Mathletics Common Core State Standards Alignment · Expanding Binomial Irrational Numbers Under...

Mathletics Common CoreState Standards Alignment

Algebra I - Integrated Math III

Supported by independent evidence-based research and practice

CCSS ready

Powerfulreporting

Studentcentered

V.13012016

CCSS StandardsAlignment with Mathletics

© 3P Learning1

Mathletics and the CCSS Standards

The team at Mathletics is committed to providing a resource that is powerful, targeted, and, most importantly, relevant to all students.

Mathletics includes well over 1,200 individual adaptive practice activities. Our team of educational publishers has created a course that specifically follows the Common Core State Standards. You can be assured that students have access to relevant and targeted content.

Courses consist of topics based on domains, clusters, and standards. Activities within each topic provide adaptive practice and each topic has a pre and post assessment. What’s more, Mathletics contains an extensive library of eBook—for use on screen or as a printable resource—that are also mapped to the requirements of the Common Core.

This document outlines this mapping and acts as a useful guide when using Mathletics in your school.

3P Learning USA

Engage Diagnose Assess Report Fluency MobileTarget


© 3P Learning2

CCSS Algebra I

Domain Cluster Standard Description Topic Activities eBooks

Conceptual Category: Number and Quantity

The Real Number System

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.

Exponents

Exponent Laws and AlgebraExponent Notation and AlgebraSimplifying with Exponent Laws 2 Fractional ExponentsIrrational Number to Exponent FormZero Exponent and Algebra

Radicals and ExponentsExponents



N.RN.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Exponents

Fractional ExponentsIrrational Number to Exponent FormZero Exponents and AlgebraSimplifying with Exponent Laws 1Multiplication with ExponentsExponent Laws and AlgebraExponent Laws with Brackets

Grade 8 Pythagoras' Theorem


Use properties of rational and irrational numbers.

N.RN.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.

Irrational Numbers

Adding and SubtractingIrrational NumbersMultiplying Irrational NumbersExpanding BinomialIrrational Numbers

Under review

Quantities

Reason quantitatively and use units to solve problems.

N.Q.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.

Under review Under Consideration Under review

© 3P Learning 3

Alignment with MathleticsCCSS Standards

CCSS Algebra I



Quantities


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


Quantities


N.Q.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Quantities and Solving Linear Equations

Error in MeasurementPercentage Error Decimals

Conceptual Category: Algebra

Seeing Structure in Expressions

Interpret the structure of expressions.

A.SSE.1.a

Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients.

Linear Expressions and Equations

Gradients for Real Write an Equation: Word Problems

Quadratic Equations and Inequalities

Vertex of a Parabola

Exponents

Compound InterestCompound Interest by FormulaDepreciationDeclining Balance Depreciation

Depreciation Interest



A.SSE.1.b

Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and afactor not depending on P.


The DiscriminantConstructing Formulae Under review



A.SSE.2

Use the structure of an expression to identify ways to rewrite it. For example, seex4 – y4 as (x2)2 – (y2)2, thusrecognizing it as a difference of squares that can be factoredas (x2 – y2)(x2 + y2).


Factoring Quadratics 1Factoring Quadratics 2 Grouping in Pairs

Expanding and Factorizing


© 3P Learning4

CCSS Algebra I




Write expressions in equivalent forms to solve problems.

A.SSE.3.a

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines.


Highest CommonAlgebraic FactorFactoring Quadratics 1Factoring Quadratics 2Grouping in Pairs

Under review



A.SSE.3.b

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.


Completing the SquareCompleting the Square 2Vertex of a Parabola

Under review



A.SSE.3.c

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.Use the properties of exponents to transform expressions for exponential functions. For example theexpression 1.15t can berewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximateequivalent monthly interestrate if the annual rate is 15%.


Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomials.

A.APR.1

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

Add, Subtract, and Multiply Polynomials

Like Terms: Add and SubtractSimplifying ExpressionsAlgebraic Fractions 1Algebraic Fractions 2Algebraic MultiplicationExpand then SimplifyExpanding Binomial ProductsSpecial Binomial Products


© 3P Learning 5


CCSS Algebra I



Creating Equations

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.


Writing Algebraic ExpressionsEquations to Solve ProblemsWriting EquationsWrite an Equation: Word Problems


Constructing Formulae

Quadratic Equations

DepreciationInterest

Creating Equations


A.CED.2

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


Equation from Point and GradientEquation from Two PointsGraphing from a Table of ValuesGraphing from a Table of Values 2Which Straight Line?y=axDetermining a Rule for a LineEquation of a Line 1Modeling Linear Relationships

Linear RelationshipsExponential and Power Graphs

Exponents Graphing Exponentials


Vertex of a Parabola Graphing Parabolas

Creating Equations


A.CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, representinequalities describingnutritional and costconstraints on combinationsof different foods.



© 3P Learning6

CCSS Algebra I



Creating Equations


A.CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.


Changing the SubjectLinear Relationships Depreciation

Reasoning with Equations and Inequalities

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.


Find the MistakeAddition PropertiesMultiplication PropertiesUsing the Distributive Property

Equations QuadraticEquations

© 3P Learning 7


CCSS Algebra I




Solve equations and inequalities in one variable.

A.REI.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Quantities and SolvingLinear Equations

Recognising Like TermsChecking Solutions Solving Simple EquationsSolving More EquationsSolve Two-Step EquationsEquations with Grouping SymbolsSolve Multi-Step EquationsEquations: Variables, Both SidesEquations with DecimalsEquations with FractionsSimple SubstitutionSimple Substitution 3Real Formulae

EquationsEquations and Inequalities


Equations to Solve ProblemsWriting EquationsWrite an Equation: Word Problems


Linear Inequalities

Solve One-Step Inequalities 1Solve One-Step Inequalities 2Solve Two-Step Inequalities Solving Inequalities 1Solving Inequalities 2Solving Inequalities 3Graphing Inequalities 1Graphing Inequalities 2Graphing Inequalities 3

InequalitiesEquations and Inequalities



A.REI.4.a.

Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.


