Mafs 912 g co 3.9 answers

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)

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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)

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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)

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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)

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

Amended Standard New Standard Deleted Standard

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)

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

Amended Standard New Standard Deleted Standard

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)

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

Amended Standard New Standard Deleted Standard

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)

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

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)

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

Amended Standard New Standard Deleted Standard

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)

Next Generation Sunshine State Standards (NGSSS) for Mathematics (MA) 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)

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

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