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Topic 5 – Class Profile

Student Name

Grade

English Language Learner

Socio-economic Status

Ethnicity

Gender

IEP/504

Other

Reading Performance Level

Student Interests

Eduardo

8

Low Intermediate

Mid SES

Hispanic

Male

No

Tier 2 RTI for reading

One year below grade level

Playing percussion in the school band

Jade

9

No

High SES

African American

Female

No

None

At grade level

Cheerleading; reading young adult literature

Lolita

10

No

Mid SES

Native American/
Pacific Islander

Female

None

Little access to technology at home

One year above grade level

Basketball team member; taking care of her two younger siblings

Kent

11

No

High SES

White

Male

Emotionally disabled

None

At grade level

Alternative music; drawing and art class

Ines

12

High Intermediate

Low SES

Hispanic

Female

Learning disabled (Dyscalculia)

Tier 2 RTI for math

One year below grade level

Working at the local coffee shop; member of the soccer team

© 2019. Grand Canyon University. All Rights Reserved.

© 2019. Grand Canyon University. All Rights Reserved.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

GRADE: 912

Domain: NUMBER & QUANTITY: THE REAL NUMBER SYSTEM
Cluster 1: Extend the properties of exponents to rational exponents.

Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the

major work of the grade with the supporting clusters.

STANDARD CODE STANDARD

MAFS.912.N-RN.1.1 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. For example, we define to be the cube root of 5

because we want = to hold, so must equal 5.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of
exponents.

Cognitive Complexity: Level 1: Recall

Cluster 2: Use properties of rational and irrational numbers.

Algebra 1 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.N-RN.2.3 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: NUMBER & QUANTITY: QUANTITIES
Cluster 1: Reason quantitatively and use units to solve problems.

Algebra 1 – Supporting Cluster

Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD
MAFS.912.N-Q.1.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; choose and interpret units consistently in formulas; choose and interpret the
scale and the origin in graphs and data displays.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-Q.1.2 Define appropriate quantities for the purpose of descriptive modeling.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-Q.1.3 Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: NUMBER & QUANTITY: THE COMPLEX NUMBER SYSTEM
Cluster 1: Perform arithmetic operations with complex numbers.

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.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.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.1.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to
add, subtract, and multiply complex numbers.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.1.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of
complex numbers.

Cognitive Complexity: Level 1: Recall

Cluster 2: Represent complex numbers and their operations on the complex plane.

STANDARD CODE STANDARD
MAFS.912.N-CN.2.4 Represent complex numbers on the complex plane in rectangular and polar form

(including real and imaginary numbers), and explain why the rectangular and polar
forms of a given complex number represent the same number.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-CN.2.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers
geometrically on the complex plane; use properties of this representation for
computation. For example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

argument 120°.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-CN.2.6 Calculate the distance between numbers in the complex plane as the modulus of the
difference, and the midpoint of a segment as the average of the numbers at its
endpoints.

Cognitive Complexity: Level 1: Recall

Cluster 3: Use complex numbers in polynomial identities and equations.

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.3.8 Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x
+ 2i)(x – 2i).

Cognitive Complexity: Level 1: Recall

MAFS.912.N-CN.3.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.

Cognitive Complexity: Level 1: Recall

Domain: NUMBER & QUANTITY: VECTOR & MATRIX QUANTITIES
Cluster 1: Represent and model with vector quantities.

STANDARD CODE STANDARD
MAFS.912.N-VM.1.1 Recognize vector quantities as having both magnitude and direction. Represent vector

quantities by directed line segments, and use appropriate symbols for vectors and their
magnitudes (e.g., v, |v|, ||v||, v).

Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.1.2 Find the components of a vector by subtracting the coordinates of an initial point from
the coordinates of a terminal point.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.1.3 Solve problems involving velocity and other quantities that can be represented by
vectors.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Perform operations on vectors.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD
MAFS.912.N-VM.2.4 Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule.
Understand that the magnitude of a sum of two vectors is typically not the sum
of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude
and direction of their sum.

c. Understand vector subtraction v – w as v + (–w), where –w is the additive
inverse of w, with the same magnitude as w and pointing in the opposite
direction. Represent vector subtraction graphically by connecting the tips in the
appropriate order, and perform vector subtraction component-wise.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.2.5 Multiply a vector by a scalar.

a. Represent scalar multiplication graphically by scaling vectors and possibly
reversing their direction; perform scalar multiplication component-wise, e.g., as

c = .
b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the

direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v
(for c > 0) or against v (for c < 0).

Cognitive Complexity: Level 1: Recall

Cluster 3: Perform operations on matrices and use matrices in applications.

STANDARD CODE STANDARD
MAFS.912.N-VM.3.10 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable
dimensions to produce another vector. Work with matrices as transformations of
vectors.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.12 Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute
value of the determinant in terms of area.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.N-VM.3.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

a game are doubled.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.3.8 Add, subtract, and multiply matrices of appropriate dimensions.