Quadratic Equations 1Quadratic Equations 2Roots of the Quadratic

Quadratic Equations


© 3P Learning8

CCSS Algebra I





A.REI.4.b

Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.


Quadratic Equations 1Quadratic Equations 2Quadratic FormulaThe DiscriminantGrouping in Pairs Quadratic Inequalities

Equations and InequalitiesFactorizingQuadratic Equations


Solve systems of equations. A.REI.5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Under review Under ConsiderationEquations and Inequalities



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

Systems of Linear Equations

Solve Systems by GraphingAre they Parallel?Simultaneous Linear EquationsBreakeven PointSimultaneous Equations 1Simultaneous Equations 2

Equations and Inequalities



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.

Linear and Quadratic Systems

Intersection: Line & ParabolaSimultaneous Equations 3Intersection: Line & Circle

Quadratic Equations


Represent and solve equations and inequalities graphically.

A.REI.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).


Reading Values from a Line Under review

© 3P Learning 9


CCSS Algebra I





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.

Under review UnderConsideration Under review



A.REI.12

Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities

Linear RegionsIntersecting Linear Regions

Under review

Conceptual Category: Functions

Interpreting Functions

Understand the concept of a function and use function notation.

F.IF.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).

Functions

Function Rules and TablesHorizontal and Vertical Lines

Functions



F.IF.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Functions

Function Notation 1Function Notation 2Function Notation 3

Functions


© 3P Learning10

CCSS Algebra I





F.IF.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.

Arithmetic and Geometric Sequences

Table of ValuesTerms: Arithmetic ProgressionsTerms: Geometric Progressions 1Terms: Geometric Progressions 2

Sequences & Series: ArithmeticSequences & Series: Geometric


Interpret functions that arise in applications in terms of a context.

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.


InterceptsSlope of a Liney=axGradients for Real

Linear Relationships


Vertex of a ParabolaGraphing ParabolasParabolas and RectanglesParabolas and Marbles

Parabolas



F.IF.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Under review Under Consideration Functions


Interpret functions that arise in applications in terms of the context.

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.


Equation from Two Points Under review

© 3P Learning 11


CCSS Algebra I




Analyze functions using different representations.

F.IF.7.a

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima.


Graphing from a Table of ValuesGraphing from a Table of Values 2 Which Straight Line?



Graphing Parabolas Parabolas



F.IF.7.b

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value, Step, and Piecewise

Absolute Value ExpressionsAbsolute Value EquationsAbsolute Value GraphsStep GraphsPiecemeal Functions

Under review



F.IF.7.e

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.


Exponential and Power Graphs



F.IF.8.a

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.


Factoring Quadratics 1Factoring Quadratics 2Grouping in PairsCompleting the SquareCompleting the Square 2Vertex of a Parabola

Factorizing ParabolasQuadratic Equations


© 3P Learning12

CCSS Algebra I





F.IF.8.b

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

Exponents Multiplication with Exponents Under review



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.

Under review Under Consideration


Building Functions

Build a function that models a relationship between two quantities.

F.BF.1.a

Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.


Modeling Linear Relationships Under review

Exponents

Compound InterestCompound Interest by FormulaDepreciationDeclining Balance Depreciation



Constructing Formulae Parabolas

© 3P Learning 13


CCSS Algebra I



Building Functions


F.BF.1.b

Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.


Building 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.


Table of ValuesTerms: Arithmetic ProgressionsTerms: Geometric Progressions 1Terms: Geometric Progressions 2


Building Functions

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 giventhe graphs. Experimentwith cases and illustrate anexplanation of the effects onthe graph using technology.Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Under review UnderConsideration

Exponential and PowerGraphs Functions Parabolas

Building Functions


F.BF.4.a

Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x + 1)/(x – 1) for x ≠ 1.

Functions Inverse Functions Functions


© 3P Learning14

CCSS Algebra I



Linear, Quadratic, and Exponential Models

Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.1.a

Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.





F.LE.1.b

Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Functions What Type of Function?

Straight LinesSequences & Series: Arithmetic



F.LE.1.c

Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Functions What Type of Function?

Depreciation InterestSequences & Series: Geometric



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).

Functions Find the Function Rule

Sequences & Series: Arithmetic


Equations to Solve ProblemsWriting EquationsWrite an Equation: Word ProblemsEquation from Two PointsEquation of a Line 1Modeling Linear Relationships


Terms: Geometric Progressions 2


© 3P Learning 15


CCSS Algebra I





F.LE.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.



Interpret expressions for functions in terms of the situation they model.

F.LE.5Interpret the parameters in a linear or exponential function in terms of a context.


Gradients for Real Under review

Conceptual Category: Statistics and Probability

Interpreting Categorical and Quantitative Data

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

S.ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

Descriptive Statistics

Dot Plots Histograms Box-and-Whisker Plots 1Box-and-Whisker Plots 2

DataInterpreting Data



S.ID.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.


Data Terms MeanMean 1MedianMedian 1ModeCalculating InterquartileRange CalculatingStandard DeviationInterpreting Standard Deviation

DataInterpreting Data



S.ID.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Descriptive Statistics Skewness of Data Interpreting

Data


© 3P Learning16

CCSS Algebra I




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

S.ID.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.

Under review

Under Consideration Under review



S.ID.6.a

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

Under review




S.ID.6.b

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Informally assess the fit of a function by plotting and analyzing residuals.

Under review




S.ID.6.cFit a linear function for a scatter plot that suggests a linear association.


Data Analysis: Scatter Plots Scatter Plots

Under review


Interpret linear models. S.ID.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Under review




Compute (using technology) and interpret the correlation coefficient of a linear fit.

Descriptive Statistics Correlation Under review


Interpret linear models. S.ID.9 Distinguish between correlation

and causationUnder review


© 3P Learning 17


CCSS Geometry


Conceptual Category: Geometry

CongruenceExperiment with transformations in the plane.

G.CO.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.

Line and Angle Basics

What Line Am I?Classifying AnglesLabelling AnglesAngles in a Revolution

Under review


G.CO.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).

Rigid Transformations

TransformationsTransformations: Coordinate PlaneRotations: Coordinate Plane

Under review


G.CO.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.


