Prologue: Why math isn't an awful nerd -- Basic number properties -- Basic arithmetic -- Let the game begin! -- Looking for patterns in numbers -- Exponents and perfect squares -- A surprising sequence of numbers --
pt. I: What is algebra, really? -- ch. 1. Taking algebra to the streets -- The secret algebra you've already been doing -- Using variables -- Writing equations -- What's the point of algebra? -- Square roots -- The Pythagorean Theorem -- Why algebra matters in the real world -- Algebra in your backyard -- How to make a graph -- Challenge problems -- ch. 2. Algebra basics -- What are variables? -- How do variables work? -- What are algebraic expressions? -- The order of operations -- Practice problem -- Intro to equations -- Halftime recap -- How you should think about equations -- How to solve an equation -- How to solve an algebra problem --
pt. II: Understanding algebra better -- ch. 3. Walk the number line -- A brief history of numbers -- Algebra and decimal numbers -- Algebra and the number line -- Absolute values -- Number boot camp -- Linear equations -- How to solve single variable linear equations -- Linear equations with absolute values -- How to solve absolute value equations -- Linear inequalities -- How to solve linear inequalities -- ch .4. Arithmetic 2.0 : math with variables, exponents, and roots -- Arithmetic 1.0 : preparing for algebra -- Doing arithmetic with "real" numbers -- Arithmetic 2.0 (here comes the algebra) -- How to simplify expressions -- Math properties -- How to combine like terms -- Exponentiation -- Roots -- Exponentiation and roots combined -- Irrational exponents -- Can you remind me of the point of algebra? -- Final exam --
pt. III: Solving algebra problems -- ch. 5. Polynomials, functions, and beyond -- What are polynomials? -- Evaluating polynomials -- Functions -- Visualizing polynomial functions -- How to solve problems with polynomials -- How to find and write the equations of lines -- Equations of horizontal and vertical lines -- Systems of equations -- How to solve a system of equations -- Systems of inequalities -- How to solve a system of inequalities -- Challenge problem #1 -- Final exam -- ch. 6. The root of the problem -- Challenge problem #2 -- Roots of polynomials -- Factoring polynomials -- How to factor polynomials -- Solving quadratic equations -- Challenge problem #3 -- Game over? -- Final exam.
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