Cognitive Complexity: Level 1: Recall

MAFS.912.N-VM.3.9 Understand that, unlike multiplication of numbers, matrix multiplication for square
matrices is not a commutative operation, but still satisfies the associative and
distributive properties.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: ALGEBRA: SEEING STRUCTURE IN EXPRESSIONS
Cluster 1: Interpret the structure of expressions

Algebra 1 – Major Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context.

a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a

single entity. For example, interpret as the product of P and a factor
not depending on P.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4- y4
as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x²
– y²)(x² + y²).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Write expressions in equivalent forms to solve problems

Algebra 1 – Supporting Cluster

Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain

properties of the quantity represented by the expression.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or

minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential

functions. For example the expression can be rewritten as
≈ to reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-SSE.2.4 Derive the formula for the sum of a finite geometric series (when the common ratio is
not 1), and use the formula to solve problems. For example, calculate mortgage
payments.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: ALGEBRA: ARITHMETIC WITH POLYNOMIALS & RATIONAL EXPRESSIONS
Cluster 1: Perform arithmetic operations on polynomials

Algebra 1 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-APR.1.1 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.

Cognitive Complexity: Level 1: Recall

Cluster 2: Understand the relationship between zeros and factors of polynomials

Algebra 1 – Supporting Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-APR.2.2 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).

Cognitive Complexity: Level 1: Recall

MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the
zeros to construct a rough graph of the function defined by the polynomial.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cognitive Complexity: Level 1: Recall

Cluster 3: Use polynomial identities to solve problems

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships. For

example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate
Pythagorean triples.

Cognitive Complexity: Level 1: Recall

MAFS.912.A-APR.3.5 Know and apply the Binomial Theorem for the expansion of (x in powers of x and
y for a positive integer n, where x and y are any numbers, with coefficients determined
for example by Pascal’s Triangle.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 4: Rewrite rational expressions

Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-APR.4.6 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-APR.4.7 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: ALGEBRA: CREATING EQUATIONS
Cluster 1: Create equations that describe numbers or relationships

Algebra 1 – Major Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve

problems. Include equations arising from linear and quadratic functions, and
simple rational, absolute, and exponential functions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities;

graph equations on coordinate axes with labels and scales.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints
on combinations of different foods.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-CED.1.4 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.

Cognitive Complexity: Level 1: Recall

Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES
Cluster 1: Understand solving equations as a process of reasoning and explain the reasoning

Algebra 1 – Major Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-REI.1.1 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing
how extraneous solutions may arise.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 2: Solve equations and inequalities in one variable

Algebra 1 – Major Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

STANDARD CODE STANDARD
MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with

coefficients represented by letters.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.

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.

b. 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Solve systems of equations

Algebra 1 – Additional Cluster
Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-REI.3.5 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.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.

Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.3.7 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.3.8 Represent a system of linear equations as a single matrix equation in a vector variable.

Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.3.9 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).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cluster 4: Represent and solve equations and inequalities graphically

Algebra 1 – Major Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.A-REI.4.10 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).

Cognitive Complexity: Level 1: Recall

MAFS.912.A-REI.4.11 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (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 half-planes.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: INTERPRETING FUNCTIONS
Cluster 1: Understand the concept of a function and use function notation

Algebra 1 – Major Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-IF.1.1 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).

Cognitive Complexity: Level 1: Recall

MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain
is a subset of the integers. For example, the Fibonacci sequence is defined recursively
by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Interpret functions that arise in applications in terms of the context

Algebra 1 – Major Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-IF.2.4 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.2.5 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.2.6 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Analyze functions using different representations

Algebra 1 – Supporting Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by

hand in simple cases and using technology for more complicated cases.

a. Graph linear and quadratic functions and show intercepts, maxima, and
minima.

b. Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.

d. Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

e. Graph exponential and logarithmic functions, showing intercepts and
end behavior, and trigonometric functions, showing period, midline, and
amplitude, and using phase shift.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and

explain different properties of the function.

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.

b. Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such as y =

, y = , y = , y = , and classify them as
representing exponential growth or decay.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a graph
of one quadratic function and an algebraic expression for another, say which has the
larger maximum.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: BUILDING FUNCTIONS
Cluster 1: Build a function that models a relationship between two quantities

Algebra 1 – Supporting Cluster
Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-BF.1.1 Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation
from a context.

b. 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.

c. Compose functions. For example, if T(y) is the temperature in the atmosphere
as a function of height, and h(t) is the height of a weather balloon as a function
of time, then T(h(t)) is the temperature at the location of the weather balloon as
a function of time.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula,

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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use them to model situations, and translate between the two forms.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Build new functions from existing functions

Algebra 1 – Additional Cluster
Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-BF.2.3 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-BF.2.4 Find inverse functions.

a. 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.

b. Verify by composition that one function is the inverse of another.
c. Read values of an inverse function from a graph or a table, given that the

function has an inverse.
d. Produce an invertible function from a non-invertible function by restricting the

domain.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.F-BF.2.5 Understand the inverse relationship between exponents and logarithms and use this

relationship to solve problems involving logarithms and exponents.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-BF.2.a Use the change of base formula.

