algebra ii - jmcss.org

Algebra II The HS Scope and clarification column for each standard appears below its standard here. It is included only for major changes, otherwise does not appear.

Major work of the grade indicated by green colored cluster heading. All other standards are to be considered as supporting standards. Changes are highlighted in yellow. Explanation of changes, if any, appear in the Notes column.

CCSS Standard (OLD) Notes TN Standard (NEW)

Conceptual Category: Number and Quantity

Domain: The Real Number System (N.RN)

Cluster A: Extend the properties of exponents to rational exponents.

N-RN.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 51/3 to be the cube root of 5

because we want (51/3)3 = 𝟓(𝟏

𝟑)𝟑

to hold, so (51/3)³ must equal 5.

Example moved to scope and clarifications

A2.N-RN.A.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.

N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

No Change

A2.N-RN.A.2 Rewrite expressions involving radicals and rational

exponents using the properties of exponents.

Domain: Quantities ★ (N.Q)

Cluster A: Reason quantitatively and use units to solve problems.

N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.

Note code change. Define is a broad word that needs clarification in terms of the expectations. The scope and

clarification needs adjustment to give a better explanation of what is included.

A2.N.Q.A.1 Identify, Interpret, and justify appropriate quantities for the purpose of descriptive modeling. Understanding/interpreting graphs. Identifying extraneous information, choosing appropriate units, etc.)

The Complex Number System Domain (N.CN)

Cluster A: Perform arithmetic operations with complex numbers

N- CN.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.

No Change

A2.N.CN.A.1

Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

N- CN.2

Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Added the word “Know” to make “Know and use” to indicate that students are not only to

use the relation but are to know it as well indicating fluency.

A2.N.CN.A.2 Know and use the relation i2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Cluster B: Use complex numbers in quadratic equations.

N-CN.7 Solve quadratic equations with real coefficients that have complex solutions

Note code change. A2.N.CN.B.3 Solve quadratic equations with real coefficients that have complex solutions

Conceptual Category: Algebra

Domain: Seeing Structure in Expressions (A.SSE)

Cluster A: Interpret the structure of expressions

A-SSE.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)).

Note code change.

Example moved to scope and clarification and

the example itself was changed as well.

A2.A.SSE.A.1

Use the structure of an expression to identify ways to rewrite it.

Scope & Clarification:

(i) Tasks are limited to polynomial, rational, or exponential expressions.

(ii) Examples: 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)) In the equation (x² + 2x + 1 + y² = 9), see an opportunity to rewrite the first three terms as (x + 1)² , thus recognizing the equation of a

For A2.A.SSE.A.1 Scope & Clarification:

For example, see 2x⁴ + 3x² - 5 as its factors (x² - 1)

and (2x² + 5) ; 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); see (x² + 4)/(x² + 3) as

((x² + 3) + 1)/ (x² + 3), thus recognizing an opportunity to write it as 1 + 1/(x² + 3).

circle with radius (3) and center (-1, 0). See ((x² + 4) over (x² + 3)) as ((x² + 3) + 1)/ (x² + 3)), thus recognizing

an opportunity to write it as (1 + 1)/ (x² + 3).

Tasks are limited to polynomial, rational, or exponential expressions.

Cluster B: Use expressions in equivalent forms to solve problems.

A-SSE.3 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★

c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Note code changes.

In part c of old note that “transform” was changed to “rewrite”

Example was moved to scope/clarification.

A2.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Use the properties of exponents to rewrite expressions for exponential functions.


(i) Tasks have a real-world context. As described in the

standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and

producing an equivalent form of the expression reveals something about the situation

ii) Tasks are limited to exponential expressions with

rational or real exponents.

For A2.A.SSE.B.2 Scope & Clarification:

For example the expression 1.15t

can be rewritten as ((1.15)1/12)12t

1.01212t to reveal that the approximate equivalent monthly interest rate is 1.2% if the annual

rate is 15%.

i) Tasks have a real-world context. As described in the standard, there

is an interplay between the mathematical structure of the

expression and the structure of the situation such that choosing and

producing an equivalent form of the expression reveals something about

the situation.

ii) Tasks are limited to exponential expressions with rational or real

exponents.

