Math - Clovis Municipal School District - COLLEGE … · COLLEGE PREP MATH COMMON CORE STANDARDS 1st Nine Weeks Extend the properties of exponents to rational exponents. N-RN.1 Explain

Math

Curriculum Guide

Clovis Municipal Schools

College Prep Math

Revised Spring 2016

COLLEGE PREP MATH COMMON CORE STANDARDS1st Nine Weeks

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 interger exponents to those values, allowing for a notation for radicals in terms of rational exponents. N- RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Interpret the structure of expressionsA-SSE.1 Interpret expressions that represent a quantity in terms of its context. A-SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.A-SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single enntity.

Write expressions in equivalent forms to solve problems.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A-SSE.3c Use the properties of exponents to transform expressions for exponential functions.

Perform arithmetic operations on polynomialsA-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.CMS Factor polynomials of various types (e.g., difference of squares, perfect square trinomials, sum and difference of cubes).

2nd Nine WeeksRewrite rational expressions

A-APR.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Create equations that describe numbers or relationshipsA-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solve equations and inequalities in one variableA-REI.4 Solve quadratic equations in one variable. A-REI.4a Use the method of completing the square to transform any quadratic equation in "x" into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.A-REI.4b 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".

Understand the concept of a function and use function notationF-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).

Interpret functions that arise in applications in terms of the contextF-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.

Analyze functions using different representationsF-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F-IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

revised May 2016

COLLEGE PREP MATH COMMON CORE STANDARDS3rd Nine Weeks

Create equations that describe numbers or relationshipsA-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Represent and solve equations and inequalities graphicallyA-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Analyze functions using different representationsF-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F-IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. (linear)F-IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. (step/piecewise)F-IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.F-IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.F-IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Extend the domain of trigonometric functions using the unit circleF-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.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.F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for "x", where "x" is any real number.

Prove and apply trigonometric identitiesF-TF.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.

Define trigonometric ratios and solve problems involving right trianglesG-SRT.8 Use trigonometric ratio and Pythagorean Theorem to solve right triangles in applied problems.

Use coordinates to prove simple geometric theorems algebraicallyG-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).

Major Clusters-areas of intensive focus, where students need fluent understanding and application of the core concepts (approximately 70%).Supporting Clusters-rethinking and linking; areas where some material is being covered, but in a way that applies core understandings (approximately 20%).Additional Clusters-expose students to other subjects, though at a distinct level of depth and intensity (approximately 10%).

revised May 2016

COLLEGE PREP MATH COMMON CORE STANDARDS4th Nine Weeks

Understand the concept of a function and use function notationF-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).

Interpret functions that arise in applications in terms of the contect.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Extend the domain of trigonometric functions using the unit circleF-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for "x", where "x" is any real number.

Prove geometric theoremsG-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.

Prove theorems involving similarityG-SRT.5 Use congruence ( 2nd nine weeks) and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios and solve problems involving right trianglesG-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Understand and apply theorems about circlesG-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 radius intersects the circle.

Translate between the geometric description and the equation for a conic sectionG-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.

Apply geometric concepts in modeling situationsG-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).

Major Clusters-areas of intensive focus, where students need fluent understanding and application of the core concepts (approximately 70%).Supporting Clusters-rethinking and linking; areas where some material is being covered, but in a way that applies core understandings (approximately 20%).Additional Clusters-expose students to other subjects, though at a distinct level of depth and intensity (approximately 10%).

revised May 2016

Common Core State Standards-Mathematics

RN- Real Number System

Extend the properties of exponents to rational exponentsCluster:

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10-12 College Prep Math

2

Performance Standards

Domain:

Grade: Page # : 01May 2016Revision Date:

VocabularyVerbs- Level of Learning

Standard ResourcesMathematical Practices Explanations/Assessments

Key :

Understand the properties of exponents.

Understand that the denominator of the rational exponent isthe root index and the numerator is the exponent of theradicand. For example, 51/2=√5

Students may explain orally or in written format.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 28 #61

Algebra 2 Common Core, Pearson, 2012 - p.34 #9 - p. 429 #7 - p. 20 #2-4

N-RN.1Explain how the definition of the meaningof rational exponents follows fromextending the properties of integerexponents to those values, allowing for anotation for radicals in terms of rationalexponents. For example, we define 51/3 tobe the cube root of 5 because we want (5 1/3) 3 = 5 ( 1/3) 3 to hold, so (5 1/3) 3 mustequal 5.