Symmetry or Not 1Symmetry or Not?Rotational Symmetry

Under review


G.CO.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.



G.CO.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.



© 3P Learning18

CCSS Geometry



Congruence

Understand congruence in terms of rigid motions.

G.CO.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.


Congruent Figures (Grid)Congruent Figures (Dots)

Under review

Congruence


G.CO.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 are congruent.


Congruent Triangles

Similarity and Congruence

Congruence


G.CO.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Under review Under Consideration


CongruenceProve Geometric Theorems.

G.CO.9

Prove theorems about lines and angles. 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.

Geometric Theorems

Parallel Lines Angles and Parallel Lines

Under review

CongruenceProve Geometric Theorems.

G.CO.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; 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.

Geometric Theorems

Angle Measures in a TrianglePlane Figure TheoremsRatio of Intercepts

Polygons and Angles

© 3P Learning 19


CCSS Geometry



Congruence Prove geometric theorems. G.CO.11

Prove theorems about parallelograms. 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.

Geometric Theorems

Plane Figure Theorems Under review

Congruence Make geometric constructions. G.CO.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.

Under review Under Consideration Constructions


Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Under review Under Consideration Constructions

Similarity, Right Triangles, and Trigonometry

Understand similarity in terms of similarity transformations.

G.SRT.1.a

Verify experimentally the properties of dilations given by a center and a scale factor: 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.



© 3P Learning20

CCSS Geometry





G.SRT.1.b

Verify experimentally the properties of dilations given by a center and a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

SimilarityScale MeasurementScale Factor

Under review



G.SRT.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.

Similarity Similar Figures Similar Figures 1




G.SRT.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Similarity Similarity ProofsSimilarity and Congruence


Prove theorems involving similarity.

G.SRT.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.

Geometric Theorems

Ratio of Intercepts Under review



G.SRT.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CongruenceCongruent Figures: Find Values


Similarity

Using Similar TrianglesUsing Similar Triangles 1


© 3P Learning 21


CCSS Geometry




Define trigonometric ratios and solve problems involving right triangles.

G.SRT.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.

Trigonometry

Exact TrigonometricRatiosSin ACos ATan A

Trigonometry



G.SRT.7

Explain and use the relationship between the sine and cosine of complementary angles.


Trigonometric Relationships



G.SRT.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Trigonometry

Pythagorean Theorem Find Unknown SidesFind Unknown AnglesElevation and DepressionTrigonometry Problems 2

Pythagorean TheoremTrigonometry


Apply trigonometry to general triangles.

G.SRT.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.

TrigonometryArea Rule 1Area Rule 2Area Problems

Non Right Angled Triangles



G.SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.

TrigonometrySine Rule 1Cosine Rule 1Cosine Rule 2




G.SRT.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).



CirclesUnderstand and apply theorems about circles.

G.C.1 Prove that all circles are similar. Under review Under

Consideration Under review


© 3P Learning22

CCSS Geometry




G.C.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 radiusintersects the circle.

Circles

Circle Terms Circle TheoremTangents and Secants

Tangents and SecantsChords and Angles


G.C.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.



G.C.4Construct a tangent line from a point outside a given circle to the circle.

Circles Intersection: Line & Circle Constructions

CirclesFind arc lengths and areas of sectors of circles.

G.C.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.

Circles

Converting Radians and DegreesPerimeter and CirclesArc LengthLength of an ArcArea of a Sector (degrees and radians)

Perimeter and Area

Expressing Geometric Properties with Equations

Translate between the geometric description and the equation for a conic section.

G.GPE.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.

CirclesCentre and Radius 1Centre and Radius 2Graphing Circles

Circle Graphs



G.GPE.2Derive the equation of a parabola given a focus and directrix.

Equations of Parabolas

Vertex of a ParabolaGraphing Parabolas Focus and Directrix 1Focus and Directrix 2Focus and Directrix 3Focus and Directrix 4

Under review

© 3P Learning 23


CCSS Geometry




Use coordinates to prove simple geometric theorems algebraically.

G.GPE.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).

Connecting Geometry and Algebra

Coordinate Methods inGeometryPerpendicular Distance 1Perpendicular Distance 2

Coordinate GeometryCircle Graphs

Circles Intersection: Line & Circle Circle Graphs



G.GPE.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).


Are they Parallel?Are they Perpendicular?Equation of a Line 3Equation from Point and Gradient

Linear Relationships Straight Lines



G.GPE.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.


Midpoint by Formula

Coordinate Geometry



G.GPE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.


Distance Between Two Points

Coordinate Geometry

Geometric Measurement and Dimension

Explain volume formulas and use them to solve problems.

G.GMD.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.



© 3P Learning24

CCSS Geometry





G.GMD.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Three-Dimensional Figures

Volume: Triangular PrismsVolume: Prisms Volume: CylindersVolume PyramidsWhat Pyramid am I?Volume: ConesVolume: SpheresVolume Composite FiguresVolume: Rearrange Formula

Measuring Solids


Visualize relationships between two- dimensional and three-dimensional objects.

G.GMD.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.


Relate Shapes and SolidsNets

Under review

Modeling with Geometry

Apply geometric concepts in modeling situations.

G.MG.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).


Right and Oblique ObjectsMatch the Solid 2

Measuring Solids



G.MG.2

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




G.MG.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).

Trigonometry Trigonometry Problems 2 Under review

© 3P Learning 25


CCSS Geometry



Conditional Probability and the Rules of Probability

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”).

Probability

Complementary Events Venn Diagrams Probability - 'And' and 'Or'

Probability



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.

Under review UnderConsideration Probability



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 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 randomsample of students in yourschool on their favorite subjectamong math, science, andEnglish. Estimate the probabilitythat a randomly selectedstudent from your school will favor science given that thestudent is in tenth grade. Dothe same for other subjects andcompare the results.

ProbabilityTwo-way Table Probability Probability Tables

Probability


© 3P Learning26

CCSS Geometry





S.CP.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, comparethe chance of havinglung cancer if you are asmoker with the chanceof being a smoker if youhave lung cancer.



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.




S.CP.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.

Probability Find the Probability Under review



S.CP.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.

