Math Foundations VIII | Pre-Algebra Part 2

Placement Information

Placement Process
One critical factor for restful learning is the proper placement of students. If you are unsure which level is the best fit for your student, reach out to the instructor you are considering. Once registered, anticipate contact regarding placement evaluations from instructors by May 15th and throughout the summer. Students must be registered to enter the placement process. Early placement exams may allow time for tutoring or additional review based on the outcomes. See more about placement evaluations in our Student-Parent Handbook.

Math Placement Process
For registered students, please anticipate contact regarding placement evaluations from instructors by May 15th and throughout the summer. Students must be registered in a math course to receive a placement assessment. Math classes have a detailed and specific placement process.
Read more about the math placement process here.

Watch the math placement process video with our department chair, Dr. Fransell Riley, here.

See the Math Scope and Sequence here.

Content
Foundations VIII is the continuation of the gradual transition from arithmetic to algebra that began in Foundations VII. Students will build upon skills learned in arithmetic and master solving equations. Students will build on their fluency in rational numbers and expand their knowledge to roots and irrational numbers. They will develop fluency in the laws of exponents, and solving complex multistep equations and inequalities. They will take their first steps towards understanding relations and functions, domain and range, and systems of equations. Expanding on their geometry foundation, students will learn the Pythagorean Theorem and its uses as well as transformations, congruence, and similarity of shapes. They will develop 21st-century skills in analyzing data. Students will develop and practice problem-solving skills by working on challenging problems, including competition-level problems. Students will delve into the history of Algebra and participate in philosophical discussions of the course content.
They will complete portfolio projects that deepen their understanding of the concepts, appreciate the role of mathematics in God’s creation, and lead them to explore real-world applications of mathematics. Throughout the course, students will be led to see mathematics as a tool to solve real-world problems. They will practice different problem-solving strategies: Solve an Easier Problem and Solve a Subproblem.
Experience
The teaching of a new concept opens with a brief review of previously covered content. This review connects the previous lesson to the current lesson. The premise of the current lesson is presented via a question or idea. The students now have a puzzle or idea that they want to explore. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We use our prior knowledge and intuition to uncover a new truth about mathematics. Once this truth has been uncovered, we begin to work examples; first as a class and then as individuals or in groups. As our understanding of the concept deepens, we extend our knowledge base to include specific cases or situations that lead to minor adjustments in the truth that we have uncovered – thus expanding the truth. We use a variety of methods to uncover new truths. The most frequent method is a Socratic-style discussion that the entire class participates in. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application).

Delivery
Each teacher has a unique presentation style in delivering the aforementioned experience. Sometimes the teacher leads the discussion using questions; following the example set by Socrates.. Sometimes a problem is presented and the students take the lead in finding a solution based on extending previous knowledge. Sometimes students participate in a hands-on activity to discover new truths. Sometimes a short lecture or presentation is required, however, we aim to minimize lecturing, especially before high school.
Methodology
Students continue to study the new truth and deepen their understanding of it via homework, classwork, projects, and assessments. Since our classes do not meet 5 days per week, students must spend time studying the concepts outside of class. This also helps students grow in their ability to think and work math concepts independently which is required for future math classes. For this reason, we ask that parents minimize the assistance that students are given on assignments. If a student receives an A on an assignment, it should be a true indication of their independent ability as the teacher interprets this A as independent mastery.
Review assignments or classroom review activities are utilized to assist students with opportunities to retain or improve their mastery. Assessments are directly or indirectly cumulative and serve as an opportunity to deepen their learning. Assessments are not meant to be a regurgitation of previous homework assignments.
Preparedness
Students who are adequately prepared to take this course will have mastered (can work independently without prompting):

Can add, subtract, multiply, and divide negative number including negative fractions and decimals.
Solve percent problems (taxes, tips, interest, etc…)
Understands proportional relationships and can solve proportions
Solve 3-step equations; ex: 3(6x - 4) = 15
Calculate probability of simple and compound events
Classify Angles
Calculate Area of Polygons, Circles, and Composite Figures
Calculate Volume and Surface Area of 3D Figures
Translate multi-step verbal problems into expressions or equations

Required Materials:
Books and supplies are not included in the purchase of the course.

All Sections:

Digital tablet
- Choose from: Wacom Intuos, Huion, XP-Pen, or other
- A separate tablet/iPad with a stylus pen might also suffice
Scientific Calculator (preferences by instructor may be noted later in the materials list)
- TI, Sharp, other
Free web accounts
- Ziteboard.com, Desmos.calculator,
- Ziteboard is used often as a virtual classroom chalkboard.
Binder
- Three-ring binder with five dividers to keep math work together including notebook paper and a small amount of graph paper
Multiple sharpened pencils, erasers
Throughout the year, students/parents may need to print handouts or assignments.
Optional Mathematics for the Nonmathematician
- Excerpts (used print or digital is ok)
- This text will be used to learn some of the related history and philosophy of the concepts covered.

