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

Learn
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!
Learn
Graph interpretation word problem: temperatureGraph interpretation word problem: basketballLinear graphs word problemsLinear graphs word problem: catsSystem of equations word problem: walk & ride
Practice
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!
Learn
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!
Learn
Adding polynomials: two variables (intro)Subtracting polynomials: two variables (intro)Subtracting polynomials: two variablesFinding an error in polynomial subtraction
Practice
Add & subtract polynomials: two variablesGet 3 of 4 questions to level up!
Learn
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!
Learn
Multiplying monomials by polynomials: area modelMultiplying monomials by polynomialsMultiplying monomials by polynomials challenge
Practice
Multiply monomials by polynomialsGet 3 of 4 questions to level up!
Learn
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!
Learn
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!
Learn
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!
Learn
Compound inequalities: ORCompound inequalities: ANDA compound inequality with no solutionDouble inequalitiesCompound inequalities examples
Practice
Compound inequalitiesGet 3 of 4 questions to level up!
Learn
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!
Learn
Two-variable linear equations introSolutions to 2-variable equationsWorked example: solutions to 2-variable equationsCompleting solutions to 2-variable equations
Practice
Solutions to 2-variable equationsGet 3 of 4 questions to level up!
Learn
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!
Learn
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!
Learn
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!
Equivalent systems of equationsGet 3 of 4 questions to level up!
Learn
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!
Learn
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!

About this unit

"In this module students analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem. They reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities. They master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations. They learn the terminology specific to polynomials and understand that polynomials form a system analogous to the integers." Eureka Math/EngageNY (c) 2015 GreatMinds.org