Mathematics

Schola’s mathematics department strives to teach real math: conceptual math with plenty of practical application problems. Why is this important?

It is well known that most U.S. high school math scores are in the bottom third of developed nations. Sadly, most homeschoolers don’t fare much better. Why not? Students who do not have access to a qualified instructor are often relegated to self-instruction. Conceptual math is hard, if not impossible, for students to self teach. The struggling student often changes math programs one or more times, hoping to find one that “works” – always opting for a less rigorous, less conceptual program.

Standardized test scores are the most heavily weighted single factor in college admission. Mathematics comprises half of the SAT score. It should be noted that the SAT test includes problem-solving oriented math (rather than application of formulas, which is where most homeschool math focuses). A conceptual mathematics education is a must for students seeking scholarships and/or admittance into highly competitive universities.

Does a student who is not planning on pursing a math, science, or engineering field need conceptual math? Yes! Studying conceptual mathematics develops solid logic and critical thinking skills. It trains the mind in important thinking processes for problem solving and decision-making, both of which affect performance in other areas. Historically, the study of conceptual math has been a staple of a good education, including even a "classical" humanities education; good thinking skills are necessary in every facet of life.

A conceptual math program, such as Schola’s, focuses on both inductive thinking (coming up with how to solve the problem) and deductive thinking (coming up with the right answer from the approach you have chosen) – preparing the student for adult life as well as fields of study in which math is foundational. Most math curricula designed specifically for homeschoolers – which are all formula-based, so they are easier to study at home – aren’t as effective at preparing the student for life beyond high school.

Schola’s mathematic instruction occurs one day a week. Because of the nature of mathematics, instruction given only one day per week may make comprehension difficult for some students. For this reason, supplemental video instruction may be purchased from the various options listed on the book lists for each math class.

The learning of mathematics, unlike subjects that rely heavily on reading comprehension for the acquisition of knowledge (like history, for example), must be done “little by little” over a “long period of time.” In other words, optimally math should be taught in small “chunks,” practiced daily, and repeated for mastery. Class time will be used to introduce new concepts, answer questions, and check progress. At-home time is used for daily homework and study.

Enrollment
Mathematics classes meet on various days (see schedule ) . Mathematics requires a consistent study habit each day. The average student should plan to devote approximately 45-60 minutes four days each week to math studies. Students should not enroll in upper-level mathematics courses (Geometry, Algebra 2, Pre-calculus) if consistent daily study time is not available.

Students in grades 4 though 8 may benefit from Math Games to strengthen their recall of basic math facts.

Class Size
  • Minimum: 4
  • Maximum: 17
Tuition and Fees
Suggested Class Sequence
Math Prep
Pre-Algebra
Algebra 1
Geometry OR Algebra 2
Algebra 2 OR Geometry
Pre-Calculus

Each class lists prerequisites and appropriate age, based on the typical level of academic experience and emotional maturity required to complete course material. We understand parents sometimes feel their students can benefit from taking classes before the recommended age or without prerequisite knowledge. We value our parents expertise; however, if you decide to enroll a child who is younger than the recommended guidelines or who lacks prerequisite skills, and this results in that student requiring significant additional support to be successful in the class, you will need to be prepared to provide that additional support.

If you are requesting young age admittance, their admittance will be based on their math report card and a letter of recommendation which addresses their social maturity.


Math Prep (Saxon 7/6)
provides excellent review and practice of basic arithmetic including extensive practice with fraction/decimal/percent conversions and unit multipliers as well as plenty of math facts practice. In addition, students will be introduced to new concepts needed for upper-level algebra and geometry. Lessons include word problems, functions and coordinate graphing, integers, exponential expressions, prime factorization. After every tenth lesson is an investigations of a specific math topic, discussed at length to ensure solid understanding.
Prerequisite
  • Student must be 11 years of age by September 1st of the current school year.
Text & Materials


Pre-Algebra (Saxon 8/7)
bridges the gap between elementary math and algebra by building a strong foundation in basic mathematics. This strong foundation becomes the launching pad for higher order math courses, such as Algebra 1, as well as science courses, such as physical science. Students will become successful in the mastery of arithmetic calculation, fractions, percents, decimals and ratios, measurements, basic geometry, and other foundational concepts and skills, as well as extensive pre-algebra exercises, preparing the student for upper-level mathematics.
Prerequisite
  • Saxon 7/6
  • Student must be 12 years of age by September 1st of the current school year.
Text & Materials


Algebra 1 ( Foerster )
is where math begins to be applied. Students will learn how to apply arithmetic skills to find solutions to real problems. Algebra 1 begins with a review of basic concepts, and moves into more logical and abstract mathematics. Algebra 1 is a gentle course. Students who struggle often have not yet developed their logical/abstract thinking skills. For many students the ability to think and reason abstractly develops around age 14, but every student is unique. Some students reach this point sooner, and others later. Be sure you evaluate your student before beginning Algebra 1.
Prerequisite
  • Successful completion of Saxon Math 8/7, Saxon Algebra ½, or equivalent with a final course grade of 85% or higher.
  • Student must be 13 years of age by September 1st of the current school year.
Text & Materials




