Download Honors Algebra 2 Learning Standards

[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 1.1
Standard: A.SSE.1A
Interpret expressions that represent a quantity in terms of its context.--Interpret parts of an expression, such as terms, factors,
and coefficients.
A.SSE.1B Interpret expressions that represent a quantity in terms of its context.--Interpret complicated expressions by viewing one or more of their
parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A.CED.1 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.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law
V =IR to highlight resistance R.
A.REI.1 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.
A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise
AREI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Essential Learning Objective: 1.
Students will create and solve multi-step equations, inequalities, and absolute value equations and inequalities,
including graphical, numerically, analytically, and in words.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Students will create situations that can be modeled with linear equations or inequalities
applied to theoretical or real world applications.
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
1. Students will create and solve multi-step equations, inequalities, and absolute
value equations and inequalities, including graphical, numerically, analytically, and
in words.
1
[Department: Honors Algebra II]
Grade Level: 10 - 11
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: reciprocal, opposite, power, exponent,
base, variable, coefficients, variable, terms, constant, like terms, equivalent expressions, linear
equations, equivalent equations, solve for a variable, linear inequality, compound inequality,
absolute value, extraneous solution, compound inequality.

perform basic processes, such as:
1) Apply properties of addition and multiplication.
2) Evaluate and simplify algebraic expressions.
3) Use verbal model to solve a problem.
4) Solve linear equations.
5) Rewrite formulas and equations.
6) Solve linear inequalities.
7) Solve absolute value equations and inequalities.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
2
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 1.2
Standard: F.IF.1
F.IF.4 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.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function
h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for
the function.
F.IF.6 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.
F.IF.7A Graph functions expressed symbolically and show key features of
the graph, by hand in simple cases and using technology for more
complicated cases.-Graph linear and quadratic functions and show intercepts, maxima, and minima.
A.CED.1 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.
S.ID.6A Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.--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.
S.ID.6B Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.--Informally assess the fit of a
function by plotting and analyzing residuals.
S.ID.6C Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.--Fit a linear function for a scatter
plot that suggests a linear association
Essential Learning Objective: 2.
Students will analyze linear functions graphically, analytically, numerically, and in words.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
3
[Department: Honors Algebra II]
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
standard. The student will:
 Students will create situations that can be modeled with linear functions as applied to
theoretical or real world applications.
3.5
Level 3
Grade Level: 10 - 11

Example Activities
Modeling unit change (i.e. temperature C/F)
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:

Students will analyze linear functions graphically, analytically, numerically, and in words.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: relation, domain, range, function,
function notation, equations in two variables, solution to equation in two variables,
independent variable, dependent variable, linear function, function notation, slope, parallel,
perpendicular, rate of change, parent function, y-intercept, slope-intercept form, x-intercept,
standard form of a linear equation, point-slope form, direct variation, scatter plot, positive
correlation, negative correlation, linear inequality in two variables, solutions to a linear
inequality in two variables, discrete, continuous.

perform basic processes, such as:
1) Classify and evaluate functions: (linear-non linear)
2) Find slope and rate of change given a table, graph, algebraic equation, ordered pairs, or
verbal model.
3) Use properties of parallel and perpendicular lines.
4) Graph equations of lines in standard, point slope, and slope intercept.
5) Given a table (or points), graph, or verbal model, write the algebraic equation.
6) Draw scatter plots and best fitting lines.
7) Graph linear inequalities in 2 variables.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
4
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 1.3
Standard: A.REI.5 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.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example,
find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
A.REI.8 Represent a system of linear equations as a single matrix equation in a vector variable.
A.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or
greater).
A.REI.11 Explain why the x-coordinates 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
N.VM.6 Use matrices to represent and manipulate data,e.g.,to represent payoffs or incidence relationships in a network.
N.VM.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N.VM.8 Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still
satisfies the associative and distributive properties.
N.VM.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real
numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
N.VM.12 Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Essential Learning Objective: 3. Students will create and solve linear systems of equations and inequalities graphically, numerically, analytically, and in
words.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
5
[Department: Honors Algebra II]
Grade Level: 10 - 11
standard. The student will:
 Students will model situations with linear systems in 3 or more variables applied to
theoretical or real world applications with the use of technology.
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Create and solve linear systems of equations and inequalities graphically, numerically, analytically,
and in words.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: System of two linear equations in two
variables, solution of a system of linear equations, substitution method, elimination method,
system if linear inequalities in two variables, matrix, elements of a matrix, dimensions of a
matrix, scalar, scalar multiplication

perform basic processes, such as:

1) Solve linear systems by graphing.