A-SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the

Note Standard Number Change

Derive implies that students will need to create a specific formula given a problem.

A2.A.SSE.B.3

Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context

formula to solve problems. For example, calculate

mortgage payments.★

Students do not need to derive a formula, but need to be able to use the formula.

Added “Know” indicating fluency, the word “sum” included for clarity, and “in context”

added to clarify intent of standard.

Example was deleted.

Domain: Arithmetic with Polynomials and Rational Expressions (A.APR)

Cluster A: Understand the relationship between zeros and factors of polynomials.

A-APR.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)).

Note Code Change

A2.A.APR.A.1

Know and apply the Remainder Theorem: For a polynomial (p(x)) and a number (a), the remainder on division by (x - a) is (p(a)), so (p(a) = 0) if and only if ((x - a)) is a factor of (p(x)).

A-APR.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.

Note Code Change

A2.A.APR.A.2

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.

Cluster B: Use polynomial identities to solve problems.

A-APR.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.

Note the code change.

“Prove” was changed to “use” and the example was changed and moved to

scope/clarification.

A2.A.APR.B.3 Use polynomial identities to describe numerical relationships.


There is no additional scope or clarification information for this standard.

For A2.A.APR.B.3 Scope & Clarification:

For example, compare (31)(29) = (30 + 1) (30 1) = 302 12 with (x + y) (x y) = x2 y2.

There are no assessment limits for this standard. The entire standard is assessed in this course.

Cluster C: Rewrite rational expressions

A-APR.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.

Note Code Change

High schools do not have equal access to computer algebra systems so that is being deleted. This standard can incorporate many other examples of rewriting rational expressions without implying long division.

A2.A.APR.C.4

Rewrite simple rational expressions in different forms.

Domain: Creating Equations ★ (A.CED)

Cluster A: Create equations that describe numbers or relationships

A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Delete the word simple to allow for the

numerator to be a rational function and not just a constant value. Move “include…”

clarification to scope/clarification.

A2.A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems.


(i) Tasks are limited to exponential equations with rational or real exponents and rational functions.

(ii) Tasks have a real-world context.

For A2.A.CED.A.1 Scope & Clarification:

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

Tasks have a real-world context.

No parallel – new standard

This standard is new to Alg 2 and is a continuation from Alg 1 standard

A1.A.CED.A.4

A2.A.CED.A.2

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.


No parallel – New standard scope/clarification

For A2.A.CED.A.2

Compare scope/clarification for Alg 1: Tasks are limited to linear, quadratic,

piecewise, absolute value, and exponential equations with integer exponents.


i) Tasks are limited to square root, cube root, polynomial, rational, and logarithmic functions.

ii) Tasks have a real-world context.

Domain: Reasoning with Equations and Inequalities (A.REI)

Cluster A: Understand solving equations as a process of reasoning and explain the reasoning

A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method

Delete the word simple. It is a matter of opinion in this one as to what simple would

constitute.

A2.A.REI.A.1

Explain each step in solving an 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.


(i) Tasks are limited to simple rational or radical equations).

For A2.A.REI.A.1 Scope & Clarification:

Tasks are limited to square root, cube root, polynomial, rational, and logarithmic functions

A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Delete the word simple to allow for the numerator to be a rational functions and not just a constant value. Students need to be able to recognize extraneous solutions, but giving examples of how they arise is outside

an appropriate scope of this course.

A2.A.REI.A.2

Solve rational and radical equations in one variable, and identify extraneous solutions if they exist.

Cluster B: Solve equations and inequalities in one variable.

A-REI.4 Solve quadratic equations in one variable.

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.

Note code change.

Added “knowing and applying” for standard intent clarification.

A2.A.REI.B.3 Solve quadratic equations and inequalities in one variable. a. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, knowing and applying 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.

Cluster C: Solve systems of equations.

A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables

Note code change Systems of equations in two variables is in the Algebra 1 standards, as well as 8th grade. Specify the problem with three variables. This

A2.A.REI.C.4 Write and solve a system of linear equations in context.

is a more appropriate level for Algebra 2 and context is an important part of the problem.


