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Algebra I

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#### Course content

#### Algebra foundations

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#### Solving equations & inequalities

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#### Working with units

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#### Linear equations & graphs

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#### Forms of linear equations

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#### Systems of equations

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#### Inequalities (systems & graphs)

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#### Functions

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#### Absolute value & piecewise functions

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#### Exponents & radicals

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#### Exponential growth & decay

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#### Quadratics: Multiplying & factoring

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388 Lessons

Overview and history of algebra

Origins of algebra

Abstract-ness

The beauty of algebra

Intro to the coordinate plane

Why all the letters in algebra?

What is a variable?

Introduction to variables

Why aren’t we using the multiplication sign?

Evaluating an expression with one variable

Substitution and evaluating expressions

Evaluating expressions with two variables

Evaluating expressions with two variables: fractions & decimals

Combining like terms

Intro to combining like terms

Simplifying expressions

Combining like terms challenge problem

Simplifying expressions with rational numbers

Introduction to equivalent expressions

Equivalent expressions

Division by zero

Why dividing by zero is undefined

The problem with dividing zero by zero

Undefined & indeterminate expressions

Linear equations with variables on both sides

Why we do the same thing to both sides: Variable on both sides

Intro to equations with variables on both sides

Equations with variables on both sides: 20-7x=6x-6

Equation with variables on both sides: fractions

Equation with the variable in the denominator

Linear equations with parentheses

Equations with parentheses

Analyzing the number of solutions to linear equations

Number of solutions to equations

Worked example: number of solutions to equations

Creating an equation with no solutions

Creating an equation with infinitely many solutions

Linear equations with unknown coefficients

Linear equations with unknown coefficients

Multi-step inequalities

Inequalities with variables on both sides

Inequalities with variables on both sides (with parentheses)

Multi-step inequalities

Compound inequalities

Compound inequalities: OR

Compound inequalities: AND

A compound inequality with no solution

Double inequalities

Compound inequalities examples

Rate conversion

Intro to dimensional analysis

Same rate with different units

Appropriate units

Appropriate units

Interpreting units in formulas

Interpreting units in formulas: novel units

Word problems with multiple units

Worked example: Rate problem

Multiple units word problem: road trip

Measurement word problem: running laps

Multiple units word problem: drug dosage (advanced)

Two-variable linear equations intro

Two-variable linear equations intro

Solutions to 2-variable equations

Worked example: solutions to 2-variable equations

Completing solutions to 2-variable equations

Slope

Intro to slope

Positive & negative slope

Worked example: slope from graph

Graphing a line given point and slope

Calculating slope from tables

Worked example: slope from two points

Horizontal & vertical lines

Slope of a horizontal line

Horizontal & vertical lines

x-intercepts and y-intercepts

Intro to intercepts

x-intercept of a line

Intercepts from an equation

Intercepts from a table

Applying intercepts and slope

Slope, x-intercept, y-intercept meaning in context

Slope and intercept meaning in context

Slope and intercept meaning from a table

Finding slope and intercepts from tables

Linear functions word problem: fuel

Intro to slope-intercept form

Intro to slope-intercept form

Slope and y-intercept from equation

Worked examples: slope-intercept intro

Linear equation word problems

Graphing slope-intercept equations

Graph from slope-intercept equation

Writing slope-intercept equations

Slope-intercept equation from graph

Slope-intercept equation from slope & point

Slope-intercept equation from two points

Constructing linear equations from context

Point-slope form

Intro to point-slope form

Point-slope & slope-intercept equations

Standard form

Intro to linear equation standard form

Graphing a linear equation: 5x+2y=20

Clarifying standard form rules

Converting from slope-intercept to standard form

Summary: Forms of two-variable linear equations

Slope from equation

Writing linear equations in all forms

Introduction to systems of equations

Systems of equations: trolls, tolls (1 of 2)

Systems of equations: trolls, tolls (2 of 2)

Testing a solution to a system of equations

Systems of equations with graphing: y=7/5x-5 & y=3/5x-1

Systems of equations with graphing: exact & approximate solutions

Setting up a system of equations from context example (pet weights)

Setting up a system of linear equations example (weight and price)

Interpreting points in context of graphs of systems

Solving systems of equations with substitution

Systems of equations with substitution: potato chips

Systems of equations with substitution: -3x-4y=-2 & y=2x-5

Systems of equations with elimination: potato chips

Systems of equations with elimination (and manipulation)

Worked example: equivalent systems of equations

Worked example: non-equivalent systems of equations

Equivalent systems of equations and the elimination method

Systems of equations with elimination: King’s cupcakes

Why can we subtract one equation from the other in a system of equations?

