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# Module 1: Relationships between quantities and reasoning with equations and their graphs

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Introduction to piecewise functionsWorked example: evaluating piecewise functionsParabolas introIntro to exponential functionsExponential vs. linear growthExponential vs. linear models: verbalExponential vs. linear models: table

Practice

Evaluate piecewise functionsGet 3 of 4 questions to level up!

Evaluate step functionsGet 3 of 4 questions to level up!

Parabolas introGet 5 of 7 questions to level up!

Warmup: exponential vs. linear growthGet 3 of 3 questions to level up!

Exponential vs. linear growthGet 3 of 4 questions to level up!

Exponential vs. linear modelsGet 3 of 4 questions to level up!

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Graph interpretation word problem: temperatureGraph interpretation word problem: basketballLinear graphs word problemsLinear graphs word problem: catsSystem of equations word problem: walk & ride

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Graph interpretation word problemsGet 3 of 4 questions to level up!

Linear equations word problems: graphsGet 3 of 4 questions to level up!

Systems of equations word problemsGet 3 of 4 questions to level up!

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Lessons 6-7: No content yet

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Polynomials introThe parts of polynomial expressionsEvaluating polynomialsSimplifying polynomialsAdding polynomialsSubtracting polynomialsPolynomial subtractionAdding & subtracting multiple polynomials

Practice

Polynomials introGet 3 of 4 questions to level up!

Add polynomials (intro)Get 3 of 4 questions to level up!

Subtract polynomials (intro)Get 3 of 4 questions to level up!

Add & subtract polynomialsGet 3 of 4 questions to level up!

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Adding polynomials: two variables (intro)Subtracting polynomials: two variables (intro)Subtracting polynomials: two variablesFinding an error in polynomial subtraction

Practice

Add & subtract polynomials: two variables (intro)Get 3 of 4 questions to level up!

Add & subtract polynomials: two variablesGet 3 of 4 questions to level up!

Add & subtract polynomials: find the errorGet 3 of 4 questions to level up!

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Multiplying monomialsMultiplying monomials to find area: two variablesMultiplying monomials to find areaMultiplying monomials challenge

Practice

Multiply monomials Get 3 of 4 questions to level up!

Multiply monomialsGet 3 of 4 questions to level up!

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Multiplying monomials by polynomials: area modelMultiplying monomials by polynomialsMultiplying monomials by polynomials challenge

Practice

Multiply monomials by polynomials: area modelGet 3 of 4 questions to level up!

Multiply monomials by polynomialsGet 3 of 4 questions to level up!

Multiply monomials by polynomials challengeGet 3 of 4 questions to level up!

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Multiplying binomials: area modelMultiplying binomials introMultiplying binomials

Practice

Multiply binomials: area modelGet 3 of 4 questions to level up!

Warmup: multiplying binomials introGet 3 of 4 questions to level up!

Multiply binomials introGet 3 of 4 questions to level up!

Multiply binomialsGet 3 of 4 questions to level up!

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Testing solutions to equationsIntro to equationsNumber of solutions to equationsWorked example: number of solutions to equationsCreating an equation with no solutionsCreating an equation with infinitely many solutionsSame thing to both sides of equationsRepresenting a relationship with an equationDividing both sides of an equationWhy we do the same thing to both sides: Variable on both sides

Practice

Testing solutions to equationsGet 5 of 7 questions to level up!

Number of solutions to equationsGet 3 of 4 questions to level up!

Number of solutions to equations challengeGet 3 of 4 questions to level up!

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Testing solutions to inequalitiesPlotting inequalitiesPlotting an inequality exampleOne-step inequalities examplesOne-step inequalities: -5c ≤ 15Two-step inequalitiesInequalities with variables on both sidesInequalities with variables on both sides (with parentheses)Multi-step inequalities

Practice

Testing solutions to inequalitiesGet 3 of 4 questions to level up!

Plotting inequalitiesGet 3 of 4 questions to level up!

One-step inequalitiesGet 5 of 7 questions to level up!

Two-step inequalitiesGet 5 of 7 questions to level up!

Multi-step linear inequalitiesGet 3 of 4 questions to level up!

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Compound inequalities: ORCompound inequalities: ANDA compound inequality with no solutionDouble inequalitiesCompound inequalities examples

Practice

Compound inequalitiesGet 3 of 4 questions to level up!

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Zero product propertySolving quadratics by factoringSolving quadratics by factoringLesson 18: No content yetLinear equations with unknown coefficients

Practice

Zero product propertyGet 3 of 4 questions to level up!

Quadratics by factoring (intro)Get 3 of 4 questions to level up!

Linear equations with unknown coefficientsGet 3 of 4 questions to level up!

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Two-variable linear equations introSolutions to 2-variable equationsWorked example: solutions to 2-variable equationsCompleting solutions to 2-variable equations

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Solutions to 2-variable equationsGet 3 of 4 questions to level up!

Complete solutions to 2-variable equationsGet 3 of 4 questions to level up!

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Testing solutions to inequalitiesIntro to graphing two-variable inequalitiesGraphing two-variable inequalitiesTwo-variable inequalities from their graphs

Practice

Solutions of inequalities: algebraicGet 3 of 4 questions to level up!

Solutions of inequalities: graphicalGet 3 of 4 questions to level up!

Graphs of inequalitiesGet 3 of 4 questions to level up!

Two-variable inequalities from their graphsGet 3 of 4 questions to level up!

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Testing a solution to a system of equationsSystems of equations with graphing: y=7/5x-5 & y=3/5x-1Systems of equations with graphing: exact & approximate solutionsTesting solutions to systems of inequalitiesIntro to graphing systems of inequalitiesGraphing systems of inequalities

Practice

Solutions of systems of equationsGet 3 of 4 questions to level up!

Systems of equations with graphingGet 3 of 4 questions to level up!

Solutions of systems of inequalitiesGet 3 of 4 questions to level up!

Systems of inequalities graphsGet 3 of 4 questions to level up!

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Systems of equations with elimination: King's cupcakesSystems of equations with elimination: x-4y=-18 & -x+3y=11Systems of equations with elimination: potato chipsSystems of equations with elimination (and manipulation)Why can we subtract one equation from the other in a system of equations?Worked example: equivalent systems of equationsWorked example: non-equivalent systems of equations

Practice

Systems of equations with eliminationGet 3 of 4 questions to level up!

Systems of equations with elimination challengeGet 3 of 4 questions to level up!

Equivalent systems of equationsGet 3 of 4 questions to level up!

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Age word problem: ImranAge word problem: Ben & WilliamAge word problem: Arman & DiyaModeling with systems of inequalitiesWriting systems of inequalities word problemSolving systems of inequalities word problemGraphs of systems of inequalities word problem

Practice

Age word problemsGet 3 of 4 questions to level up!

Systems of inequalities word problemsGet 3 of 4 questions to level up!

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Worked example: Rate problemSequences introEvaluating sequences in recursive form

Practice

Rate problems 2Get 3 of 4 questions to level up!

Evaluate sequences in recursive formGet 3 of 4 questions to level up!