Course Textbook
Each section has different requirements for textbooks. Please refer to the materials list for your section and please do not purchase any textbooks until your instructor provides instructions - in late July / early August.

For Sections with Natalie Dignoti
- Details coming soon!

Natalie Dignoti

Natalie Dignoti earned a Bachelor's of Science in Elementary Education (Social Studies Cognate) and Master's of Arts in Cross-Cultural & International Education. After these studies, she taught at a charter school outside of Boston, Massachusetts. During her time there, she served in both 4th and 6th grade classrooms and as an after-school violin teacher. After 3 years, she and her husband moved to Bowling Green, Ohio to pursue graduate degrees. While there, she partnered with the university's College of Education to provide online math and reading intervention for students. She has also taught English Language Arts at a local homeschool cottage school and provided individual tutoring services in math and other subjects.

Quarter 1

Laws of Exponents (include problems that require 4+ steps)
Scientific Notation
Operation with Scientific Notation (without converting to standard form)
Terminating and Repeating Decimals
Compare and Order Rational Numbers
Roots
Solve 3+ Step Equations and Advanced Equations (with fractions)

The order in which topics are presented may vary according to instructor and course section.

Quarter 2

Identify and Compare Functions
Properties of Functions (linear and nonlinear)
Dimensional Analysis (Create Conversions Factors)
Solve Systems of Equations (using substitution and graphing)
Determine the number of solutions in a system of equations
Factor algebraic expressions

The order in which topics are presented may vary according to instructor and course section.

Quarter 3

Slope of a Line
Direct Variation
Slope Intercept Form
Scatterplots
Lines of Fit
Two-way Tables
Interpret qualitative graphs

The order in which topics are presented may vary according to instructor and course section.

Quarter 4

Similar Triangles (using proportions NOT SAS, SSS, ASA, etc)
Angle Relationships and Parallel Lines
Pythagorean Theorem and Converse
Distance and Midpoint Formula
TransformationsCongruence and Silimarity
Volume of Cylinders, Cones, and Spheres

The order in which topics are presented may vary according to instructor and course section.

Computer: You will need a stable, reliable computer, running with a processor with a speed of 1 GHz or better on one of the following operating systems: Mac OS X with Mac OS 10.7 or later; Windows 8, 7, Vista (with SP1 or later), or XP (with SP3 or later). We do not recommend using an iPad or other tablet for joining classes. An inexpensive laptop or netbook would be much better solutions, as they enable you to plug an Ethernet cable directly into your computer. Please note that Chromebooks are allowed but not preferred, as they do not support certain features of the Zoom video conference software such as breakout sessions and annotation, which may be used by our teachers for class activities.

High-Speed Internet Connection: You will also need access to high-speed Internet, preferably accessible via Ethernet cable right into your computer. Using Wi-Fi may work, but will not guarantee you the optimal use of your bandwidth. The faster your Internet, the better. We recommend using a connection with a download/upload speed of 5/1 Mbps or better. You can test your Internet connection here.

Webcam: You may use an external webcam or one that is built in to the computer. Webcam Recommendations: Good (PC only) | Best (Mac and PC)

Headset: We recommend using a headset rather than a built-in microphone and speakers. Using a headset reduces the level of background noise heard by the entire class. Headset Recommendations: USB | 3.5mm

Zoom: We use a web conferencing software called Zoom for our classes, which enables students and teachers to gather from around the globe face to face in real time. Zoom is free to download and easy to use. To download Zoom:

Visit zoom.us/download.
Click to download the first option listed, Zoom Client for Meetings.
Open and run the installer on your computer.
In August, students will be provided with instructions and a link for joining their particular class.

Scanner: In this class, students frequently submit homework assignments by scanning pages from their workbooks. Students and/or their parents should have easy access to a scanner and the ability to use it.

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First, read the available course descriptions, noting prerequisites, target grades, and course objectives. If you think your student is prepared for the course, go ahead and register. After registration, a placement assessment may be provided to students, depending on the course and the student's previous enrollment with Scholé Academy. Registration is finalized when the student's placement assessment has been returned by the course instructor with placement confirmation.

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Our Assistant to the Principal will be in touch with you after your enrollment to help you with next steps, including any placement evaluations that may be required for your course selections.

This registration will be finalized when the student's placement assessment has been returned by the course instructor with placement confirmation.