Probability

Probability With ReplacementProbability Without Replacement

Under review



S.CP.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

Probability

Counting Techniques 1Counting Techniques 2Tree Diagrams

Under review

Using Probability to Make Decisions

Use probability to evaluate outcomes of decisions.

S.MD.6

Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability Fair Games Under review

© 3P Learning 27


CCSS Geometry





S.MD.7

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



© 3P Learning28

CCSS Algebra II



The Complex Number System

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.

Complex Numbers

Introduction toComplex Numbers Under review



N.CN.2

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

Complex Numbers

Powers of iAdding ComplexNumbers Subtracting ComplexNumbersComplex Multiplication

Under review


Use complex numbers in polynomial identities and equations.

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




N.CN.8

Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).




N.CN.9

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.





A.SSE.1.a


Modeling with Functions

Gradients for RealExponential Growth and Decay

Sketching Polynomials



A.SSE.1.b

Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P.

Solving Higher Order Equations

Factoring ExpressionsEquations Reducible to Quadratics

Geometric Series in Finance

© 3P Learning 29


CCSS Algebra II





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).


Equations Reducible to Quadratics Factorizing

Polynomial Arithmetic

Polynomial Long DivisionSimplifying Binomial Expressions

Factorizing



A.SSE.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.

Sequences and Series

Limiting SumTerms: Geometric Progressions 1Terms: Geometric Progressions 2 Sum: Geometric Progressions

Sequences & Series: GeometricGeometric Series and Loan RepaymentsGeometric Series in Finance



A.APR.1



Like Terms: Add, SubtractAlgebraic MultiplicationMultiplication with ExponentsDividing ExpressionsAlgebraic Fractions 1Indirect VariationSpecial Binomial ProductsExpanding BracketsExpand then SimplifyExpanding Binomial Products

Polynomials EquationsExpanding and FactorizingSimplifying AlgebraBinomials and Pascal's Triangle


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).


Polynomial Factor TheoremMore Substitution in FormulaeRationalising the DenominatorRationalising and Binomials

Polynomials


Understand the relationship between zeros and factors of polynomials.

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.


Factoring ExpressionsEquations Reducible to QuadraticsPolynomial Factor Theorem Graphing Cubics

Factorizing PolynomialsSketching Polynomials


© 3P Learning30

CCSS Algebra II




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.


Equations Reducible to Quadratics

Factorizing



A.APR.5

Know and apply the Binomial Theorem for the expansion of (x + y)n 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.

Under review

Under Consideration

The Binomial TheoremBinomials and Pascal's Triangle


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.



Polynomials



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.

Rational Equations

Algebraic Fractions 2Algebraic Fractions 3Factoring and Fractions 1Factoring and Fractions 2

Factorizing

Creating Equations


A.CED.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arisingfrom linear and quadratic functions,and simple rational and exponentialfunctions.


Write an Equation: Word Problems

Under review

Creating Equations


A.CED.2



y=axFind the Function RuleModeling Linear RelationshipsLinear ModellingParabolas and MarblesParabolas and Rectangles

Under review

© 3P Learning 31


CCSS Algebra II



Creating Equations


A.CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example,represent inequalities describingnutritional and cost constraints oncombinations of different foods.

Under review


Creating Equations


A.CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

Inverse Functions Inverse Functions Under review

Exponents and Logarithms

Change of Base Logarithms

Radical Equations

Surface Area: Rearrange FormulaVolume: Rearrange FormulaRearranging the Equation

Under review



A.REI.2

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

Radical Equations

Equations with Square RootsEquations with Cube RootsMore Substitution in FormulaeRationalising the DenominatorRationalising and Binomials

Under review



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.


Solve Systems by Graphing Under review

Rational Equations

Graphing Hyperbolas Under review


© 3P Learning32

CCSS Algebra II





F.IF.4



Gradients for RealParabolas and MarblesParabolas and Rectangles




F.IF.5



Perpendicular Distance 1Absolute Value GraphsConversion GraphsWhat Type of Function? DomainDomain and Range

Functions



F.IF.6





F.IF.7.b


Inverse Functions

Graphing Inverse FunctionsPiecemeal Functions

Under review

© 3P Learning 33


CCSS Algebra II





F.IF.7.c

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.


Graphing Cubics

Exponential and PowerGraphs Sketching Polynomials



F.IF.7.e


Trigonometric Functions

Sine and Cosine CurvesTrig Graphs in RadiansGraph Inverse Trig Functions



Graphing ExponentialsExponential or Log Graph?

Logarithms SimpleNonlinear Graphs



F.IF.8.a







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 ofone quadratic function andan algebraic expression foranother, say which has the largermaximum.



© 3P Learning34

CCSS Algebra II



Building Functions


F.BF.1.a



Gradients for RealWrite an Equation: Word Problems

Under review

Building Functions


F.BF.1.b



Building 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.


Odd and Even Functions

Exponential and Power GraphsFunctions Sketching Polynomials

Building Functions


F.BF.4.a

Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x + 1)/(x – 1) for x ≠ 1.

Inverse Functions Inverse Functions Under review



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.


Log LawsEquations with LogsLog Base 'e'

Logarithms

© 3P Learning 35


CCSS Algebra II




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.


Converting Radians and DegreesUnit Circle Reductions

Under review



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.


Sign of the AngleUnit Circle ReductionsTrigonometric RelationshipsTrigonometric InterceptsInverse Trigonometric Functions



Model periodic phenomena with trigonometric functions.

F.TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.


Period and Amplitude Under review


Prove and apply trigonometric identities.

F.FT.8

Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.


Rationalising the DenominatorTrig Equations 1Trig Equations 2Trig Equations 3Trig Equations 4

Under review




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.

Collecting and Analyzing Data

Normal DistributionCalculating z-scoresComparingz-scoresEquivalentz-scores

Under review


© 3P Learning36

CCSS Algebra II



Making Inferences and Justifying Conclusions

Understand and evaluate random processes underlying statistical experiments.

S.IC.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Collectingand AnalyzingData

Capture Recapture Technique Probability TablesTwo-way Table Probability

Under review



S.IC.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?



Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

S.IC.3

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




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.




S.IC.5

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




S.IC.6 Evaluate reports based on data. Under review Under

Consideration Under review

© 3P Learning 37


CCSS Algebra II





S.MD.6



Fair Games Under review



S.MD.7




© 3P Learning38

Integrated Math I



Quantities


N.Q.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.

Under review Under review Under review

Quantities


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


Quantities


N.Q.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Number and Quantity

Error in MeasurementPercentage Error

Decimals




A.SSE.1.a


Writing and Graphing Linear Equations

Gradients for RealWrite an Equation: Word Problems

Under review



A.SSE.1.a


Exponential Equations and Functions

Compound Interest by FormulaDepreciation DecliningBalance Depreciation




A.SSE.1.b



Compound Interest by FormulaDepreciation Declining Balance Depreciation


© 3P Learning 39


Integrated Math I



Creating Equations


A.CED.1



Writing Algebraic ExpressionsEquations to Solve ProblemsWriting EquationsWrite an Equation: Word Problems

Under review

Creating Equations


A.CED.1





Creating Equations


A.CED.2



Equation from Point and GradientEquation from Two Pointsy=axDetermining a Rule for a LineModeling Linear Relationships


Creating Equations


A.CED.2



Which Straight Line?Equation of a Line 1

Straight Lines

Creating Equations


A.CED.2



Graphing Exponentials Under review

Creating Equations


A.CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.



© 3P Learning40

Integrated Math I



Creating Equations


A.CED.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V=IR to highlight resistance R.

Number and Quantity Changing the Subject

Linear Relationships Depreciation



A.REI.1


Solving Linear Equations and Systems

Find the MistakeAddition PropertiesMultiplication PropertiesUsing the Distributive Property

Equations



A.REI.1



Exponent Laws and AlgebraExponent Laws with Brackets

Exponents



A.REI.3



Solving Simple EquationsSolving More EquationsSolve Two-Step EquationsEquations with Grouping SymbolsSolve Multi-Step EquationsEquations: Variables, Both SidesEquations with DecimalsEquations with Fractions


© 3P Learning 41


Integrated Math I





A.REI.3



Equations to Solve ProblemsWriting EquationsWrite an Equation: Word Problems




A.REI.3


Linear Inequalities

Solve One-Step Inequalities 1Solve One-Step Inequalities 2Solve Two-Step Inequalities Solving Inequalities 1Solving Inequalities 2Solving Inequalities 3Graphing Inequalities 1Graphing Inequalities 2Graphing Inequalities 3

InequalitiesEquations and Inequalities



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.

Under review Under reviewEquations and Inequalities



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


Solve Systems by GraphingSimultaneous Linear EquationsBreakeven PointSimultaneous Equations 1Simultaneous Equations 2

Equations and Inequalities



A.REI.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).


Reading Values from a Line Under review


© 3P Learning42

Integrated Math I





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.




A.REI.12

Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities

Linear Regions Intersecting Linear Regions

Under review




F.IF.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).

Functions and Sequences

Function Rules and Tables Functions



F.IF.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.


Function Notation 1Function Notation 2Function Notation 3

Functions

© 3P Learning 43


Integrated Math I





F.IF.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.


Terms: Arithmetic ProgressionsTerms: Geometric Progressions 1Terms: Geometric Progressions 2




F.IF.4



Intercepts Slope of a Liney=axGradients for Real




F.IF.5


Under review Under review Functions



F.IF.6





© 3P Learning44

Integrated Math I





F.IF.7.a



Which Straight Line?




F.IF.7.e



Graphing Exponentials




F.IF.9


Under review Under review


Building Functions


F.BF.1.a



Modeling Linear Relationships

Under review

Building Functions


F.BF.1.a



Compound InterestCompound Interest by FormulaDepreciation DecliningBalance Depreciation


© 3P Learning 45


Integrated Math I



Building Functions


F.BF.1.b



Building 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.


Table of Values Terms: Arithmetic ProgressionsTerms: Geometric Progressions 1Terms: Geometric Progressions 2Linear Expression for the Nth Term


Building 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 thegraphs. Experiment with casesand illustrate an explanationof the effects on the graphusing technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.


Vertical and horizontal shift

Exponential and PowerGraphs Functions



F.LE.1.a

Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.




© 3P Learning46

Integrated Math I





F.LE.1.b

Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.


Terms: Arithmetic Progressions

Straight LinesSequences & Series: Arithmetic



F.LE.1.c

Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


Terms: Geometric Progressions 1Terms: Geometric Progressions 2




F.LE.2



Find the Function Rule

Sequences & Series: Arithmetic



F.LE.2



Equations to Solve Problems WritingEquations Write an Equation: Word ProblemsEquation from Two PointsEquation of a Line 1Modeling Linear Relationships

Under review



F.LE.2



Terms: Geometric Progressions 2


© 3P Learning 47


Integrated Math I





F.LE.3




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.


Gradients for Real Under review



G.CO.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.

Line and Angle Basics

What Line Am I?Classifying AnglesLabelling Angles Angles in a Revolution

Under review


G.CO.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).


TransformationsTransformations: Coordinate PlaneRotations: Coordinate Plane

Under review


G.CO.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.


Symmetry or Not?Rotational Symmetry

Under review


© 3P Learning48

Integrated Math I




G.CO.4

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.



G.CO.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.


Congruence


G.CO.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.


Congruent Figures (Grid)Congruent Figures (Dots)

Under review

Congruence


G.CO.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 are congruent.


Congruent Triangles


Congruence


G.CO.8

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Under review Under reviewSimilarity and Congruence

© 3P Learning 49


Integrated Math I




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; bisectinga segment; bisectingan angle; constructingperpendicular lines, includingthe perpendicular bisectorof a line segment; andconstructing a line parallel toa given line through a pointnot on the line.

Under review Under review Constructions


Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.




G.GPE.4

Use coordinates to prove simple geometric theorems algebraically. For example,prove or disprove that a figuredefined by four given pointsin the coordinate plane is arectangle; prove or disprovethat the point (1, √3) lies onthe circle centered at theorigin and containing thepoint (0, 2).