Domain: FUNCTIONS: LINEAR, QUADRATIC, & EXPONENTIAL MODELS
Cluster 1: Construct and compare linear, quadratic, and exponential models and solve problems

Algebra 1 – Supporting Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with

exponential functions.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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a. Prove that linear functions grow by equal differences over equal intervals, and
that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit
interval relative to another.

c. Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning
MAFS.912.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).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually
exceeds a quantity increasing linearly, quadratically, or (more generally) as a
polynomial function.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-LE.1.4 For exponential models, express as a logarithm the solution to = d where a, c, and
d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Interpret expressions for functions in terms of the situation they model

Algebra 1 – Supporting Cluster
Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: FUNCTIONS: TRIGONOMETRIC FUNCTIONS
Cluster 1: Extend the domain of trigonometric functions using the unit circle

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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subtended by the angle; Convert between degrees and radians.

Cognitive Complexity: Level 1: Recall
MAFS.912.F-TF.1.2 Explain how the unit circle in the coordinate plane enables the extension of

trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.1.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for
π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and
tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real
number.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.1.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Model periodic phenomena with trigonometric functions

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude,

frequency, and midline.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.2.6 Understand that restricting a trigonometric function to a domain on which it is always
increasing or always decreasing allows its inverse to be constructed.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.2.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts;
evaluate the solutions using technology, and interpret them in terms of the context.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Prove and apply trigonometric identities

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.F-TF.3.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric

ratios.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.F-TF.3.9 Prove the addition and subtraction, half-angle, and double-angle formulas for

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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Amended Standard New Standard Deleted Standard

sine, cosine, and tangent and use these formulas to solve problems.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: GEOMETRY: CONGRUENCE
Cluster 1: Experiment with transformations in the plane

Geometry – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.

Cognitive Complexity: Level 1: Recall

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as inputs
and give other points as outputs. Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus horizontal stretch).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed
figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence
of transformations that will carry a given figure onto another.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Understand congruence in terms of rigid motions

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect

of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are
congruent if and only if corresponding pairs of sides and corresponding pairs of angles

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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are congruent.

Cognitive Complexity: Level 1: Recall

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and
Hypotenuse-Leg) follow from the definition of congruence in terms of rigid
motions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Prove geometric theorems

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to

solve problems. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line
segment are exactly those equidistant from the segment’s endpoints.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning
MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems.

Theorems include: measures of interior angles of a triangle sum to 180°; triangle
inequality theorem; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side
and half the length; the medians of a triangle meet at a point.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning
MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to

solve problems. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 4: Make geometric constructions

Geometry – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment;
and constructing a line parallel to a given line through a point not on the line.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: SIMILARITY, RIGHT TRIANGLES, & TRIGONOMETRY
Cluster 1: Understand similarity in terms of similarity transformations

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-SRT.1.1 Verify experimentally the properties of dilations given by a center and a scale factor:

a. A dilation takes a line not passing through the center of the dilation to a parallel
line, and leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale
factor.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity transformations to

decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two
triangles to be similar.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Prove theorems involving similarity

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a

triangle divides the other two proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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Amended Standard New Standard Deleted Standard

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 3: Define trigonometric ratios and solve problems involving right triangles

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in

the triangle, leading to definitions of trigonometric ratios for acute angles.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 4: Apply trigonometry to general triangles

STANDARD CODE STANDARD
MAFS.912.G-SRT.4.10 Prove the Laws of Sines and Cosines and use them to solve problems.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-SRT.4.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown
measurements in right and non-right triangles (e.g., surveying problems, resultant
forces).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-SRT.4.9 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary
line from a vertex perpendicular to the opposite side.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: CIRCLES
Cluster 1: Understand and apply theorems about circles

Geometry – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.912.G-C.1.1 Prove that all circles are similar.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include
the relationship between central, inscribed, and circumscribed angles; inscribed angles
on a diameter are right angles; the radius of a circle is perpendicular to the tangent
where the radius intersects the circle.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-C.1.4 Construct a tangent line from a point outside a given circle to the circle.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Find arc lengths and areas of sectors of circles

Geometry – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is

proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: GEOMETRY: EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS
Cluster 1: Translate between the geometric description and the equation for a conic section

Geometry – Additional Cluster
Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean

Theorem; complete the square to find the center and radius of a circle given by an
equation.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.1.2 Derive the equation of a parabola given a focus and directrix.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.1.3 Derive the equations of ellipses and hyperbolas given the foci and directrices.

