Algebra 1

Scope & Sequence

Semester 1 

Semester 2 

Topic 1: Equations and Inequalities 

  • 1.2 Properties of equality, solve one-variable equations (A.CED.1; A.REI.1, 3) 

  • 1.3 Variables on both sides, types of solutions (N.Q.2; A.CED.1; A.REI.1, 3) 

  • 1.4 Using formulas, isolating variables (N.Q.1; A.CED.1, 4) 

  • 1.5 Inequalities in one variable (A.CED.1, 3; A.REI.3) 


Topic 2: Linear Equations 

  • 2.1 Slope-intercept form (A.CED.2; S.ID.7) 

  • 2.2 Point-slope form (F.LE.2; A.CED.2) 

  • 2.3 Standard form (A.CED.2, 3) 

  • 2.4 Parallel and perpendicular lines (A.CED.2; F.IF.7A) 


Topic 3: Functions 

  • 3.1 Function definition, domain (F.IF.1) 

  • 3.2 Function notation, linear functions, multiple representations, context (F.IF.2, 5; F.LE.2) 


Topic 4: Systems of Linear Equations 

  • 4.1 Graph to approximate solutions, model real-world problems (A.REI.6) 

  • 4.2 Substitution, interpret solutions in context (A.CED.3; A.REI.6) 

  • 4.3 Elimination, represent constraints in context (A.CED.3; A.REI.6) 


Topic 6: Exponents 

  • 6.1 Properties of integer and radical exponents (N.RN.1, 2) 

  • 6.2 Exponential functions (F.IF.4; F.BF.1; F.LE.1, 1.A) 

  • 6.5 Translate exponential graphs, identify effects of h and k on graphs  
    (F.IF.4, 9; F.BF.3) 

Topic 5: Absolute Value 

  • 1.7 Solve absolute value equations (no inequalities) (A.CED.1) 

  • 5.1 Graphs of absolute value functions, rate of change (F.IF.4, 5, 6, 7.B; F.BF.3) 

  • 5.4 Transform absolute value functions (a, h, k) (F.IF.7.B; F.BF.3) 


Topic 7: Polynomials 

  • 7.1 Identify parts, classify (by terms/degree), standard form, add/subtract (A.SSE.1a; A.APR.1) 

  • 7.2 Multiply polynomials (A.SSE.1a; A.APR.1) 

  • 7.3 Square binomials, difference of squares (A.APR.1) 

  • 7.4 GCF, factor using the structure of a polynomial (A.SSE.2) 

  • 7.5 Factor x^2 + bx + c (A.SSE.2) 

  • 7.6 Factor ax^2 + bx + c (A.SSE.2) 


Topic 8: Graphs of Quadratics 

  • 8.1 Key features of parabolas from multiple reps of quadratics (F.IF.6; F.BF.3) 

  • 8.2 Vertex form (F.IF.4, 7A; F.BF.3) 

  • 8.3 Standard form (F.IF.4, 7A, 9) 


Topic 9: Zeros of Quadratics 

  • 9.1 Solve by graphing, intercepts as solutions (A.REI.11) 

  • 9.2 Zero product property, using zeros to graph or write factored equations (A.SSE.3A; A.APR.3; A.REI.4B; F.IF.8A) 

  • 9.3 Radical expressions (N.RN.2; A.SSE.2) 

  • 9.4 Solve using square roots (A.REI.4B; A.CED.1) 

  • 9.6 Solve with the quadratic formula, use the discriminant (A.REI.4A, 4B; A.SSE.3B; A.CED.1) 



Essential Learnings  


Semester 1 

Topic 1 

1.2    A.CED.1, A.REI.1, A.REI.3 

  • Explain that each step in solving a linear equation follows from the asserted equality in the previous step. 

  • Create and solve linear equations with one variable using the properties of equality 

1.3     N.Q.2, A.CED.1, A.REI.1, A.REI.3 

  • Use the properties of equality to solve linear equations with a variable on both sides 

  • Identify whether linear equations have one solution, infinitely many solutions, or no solution 

1.4     N.Q.1, A.CED.1, A.CED.4 

  • Rearrange formulas and equations to highlight a quantity of interest by isolating the variable using the same reasoning used to solve equations 

  • Use formulas and equations to solve problems 

1.5     A.CED.1, A.CED.3, A.REI.3 

  • Create and solve inequalities in one variable 

  • Interpret solutions to inequalities within the context 

  • Identify inequalities as true or false based on the number of solutions 





Topic 2 

2.1     A.CED.2, S.ID.7 

  • Write linear equations in two variables using slope-intercept form to represent the relationship between two quantities 

  • Interpret the slope and the intercept of a linear model 

2.2     F.LE.2, A.CED.2 

  • Write and graph linear equations in point-slope form 

  • Analyze different forms of a line to interpret the slope and y-intercept of a linear model in the context of data 

2.3     A.CED.2, A.CED.3 

  • Write and graph linear equations in standard form 

  • Use linear equations in standard form to interpret both the x- and y-intercepts in the context of given data 