(i) Tasks are limited to 3x3 systems

For A2.A.REI.C.4 Scope & Clarification: When solving algebraically, tasks are limited to systems of at most three equations and three variables. With graphic solutions, systems are

limited to only two variables.

A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x² + y² = 3

Note code change Circles are not a part of the standards so the intersection should be between a linear and a quadratic. No example is needed. Remove the word simple.

A2.A.REI.C.5 Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Cluster D: Represent and solve equations graphically.

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,

exponential, and logarithmic functions. ★

Note code change.

Successive approximations should be moved to a course beyond

Algebra 2.

“Include…” moved to scope/clarification

A2.A.REI.D.6

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, using technology. ★


(i) Tasks may involve any of the function types mentioned in the standard.

For A2.A.REI.D.6 Scope & Clarification: Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and

logarithmic functions.

Tasks may involve any of the function types mentioned in the standard.

Conceptual Category: Functions

Domain: Interpreting Functions (F.IF)

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

F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the

Moved to Pre-Calculus

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. (i) This standard is Supporting work in Algebra II. This standard should support the Major work in F-BF.2 for coherence.

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the

relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums;

symmetries; end behavior; and periodicity. ★

Note code change.

Trigonometric graphing is being moved to

Pre-Calculus so periodicity is not needed in this standard.

“Key features …” moved to

scope/clarification.

A2.F.IF.A.1

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of

the relationship. ★

Scope & Clarification: (i) Tasks have a real-world context

(ii) Tasks may involve polynomial, exponential, logarithmic, and trigonometric functions. Compare note

(ii) with standard F-IF.7.

The function types listed here are the same as those listed in the Algebra II column for standards F-IF.6 and

F-IF.9).

For A2.F.IF.A.1 Scope & Clarification: Key features include: intercepts; intervals where the

function is increasing, decreasing, positive, or

negative; relative maximums and minimums;

symmetries; end behavior.

(i) Tasks have a real-world context.

(ii) Tasks may involve square root, cube root,

polynomial, exponential, and logarithmic functions.

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a

graph. ★

Note code change.

A2.F.IF.A.2

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. ★

Scope & Clarification: (i) Tasks have a real-world context.

(ii) Tasks may involve polynomial, exponential, logarithmic, and trigonometric functions.

The function types listed here are the same as those listed in the Algebra II column for standards F-IF.4 and

F-IF.9.

For A2.F.IF.A.2 Scope & Clarification: (i) Tasks have a real-world context.

(ii) Tasks may involve polynomial, exponential, and

logarithmic functions

Cluster B: Analyze functions using different representations.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and

using technology for more complicated cases. ★

c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Note code change.

Take out trigonometric functions and items related to it because the graphing will move to

Pre-Calculus

Note: Scope/Clarification has limitations on part a.

A2.F.IF.B.3a: Tasks are limited to square root and cube root functions. The other functions

are assessed in Algebra 1.

A2.F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using

technology. ★

a. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. b. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior. c. Graph exponential and logarithmic functions, showing intercepts and end behavior.

F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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

y = (1.02)ᵗ, y = (0.97)ᵗ , y = (1.01)¹²ᵗ, y =( 1.2)𝑡/10, and classify them as representing exponential growth or decay.

Note code change.

The example given really doesn't accomplish

what is outlined in the meaning of the standard. Revising the example and giving

more appropriate problems will enhance the explanation of the standard. Example moved

to Scope/Clarification

A2.F.IF.B.4 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Know and use the properties of exponents to interpret expressions for exponential functions



For A2.F.IF.B.4 Scope & Clarification: For example, identify percent rate of change in

functions such as y = 2𝑥 , y = (1

2)𝑥 , y = −2𝑥,

y = (1

2)−𝑥


F-IF.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.

Note code change. Take out the specificity of the example so the standard could be used to compare different types of functions as well as similar functions

represented in different ways.

A2.F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Scope & Clarification: For A2.F.IF.B.5 Scope & Clarification:

i) Tasks may involve polynomial, exponential, logarithmic, and trigonometric functions. (The function types listed here are the same as those listed in the Algebra II column for standards F-IF.4 and FIF.6.