Elimination strategies

Systems of equations with elimination: x-4y=-18 & -x+3y=11

Number of solutions to systems of equations

Systems of equations number of solutions: fruit prices (1 of 2)

Systems of equations number of solutions: fruit prices (2 of 2)

Solutions to systems of equations: consistent vs. inconsistent

Solutions to systems of equations: dependent vs. independent

Number of solutions to a system of equations

Number of solutions to a system of equations graphically

Number of solutions to a system of equations algebraically

How many solutions does a system of linear equations have if there are at least two?

Systems of equations word problems

Age word problem: Imran

Age word problem: Ben & William

Age word problem: Arman & Diya

System of equations word problem: walk & ride

System of equations word problem: no solution

System of equations word problem: infinite solutions

Systems of equations with elimination: TV & DVD

Systems of equations with elimination: apples and oranges

Systems of equations with substitution: coins

Systems of equations with elimination: coffee and croissants

Checking solutions of two-variable inequalities

Testing solutions to inequalities

Testing solutions to systems of inequalities

Graphing two-variable inequalities

Intro to graphing two-variable inequalities

Graphing two-variable inequalities

Two-variable inequalities from their graphs

Intro to graphing systems of inequalities

Graphing systems of inequalities

Modeling with linear inequalities

Writing two-variable inequalities word problem

Solving two-variable inequalities word problem

Graphs of two-variable inequalities word problem

Interpreting two-variable inequalities word problem

Modeling with systems of inequalities

Writing systems of inequalities word problem

Solving systems of inequalities word problem

Graphs of systems of inequalities word problem

Evaluating functions

What is a function?

Worked example: Evaluating functions from equation

Worked example: Evaluating functions from graph

Evaluating discrete functions

Worked example: evaluating expressions with function notation

Inputs and outputs of a function

Worked example: matching an input to a function’s output (equation)

Worked example: matching an input to a function’s output (graph)

Worked example: two inputs with the same output (graph)

Functions and equations

Equations vs. functions

Obtaining a function from an equation

Interpreting function notation

Function notation word problem: bank

Function notation word problem: beach

Introduction to the domain and range of a function

Intervals and interval notation

What is the domain of a function?

What is the range of a function?

Worked example: domain and range from graph

Determining the domain of a function

Determining whether values are in domain of function

Examples finding the domain of functions

Worked example: determining domain word problem (real numbers)

Worked example: determining domain word problem (positive integers)

Worked example: determining domain word problem (all integers)

Recognizing functions

Recognizing functions from graph

Does a vertical line represent a function?

Recognizing functions from table

Recognizing functions from verbal description

Recognizing functions from verbal description word problem

Maximum and minimum points

Introduction to minimum and maximum points

Worked example: absolute and relative extrema

Intervals where a function is positive, negative, increasing, or decreasing

Increasing, decreasing, positive or negative intervals

Worked example: positive & negative intervals

Interpreting features of graphs

Graph interpretation word problem: temperature

Graph interpretation word problem: basketball

Average rate of change

Introduction to average rate of change

Worked example: average rate of change from graph

Worked example: average rate of change from table

Average rate of change word problem: table

Average rate of change word problem: graph

Intro to inverse functions

Intro to inverse functions

Inputs & outputs of inverse functions

Graphing the inverse of a linear function

Finding inverse functions: linear

Introduction to arithmetic sequences

Sequences intro

Intro to arithmetic sequences

Extending arithmetic sequences

Using arithmetic sequences formulas

Worked example: using recursive formula for arithmetic sequence

Constructing arithmetic sequences

Recursive formulas for arithmetic sequences

Explicit formulas for arithmetic sequences

Arithmetic sequence problem

Converting recursive & explicit forms of arithmetic sequences

Introduction to geometric sequences

Intro to geometric sequences

Extending geometric sequences

Using explicit formulas of geometric sequences

Using recursive formulas of geometric sequences

Explicit & recursive formulas for geometric sequences

Constructing geometric sequences

Converting recursive & explicit forms of geometric sequences

Modeling with sequences

Sequences word problems

Evaluating sequences in recursive form

General sequences

Graphs of absolute value functions

Shifting absolute value graphs

Scaling & reflecting absolute value functions: equation

Scaling & reflecting absolute value functions: graph

Graphing absolute value functions

Piecewise functions

Introduction to piecewise functions

Worked example: evaluating piecewise functions

Worked example: graphing piecewise functions

Worked example: domain & range of step function

Worked example: domain & range of piecewise linear functions

Exponent properties review

Multiplying & dividing powers (integer exponents)