Geometry (Jacobs)
includes all topics in a typical high school geometry course: lines and angles, congruence, inequalities, parallel lines, quadrilaterals, transformations of the plane, area, similarity, right triangle trigonometry, circles, concurrence theorems, regular polygons in relation to the circle, geometric solids, and non-Euclidean geometries. Students learn how to apply and calculate measurements of lengths, heights, circumference, areas, and volumes using diverse examples from around the world. Students will use logic to create proofs and constructions, and they will work with key geometry theorems and proofs in the less formal paragraph format. SAT problems are included in the exercise sets. Each chapter contains an algebra review so students are not “rusty” when entering Algebra 2 or Pre-Calculus. Harold Jacobs writes in understandable, interesting, and engaging English and focuses on guided discovery to help students develop geometric intuition.
Prerequisite
  • Successful completion of a rigorous, conceptual Algebra 1 course that focuses on practical application with a final course grade of 85% or higher.
Text & Materials


Algebra 2 ( Foerster )
covers all topics that are traditionally covered in a second-year algebra course as well as basic geometry facts that are typically asked on the SAT test. Real-world problems are included along with applications to other subjects such as physics and chemistry. Students will be encouraged to develop proficiency in concepts they've already learned, such as working with linear and quadratic equations; powers and roots; as well as an introduction to new topics including matrices, logarithms, trigonometry, and conic sections. Other topics covered include solving systems of linear and nonlinear equations, statistics and probability, graphing and developing equations from experimental data, and basic trigonometry.


FAQ: Is Algebra 2 still required?
Math comprises half of a student’s SAT score. As the most heavily weighted single factor in college admission today, a student's thorough and proficient knowledge of the concepts taught in this course is crucial. Although some States have declared that “Algebra 2” is no longer required, the concepts taught in the course remain necessary. Trigonometry was “removed” as a required course many years ago, however its content is found in a typical Pre-calculus textbook – a rose by any other name is still a rose – algebra, by any other name is still algebra.
Prerequisite
  • Successful completion of a rigorous, conceptual Algebra 1 course that focuses on practical application with a final course grade of 85% or higher.
Text & Materials
  • Algebra 2 Text and Materials
  • Highly recommended: In-class access to internet via laptop, tablet or phone. in order to access free website/app DESMOS.


Pre-Calculus with Trigonometry ( Foerster )
guides students through an extensive study of trigonometry and functions including quadratics, exponentials, polynomials, logarithmic, and rational functions. Emphasis will be placed on visual representation of functions (via a graphing calculator) and algebraic manipulation of equations, as well as applications in the world of business and science, primarily physics. Students will also explore a variety of other pertinent topics including conics, vectors, complex numbers, polar coordinates (applied to conics), and parametric equations.


This course carefully integrates and coordinates print, media, and technology products for successful teaching and learning.


Class time includes testing, lecture, and in-class practice. Several on-line resources will be used during class and therefore students are encouraged to bring a device with internet access to class (laptop, tablet, or phone). Homework is completed on-line and thus at-home internet access is required. As part of the on-line homework experience, students have access to supplemental video instruction, instant homework feedback, and access to the solutions manual for assigned problems.
Prerequisite
  • Successful completion of a rigorous, conceptual Algebra 2 course that focuses on practical application with a final course grade of 85% or higher.
Text & Materials
  • Pre-Calculus Text and Materials
  • Required: at home internet access to complete interactive daily homework assignments. Please note - all homework is completed on line.
  • Highly recommended: In-class access to internet via laptop, tablet or phone.




Calculus (Larson)
offers a substantial and thorough introduction to the three main ideas of calculus: limits, derivatives, and integrals. Following a condensed summary of key algebra, trigonometry, and analytic geometry topics, students proceed to develop a concept of limits. They apply this concept to define the derivative and explore its applications, and then return to define the integral, exploring its relation to the derivative. Numerous integration techniques and applications are discussed.


This course carefully integrates and coordinates print, media, and technology products for successful teaching and learning.


Class time includes testing, lecture, and in-class practice. Several on-line resources will be used during class and therefore students are encouraged to bring a device with internet access to class (laptop, tablet, or phone). Homework is completed on-line and thus at-home internet access is required. As part of the on-line homework experience, students have access to supplemental video instruction, instant homework feedback, and access to the solutions manual for assigned problems.
Prerequisite
  • Successful completion of a rigorous, conceptual Pre-Calculus course that focuses on practical application with a final course grade of 85% or higher.
Text & Materials
  • Calculus Text and Materials
  • Required: at home internet access to complete interactive daily homework assignments. Please note - all homework is completed on line.
  • Highly recommended: In-class access to internet via laptop, tablet or phone.