Coordinate Methods in GeometryPerpendicular Distance 1Perpendicular Distance 2

Coordinate Geometry



G.GPE.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).


Are they Parallel?Are they Perpendicular?Perpendicular and Parallel LinesEquation of a Line 3

Linear Relationships Straight Lines



G.GPE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.


Distance Between Two Points

Coordinate Geometry


© 3P Learning50

Integrated Math I




Summarize, represent, and interpret data on a single count or measurement variable

S.ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).


Dot Plots Histograms Box-and-Whisker Plots 1Box-and-Whisker Plots 2

Data Interpreting Data



S.ID.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.


MeanMean 1MedianMedian 1ModeCalculating Interquartile RangeCalculating Standard DeviationInterpreting Standard Deviation

Data Interpreting Data



S.ID.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).


Skewness of Data

Interpreting Data


Summarize, represent, and interpret data on two categorical and quantitative variables

S.ID.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.


© 3P Learning 51


Integrated Math I





S.ID.6.a

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.




S.ID.6.b

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Informally assess the fit of a function by plotting and analyzing residuals.




S.ID.6.c

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a linear function for a scatter plot that suggests a linear association.

Descriptive Statistics Scatter Plots Under review



Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.




Compute (using technology) and interpret the correlation coefficient of a linear fit.

Descriptive Statistics Correlation Under review


Interpret linear models. S.ID.9 Distinguish between

correlation and causation. Under review Under review Under review


© 3P Learning52

Integrated Math II





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.

Exponents

Fractional ExponentsIrrational Number to Exponent FormZero Exponents and Algebra

Radicals and ExponentsExponents



N.RN.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Exponents

Fractional ExponentsIrrational Number to Exponent FormZero Exponents and AlgebraSimplifying with Exponent Laws 1Simplifying with Exponent Laws 2Multiplication with ExponentsExponent Laws and AlgebraExponent Laws with Brackets

Radicals and Exponents Exponents


Use properties of rational and irrational numbers.

N.RN.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.

Irrational Numbers

Adding and SubtractingIrrational NumbersMultiplying Irrational NumbersExpanding BinomialIrrational Numbers

Under review



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.

Complex Numbers

Introduction to Complex Numbers

Under review

© 3P Learning 53


Integrated Math II





N.CN.2

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

Complex Numbers

Powers of iAdding Complex NumbersSubtracting Complex Numbers Complex Multiplication

Under review



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




N.CN.8





N.CN.9






A.SSE.1.a


Quadratic Functions and Equations

Vertex of a Parabola Parabolas



A.SSE.1.b

Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P anda factor not depending on P.


The DiscriminantConstructing FormulaeEquations Reducible to Quadratics

Under review


© 3P Learning54

Integrated Math II





A.SSE.1.b


Exponents

Fractional ExponentsCompound Interest by FormulaDepreciationDeclining Balance Depreciation




A.SSE.2



Factoring Quadratics 1Factoring Quadratics 2Equations Reducible to Quadratics




A.SSE.3.a

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines.

Solving Quadratic Equations

Highest CommonAlgebraic FactorFactoring Quadratics 1Factoring Quadratics 2Grouping in Pairs

Quadratic Equations



A.SSE.3.b

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.


Completing the SquareCompleting the Square 2Vertex of a Parabola

Quadratic Equations



A.SSE.3.c

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal theapproximate equivalent monthlyinterest rate if the annual rate is 15%.


© 3P Learning 55


Integrated Math II





A.APR.1



Like Terms: Add and SubtractSimplifying ExpressionsAlgebraic Fractions 1Algebraic Fractions 2Algebraic MultiplicationExpand then SimplifyExpanding BracketsExpanding Binomial ProductsSpecial Binomial ProductsMultiplication with Exponents

Polynomials Equations Expanding and Factorizing Simplifying Algebra Binomials and Pascal's Triangle

Creating Equations


A.CED.1

Create equations and inequalities in one variable and use them to solve problems. Include equationsarising from linear andquadratic functions,and simple rational andexponential functions.


Constructing Formulae

Quadratic Equations

Creating Equations


A.CED.1

Create equations and inequalities in one variable and use them to solve problems. Include equationsarising from linear andquadratic functions,and simple rational andexponential functions.

Exponents

Compound Interest by Formula Depreciation Declining Balance Depreciation

"Depreciation Interest"

Creating Equations


A.CED.2




Creating Equations


A.CED.2



Vertex of a ParabolaGraphing Parabolas Constructing Formulae

Parabolas


© 3P Learning56

Integrated Math II



Creating Equations


A.CED.4


Functions Changing theSubject

Linear Relationships Depreciation



A.REI.4.a.

Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2=q that has the same solutions. Derive the quadratic formula from this form.


Quadratic Equations 1Quadratic Equations 2

Quadratic Equations



A.REI.4.b

Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.


Quadratic Equations 1Quadratic Equations 2Quadratic FormulaThe DiscriminantFactoring Quadratics 1Factoring Quadratics 2Checking QuadraticEquations

Equations and InequalitiesFactorizing Quadratic Equations



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.

Linear and Quadratic Systems

Intersection: Line & ParabolaSimultaneous Equations 3Intersection: Line & Circle

Quadratic Equations

© 3P Learning 57


Integrated Math II





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 thefunction is increasing, decreasing,positive, or negative; relativemaximums and minimums;symmetries; end behavior; andperiodicity.


Vertex of a ParabolaGraphing ParabolasParabolas and RectanglesParabolas and Marbles

Parabolas



F.IF.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) givesthe number of person-hours ittakes to assemble n engines in afactory, then the positive integerswould be an appropriate domainfor the function.

FunctionsDomain Domain and Range

Functions



F.IF.6


Functions Equation from Two Points Under review



F.IF.7.a



Graphing Parabolas Parabolas



F.IF.7.b


Absolute Value, Step, and Piecewise

Absolute Value GraphsStep GraphsPiecemeal Functions

Under review


© 3P Learning58

Integrated Math II





F.IF.8.a



Factoring Quadratics 1Factoring Quadratics 2Grouping in PairsCompleting the SquareCompleting the Square 2Vertex of a Parabola

Factorizing Parabolas Quadratic Equations



F.IF.8.b

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identifypercent rate of change in functionssuch as y=(1.02)t, y=(0.97)t, y=(1.01)12t, y=(1.2)t/10, and classify them asrepresenting exponential growth ordecay.