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 2: Use coordinates to prove simple geometric theorems algebraically

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove

or disprove that a figure defined by four given points in the coordinate plane is a
rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin
and containing the point (0, 2).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
line that passes through a given point).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the
segment in a given ratio.

Cognitive Complexity: Level 1: Recall

MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and
rectangles, e.g., using the distance formula.

Cognitive Complexity: Level 1: Recall

Domain: GEOMETRY: GEOMETRIC MEASUREMENT & DIMENSION
Cluster 1: Explain volume formulas and use them to solve problems

Geometry – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a

circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s
principle, and informal limit arguments.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-GMD.1.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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a sphere and other solid figures.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Visualize relationships between two-dimensional and three-dimensional objects

Geometry – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and

identify three-dimensional objects generated by rotations of two-dimensional objects.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: GEOMETRY: MODELING WITH GEOMETRY
Cluster 1: Apply geometric concepts in modeling situations

Geometry – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects (e.g.,

modeling a tree trunk or a human torso as a cylinder).

Cognitive Complexity: Level 1: Recall

MAFS.912.G-MG.1.2 Apply concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost; working with typographic grid
systems based on ratios)

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: STATISTICS & PROBABILITY: INTERPRETING CATEGORICAL & QUANTITATIVE
DATA
Cluster 1: Summarize, represent, and interpret data on a single count or measurement variable

Algebra 1 – Additional Cluster
Algebra 2 – Additional Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.2 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to
estimate population percentages. Recognize that there are data sets for which such a
procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate
areas under the normal curve.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Summarize, represent, and interpret data on two categorical and quantitative
variables

Algebra 1 – Supporting Cluster
Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way 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.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related.

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, and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 3: Interpret linear models

Algebra 1 – Major Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard
Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in

the context of the data.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-ID.3.9 Distinguish between correlation and causation.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: MAKING INFERENCES & JUSTIFYING
CONCLUSIONS
Cluster 1: Understand and evaluate random processes underlying statistical experiments

Algebra 2 – Supporting Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters

based on a random sample from that population.

Cognitive Complexity: Level 1: Recall

MAFS.912.S-IC.1.2 Decide if a specified model is consistent with results from a given data-generating
process, e.g., using simulation. For example, a model says a spinning coin falls heads
up with probability 0.5. Would a result of 5 tails in a row cause you to question the
model?

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Make inferences and justify conclusions from sample surveys, experiments, and
observational studies

Algebra 2 – Major Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and

observational studies; explain how randomization relates to each.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-IC.2.4 Use data from a sample survey to estimate a population mean or proportion; develop a
margin of error through the use of simulation models for random sampling.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to
decide if differences between parameters are significant.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-IC.2.6 Evaluate reports based on data.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: CONDITIONAL PROBABILITY & THE RULES OF
PROBABILITY
Cluster 1: Understand independence and conditional probability and use them to interpret data

Algebra 2 – Additional Cluster

Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using

characteristics (or categories) of the outcomes, or as unions, intersections, or
complements of other events (“or,” “and,” “not”).

Cognitive Complexity: Level 1: Recall

MAFS.912.S-CP.1.2 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.

Cognitive Complexity: Level 1: Recall

MAFS.912.S-CP.1.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the
same as the probability of A, and the conditional probability of B given A is the same as
the probability of B.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.1.4 Construct and interpret two-way frequency tables of data when two categories are
associated with each object being classified. Use the two-way table as a sample space
to decide if events are independent and to approximate conditional probabilities. For
example, collect data from a random sample of students in your school on their favorite
subject among math, science, and English. Estimate the probability that a randomly
selected student from your school will favor science given that the student is in tenth
grade. Do the same for other subjects and compare the results.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.1.5 Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations. For example, compare the chance of
having lung cancer if you are a smoker with the chance of being a smoker if you have
lung cancer.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Use the rules of probability to compute probabilities of compound events in a uniform
probability model

Algebra 2 – Additional Cluster

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard
Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.

STANDARD CODE STANDARD
MAFS.912.S-CP.2.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also

belong to A, and interpret the answer in terms of the model.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer
in terms of the model.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-CP.2.9 Use permutations and combinations to compute probabilities of compound events and
solve problems.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Domain: STATISTICS & PROBABILITY: USING PROBABILITY TO MAKE DECISIONS
Cluster 1: Calculate expected values and use them to solve problems

STANDARD CODE STANDARD
MAFS.912.S-MD.1.1 Define a random variable for a quantity of interest by assigning a numerical value to

each event in a sample space; graph the corresponding probability distribution using the
same graphical displays as for data distributions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.2 Calculate the expected value of a random variable; interpret it as the mean of the
probability distribution.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.3 Develop a probability distribution for a random variable defined for a sample space in
which theoretical probabilities can be calculated; find the expected value. For example,
find the theoretical probability distribution for the number of correct answers obtained by
guessing on all five questions of a multiple-choice test where each question has four
choices, and find the expected grade under various grading schemes.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.1.4 Develop a probability distribution for a random variable defined for a sample space in
which probabilities are assigned empirically; find the expected value. For example, find
a current data distribution on the number of TV sets per household in the United States,
and calculate the expected number of sets per household. How many TV sets would
you expect to find in 100 randomly selected households?

