subscribe to the online math platform, IXL (https://www.ixl.com/). As an alternate, parents can purchase the textbook on audio-CD for any students who struggle with reading (ISBN #978-0618478828). Finally, although Pre-Algebra is often taught without the use of calculators, if a student is slow with some math facts or computation by hand, a TI-34 calculator is recommended so the student can keep up with the problems.

### Mental Math Fun: Logic & Reasoning Puzzles

Quarter 3: Starts on January 9, 2019

Class Time: 12:00 pm Duration: 55 min

Instructor: David Chelf

Grade Range: 3rd-4th

Prerequisites:

Students will tackle a variety of puzzles, games, and riddles each week that will develop their mathematical thinking and problem-solving skills while having loads of fun in class! Hands-on activities may use cards, dice, coins, cubes, toothpicks, and of course, lots of numbers. Every activity is in essense a math problem, and students will learn tips and techniques for tackling the challenges. Race to sum numbers in the game "Thirty One"; take turns moving squares on a grid in "Cartesian Chase"; and use lines to separate colors in the game "Patchwork." How many squares- of all sizes- are there on chess board? For each puzzle, students will learn to ask, "what is the winning strategy?" or "what is the fewest number of moves?"

For each new puzzle, game, and riddle, students will learn concepts and strategies that they can apply to solving ANY math challenge, such as: the phases of solving a problem, what to do when you get stuck, how to make predictions, how to generalize from specific cases, and how to become your own questioner. Through these weekly activities, students will learn that math isn t just something done at a desk with pencil and paper, but is present everywhere you look, and that the ability to think mathematically can not only be useful, but also fun!

### Real Life Math: Exploring Exponents

Quarter 3: Starts on January 9, 2019

Class Time: 1:00 pm Duration: 55 min

Instructor: David Chelf

Grade Range: 7th-8th

Prerequisites:

How have video game console speeds changed over time? How much do you really pay when you use a credit card? How long does it take a disease to infect the entire population? How much can you trust your memory? Exponents are used in a variety of ways in everyday and scientific applications. Whether describing computer memory, measuring long distances, or recording the strength of earthquakes, exponents are necessary to understand and quantify phenomena that occur in the real world. In this class, students will learn to represent numbers as exponents, as well as add, subtract, multiply, and divide exponents and move between different representations using real life examples to demonstrate and answer the question, "Why do I have to learn this?"

In Real Life Math, each skillset is reviewed independently, with tips and tricks given and sample word problems worked. In addition to improving specific math skills, students will become more comfortable moving between word problems and abstract mathematical representation by working with tangible examples. The class serves as a solid complement to middle school math. Topics in this year's class series include: Investigating Integers (2nd quarter), Exploring Exponents and Orders of Magnitude (3rd quarter), and Rates/Ratios (4th quarter).

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