## 180 Aims for Algebra (file)

**Common Core Algebra I – Suggested Aims**

__Unit 1 – Foundations and Review__- How do we classify the
**sets of real numbers**? (Natural numbers, whole numbers, integers, and rational numbers) - How do we use the
**properties of real numbers**? - How do we perform
**operations with****integers**? - How do we perform
**operations with fractions**? (Graphing calculator-based review strongly encouraged if this specific skill gap is identified) - How do we use the
**order of operations**to evaluate expressions? (Include applications to integers, fractions, and absolute values) - How do we write
**algebraic expressions**based on key words, patterns, and real-world situations? - How do we apply the
**distributive property**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 1? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 2 – Linear Equations in One Variable__- How do we solve and check
**one-step equations**? - How do we solve and check
**two-step equations**? - How do we solve and check
**multi-step equations**, including combining like-terms and the distributive property? - How do we solve and check
**equations with variables on both sides**? - How do we work with
**rates, ratios, and conversions?** - How do we solve
**proportions**? - How do we evaluate
**percentages**? (2 days) - How do we solve
**literal equations and formulas**for a given variable? - How do we
**use equations to model and solve real-world situations**? (2 days) - How do we solve, graph, and check
**absolute-value equations**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 2? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 3 – Linear Inequalities in One Variable__- How do we
**write, graph, and identify solutions of inequalities**? - How do we solve, graph and check
**one-step inequalities**using addition and subtraction? - How do we solve, graph and check
**two-step inequalities**using multiplication and division? - How do we solve, graph and check
**multi-step inequalities**? (Include practice with like-terms, distributive property, and variables on both sides) (2 days) - How do we
**use inequalities to****model and solve real-world situations**? (2 days) - : How do we solve, graph, and check
**compound inequalities**? - : How do we solve, graph, and check
**absolute-value inequalities**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 3? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 4 – Basic Concepts of Functions__- How do we define and identify
**relations and functions**? - How do we use
**function notation**and**domain and range**to**evaluate functions**? - What are the general characteristics of the main
**families of functions**we will encounter this year? (Linear, quadratic, absolute-value, exponential, radical, and piecewise functions; time-permitting, extend to include rational functions) (2 days) - How do we use the characteristics of families of functions to perform
**transformations**on them? (2 days) - How do we
**represent (simple) functions**algebraically, graphically, numerically in tables, or from verbal descriptions? (2 days) - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 4? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 5 – Linear Equations In Two Variables (Linear Functions)__- How do we define, find, and interpret
**rates of change**for real-world scenarios? - How do we calculate the
**slopes**of lines using the formula and the visual definition? - How do we write linear functions in
**slope-intercept form y = mx + b**? - How do we
**use the slope-intercept form to graph lines**? - How do we
**write the equation of a line in slope-intercept form**given different scenarios? (the slope and y-intercept; the slope and a point; two points; the graph of a line) (2 days) - How do we
**apply the slope-intercept form of linear equations to solve real-world situations**? (2 days) - How do we use the
**standard form of lines Ax + By = C**to find their**x- and y-intercepts**and graph them? - How do we
**apply the standard form of linear equations to solve real-world situations**? (2 days) - How do we write and graph lines in
**point-slope form**? - How and when should we
**convert between the different forms of lines**? - How do we
**create scatter plots and apply linear regression models to analyze real-world data**? (Include correlation coefficient) (3 days) - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 5? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 6 – Systems of Linear Equations and Inequalities in Two Variables__- How do we solve and check systems of linear equations graphically/by
**graphing**? - How do we solve systems of linear equations using
**substitution**? - How do we solve systems of linear equations using
**elimination**? - How do we choose the best/
**most appropriate method**to solve a given system of equations? (Review of all three methods learned) - How do we solve a system by more than one method? (
**Review**of all three methods learned) - How do we
**use systems of linear equations to model and solve real-world applications**? (2 days) - How do we solve, graph, and check
**linear inequalities**? - How do we
**apply our knowledge of linear inequalities to real-world situations**? (2 days) - How do we solve, graph, and check
**systems of linear inequalities**? - How do we
**apply our knowledge of systems of linear inequalities to real-world situations**? (2 days) - : How do we solve
**systems of inequalities involving linear as well as non-linear equations/functions**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 6? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 7 – Exponents and Exponential Functions__- How do we apply the
**properties of exponents**to evaluate algebraic expressions? (4-5 days) - : How do we work with
**rational exponents**? - How do we identify, graph, and evaluate
**exponential functions**? - How do we identify and model exponential
**growth and decay**? - How do we apply the
**Compound****Interest Formula**to model and solve real-world situations? (2 days) - How do we
**apply scatter plots and exponential regression models to analyze real-world data**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 7? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 8 – Polynomials__- How do we
**classify polynomials**by degree and number of terms? - How do we
**add and subtract polynomials**? - How do we
**multiply polynomials**? (Scaffold to include all cases, i.e., a binomial by a trinomial) (2 days) - How do we factor polynomials with the
**GCF**method? - How do we factor polynomials of the form ax2 + bx + c with a = 1 using the
**Sum/Product**method? - How do we factor a polynomial of the form
**ax2 + bx + c with a>1**using the Sum/Product method? - How do we factor polynomials using the
**Difference of Squares**method? - How do we factor
**special case polynomials**which are**perfect squares trinomials**? - How do we factor polynomials by
**Grouping**? - How can we ensure that we
**factor a polynomial completely**? - How can we determine the
**appropriate method****to factor**a polynomial? (A**review**of all of the methods learned) (2 days) - : Introduce students to “dividing” polynomials by factoring, i.e., simplifying rational expressions; this will be explored in more depth in a later unit
- How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 8? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 9 – Quadratics__- How do we graph and find the characteristics of simple quadratic functions of the form

