Essential Foundations of Math

(designed to be taken prior to Pre-Algebra, this course covers the most important skills students need prior to taking Pre-Algebra))


Ages: 11-13

Ray Carty

This is a year long course

Students will need to provide a calculator, binder, paper and pencils.

Homework:  YES.  

Homework assignments will be provided and will vary from 40 - 90 minutes / week, because Math is a Language and a skill set.   If you don’t practice Italian or Spanish you will lose it. If you don’t practice playing piano, you will lose that ability to play piano well.


In this projects, games and activities based math class, we will master concepts that students need to be solid on before advancing to pre-algebra. We will have strong focus on advanced fraction work and negative integer work in our first quarter together. Negative integer work becomes more fun when we measure sea levels, population levels, budgets and temperatures. It starts to make more sense, and students get lots of practice using their skills over and over in ways that matter. 


Fall:  Negative Integer & exponents operations, simple and advanced fraction operations, Basic Algebra Equations and Inequalities, How does one know they are actually doing Algebra? the Real number system and its symbolic representations, definition of rational numbers and irrationals numbers and their properties and operations, radical representations of irrationals, radical representation of rational exponents, ordering of irrationals, the Divisibility rules up to 12, to (GCF/LCM), Euclidian Algorithm for finding GCF, What is Infinity? The TWO types of Infinity and why are there two types? What does it REALLY mean to be “ undefined “ and why we can see it’s just a simple logical consequence of the definition of the multiplication operation of real numbers. Includes the introduction of standard international notation.

Winter:  Continued work on fraction/decimal/percent conversions including multi-digit repeating decimal expressions conversion into their fraction equivalents, Proof  that 0.999 repeating is the same as the number 1( fun topic! ). Advanced Proportions, Linear expressions, Cartesian coordinate system or Euclidian two dimension plane, multi-step equalities and multi-step inequalities.

Spring:  Basic Euclidian geometry including Euclid’s parallel postulate and other postulates, Definitions Axioms, Identities, Theorems, Postulates, Conjectures, Definitions of area, perimeter, circumference, distance, rates and their calculations. The difference between Euclidian Geometry and Non Euclidean Geometry: Origins of the 360 degree convention for a circle and its consequences. Introduction of standard international notation.  We’ll have lots of fun with our explanation of why all three angles of a triangle add up to 180 degrees!  Various shapes will be included from Parallelograms, Rectangles to Trapezoids, Triangles, Kites, Circles, etc.