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 2: Use probability to evaluate outcomes of decisions

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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STANDARD CODE STANDARD
MAFS.912.S-MD.2.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values

and finding expected values.

a. Find the expected payoff for a game of chance. For example, find the expected
winnings from a state lottery ticket or a game at a fast-food restaurant.

b. Evaluate and compare strategies on the basis of expected values. For
example, compare a high-deductible versus a low-deductible automobile
insurance policy using various, but reasonable, chances of having a minor or a
major accident.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.2.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number
generator).

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.S-MD.2.7 Analyze decisions and strategies using probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at the end of a game).

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

GRADE: K12

Domain: MATHEMATICAL PRACTICE
Cluster 1: Make sense of problems and persevere in solving them.

STANDARD CODE STANDARD
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a
problem and looking for entry points to its solution. They analyze givens, constraints,
relationships, and goals. They make conjectures about the form and meaning of the
solution and plan a solution pathway rather than simply jumping into a solution attempt.
They consider analogous problems, and try special cases and simpler forms of the
original problem in order to gain insight into its solution. They monitor and evaluate their
progress and change course if necessary. Older students might, depending on the
context of the problem, transform algebraic expressions or change the viewing window
on their graphing calculator to get the information they need. Mathematically proficient
students can explain correspondences between equations, verbal descriptions, tables,
and graphs or draw diagrams of important features and relationships, graph data, and
search for regularity or trends. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient students
check their answers to problems using a different method, and they continually ask
themselves, “Does this make sense?” They can understand the approaches of others to
solving complex problems and identify correspondences between different approaches.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 2: Reason abstractly and quantitatively.

STANDARD CODE STANDARD
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in
problem situations. They bring two complementary abilities to bear on problems
involving quantitative relationships: the ability to decontextualize—to abstract a given
situation and represent it symbolically and manipulate the representing symbols as if
they have a life of their own, without necessarily attending to their referents—and the
ability to contextualize, to pause as needed during the manipulation process in order to
probe into the referents for the symbols involved. Quantitative reasoning entails habits
of creating a coherent representation of the problem at hand; considering the units
involved; attending to the meaning of quantities, not just how to compute them; and
knowing and flexibly using different properties of operations and objects.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cluster 3: Construct viable arguments and critique the reasoning of others.

STANDARD CODE STANDARD
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions,
and previously established results in constructing arguments. They make conjectures
and build a logical progression of statements to explore the truth of their conjectures.
They are able to analyze situations by breaking them into cases, and can recognize and
use counterexamples. They justify their conclusions, communicate them to others, and
respond to the arguments of others. They reason inductively about data, making
plausible arguments that take into account the context from which the data arose.
Mathematically proficient students are also able to compare the effectiveness of two
plausible arguments, distinguish correct logic or reasoning from that which is flawed,
and—if there is a flaw in an argument—explain what it is. Elementary students can
construct arguments using concrete referents such as objects, drawings, diagrams, and
actions. Such arguments can make sense and be correct, even though they are not
generalized or made formal until later grades. Later, students learn to determine
domains to which an argument applies. Students at all grades can listen or read the
arguments of others, decide whether they make sense, and ask useful questions to
clarify or improve the arguments.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 4: Model with mathematics.

STANDARD CODE STANDARD
MAFS.K12.MP.4.1 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve
problems arising in everyday life, society, and the workplace. In early grades, this might
be as simple as writing an addition equation to describe a situation. In middle grades, a
student might apply proportional reasoning to plan a school event or analyze a problem
in the community. By high school, a student might use geometry to solve a design
problem or use a function to describe how one quantity of interest depends on another.
Mathematically proficient students who can apply what they know are comfortable
making assumptions and approximations to simplify a complicated situation, realizing
that these may need revision later. They are able to identify important quantities in a
practical situation and map their relationships using such tools as diagrams, two-way
tables, graphs, flowcharts and formulas. They can analyze those relationships
mathematically to draw conclusions. They routinely interpret their mathematical results
in the context of the situation and reflect on whether the results make sense, possibly
improving the model if it has not served its purpose.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

Cluster 5: Use appropriate tools strategically.