MP.2 Reason abstractly andquantitatively.

MP.3 Construct viablearguments and critique thereasoning of others.

MP.7 Look for and make useof structure.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P, Section 2

Algebra 2 Common Core, Pearson, 2012 - Chapter 7, Section 2-4

ACTCoachMathematics,TriumphLearning,2014

Convert from radical representation to using rationalexponents and vise versa.


Algebra 2 Common Core, Pearson, 2012 - p. 386 #19-24

ACTCoachMathematics,TriumphLearning,2014#3-4

N-RN.2Rewrite expressions involving radicals andrational exponents using the properties ofexponents.

MP.1 Make sense ofproblems and persevere insolving them.


Algebra 2 Common Core, Pearson, 2012 - Chapter 6, Section 4



SSE-Seeing Structure in Expressions

Interpret the structure of expressions

★ Modeling Standard

Cluster:

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Domain:

Grade: Page # : 02-03May 2016Revision Date:



Key :

Identify the different parts of the expression and explain theirmeaning within the context of a problem. Decomposeexpressions and make sense of the multiple factors and termsby explaining the meaning of the individual parts. Studentsshould understand the vocabulary for the parts that make upthe whole expression and be able to identify those parts andinterpret their meaning in terms of a context when doingorder of operations working problems that include decimalsand fractions by hand without using any technology (e.g.,7.13 x 24.6).



A-SSE.1Interpret expressions that represent aquantity in terms of its context. ★



MP.4 Model withmathematics.




Students manipulate the terms, factors, and coefficients indifficult expressions to explain the meaning of the individualparts of the expression. Use them to make sense of themultiple factors and terms of the expression. For example,the expression $10,000 (1.055)5 represents the amount ofmoney I have in an account. My account has a starting valueof $10,000 with a 5.5% interest rate every 5 years, where10,000 and (1+.055)are factors, and the $10,000 does notdepend on the amount the account is increased by.


A-SSE.1aInterpret parts of an expression, such asterms, factors, and coefficients. ★







SSE-Seeing Structure in Expressions

Interpret the structure of expressions


Cluster:

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3


Domain:




Key :

Students group together parts of an expression to revealunderlying structure.


A-SSE.1bInterpret complicated expressions byviewing one or more of their parts as asingle entity. For example, interpret P(1+r) n as the product of P and a factor notdepending on P. ★







SSE- Seeing Structure in Expressions

Write expressions in equivalent forms to solve problems


Cluster:

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2


Domain:




Key :

Students will use the properties of operations to createequivalent expressions.

Example:

• Express 2(x3 – 3x2 + x – 6) – (x – 3)(x + 4) in factored formand use your answer to say for what values of x theexpression is zero.



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



Algebra 2 Common Core, Pearson, 2012 - Chapter 4, Section 4 and 6

Use properties of exponents to write an equivalent formof an exponential function to reveal and explain specificinformation about the rate of growth or decay.

Example: The equation y=14000(0.8)x represents the value ofan automobile x years after purchase. Find the yearly and themonthly rate of depreciation of the car.



A-SSE.3cUse the properties of exponents totransform expressions for exponentialfunctions.

For example the expression 1.15t can berewritten as (1.151/12)12t ≈ 1.01212t toreveal the approximate equivalent monthlyinterest rate if the annual rate is 15%. ★



Algebra 2 Common Core, Pearson, 2012 - Chapter 4, Section 4 and 6


APR- Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomialsCluster:

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2


Domain:




Key :

The Closure Property means that when adding, subtracting ormultiplying polynomials, the sum, difference, or product isalso a polynomial. Polynomials are not closed under divisionbecause in some cases the result is a rational expression.

Example: If the radius of a circle is (5x-2) kilometers, writean expression for the area of the circle.

Example: Explain why (4x2+3)2 does not equal (16x4+9)

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 65 #17-20 and #65-68

A-APR.1Understand that polynomials form a systemanalogous to the integers, namely, they areclosed under the operations of addition,subtraction, and multiplication; add,subtract, and multiply polynomials.




Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 53 #13-20 - Chapter P, Midchapter Test, p. 68 #28-34

Algebra 2 Common Core, Pearson, 2012 - p.221 #20-28 - p. 301 #10-12

ACTCoachMathematics,TriumphLearning,2014 - p. 166 #1

CMS APRFactor polynomials of various types (e.g.,difference of squares, perfect squaretrinomials, sum and difference of cubes).