2) Solve linear systems algebraically.
3) Graph systems of linear inequalities.
4)Perform basic matrix operations.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
6
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 1.4
Standard: N.EN.1
N.CN.1.1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.
N.CN.1.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N.CN.1.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Represent complex numbers
and their operations on the complex plane.
N.CN.3.1 Solve quadratic equations with real coefficients that have complex solutions.
A.REI.4.1 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
A.REI.2.2A Solve quadratic equations in one variable.--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.
A.REI.2.2B Solve quadratic equations in one variable.--Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing
the square, the quadratic formula and
factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi
for real numbers a and b.
A.REI.4.2 Explain why the x-coordinates 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.
F. IF 2.1 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.
F.IF.3.2A Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.-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.
F.IF.3.1A Graph functions expressed symbolically and show key features of
the graph, by hand in simple cases and using technology for more
complicated cases.-Graph linear and quadratic functions and show intercepts, maxima, and minima.
Essential Learning Objective: .
Students will analyze and solve quadratic functions graphically, numerically, analytically, and in words, including
solutions that arise in the complex number system.
7
[Department: Honors Algebra II]
Grade Level: 10 - 11
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Solving and graphing a system of quadratic
 Students will create situations that can be modeled with quadratic functions applied to
inequalities
theoretical or real world applications.
 Trajectory situations
 Rate of Change (slope)
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Analyze and solve quadratic functions graphically, numerically, analytically, and in words,
including solutions that arise in the complex number system.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: Quadratic function, standard form of
quadratic function, parabola, vertex, axis of symmetry, minimum and maximum value,
monomial, binomial, trinomial, intercept form, vertex form, quadratic equation, root of an
equation, zero of a function, square root, radical, radicand, rationalizing the denominator,
conjugates, imaginary unit, complex number, imaginary number, completing the square ,
quadratic formula, zero product property

perform basic processes, such as:
1) Graph quadratic functions in standard form.
2) Graph quadratic functions in vertex and standard form.
3) Factor and use the zero product property to solve equations of the form:
𝑥 2 + 𝑏𝑥 + 𝑐 = 0
4) Solve quadratic equations by finding square roots.
5) Perform operations with complex numbers.
6) Complete the square.
7) Use the quadratic formula and the discriminant.
8
[Department: Honors Algebra II]
Grade Level: 10 - 11
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
9
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 2.1
Standard: A.APR.1 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.
A.APR.2.1 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if
and only if (x – a) is a factor of p(x).
A.APR.2.2Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function
defined by the polynomial.
A.APR.4.1 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are
polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer
algebra system.
F.IF.3.1C Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.--Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F.BF.2.1 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.
F.BF.2.2A Find inverse functions.--Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the
inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠1
Essential Learning Objective: Students will be able to add, subtract, multiply, divide and factor polynomials and analyze the graphs of polynomials.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Students will identify intervals on which a function is decreasing/increasing, points of
inflection, concavity, and end point behavior.
 Identify intervals using correct set notation.
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Add, subtract, multiply, divide and factor polynomials and analyze the graphs of
polynomials.
10
[Department: Honors Algebra II]
Grade Level: 10 - 11
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: polynomial, polynomial function,
degree, constant term, polynomial long division,

perform basic processes, such as:

1) Use properties of exponents.
2) Add subtract and multiply polynomials.
3) Use polynomial long division.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
11
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 2.2
Standard: F.IF.3.1B Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for
more complicated cases.--Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Essential Learning Objective: . Students will analyze and solve radical functions graphically, numerically, analytically, and in words.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Students will create and solve complex radical functions as applied to theoretical
situations.
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Analyze and solve radical functions graphically, numerically, analytically, and in words.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: nth root of a, index of a radical, like
radicals, radical function, radical equations, rational numbers, rational powers,