Tasks may involve polynomial, exponential, and logarithmic functions.

Domain: Building Functions (F.BF)

Cluster A. Build a function that models a relationship between two quantities. F-BF.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.

Example was changed and moved to Scope/Clarification

A2.F.BF.A.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 F-BF.1a: (i) Tasks have a real-world context

(ii) Tasks may involve linear functions, quadratic functions, and exponential functions).

For A2.F.BF.A.1 Scope & Clarification: For example, given cost and revenue

functions, create a profit function. For A2.F.BF.A.1a

(i) Tasks have a real-world context (ii) Tasks may involve linear functions, quadratic

functions, and exponential functions).

F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

★

“Know” indicates fluency. A2.F.BF.A.2 Know and write arithmetic and geometric sequences with an explicit formula and use them to model

situations. ★

Cluster B: Build new functions from existing functions.

F-BF.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.

Moved “Include …” to Scope/Clarification and simplified to “recognizing” since graphs and expressions are implied and stated in the

standard.

A2.F.BF.B.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.

Scope & Clarification: (i) Tasks may involve polynomial, exponential,

logarithmic, and trigonometric functions

For A2.F.BF.B.3 Scope & Clarification: i) Tasks may involve polynomial, exponential, and

logarithmic functions.

(ii) Tasks may involve recognizing even and odd functions.

The function types listed in note (i) are the same as those listed in the Algebra II column for standards

F-IF.4, F-IF.6, and F-IF.9.

ii) Tasks may involve recognizing even and odd functions.

F-BF.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) = 2x³ or f(x) = (x + 1)/(x – 1) for x ≠ 1.

The portion of the standard saying f(x) = c is a confusing part of the standard. Reword a, but keep it to retain the numbering and labeling

features of the standards. To find an inverse it would need to be one-to-one so include that

in the standard.

A2.F.BF.B.4 Find inverse functions. a. Find the inverse function when a given function is one-to-one.

Domain: Linear, Quadratic, and Exponential Models ★ (F.LE)

Cluster A: Construct and compare linear quadratic, and exponential models and solve problems. F-LE.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).

Note code change. “table” was moved into standard as opposed to parenthetical statement. Scope/Clarification limitations removed:

(i) Tasks will include solving multi-step problems by constructing linear and

exponential functions).

A2.F.LE.A.1 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.

F-LE.4 For exponential models, express as a logarithm the solution to 𝑎𝑏𝑐𝑡 = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Note code change.

A2.F.LE.A.2 For exponential models, express as a logarithm the solution to 𝑎𝑏𝑐𝑡 = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Cluster B: Interpret expressions for functions in terms of the situation they model. F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Note code change.

Parameters need to be defined. An example added for clarification in Scope/Clarification.

A2.F.LE.A.2 Interpret the parameters in a linear or exponential function in terms of a context.

Scope & Clarification: (i) Tasks have a real-world context.

(ii) Tasks are limited to exponential functions with domains not in the integers

For A2.F.LE.A.2 Scope & Clarification:

For example, the equation y = 5000 (1.06)𝑥 models the rising population of a city with 5000 residents

when the annual growth rate is 6 percent. What will be the effect on the equation if the city's growth rate

was 7 percent instead of 6 percent?

Domain: Trigonometric Functions: (F.TF) Cluster A: Extend the domain of trigonometric functions using the unit circle. F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Expanded the standard to have parts a and b to clarify intent and to emphasize unit circle

usage.

Scope/Clarification added: Commonly recognized angles include all multiples of nπ/6 and nπ/4 where n is an

integer.

A2.F.TF.A.1 Understand and use radian measure of an angle. a. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. b. Use the unit circle to find sin ϴ cos ϴ, and tan ϴ when ϴ is a commonly recognized angle between 0 and 2π.

F-TF.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.

Extends A2.F.TF.A.1.

No change.

A2.F.TF.A.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.

