# One Day Academy SUMMER

# NOTE: Not all courses are offered each summer. Please see Summer Course Schedules.

## Summer Mathematics

##### Solid Foundations

We look at all the content which is required to make sure that a child is completely ready for transition mathematics. We work on flashcard facts, both content and speed. We work on basic operations, especially longhand multiplication and division. We introduce the concepts of partial amounts with fractions and decimals. Plus place value on both sides of the decimal point will be emphasized.

##### Fractions, Decimals, and Percents

We cover a basic overview of the meanings and definitions of these 3 forms of describing portions. We look at the 4 basic operations for decimals and fractions. We look at how to convert among fractions, decimals, and percents. And we look at how to properly understand and manipulate mixed fractions. Part of each step is working with fractions which contain, not just numbers, but also variables as well.

##### Intro to Algebra

We cover a basic overview of the rules and procedures of working with signed numbers, as well as the conceptual foundations of understanding and solving first degree equations. We also explore operations with signed numbers as they apply to variables. We examine the fundamental principles of exponents, and how they provide the building blocks for handling polynomial expressions. Finally, we introduce two dimensional graphing, including how to graph lines.

##### Algebra Applications

A special emphasis will be placed on how to think in approaching a word problem.

Each of the 10 weeks will be spent looking at a major type of appliaction in algebra, and the skills which are required to support working the application problems. Topics include percents (tax, increase, profit), variation, ratios and proportions, rate and distance, total value, and linear modeling.

##### Intro to Geometry

We will prepare students to understand and work with the 5 major components of high school geometry: logic and proofs, constructions, area/volume/surface area, solving triangles, and circle properties. Other topics will be addressed, with an emphasis on those topics which are most difficult to learn the first time through.

##### Intro to Algebra II

Following Introduction to Algebra, we will look at the major components of higher level algebra: solving non-linear equations, higher order polynomials, solving systems, non-whole number exponents, rational expressions, and several levels of difficulty of writing linear equations from data.

##### Intro to Trig and Pre-cal

We look at a variety of topics, including graphing, triangle solution and application, proofs, angular velocity, and equations. A special emphasis is placed on learning the theory behind the unit circle, and how to use this theory to learn all the exact values which trig work expects a student to memorize.

##### Intro to Calculus

We look at a variety of topics, including limits, continuity, derivates, integrals, and related rates. A special emphasis is placed on difference quotients and understanding the foundation of calculus: finding the limit of adding a finite number of calculations as the number of calculations goes to infinity.

##### Advanced Proofs

This course introduces the student to several major areas of mathematical reasoning: set theory, number theory, algebraic theory, and real number analysis. Students learn to understand and direct the flow of thought required to do a proof, and practice proofs each week, both in class and outside of class. A major emphasis is placed on logical reasoning and the sequential flow of implication. 100% of the course work for this course will be graduate level mathematics, designed to prepare the student for any advanced/post-calculus coursework.