


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

1 ) Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. [NRN1]
Example: We define 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)}^{3} to hold, so (5^{1/3})^{3} must equal 5.
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

2 ) Rewrite expressions involving radicals and rational exponents using the properties of exponents. [NRN2]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

3 ) Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [NRN3]
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
2 
Learning Activities: 
2 

4 ) Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

5 ) Define appropriate quantities for the purpose of descriptive modeling. [NQ2]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

6 ) Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3]
Alabama Alternate Achievement Standards




Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
2 
Learning Activities: 
2 

7 ) Interpret expressions that represent a quantity in terms of its context.* [ASSE1]
a. Interpret parts of an expression such as terms, factors, and coefficients. [ASSE1a]
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [ASSE1b]
Example: Interpret P(1+r)^{n} as the product of P and a factor not depending on P.
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

8 ) Use the structure of an expression to identify ways to rewrite it. [ASSE2]
Example: See x^{4}  y^{4} as (x^{2})^{2}  (y^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (x^{2}  y^{2})(x^{2} + y^{2}).


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

9 ) Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3]
a. Factor a quadratic expression to reveal the zeros of the function it defines. [ASSE3a]
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. [ASSE3b]
c. Determine a quadratic equation when given its graph or roots. (Alabama)
d. Use the properties of exponents to transform expressions for exponential functions. [ASSE3c]
Example: The expression 1.15^{t} can be rewritten as (1.15^{1/12})^{12t} ≈ 1.012^{12t} to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
2 
Learning Activities: 
2 

10 ) Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [AAPR1]


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

11 ) (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. [AAPR7]
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

12 ) Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1]

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

13 ) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2]

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

14 ) Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3]
Example: Represent inequalities describing nutritional and cost constraints on combinations of different foods.

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
2 
Lesson Plans: 
2 

15 ) Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [ACED4]
Example: Rearrange Ohm's law V = IR to highlight resistance R.



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [AREI1]


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

17 ) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [AREI3]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
2 
Learning Activities: 
2 

18 ) Solve quadratic equations in one variable. [AREI4]
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x  p)^{2} = q that has the same solutions. Derive the quadratic formula from this form. [AREI4a]
b. Solve quadratic equations by inspection (e.g., for x^{2} = 49), taking square roots, completing the square and the quadratic formula, and factoring as appropriate to the initial form of the equation. [AREI4b] (Alabama)
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

19 ) Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [AREI5]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

20 ) Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

21 ) Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [AREI7]
Example: Find the points of intersection between the line y = 3x and the circle x^{2} + y^{2} = 3.
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

22 ) Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

23 ) Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

24 ) Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. [AREI12]
Alabama Alternate Achievement Standards




Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

25 ) Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

26 ) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

27 ) Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3]
Example: The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n ≥ 1.
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

28 ) For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5]
Example: If the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

30 ) Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

31 ) Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7]
a. Graph linear and quadratic functions, and show intercepts, maxima, and minima. [FIF7a]
b. Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. [FIF7b]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

32 ) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8]
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. [FIF8a]
b. Use the properties of exponents to interpret expressions for exponential functions. [FIF8b]
Example: Identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, and y = (1.2)^{t/10}, and classify them as representing exponential growth and decay.
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

33 ) Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9]
Example: Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Lesson Plans: 
1 

34 ) Write a function that describes a relationship between two quantities.* [FBF1]
a. Determine an explicit expression, a recursive process, or steps for calculation from a context. [FBF1a]
b. Combine standard function types using arithmetic operations. [FBF1b]
Example: Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

35 ) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

36 ) Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [FBF3]
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

37 ) Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1]
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. [FLE1a]
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. [FLE1b]
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. [FLE1c]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

38 ) Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

39 ) Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [FLE3]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

40 ) Interpret the parameters in a linear or exponential function in terms of a context. [FLE5]
Alabama Alternate Achievement Standards




Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

41 ) Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

42 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

43 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [SID3]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

44 ) Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. [SID5]
Alabama Alternate Achievement Standards

Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
0 

45 ) Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6]
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [SID6a]
b. Informally assess the fit of a function by plotting and analyzing residuals. [SID6b]
c. Fit a linear function for a scatter plot that suggests a linear association. [SID6c]
Alabama Alternate Achievement Standards


Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

46 ) Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Alabama Alternate Achievement Standards



Mathematics (2016) 
Grade(s): 9  12 
Algebra I 
All Resources: 
1 
Learning Activities: 
1 

47 ) Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2]