STANDARD CODE STANDARD
MAFS.K12.MP.5.1 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a
mathematical problem. These tools might include pencil and paper, concrete models, a
ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical
package, or dynamic geometry software. Proficient students are sufficiently familiar with
tools appropriate for their grade or course to make sound decisions about when each of
these tools might be helpful, recognizing both the insight to be gained and their
limitations. For example, mathematically proficient high school students analyze graphs
of functions and solutions generated using a graphing calculator. They detect possible
errors by strategically using estimation and other mathematical knowledge. When
making mathematical models, they know that technology can enable them to visualize
the results of varying assumptions, explore consequences, and compare predictions
with data. Mathematically proficient students at various grade levels are able to identify
relevant external mathematical resources, such as digital content located on a website,
and use them to pose or solve problems. They are able to use technological tools to
explore and deepen their understanding of concepts.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 6: Attend to precision.

STANDARD CODE STANDARD
MAFS.K12.MP.6.1 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to
use clear definitions in discussion with others and in their own reasoning. They state the
meaning of the symbols they choose, including using the equal sign consistently and
appropriately. They are careful about specifying units of measure, and labeling axes to
clarify the correspondence with quantities in a problem. They calculate accurately and
efficiently, express numerical answers with a degree of precision appropriate for the
problem context. In the elementary grades, students give carefully formulated
explanations to each other. By the time they reach high school they have learned to
examine claims and make explicit use of definitions.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Cluster 7: Look for and make use of structure.

STANDARD CODE STANDARD

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.K12.MP.7.1 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young
students, for example, might notice that three and seven more is the same amount as
seven and three more, or they may sort a collection of shapes according to how many
sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5
+ 7 × 3, in preparation for learning about the distributive property. In the expression x² +
9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the
significance of an existing line in a geometric figure and can use the strategy of drawing
an auxiliary line for solving problems. They also can step back for an overview and shift
perspective. They can see complicated things, such as some algebraic expressions, as
single objects or as being composed of several objects. For example, they can see 5 –
3(x – y)² as 5 minus a positive number times a square and use that to realize that its
value cannot be more than 5 for any real numbers x and y.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Cluster 8: Look for and express regularity in repeated reasoning.

STANDARD CODE STANDARD
MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for
general methods and for shortcuts. Upper elementary students might notice when
dividing 25 by 11 that they are repeating the same calculations over and over again,
and conclude they have a repeating decimal. By paying attention to the calculation of
slope as they repeatedly check whether points are on the line through (1, 2) with slope
3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the
regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and
(x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric
series. As they work to solve a problem, mathematically proficient students maintain
oversight of the process, while attending to the details. They continually evaluate the
reasonableness of their intermediate results.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

GRADE: 912 – CALCULUS

Standard 1: Limits and Continuity

Develop an understanding of the concept of limit by estimating limits graphically and numerically
and evaluating limits analytically. Extend the idea of a limit to one-sided limits and limits at
infinity. Use limits to define and understand the concept of continuity, decide whether a function

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

is continuous at a point, and find types of discontinuities. Understand and apply continuity
theorems.

BENCHMARK CODE BENCHMARK
MAFS.912.C.1.1 Understand the concept of limit and estimate limits from graphs and tables of

values.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.10 Decide if a function is continuous at a point.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.1.11 Find the types of discontinuities of a function.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.12 Understand and use the Intermediate Value Theorem on a function over a closed
interval.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.13 Understand and apply the Extreme Value Theorem: If f(x) is continuous over a
closed interval, then f has a maximum and a minimum on the interval.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.2 Find limits by substitution.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.3 Find limits of sums, differences, products, and quotients.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.4 Find limits of rational functions that are undefined at a point.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.5 Find one-sided limits.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.1.6 Find limits at infinity.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.7 Decide when a limit is infinite and use limits involving infinity to describe
asymptotic behavior.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.8
Find special limits such as

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.1.9 Understand continuity in terms of limits.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

Standard 2: Differential Calculus

Develop an understanding of the derivative as an instantaneous rate of change, using
geometrical, numerical, and analytical methods. Use this definition to find derivatives of
algebraic and transcendental functions and combinations of these functions (using, for example,
sums, composites, and inverses). Find second and higher order derivatives. Understand and
use the relationship between differentiability and continuity. Understand and apply the Mean

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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Value Theorem. Find derivatives of algebraic, trigonometric, logarithmic, and exponential
functions. Find derivatives of sums, products, and quotients, and composite and inverse
functions. Find derivatives of higher order, and use logarithmic differentiation and the Mean
Value Theorem.

