‘Foundations: Algebra 1’ is designed to provide 7th-10th grade students with an adaptable sequence that moves from the final phases of pre-algebra into the heart of Algebra 1, and for advanced or older students finishes by building a bridge of understanding which connects Algebra to Geometry.

The course goal is to gradually lead students into developing their own natural understanding of core competencies that lie at the heart of Algebra 1 while providing plenty of practice with hard skills and processes necessary for mastering Algebra. Some methods students will master include simplifying, solving multi step equations, systems, functions, graphing on the coordinate plane, factoring polynomials, working with exponents and radicals, and more. Also, students will gain useful techniques for attacking multi-step word problems that deal with real-world scenarios, translating sentences into algebraic statements and equations, and key phrases for finding algebra in unlikely places like English grammar and story-telling.

By the end of the course, students will be able to show an intuitive grasp of core concepts found in Algebra 1 and will be able to demonstrate their ability to use Algebraic reasoning on traditional tests, multiformat worksheets, and in oral convseration explaining their thinking aloud through verbalizing their knowledge and even teaching others.

The course is comprised of 5 units, all of which are aligned to curtrent common core standards for Algebra 1. Students will show their mastery level with written and oral assessments to monitor thier progress with developing an intuitive grasp of Algebra 1 concepts and methods according to independence and accuracy.

Foundations: Algebra 1

5-Unit Course Concept Map

Expressions

  • Features of expressions vs equations
    • What does it mean to “combine like terms” and “simplify”
    • distributive property , associative property, communicative property- why are these useful?
  • Labeling unknowns (aka variables)
    • What do variables mean and why do we use letters to represent ‘unknowns?
  • Order of operations- what we do
    • The rules for how we simplify the parts of expressions
    • Lots of practice, practice, practice!
  • Simplify vs Plug-in Value (Substitute)
    • How can we simplify down to just a single number?
  • Expressions with an equal sign
    • How expressions become equations

Linear Equations

  • Evaluate and Solve
    • Assumed Multiplication
  • Inverse Operations as “opposites”
    • Single-Step to Multi-Step
    • Integers and Rational Numbers
  • Proportional Relationships
    • Inputs and Outputs
    • Using a rule
    • Direct Proportionality
  • Linear Equations and Functions
    • Arithmetic series
    • Simple interest
  • Systems Of Equations
  • Inequalities and Absolute Value
  • Models For Real World Patterns

Exponential Equations

  • From Lines to Curves
  • Laws of Exponents
  • Exponential Equations
  • Compound Interest
  • Geometric series
  • Applications in Science

Polynomials and Factoring

  • Monomials to Polynomials
  • Radicals
  • Quadratics
  • Factoring

Algebra into Geometry

  • Algebraic Reasoning and shapes
  • Rigid / Non-rigid transformations
  • Angles
  • Side Lengths and Midpoints
  • Triangles