For math students there are three levels of knowing to be considered:  How, What, Why.  How is procedural ability, they can follow steps.  What is the understanding of the How, an explanation of the steps.  Why is the understanding of the conceptual consequences from which procedure is derived. 

There are practically a limitless number of Hows in math.  Students that struggle the most focus on How and are continually confusing or forgetting steps.  Here we focus on Why, balancing the How and What to develop a well-balanced and prepared student.  Read more about the design and approach behind the materials you will find on this site in the Teaching Philosophy tab below.

Algebra 1 IS the cornerstone mathematics course.  As such it deserves careful consideration by teachers, students, parents and administration.  The conceptual understanding developed in this course needs to support the acquisition of mathematical literacy.  A student that possess both conceptual understanding and mathematical literacy will thrive as they move forward through other math and science subjects.

The materials you will find here are not designed to help students arrive at easy solutions by tricks.  Instead, the materials are designed to develop procedural fluency as a consequence of conceptual understanding and literacy.  The end result is that students will have a practical balance between conceptual understanding, mathematical literacy, and procedural proficiency.

This curriculum is broken down into six units: Number Unit, Foundations of Algebra, Functions, Linear Equations, Polynomials, and Quadratic Equations.  

Each of the units has multiple chapters, which can be navigated on the unit page.  Refer to the scope and sequence to help you pace the course.

Below you will find links to the topics taught in Algebra 1.  

Number UnitFoundationsFunctions
Prime NumbersWhat is Algebra?Relations
Real NumbersReading EquationsFunction Notation
Square RootsInverse OperationsArithmetic
ExponentsRational Equations Pt 1Composition of Functions
Rational ExponentsInequalitiesInverse Functions
Order of OperationsCompound InequalitiesReading Graphs of Functions
Algebraic FractionsAbsolute Value Inequalities
PercentagesVariation
Conversion of UnitsWriting Equations
Rates
Distance, Rate and Time
 

Linear EquationsPolynomialsQuadratics
Coordinate PlaneMonomials, Binomials, etc.Basics
Understanding GraphsDistribute Combine Like TermsUnderstanding Graphs
SlopeMultiplicationVertex
InterceptsFactoring BasicsIntercepts and Factoring
Writing EquationsFactoring QuadraticsCompleting the Square
Graphing EquationsFactoring Special CasesQuadratic Formula
Parallel and Perpendicular LinesGraphing
Linear InequalitiesWriting Equations
Systems of EquationsSystems of Quadratic Equations
Systems of Inequalities

Quarter 1:  Number Unit

In the Number Unit students will simultaneously firm up misconceptions and procedural inefficiencies, while transferring prior knowledge to high school level mathematics.

  Unit # / Topic

Time

Notes

Resources

1.1 Number Sense

2 – 4 days

Prime numbers: any whole number can be expressed as a unique product of primes. Real Numbers: arithmetic between rational and irrational numbers.

Prime Numbers

Real Numbers

1.7 Square Roots

3 – 5  Days

Introduce square roots, what simplifying them means, and basic arithmetic.

Square Root Arithmetic

Square Roots 1

Square Roots 2

1.7 & 2.4 Exponents

3 – 4  Days

Exponent properties and “rules” not including fractional exponents. 

Exponents Page

1.7 Rational Exponents & Other Roots

2 Days

Multiple ways to manipulate, think about, and simplify various rational and radical expressions.

Exponents Page 4

1.2, 1.7, 3.1

2 – 3 Days

The order of operations, reading mathematical structure and notation.  Ex: Scientific notation is an application of the order of operations and properties of exponents.  Ex: Introducing function notation as a way to practice the order of operations.

Order of Operations

 

Test Number One

 

1.3 LCM/GCF

1 – 2 Days

Connect LCM/GCF with

algebraic expressions. 

Algebraic Fractions Page

2.10 Alg. Fractions

2 – 3 Days

Introduction to reducing and adding/subtracting simple Algebraic Fractions.

Reducing Printable

Reduce Alg. Fractions Page

Add/Sbrct Printable

Add/Sbrct Page

1.6 Percentages, Profit, Interest

One Week

Writing equations is the key skill required for students to be successful with this unit.

Printable

Percentages Page

1.4 1.9, 1.10, 1.11
D = R×T, Units and Conversions

One Week

Students will learn to use rates to convert units while dealing with problems involving time (seconds to days), as well as distance, rate and time.

Units Printable

Units Page

DRT Printable

DRT Page

Midterm Examination

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