F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Moved to Precalculus

Cluster B: Prove and apply trigonometric identities. F-TF.8 Prove the Pythagorean identity \(sin^2(\Theta) + cos^2(\Theta) = 1\) and use it to find \(sin(\Theta), cos(\Theta)\), or \(tan(\Theta)\) given \(sin(\Theta), cos(\Theta)\), or \(tan(\Theta)\) and the quadrant of the angle.

This standard has been rewritten to create an overarching standard with two parts.

A2.F.TF.B.3 Know and use trigonometric identities to find values of trig functions. a. Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin ϴ, cos ϴ, and tan ϴ to evaluate the trigonometric functions. b. Given the quadrant of the angle, use the identity sin2ϴ + cos2ϴ = 1 to find sin ϴ given cos ϴ, or vice versa.

Conceptual Category: Geometry

Domain: Expressing Geometric Properties with Equations (G.GPE) Cluster A: Translate between the geometric description and the equation for a conic section.

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

Moved to Precalculus.

Conceptual Category: Statistics and Probability

Domain: Interpreting Categorical and Quantitative Data (S.ID)

Cluster A: Summarize, represent, and interpret data on a single count or measurement variable.

S-ID.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

Note code change.

This standard will not include the use of z-scores. It is only to include the Empirical Rule.

No calculators or estimates of areas will be used.

A2.S.ID.A.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.

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

S-ID.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, quadratic, and exponential models

Note code change.

Moved “Use given…” to scope/clarification.

A2.S.ID.B.2 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.


i) Tasks have a real-world context.

ii) Tasks are limited to exponential functions with domains not in the integers and trigonometric functions

For A2.S.ID.B.2 Scope & Clarification: Use given functions or choose a function suggested

by the context. Emphasize linear, quadratic, and exponential models.

i) Tasks have a real-world context.

ii) Tasks are limited to exponential functions with

domains not in the integers.

Domain: Making Inferences and Justifying Conclusions (S.IC) Cluster A: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Removed. Covered in Statistics.

S-IC.2 Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin

Removed. Covered in Statistics

falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Note code change.

No change to standard but added example in scope/clarification

A2.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Scope and Clarification:


For A2.S.IC.A.1 Scope and Clarification: For example, in a given situation, is it more

appropriate to use a sample survey, an experiment, or an observational study? Explain how

randomization affects the bias in a study.


S-IC.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

Note code change.

Some of the strict statistics vocabulary is being moved to a statistics class to more fully

develop the concepts. A more general introduction will be kept in Algebra 2.

A2.S.IC.A.2 Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.

S-IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Moved to Statistics

S-IC.6 Evaluate reports based on data.

Dropped.

Domain: Conditional Probability and the Rules of Probability (S.CP) Cluster A: Understand independence and conditional probability and use them to interpret data. S.CP.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").

No Change. A2.S.CP.A.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”).

S-CP.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.

No Change A2.S.CP.A.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.

S-CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B

No Change A2.S.CP.A.3 Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret

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.

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.

S-CP.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.

Moved to Statistics Course

S-CP.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.

Note code change.

Moved example to Scope/Clarification, otherwise no change.

A2.S.CP.A.4 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Scope and Clarification

There is no additional scope or clarification information for this standard

For A2.S.CP.A.4 Scope and Clarification 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. There are no assessment limits for this standard. The entire standard is assessed in this course.

Cluster B: Use the rules of probability to compute probabilities of compound events in a uniform probability model. S-CP.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.

Note code change. A2.S.CP.B.5 Find the conditional probability of A given B as the fraction of B belong to A and interpret the answer in terms of the model.



For A2.S.CB.B.5

Added example to scope/clarification

Scope and Clarification For example, a teacher gave two exams. 75 percent passed the first quiz and 25 percent passed both. What percent who passed the first quiz also passed the second quiz? There are no assessment limits for this standard. The entire standard is assessed in this course.

S-CP.7 Note code change. A2.S.CP.B.6

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.

Added example to scope/clarification

Know and 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.



For A2.S.CP.B.6 Scope and Clarification For example, in a math class of 32 students, 14 are boys and 18 are girls. On a unit test 6 boys and 5 girls made an A. If a student is chosen at random from a class, what is the probability of choosing a girl or an A student? There are no assessment limits for this standard. The entire standard is assessed in this course.

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