2.4     A.CED.2, F.IF.7a 

  • Create equations to represent lines that are parallel or perpendicular to a given line 

  • Graph lines to show an understanding of the relationship between the slopes of parallel and perpendicular lines 

  • Solve real-world problems with parallel or perpendicular lines 


Topic 3 

3.1     F.IF.1 

  • Understand that a relation is a function if each element of the domain is assigned to exactly one element in the range 

  • Determine a reasonable domain and identify constraints on the domain based on the context of a real-world problem 

3.2     F.IF.2, F.IF.5, F.LE.2 

  • Evaluate linear functions using function notation 

  • Graph a linear function and relate the domain of a function to its graph 

  • Interpret functions represented by graphs, tables, verbal descriptions, and function notation in terms of a context 


Topic 4 

4.1     A.REI.6 

  • Graph systems of linear equations in two variables to find an approximate solution 

  • Write a system of linear equations in two variables to represent real-world problems 

4.2     A.CED.3, A.REI.6 

  • Use the substitution method to solve systems of equations 

  • Represent situations as a system of equations and interpret solutions as viable/nonviable options for the situation 

4.3     A.CED.3, A.REI.6 

  • Solve systems of linear equations and prove that the sum of one equation and a multiple of the other produces a system with the same solutions as the original system. 

  • Represent constraints with a system of equations in a modeling context 




Topic 6 (this will take noticeably more time than in previous years, covered in CC8 remotely) 

6.1     N.RN.1, N.RN.2 

  • Extend the properties of integer exponents to rational exponents to rewrite radical expressions using rational exponents 

6.2     F.IF.4, F.BF.1, F.LE.1, F.LE.1.A 

  • Sketch graphs showing key features of exponential functions 

  • Write exponential functions using tables and graphs 

  • Compare linear and exponential functions 

6.5     F.IF.4, F.IF.9, F.BF.3 

  • Translate the graph of an exponential function vertically and horizontally, identifying the effect different values of h and k have on the graph of the function (graphs only) 



Semester 2 

Topic 5 

1.7     A.CED.1 

  • Solve equations that involve absolute value (no inequalities) 

5.1     F.IF.4, F.IF.5, F.IF.6, F.IF.7.B, F.BF.3 

  • Graph an absolute value function and identify the key features of the graph 

  • Calculate and interpret the rate of change of an absolute value function over a specified interval 

5.4     F.IF.7.B, F.BF.3 

  • Identify the effect of changing constants and coefficients of absolute value functions on their graphs  (no piecewise) 


Topic 7 

7.1     A.SSE.1a, A.APR.1 

  • Identify the parts of a polynomial 

  • Classify polynomials by number of terms and by degree 

  • Write a polynomial in standard form 

  • Add or subtract two polynomials 

7.2     A.SSE.1a, A.APR.1 

  • Use the Distributive Property with polynomials, recognizing that polynomials are closed under multiplication. 

  • Multiply polynomials using a table and an area model 

7.3     A.APR.1 

  • Determine the square of a binomial 

  • Find the product of a sum and difference of two squares 

7.4     A.SSE.2 

  • Find the greatest common factor of the terms of a polynomial 

  • Use the structure of a polynomial to rewrite it in factored form 

7.5     A.SSE.2 

  • Factor a trinomial in the form  by finding two binomial factors whose product is equal to the trinomial 

  • Identify the use patterns in the signs of the coefficients of the terms of a trinomial expression 

7.6     A.SSE.2 

  • Identify the common factor of the coefficients in the terms of a trinomial expression in the form  

  • Write a quadratic trinomial as a product of two binomial factors 


Topic 8 

8.1     F.IF.6, F.BF.3 

  • Identify key features of the graph of a quadratic function using graphs, tables, and equations 

  • Explain the effect of the value of a on the quadratic parent function 

8.2     F.IF.4, F.IF.7a, F.BF.3 

  • Identify key features of the graph of quadratic functions written in vertex form 

  • Graph quadratic functions in vertex form 

8.3     F.IF.4, F.IF.7A, F.IF.9 

  • Graph quadratic functions in standard form and show intercepts, maxima, and minima 


Topic 9 

9.1     A.REI.11 

  • Use a graph to identify the intercepts as solutions of a quadratic equation 

9.2     A.SSE.3A, A.APR.3, A.REI.4B, F.IF.8A 

  • Use the Zero-Product Property and factoring to find the solutions of a quadratic equation 

  • Use zeros of a quadratic equation to sketch a graph 

  • Write the factored form of a quadratic function from a graph 

9.3     N.RN.2, A.SSE.2 

  • Use properties of exponents to rewrite radical expressions 

  • Multiply radical expressions 

9.4     A.REI.4B, A.CED.1 

  • Solve quadratic equations by finding square roots 

9.6     A.REI.4A, A.REI.4B, A.SSE.3b, A.CED.1 

  • Solve quadratic equations in one variable by using the quadratic formula 

  • Use the discriminant to determine the number and type of solutions to a quadratic equation