Exponents

Multiplication with ExponentsFractional Exponents

Under review



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 onequadratic function and an algebraicexpression for another, say which has the larger maximum.


Linear Relationships Exponential and Power Graphs

Building Functions


F.BF.1.a


Exponents



Building Functions


F.BF.1.a



Constructing Formulae Parabolas

© 3P Learning 59


Integrated Math II



Building Functions


F.BF.1.b

Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. For example, builda function that models thetemperature of a cooling body byadding a constant function to adecaying exponential, and relatethese functions to the model.


Building 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 recognizingeven and odd functions from theirgraphs and algebraic expressionsfor them.

Functions

Vertical and horizontal shiftSymmetries of Graphs 1Odd and Even Functions

Functions Parabolas Sketching Polynomials

Building Functions


F.BF.4.a

Find inverse functions. Solve an equation of the form f(x)=c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x)=2x3 or f(x)=(x + 1)/(x – 1) for x≠1.

Functions Inverse Functions Functions



F.LE.3




Prove and apply trigonometric identities.

F.FT.8

Prove the Pythagorean identity sin2(θ) + cos2(θ)=1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.



© 3P Learning60

Integrated Math II



Congruence Prove Geometric Theorems G.CO.9

Prove theorems about lines and angles. Theorems include: vertical angles arecongruent; when a transversalcrosses parallel lines, alternateinterior angles are congruentand corresponding anglesare congruent; points on aperpendicular bisector of aline segment are exactly thoseequidistant from the segment’sendpoints.

Similarity, Congruence, and Theorems

Angles and Parallel LinesParallel Lines

Under review

Congruence Prove Geometric Theorems G.CO.10

Prove theorems about triangles. Theorems include: measures ofinterior angles of a triangle sumto 180°; base angles of isoscelestriangles are congruent; thesegment joining midpoints of two sides of a triangle is parallel tothe third side and half the length;the medians of a triangle meetat a point.


AngleMeasures in a TrianglePlane Figure TheoremsRatio of Intercepts

Polygons and Angles

Congruence Prove geometric theorems. G.CO.11

Prove theorems about parallelograms. Theorems include: opposite sides arecongruent, opposite angles arecongruent, the diagonals of aparallelogram bisect each other,and conversely, rectangles areparallelograms with congruentdiagonals.


Plane Figure Theorems Under review



G.SRT.1.a

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.




G.SRT.1.b

Verify experimentally the properties of dilations given by a center and a scale factor: b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.


Scale Measurement Scale Factor

Under review

© 3P Learning 61


Integrated Math II





G.SRT.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.


Similar Figures 1 Similarity and Congruence



G.SRT.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.


Similarity Proofs Similarity and Congruence



G.SRT.4

Prove theorems about triangles. Theorems include: a line parallelto one side of a triangle dividesthe other two proportionally, andconversely; the PythagoreanTheorem proved using trianglesimilarity.


Ratio of Intercepts Under review



G.SRT.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.


Similar FiguresUsing Similar TrianglesUsing Similar Triangles 1




G.SRT.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.

Trigonometry

Exact Trigonometric RatiosSin ACos ATan A

Trigonometry



G.SRT.7Explain and use the relationship between the sine and cosine of complementary angles.

Under review Under review Trigonometric Relationships



G.SRT.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Trigonometry

Find Unknown Sides Find Unknown Angles Elevation and Depression Trigonometry Problems 2

Pythagorean Theorem Trigonometry


© 3P Learning62

Integrated Math II




G.C.1 Prove that all circles are similar. Under review Under review Under review


G.C.2

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationshipbetween central, inscribed, andcircumscribed angles; inscribedangles on a diameter are rightangles; the radius of a circle isperpendicular to the tangentwhere the radius intersects the circle.

Circles and Parabolas

Circle TheoremTangents and Secants

Tangents and SecantsChords and Angles


G.C.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.



G.C.4Construct a tangent line from a point outside a given circle to the circle.


CirclesFind arc lengths and areas of sectors of circles.

G.C.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.


Converting Radians and DegreesPerimeter and CirclesArc LengthLength of an ArcArea of a Sector (degrees and radians)

Perimeter and Area



G.GPE.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.


Centre and Radius 1Centre and Radius 2

Circle Graphs



G.GPE.2Derive the equation of a parabola given a focus and directrix.


Focus and Directrix 1Focus and Directrix 2Focus and Directrix 3Focus and Directrix 4

© 3P Learning 63


Integrated Math II





G.GPE.4

Use coordinates to prove simple geometric theorems algebraically. For example, proveor disprove that a figure definedby four given points in thecoordinate plane is a rectangle;prove or disprove that the point(1, √3) lies on the circle centeredat the origin and containing thepoint (0, 2).


Centre and Radius 1Centre and Radius 2Focus and Directrix 1Focus and Directrix 2Focus and Directrix 3Focus and Directrix 4

Coordinate Geometry Circle Graphs



G.GPE.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.


Midpoint by Formula

Coordinate Geometry



G.GMD.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’sprinciple, and informal limitarguments.




G.GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.


Volume: CylindersVolume: PyramidsVolume: ConesVolume: SpheresVolume Composite FiguresVolume: Rearrange Formula

Measuring Solids




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”).

ProbabilityVenn DiagramsProbability - 'And' and 'Or'

Probability


© 3P Learning64

Integrated Math II





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.

Under review Under review Probability



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 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.

Probability ConditionalProbability Under review



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.

Probability

Two-way Table ProbabilityProbability Tables

Probability



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.


© 3P Learning 65


Integrated Math II





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.

Probability Conditionalprobability Under review



S.CP.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.

Probability Probability -'And' and 'Or' Under review



S.CP.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.