**vertex, axis of symmetry, zeros**)

- How do we graph and analyze the behavior of
**quadratic functions in the standard form**

**y = ax2 + bx + c**? (Include vertex, axis of symmetry, zeroes)

- How do we write and use
**quadratic functions in vertex form**? (2 days) - How do we identify and apply
**transformations of quadratic functions**? (2 days) - How do we solve and check simple quadratic equations of the form ax2 + c = 0 using inverse operations, i.e., by taking square roots?
- How do we
**solve**and check**quadratic equations by factoring**then using**the zero-product property**? (2 days) - How do we solve and check quadratic equations with the
**Quadratic Formula**? (2 days) - : How do we calculate and interpret the
**discriminant**of a quadratic equation? - How do we solve and check quadratic equations by
**completing the square**? (2 days) - How do we
**solve**and check**quadratic equations by graphing**the related function? - How can we determine the best/
**most appropriate method to solve a quadratic equation**? (A review of all methods learned) (2 days) - How can we solve a quadratic equation by more than one method? (A
**review**of all methods learned) (2 days) - How can we
**apply our knowledge of quadratic functions and equations to model and solve real-world situations**? (2 days) - How do we
**apply scatter plots and quadratic regression models to analyze real-world data**? - How can we
**differentiate between linear, quadratic, and exponential patterns**? (2 days) - How can we solve and check
**linear-quadratic systems**of equations? (2 days) - How can we solve and check
**quadratic systems**of equations? (2 days) - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 9? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 10 – Rational Expressions__- How do we
**simplify rational expressions**and identify excluded values? - How do we
**multiply rational expressions**? - How do we
**divide rational expressions**? - How do we
**add rational expressions with the same denominator**? - How do we
**subtract rational expressions with the same denominator**? - How do we
**add rational expressions with different denominators**? - How do we
**subtract rational expressions with different denominators**? - How do we
**simplify complex fractions**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 10? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 11– Analyzing Data__1. How do we define and calculate the measures of central tendency (

**mean, median, and mode**)? (Include definition and calculation of

**range**and applications to real-world situations)

2. How do we

**read and interpret**

**graphs**?

3. How do we

**organize and display data**?

4. How do we construct and interpret box and whisker plots/

**box plots**? (Include

**interquartile**

**range**and applications to real-world situations)

5. How do we

**prepare for the Regents Exam by reviewing and applying the main concepts**

learned in Unit 11? (Include a review session, a state test-aligned summative assessment, and/or a

performance task) (3 days)

__Unit 12 – Series and Sequences__- How do we define and generate sequences through
**recursive and explicit formulas**? - How do we define, generate, and represent
**arithmetic sequences**using function notation? - How do we define, generate, and represent
**geometric sequences**using function notation? - How do we work with
**arithmetic and geometric series**? - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 12? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

__Unit 13: Radicals__- How do we
**simplify expressions involving radicals**? - How do we
**add and subtract expressions involving radicals**? - How do we
**multiply and divide radical expressions**? - How do we
**rationalize the denominator**of a radical expression? - How do we solve and check
**radical equations**? (2 days) - How do we
**prepare for the Regents Exam by reviewing and applying the main concepts**learned in Unit 13? (Include a review session, a state test-aligned summative assessment, and/or a performance task) (3 days)

*{Additional Note*: The remaining 5-7 days (or less, if any of the extensions are covered) can be used for Regents review/preparation.}