BENCHMARK CODE BENCHMARK
MAFS.912.C.2.1 Understand the concept of derivative geometrically, numerically, and analytically,

and interpret the derivative as an instantaneous rate of change or as the slope of
the tangent line.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.2.10 Understand and use the relationship between differentiability and continuity.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.11 Understand and apply the Mean Value Theorem.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.2 State, understand, and apply the definition of derivative.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.3 Find the derivatives of functions, including algebraic, trigonometric, logarithmic,
and exponential functions.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.4 Find the derivatives of sums, products, and quotients.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.5 Find the derivatives of composite functions using the Chain Rule.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.6 Find the derivatives of implicitly-defined functions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.7 Find derivatives of inverse functions.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.2.8 Find second derivatives and derivatives of higher order.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.2.9 Find derivatives using logarithmic differentiation.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 3: Applications of Derivatives

Apply knowledge about derivatives to find slopes of curves and the related tangent lines.
Analyze and graph functions, finding where they are increasing or decreasing, their maximum
and minimum points, their points of inflection, and their concavity. Solve optimization problems,
find average and instantaneous rates of change (including velocities and accelerations), and
model rates of change. Find slopes and equations of tangent lines, maximum and minimum
points, and points of inflection. Solve optimization problems, and find rates of change.

BENCHMARK CODE BENCHMARK
MAFS.912.C.3.1 Find the slope of a curve at a point, including points at which there are vertical

tangent lines and no tangent lines.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

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MAFS.912.C.3.10 Find the velocity and acceleration of a particle moving in a straight line.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.11 Model rates of change, including related rates problems.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.12 Solve problems using the Newton-Raphson method.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.2 Find an equation for the tangent line to a curve at a point and a local linear
approximation.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.3 Decide where functions are decreasing and increasing. Understand the
relationship between the increasing and decreasing behavior of f and the sign of
f’.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.4 Find local and absolute maximum and minimum points.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.5 Find points of inflection of functions. Understand the relationship between the
concavity of f and the sign of f”. Understand points of inflection as places where
concavity changes.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.6 Use first and second derivatives to help sketch graphs. Compare the
corresponding characteristics of the graphs of f, f’, and f”.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.3.7 Use implicit differentiation to find the derivative of an inverse function.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.8 Solve optimization problems.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.3.9 Find average and instantaneous rates of change. Understand the instantaneous
rate of change as the limit of the average rate of change. Interpret a derivative as
a rate of change in applications, including velocity, speed, and acceleration.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 4: Integral Calculus

Understand that integration is used to find areas, and evaluate integrals using rectangular
approximations. From this, develop the idea that integration is the inverse operation to
differentiation — the Fundamental Theorem of Calculus. Use this result to find definite and
indefinite integrals, including using the method of integration by substitution. Apply approximate
methods, such as the Trapezoidal Rule, to find definite integrals. Define integrals using
Riemann sums, use the Fundamental Theorem of Calculus to find integrals using
antiderivatives, and use basic properties of integrals. Integrate by substitution, and find
approximate integrals.

BENCHMARK CODE BENCHMARK
MAFS.912.C.4.1 Use rectangle approximations to find approximate values of integrals.

Cognitive Complexity: Level 1: Recall

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) is now Mathematics Florida Standards (MAFS)

Amended Standard New Standard Deleted Standard

MAFS.912.C.4.2 Calculate the values of Riemann Sums over equal subdivisions using left, right,
and midpoint evaluation points.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.4.3 Interpret a definite integral as a limit of Riemann sums.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.4 Interpret a definite integral of the rate of change of a quantity over an interval as

the change of the quantity over the interval. That is, f'(x)dx = f(b) – f(a)
(Fundamental Theorem of Calculus).

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.4.5 Use the Fundamental Theorem of Calculus to evaluate definite and indefinite
integrals and to represent particular antiderivatives. Perform analytical and
graphical analysis of functions so defined.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.6 Use these properties of definite integrals:

• [f(x) + g(x)]dx = f(x)dx + g(x)dx

• k • f(x)dx = k f(x)dx

• f(x)dx = 0

• f(x)dx = – f(x)dx

• f(x)dx + f(x)dx = f(x)dx

• If f(x) ≤ g(x) on [a, b], then f(x)dx ≤ g(x)dx

Cognitive Complexity: Level 1: Recall

MAFS.912.C.4.7 Use integration by substitution (or change of variable) to find values of integrals.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.4.8 Use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite
integrals of functions represented algebraically, geometrically, and by tables of
values.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Standard 5: Applications of Integration

Apply knowledge about integrals to finding velocities from accelerations, solving separable
differential equations, and finding areas and volumes. Apply integration to model, and solve
problems in physics, biology, economics, etc. Find velocity functions and position functions from
their derivatives, solve separable differential equations, and use definite integrals to find areas
and volumes.

BENCHMARK CODE BENCHMARK
MAFS.912.C.5.1 Find specific antiderivatives using initial conditions, including finding velocity

functions from acceleration functions, finding position functions from velocity

Mathematics Common Core (MACC) is now Mathematics Florida Standards (MAFS)
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functions, and solving applications related to motion along a line.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.2 Solve separable differential equations, and use them in modeling.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.3
Solve differential equations of the form as applied to growth and decay
problems.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.4 Use slope fields to display a graphic representation of the solution to a
differential equation, and locate particular solutions to the equation.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.5 Use definite integrals to find the area between a curve and the x-axis or between
two curves.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.C.5.6 Use definite integrals to find the average value of a function over a closed
interval.