ProbabilityProbability Without Replacement

Under review



S.CP.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

Probability

Counting Techniques 1Counting Techniques 2Introduction to Permutations and CombinationsPermutations and ProbabilityCombinations and Probability

Under review



S.MD.6


Probability Fair Games Under review



S.MD.7




© 3P Learning66

Integrated Math III





N.CN.8



Complex Conjugate Under review



N.CN.9






A.SSE.1.a



Gradients for RealExponential Growth and Decay


Rational Equations

Vertical and Horizontal Asymptotes

Under review



A.SSE.1.b



Factoring ExpressionsEquations Reducible to Quadratics




A.SSE.2




Factorizing



Factorizing

© 3P Learning 67


Integrated Math III





A.SSE.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.

Sequences and Series

Sum: Geometric ProgressionsSigma Notation 1Sigma Notation 2

Sequences & Series: GeometricGeometric Series and Loan RepaymentsGeometric Series in Finance



A.APR.1



Like Terms: Add, SubtractAlgebraic MultiplicationMultiplication with ExponentsSpecial Binomial ProductsExpanding BracketsExpand then SimplifyExpanding Binomial Products

Polynomials EquationsExpanding and FactorizingSimplifying AlgebraBinomials and Pascal's Triangle


"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).


Polynomial Factor Theorem Polynomials


"Understand the relationship between zeros and factors of polynomials."

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.


Factoring ExpressionsEquations Reducible to QuadraticsPolynomial Factor TheoremGraphing Cubics




A.APR.4Prove polynomial identities and use them to describe numerical relationships. E20



Factorizing


© 3P Learning68

Integrated Math III





A.APR.5

Know and apply the Binomial Theorem for the expansion of (x + y)n 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.


Pascal's Triangle, Expansion

The Binomial TheoremBinomials and Pascal's Triangle



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 polynomialswith the degree of r(x) lessthan the degree of b(x), usinginspection, long division, or,for the more complicatedexamples, a computer algebrasystem.



Polynomials



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.

Rational Equations

Algebraic Fractions 2Algebraic Fractions 3Factoring and Fractions 1Factoring and Fractions 2

Factorizing

Creating Equations


A.CED.1



Write an Equation: Word Problems

Under review

Creating Equations


A.CED.2



y=axFind the Function RuleModeling Linear RelationshipsLinear ModelingParabolas and MarblesParabolas and RectanglesConstructing Formulae

Under review

© 3P Learning 69


Integrated Math III



Creating Equations


A.CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.


Creating Equations


A.CED.4


Inverse Functions

Inverse FunctionsGraphing Inverse Functions

Functions



A.REI.2

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

Radical Equations

Equations with Square RootsEquations with Cube Roots

Under review



A.REI.11

Explain why the x-coordinates of the pointswhere the graphs of theequations y=f(x) and y=g(x)intersect are the solutions ofthe equation f(x)=g(x); findthe solutions approximately,e.g., using technology tograph the functions, maketables of values, or findsuccessive approximations.Include cases where f(x)and/or g(x) are linear,polynomial, rational,absolute value, exponential,and logarithmic functions.


Solve Systems by Graphing Under review


© 3P Learning70

Integrated Math III





F.IF.4



Gradients for RealParabolas and MarblesParabolas and Rectangles




F.IF.5



DomainDomain and Range

Functions



F.IF.6






F.IF.7.b


Inverse Functions

Graph Inverse Functions Under review


Absolute Value GraphsPiecemeal FunctionsStep Graphs

Under review

© 3P Learning 71


Integrated Math III





F.IF.7.c

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.


Graphing Cubics




F.IF.7.e


Trigonometry

Sine and Cosine CurvesTrig Graphs in RadiansGraph Inverse Trig Functions



Graphing ExponentialsExponential or Log Graph?

Exponential and PowerGraphs LogarithmsSimple Nonlinear Graphs



F.IF.8.a







F.IF.8.b

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rateof change in functions such asy=(1.02)t, y=(0.97)t , y=(1.01)12t, y=(1.2)t/10, and classify them asrepresenting exponential growth ordecay.


Change of Base Under review


© 3P Learning72

Integrated Math III





F.IF.9



Building Functions


F.BF.1.b



Building 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.


Odd and Even FunctionsSymmetries of Graphs 1Vertical and horizontal shift

Exponential and Power Graphs FunctionsSketching Polynomials

Building Functions


F.BF.4.a

Find inverse functions. Solve an equation of the form f(x)=c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x)=2x3 or f(x)=(x + 1)/(x – 1) for x≠1.

Inverse Functions

Inverse Functions Functions

© 3P Learning 73


Integrated Math III





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.


Log LawsEquations with LogsLog Base 'e'

Logarithms



F.TF.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Trigonometry

Converting Radians and DegreesUnit Circle Reductions

Under review



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.

Trigonometry

Sign of the AngleUnit Circle ReductionsTrigonometric Relationships



Model periodic phenomena with trigonometric functions.

F.TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Trigonometry Period andAmplitude Under review




G.SRT.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.

TrigonometryArea Rule 1Area Rule 2Area Problems




G.SRT.10Prove the Laws of Sines and Cosines and use them to solve problems.





G.SRT.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).




© 3P Learning74

Integrated Math III




Visualize relationships between two-dimensional and three-dimensional objects.

G.GMD.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.


Relate Shapes and Solids Nets

Under review



G.MG.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).


Match the Solid 2

Measuring Solids



G.MG.2

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




G.MG.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).

Trigonometry TrigonometryProblems 2 Under review




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.


Normal DistributionNormal Distribution ProbabilityCalculating Standard Deviation Calculating z-scoresComparingz-scoresEquivalentz-scores

Interpreting Data



S.IC.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.


Capture Recapture Technique

Under review

© 3P Learning 75


Integrated Math III





S.IC.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?




S.IC.3

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




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.




S.IC.5

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




S.IC.6 Evaluate reports based on data. Under review Under review Under review



S.MD.6



Fair Games Under review



S.MD.7



powered by

Mathletics Common Core State Standards Alignment · Expanding Binomial Irrational Numbers Under...

Documents

Transcript of Mathletics Common Core State Standards Alignment · Expanding Binomial Irrational Numbers Under...