MP.8 Look for and expressregularity in repeatedreasoning.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P, Sections 4-5

Algebra 2 Common Core, Pearson, 2012 - Chapter 4, Section 4 - Chapter 5, Section 3



APR- Arithmetic with Polynomials and Rational Expressions

Rewrite rational expressions

(+) For advanced course: calculus, advanced statistics, etc.

Cluster:

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Domain:




Key :

Simplify rational expressions by adding, subtracting,multiplying, or dividing. Understand that rationalexpressions are closed under addition, subtraction,multiplication, and division(by a nonzero expression).

BlitzerPreCalculus,4thEdition,Pearson,2010-ChapterPtest,p.133#14-18

ACTCoachMathematics,TriumphLearning,2014-p.190#1-2

A-APR.7(+) Understand that rational expressionsform a system analogous to the rationalnumbers, closed under addition,subtraction, multiplication, and division bya nonzero rational expression; add, subtract,multiply, and divide rational expressions.



BlitzerPreCalculus,4thEdition,Pearson,2010-ChapterP,Section6



CED- Creating Equations

Create equations that describe numbers or relationships


Cluster:

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2


Domain:




Key :

Given a contextual situation, write equations in two variablesthat represent the relationship that exists between thequantities. Also graph the equation with appropriate labelsand scales. Make sure students are exposed to a variety ofequations arising from the functions they have studied.Problems should contain fractions and decimals.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 7 test , p. 802 #1-5, #12-15

ACTCoachMathematics,TriumphLearning,2014 - p. 203 #1-8

A-CED.2Create equations in two or more variablesto represent relationships betweenquantities; graph equations on coordinateaxes with labels and scales. ★




MP.5 Use appropriate toolsstrategically.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 7, Section 1-2


• The Pythagorean Theorem expresses the relation between the legs a and b of a right triangle and its hypotenuse c with the equation a2 + b2 = c2.• Why might the theorem need to be solved for c?• Solve the equation for c and write a problem situation where this form of the equation might be useful.

• Motion can be described by the formula below, where t = time elapsed, u=initial velocity, a = acceleration, and s = distance traveled

s = ut + ½at2

• Why might the equation need to be rewritten in terms of a?• Rewrite the equation in terms of a.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P test, p. 133 #48-50

A-CED.4Rearrange formulas to highlight a quantityof interest, using the same reasoning as insolving equations. For example, rearrangeOhm’s law V = IR to highlight resistanceR.★






Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P, Section 7-8


REI- Reasoning with Equations and Inequalities

Solve equations and inequalities in one variableCluster:

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3


Domain:




Key :

Students should solve by factoring, completing the square,and using the quadratic formula. The zero product property isused to explain why the factors are set equal to zero. Studentsshould relate the value of the discriminant to the type of rootto expect. A natural extension would be to relate the type ofsolutions to ax2 + bx + c = 0 to the behavior of the graph ofy = ax2 + bx + c .

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P test p. 99 #105-114 - p. 133 #36-38


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






Transform a quadratic equation written in standard form to anequation in vertex form (x - p)² = q by completing the square.Derive the quadratic formula by completing the square on thestandard form of a quadratic equation.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P test p. 99 #67-74 - p. 133 #36-38


A-REI.4aUse the method of completing the square totransform any quadratic equation in x intoan equation of the form (x – p)2 = q thathas the same solutions. Derive the quadraticformula from this form.








Solve equations and inequalities in one variableCluster:

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3


Domain:




Key :

Students should solve by factoring, completing the square,and using the quadratic formula. The zero product property isused to explain why the factors are set equal to zero. Studentsshould relate the value of the discriminant to the type of rootto expect. A natural extension would be to relate the type ofsolutions to ax2 + bx + c = 0 to the behavior of the graph ofy = ax2 + bx + c .

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter P test p. 99 #61-66


A-REI.4bSolve quadratic equations by inspection(e.g., for x2 = 49), taking square roots,completing the square, the quadraticformula and factoring, as appropriate to theinitial form of the equation. Recognizewhen the quadratic formula gives complexsolutions and write them as a ± bi for realnumbers a and b.








Represent and solve equations and inequalities graphically


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1


Domain:




Key :

Students may use graphing calculators, programs, or appletsto model and find solutions for inequalities or systems ofinequalities.Examples: • Graph the solution: y < 2x + 3. • A publishing company publishes a total of no more than100 magazines every year. At least 30 of these are women’smagazines, but the company always publishes at least asmany women’s magazines as men’s magazines. Find asystem of inequalities that describes the possible number ofmen’s and women’s magazines that the company can produceeach year consistent with these policies. Graph the solutionset.