Cognitive Complexity: Level 1: Recall

MAFS.912.C.5.7 Use definite integrals to find the volume of a solid with known cross-sectional
area, including solids of revolution.

Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.C.5.8 Apply integration to model, and solve problems in physical, biological, and social
sciences.

Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

Directions: Please read the notes from the instructor and I’ve included the outline down below as how the assignment should be answered. This is due within 30 hours!

Okay, here is the instructions for the Benchmark.

My error is submitting a blank profile. It is just for your use; it is not to create a class profile for this assignment. I do apologize. Perhaps that is where the confusion was—I take responsibility for that.

This assignment is due on Friday, March 26th.

For Part I, you will select two students from the attached profile and do a case study analysis for both of the students you selected from the list.

Please answer or address all four points for both students you selected.

You do NOT have to submit a class profile with those two students but the students must be from the list. Some students do, some dont.

Part II

Type a double spaced rationale addressing the three (3) bulleted points-support it with research.

Be sure to include a cover/title page

Do NOT submit in pdf format.

Please keep in mind your clinical hours forms are due by the last day of the course. Please do not wait until the last minute to get your forms signed. If you watched videos, I will be happy to sign the forms for you.

BENCHMARK

Diversity affects the culture of the classroom, the teacher’s instructional design, and the lesson planning process. A respect for diversity should be evident in the classroom through curricular materials and discussion, as well as instructional decisions that honor students’ diverse needs.

Use the “Class Profile” to complete the assignment.

Part I: Case Study Analysis

Select

 

two students from the “Class Profile.” Write a 150-250 word case study analysis for each student focused on your specific content area. ***My area is Secondary Algebra**** I’ll attach the benchmarks and goals.

Include the following:

· Brief description of student’s specific learning needs

· Learning goal for student (“Student will be able to…”), aligned to specific standard (include standard and code) **see attachment mathematicsfloridastandards

· Activity and strategies to support stated learning goal

· Assessment that would support student attainment of the learning goal, and the feedback it would provide the student

Part II: Rationale

In addition, write a 500-750 word rationale for your pedagogical decisions, answering the following:

· How would you incorporate multiple perspectives in the discussion of content, including attention to students’ personal, family, and community experiences and cultural norms to promote the student success?

· How has your planning been informed and affected by what you have learned about learning theory, human development, cultural diversity, and individual differences?

· What are some of your personal biases related to these students or opportunities for growth that require examination in order for you to become an effective teacher, specifically by promoting ethical practice, building stronger relationships with students and parents, and creating more relevant learning experiences for all students?

Support your ideas with 3-5 scholarly resources.

Please read carefully: This is the drafted outline!

For further clarification, I drafted an outline for the benchmark due Friday. Hopefully this quells any confusion. You do NOT have to use this outline. However, it will cover the instructions, objectives and rubric for this assignment. Please support your points with scholarly resources and use the appropriate format. Please do NOT submit in apa format. 

I typed

Student #1

and

Student #2

. However you can type the student’s names in that spot. Or you can leave it as is. HOWEVER, please type the name of the students you chose to write about.

Let me know if you have any questions. Have a good day. Dr. James

Below and attached is a great example of the outline for the benchmark due Friday.

 
 

TITLE

 
 
 
 

Benchmark- Classroom Diversity Case Study and Analysis

This introductory paragraph should culture, race, socioeconomic status, language,

ability, readiness, neurology, personal interests, and behavior as it relates to differentiated instructions. A good way to begin this process is to start with a class profile. Of course, one is provided for you. The purpose of this benchmark, therefore, is to a) provide a case study analysis for two students based on data from their class profile, and b) justify pedagogical decisions regarding two students by discussing multiple perspectives, development/learning theories, and educator dispositions.

 
Part I: Case Study Analysis

Below, I will discuss two students’ learning profiles from a data sheet entitled “Class Profile.” I have selected two students who vary in significant ways, __________ and _________.

Student #1
 

Validation

 
 

Learning Theory/Strategy Implemented

 
 

Assessment/Feedback

 
 
 
Student #2
 
Validation
 
 
 
Learning Theory/Strategy Implemented
 
 
 
Assessment/Feedback
 
 
 
 
 
Part II: Rationale

Multiple Perspectives

 
 
 

Effects of Educational Concepts on Pedagogical Decisions

 
 
 

Human Development

 
 
 

Learning Theories

 
 

Individual Differences

 
 

Reflection (Teacher’s)

 
 

Conclusion

 
 
 
 
 
 

References