Powers of products & quotients (integer exponents)

Radicals

Intro to square roots

Understanding square roots

Square root of decimal

Intro to cube roots

5th roots

Simplifying square roots

Simplifying square roots

Simplifying square roots (variables)

Simplifying square-root expressions

Exponential vs. linear growth

Intro to exponential functions

Exponential vs. linear growth

Exponential vs. linear models: verbal

Exponential vs. linear models: table

Exponential expressions

Exponential expressions word problems (numerical)

Initial value & common ratio of exponential functions

Exponential expressions word problems (algebraic)

Interpreting exponential expression word problem

Graphs of exponential growth

Exponential function graph

Graphs of exponential growth

Exponential vs. linear growth over time

Exponential vs. linear growth over time

Exponential growth & decay

Exponential decay intro

Graphing exponential growth & decay

Writing exponential functions

Writing exponential functions from tables

Writing exponential functions from graphs

Analyzing tables of exponential functions

Analyzing graphs of exponential functions

Analyzing graphs of exponential functions: negative initial value

Modeling with basic exponential functions word problem

Exponential functions from tables & graphs

Exponential vs. linear models

Linear vs. exponential growth: from data

Linear vs. exponential growth: from data (example 2)

Polynomials intro

Polynomials intro

Multiplying binomials

Multiplying binomials: area model

Multiplying binomials intro

Multiplying binomials

Special products of binomials

Special products of the form (x+a)(x-a)

Squaring binomials of the form (x+a)Â²

Special products of the form (ax+b)(ax-b)

Squaring binomials of the form (ax+b)Â²

Introduction to factoring

Intro to factors & divisibility

Factoring with the distributive property

Factoring quadratics as (x+a)(x+b)

Factoring quadratics as (x+a)(x+b) (example 2)

More examples of factoring quadratics as (x+a)(x+b)

Factoring quadratics intro

Factoring quadratics by grouping

Intro to grouping

Factoring quadratics by grouping

Factoring quadratics: common factor + grouping

Factoring quadratics: negative common factor + grouping

Factoring difference of squares: shared factors

Factoring quadratics with difference of squares

Difference of squares intro

Factoring difference of squares: leading coefficient â‰ 1

Factoring difference of squares: analyzing factorization

Perfect square factorization intro

Factoring perfect squares

Identifying perfect square form

Factoring perfect squares: negative common factor

Factoring perfect squares: missing values

Factoring perfect squares: shared factors

Factoring quadratics with perfect squares

Strategy in factoring quadratics

Strategy in factoring quadratics (part 1 of 2)

Strategy in factoring quadratics (part 2 of 2)

Intro to parabolas

Parabolas intro

Zero product property

Graphing quadratics in factored form

Quadratic word problems (factored form)

Solving and graphing with factored form

Solving by taking the square root

Solving quadratics by taking square roots

Solving quadratics by taking square roots examples

Solving quadratics by taking square roots: strategy

Quadratics by taking square roots: with steps

Vertex form

Vertex form introduction

Graphing quadratics: vertex form

Quadratic word problems (vertex form)

Solving quadratics by factoring

Solving quadratics by factoring

Solving quadratics by factoring: leading coefficient â‰ 1

Solving quadratics using structure

Quadratic equations word problem: triangle dimensions

Quadratic equations word problem: box dimensions

The quadratic formula

The quadratic formula

Worked example: quadratic formula (example 2)

Worked example: quadratic formula (negative coefficients)

Using the quadratic formula: number of solutions

Proof of the quadratic formula

Completing the square

Completing the square

Worked example: Completing the square (intro)

Worked example: Rewriting expressions by completing the square

Worked example: Solving equations by completing the square

Worked example: completing the square (leading coefficient â‰ 1)

Solving quadratics by completing the square: no solution

Quadratic standard form

Finding the vertex of a parabola in standard form

Graphing quadratics: standard form

Quadratic word problem: ball

Irrational numbers

Intro to rational & irrational numbers

Classifying numbers: rational & irrational

Worked example: rational vs. irrational expressions

Worked example: rational vs. irrational expressions (unknowns)

Sums and products of rational and irrational numbers

Proof: sum & product of two rationals is rational

Proof: product of rational & irrational is irrational

Proof: sum of rational & irrational is irrational

Sums and products of irrational numbers

Proof: âˆš2 is irrational

Proofs concerning irrational numbers

Proof: square roots of prime numbers are irrational

Proof: there’s an irrational number between any two rational numbers

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