A-REI.12Graph the solutions to a linear inequality intwo variables as a half-plane (excluding theboundary in the case of a strict inequality),and graph the solution set to a system oflinear inequalities in two variables as theintersection of the corresponding half-planes.



Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 7, Section 5



IF- Interpreting Functions

Understand the concept of a function and use function notation


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1


Domain:




Key :

The domain of a function is the set of all x-values (input),called the independent variable. The range of a function is theset of all y-values (output), and is dependent on a particularx-value, thus called the dependent variable.The idea of a function should be developed through anunderstanding that each input has exactly one output. If aspecific rule can be written which models the relationbetween the input and one unique output, then it is a function.When this relationship is established, the variable y becomesf(x), meaning y=f(x). For example in the equation y=3x+5,for every x-value, there exist one and only one y-value,therefore you may rewrite the equation using functionnotation, f(x)=3x+5.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 1 test, p. 275 #1-3


F-IF.1Understand that a function from one set(called the domain) to another set (calledthe range) assigns to each element of thedomain exactly one element of the range. Iff is a function and x is an element of itsdomain, then f(x) denotes the output of fcorresponding to the input x. The graph of fis the graph of the equation y = f(x).


MP.6 Attend to precision.




LifeAfterCollegeBudgetProject-SeeDept.Chair

The student will complete a variety of formulaic tasks withinthe Life After College Budget Project to determine the truecosts of such items as college and car loans, credit cards,retirement investments, and mortgage. Using thisinformation, in addition to determining salary and otherexpenses, the student will write a summary of the keyunderstandings of financial planning.



Interpret functions that arise in applications in terms of the contextCluster:

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2


Domain:




Key :

Given a function, determine its domain. Describe theconnections between the domain and the graph of thefunction. Know that the domain taken out of context is atheoretical domain and that the practical domain of a functionis found based on a contextual situation given, and is theinput values that make sense to the constraints of the problemcontext.

Blitzer PreCalculus 4th edition, Pearson, 2010 - p.261 #1-16


F-IF.5Relate the domain of a function to its graphand, where applicable, to the quantitativerelationship it describes. For example, ifthe function h(n) gives the number ofperson-hours it takes to assemble n enginesin a factory, then the positive integerswould be an appropriate domain for thefunction. ★




Blitzer PreCalculus 4th edition, Pearson, 2010 - Chapter 1, Section 10


Students should be able to describe patterns of changes fromtables and/or graphs of linear and exponential functions.Sample vocabulary may include, “increasing/decreasing at aconstant rate” or “increasing or decreasing at an increasingor decreasing rate.” Students should be comfortable in theirunderstanding of rates of change to apply their knowledgelinear and non-linear graphical display.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 189 #25-35 - p. 200 #13-18


F-IF.6Calculate and interpret the average rate ofchange of a function (presentedsymbolically or as a table) over a specifiedinterval. Estimate the rate of change from agraph. ★








Analyze functions using different representations


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6


Domain:




Key :

This standard should be seen as related to F-IF.4 with the keydifference being students can create graphs, by hand andusing technology, from the symbolic function in thisstandard.Example: The all-star kicker kicks a field goal for the teamand the path of the ball is modeled by f (x) = −4.9t2+20tFind the realistic maximum and minimum values for the pathof the ball and describe what each means in the context ofthis problem.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 1 test, p. 276#24-26 - Chapter 2 Midchapter test, p. 339 #8-11, #12-20 - Chapter 2 Review, p. 273 #73-75, 82-84 p. 271 #30-40


F-IF.7Graph functions expressed symbolicallyand show key features of the graph, byhand in simple cases and using technologyfor more complicated cases. ★F-IF.7aGraph linear and quadratic functions andshow intercepts, maxima, and minima.

F-IF.7bGraph square root, cube root, andpiecewise-defined functions, including stepfunctions and absolute value functions.

F-IF.7cGraph polynomial functions, identifyingzeros when suitable factorizations areavailable, and showing end behavior.



Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 1, Section 2,5,6 - Chapter 2, Section 2-6


Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 2 test, p. 386 #20-25 - Chapter 4, page 583 #14-17

F-IF.7d(+) Graph rational functions, identifyingzeros and asymptotes when suitablefactorizations are available, and showingend behavior.