perform basic processes, such as:
1) Evaluate expressions with rational exponents.
2) Solve radical equations.
3) Apply properties of rational exponents.
4) Write radical in simplest form.
5) Graph square root and cube root functions.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
12
[Department: Honors Algebra II]
1.5
Level 1
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
.5
Level 0
Grade Level: 10 - 11
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
13
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 2.3
Standard: F.LE.1.1A Distinguish between situations that can be modeled with linear functions and with exponential functions.--Prove that linear
functions grow by equal differences over equalintervals, and that exponential functions grow by equal factors
over equal intervals.
F.LE.1.1C Distinguish between situations that can be modeled with linear functions and with exponential functions.--Recognize situations in which a
quantity grows or decays by a constant percent rate per unit interval relative to another.
F.LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or
two input-output pairs (include reading these from a table).
F.LE.1.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e;
evaluate the logarithm using technology.
F.LE.2.1 Interpret the parameters in a linear or exponential function in terms of a context.
F.BF.1.1A Write a function that describes a relationship between two quantities.--Determine an explicit expression, a recursive process, or steps
for calculation from a context.
F.BF.1.1B Write a function that describes a relationship between two quantities.--Combine standard function types using arithmetic operations. For
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.
F.BF.2.1 Write a function that describes a relationship between two quantities.--Combine standard function types using arithmetic operations. For
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.
F.BF.2.3 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving
logarithms and exponents.
A.SSE.2.1C Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.--Use the properties of exponents to transform expressions for exponential
functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
Essential Learning Objective: Students will write, evaluate, and graph logarithmic and exponential functions.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
14
[Department: Honors Algebra II]
Grade Level: 10 - 11
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Growth and decay
 Students will create situations that can be modeled with exponential equations or applied
 Continuous Compound Interest
to theoretical or real world applications.
 Half-life
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Write, evaluate, and graph logarithmic and exponential functions.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 Recognize and define specific vocabulary, such as: exponential function, exponential
growth functions, growth factor, decay factor, asymptote, natural base e, interest, compound
interest.

perform basic processes, such as:
1) Graph and apply exponential growth functions.
2) Graph and apply exponential decay functions.
3) Solve compound interest problems.
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
15
[Department: Honors Algebra II]
Grade Level: 10 - 11
Proficiency Scale 2.4
Standard: A.APR.4.1 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
where a(x), b(x), q(x), and r(x)
are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a
computer algebra system.
A.APR.4.2 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.
N.RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the propertiesof integer exponents to
those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5
because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
N.RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
A.REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Essential Learning Objective: Students will analyze and solve rational functions graphically, numerically, analytically, and in words.
A proficiency scale includes statements of what students need to know and be able to do for a standard that sets out a logical progression of learning over time. Student
performance is represented by a proficiency level as determined by learning outcomes.
Correlating student performance to a proficiency scale:
 Level 4 – An example of application that is in-depth and goes beyond instruction of the standard
 Level 3 – Learning target/standard as stated in the common core
 Level 2 – Prerequisite skills and knowledge required to meet the learning target/standard
 Level 1 – Partial understanding of the simpler ideas and processes (Ex: English Language Learners and students with IEPs or 504s)
 Level 0 – Alternative curriculum required
Level 4
In addition to Level 3, in-depth inferences and applications that goes beyond instruction to the
Example Activities
standard. The student will:
 Identifying asymptotes and holes in a rational
 Students will create situations that can be modeled with rational functions applied to
function graph
theoretical or real world applications.
3.5
Level 3
In addition to Level 3 performance, in-depth inferences and applications with partial success.
The student will:
Analyze and solve rational functions graphically, numerically, analytically, and in words.
The student exhibits no major errors or omissions.
2.5
Level 2
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content.
There are no major errors or omissions regarding the simpler details and processes as the student
will:
 recognize and define specific vocabulary, such as: inverse variation, constant of variation,
joint variation, rational function, simplified form of a rational expression, complex fraction,
cross multiplying
16
[Department: Honors Algebra II]

Grade Level: 10 - 11
perform basic processes, such as:
1) Model inverse and joint variation
2) Graph simple rational functions.
3) Multiply and divide rational expressions
4) Add and subtract rational expressions
However, the student exhibits major errors or omissions regarding the more complex ideas and
processes.
1.5
Level 1
.5
Level 0
Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content.
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and
processes.
With help, a partial understanding of the 2.0 content but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
17