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

## 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

### Learn

### Practice

- Evaluate piecewise functionsGet 3 of 4 questions to level up!
- Evaluate step functionsGet 3 of 4 questions to level up!
- Parabolas introGet 3 of 4 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

### 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

### 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

### 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!

### Learn

### Practice

- Multiply monomials Get 3 of 4 questions to level up!
- Multiply monomials (advanced)Get 3 of 4 questions to level up!

### Learn

### 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!

### Learn

### 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

### 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!

### Learn

### 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

### Practice

- Zero product propertyGet 3 of 4 questions to level up!
- Quadratics by factoring (intro)Get 3 of 4 questions to level up!
- Rational equations introGet 3 of 4 questions to level up!
- Linear equations with unknown coefficientsGet 3 of 4 questions to level up!

### Learn

### Practice

- 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!

### Learn

### 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!

### Learn

### 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

### 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!
- Reasoning with systems of equationsGet 3 of 4 questions to level up!

### Learn

### Practice

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

### Learn

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- Rate problems 2Get 3 of 4 questions to level up!
- Evaluate sequences in recursive formGet 3 of 4 questions to level up!