F-IF.7eGraph exponential and logarithmicfunctions, showing intercepts and endbehavior, and trigonometric functions,showing period, midline, and amplitude.


Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 1, Section 2,5,6 - Chapter 2, Section 2-6 - Chapter 4, Section 5


TF-Trigonometric Functions

Extend the domain of trigonometric functions using the unit circle.Cluster:

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10-12 College Prep

3


Domain:




Key :

A central angle of a circle intercepts an arc on the samecircle. The length of the arc is some fraction of thecircumference of the circle and is the basis for discoveringthe radian measure of an angle. These steps lead the studentsto the definition of a radian. A radian is the measure of thecentral angle of a circle that intercepts an arc of the samemeasure. It is acceptable to let students define 1 radian asabout 57o. Through classroom discussion and investigation,(not direct instruction) the instruction should guide studentsto the more precise conversion factors of 360° = 2π and 180°= π radians.



F-TF.1Understand radian measure of an angle asthe length of the arc on the unit circlesubtended by the angle.

MP.6 Attend to precision. Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 4, Section 1


This standard should be approached by students by rotating a circularobject (i.e., Ferris Wheel) around and recording the angle formedwith the origin, the height off the ground, and the horizontal heightfrom the center of the circle. To do this, construct a coordinate axeson a large sheet of paper. Fromthe origin mark off “famous” unit circle angles. (This will create alarge asterisk like drawing.) On a separate piece of a paper, constructa large “unit” circle. Attach the center of the circle to the origin ofthe axes with a brad for rotational purpose. Students should draw orplace a sticker of a “rider” at (1,0). While not imperative, this wouldwork better if the grid was placed on a 10mm graph paper and thecircle constructed with a transparency.

Students may use applets and animations to explore the unit circleand trigonometric functions. Students may explain (orally or inwritten format) their understanding.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p.487 #21


F-TF.2Explain how the unit circle in thecoordinate plane enables the extension oftrigonometric functions to all real numbers,interpreted as radian measures of anglestraversed counterclockwise around the unitcircle.





Algebra 2 Common Core, Pearson, 2012 - Chapter 13, Section 2, 3



Extend the domain of trigonometric functions using the unit circle.Cluster:

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10-12 College Prep

3


Domain:




Key :

Use 30º-60º-90º and 45º-45º-90º triangles to determine thevalues of sine, cosine, and tangent for values of π/3, π/4, andπ/6.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - Chapter 4 midchapter test, p. 514 #2-28 (evens)


F-TF.3(+) Use special triangles to determinegeometrically the values of sine, cosine,tangent for π/3, π/4 and π/6, and use theunit circle to express the values of sine,cosine, and tangent for π–x, π+x, and 2π–xin terms of their values for x, where x isany real number.








Prove and apply trigonometric identities.


Cluster:

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Domain:




Key :

Use the unit circle to prove the Pythagorean identity sin²(θ) +cos²(θ) = 1. Given the value of the sin(θ) or cos(θ), use thePythagorean identity sin²(θ) + cos²(θ) = 1 to calculate othertrigonometric ratios.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 603 #9-12, 33-47


F-TF.8Prove 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) andthe quadrant of the angle.







C-Congruence

Prove geometric theorems.Cluster:

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1


Domain:




Key :

Jerry is laying out the foundation for a rectangular foundationfor an outdoor tool shed. He needs ensure that it is indeedfulfills the definition of a rectangle. The only tools hebrought with him are pegs (for nailing in the ground to markthe corners), string and a tape measure. Create a plan forJerry to follow so that he can be sure his foundation isrectangular. Justify why your plan works. Discuss yourmethod with another student to make sure your plan is errorproof. Connect this standard with G-CO.8 and use trianglecongruency criteria to determine all of the properties ofparallelograms and special parallelograms.

Geometry Common Core, Pearson, 2012 - pg. 425 #3-15

G-CO.11Prove theorems about parallelograms.Theorems include: opposite sides arecongruent, opposite angles are congruent,the diagonals of a parallelogram bisecteach other, and conversely, rectangles areparallelograms with congruent diagonals.




Geometry Common Core, Pearson, 2012 - Chapter 6, Section 2-5


SRT-Similarity, Right Triangles, and Trigonometry

Prove theorems involving similarity.Cluster:

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1


Domain:




Key :

Similarity postulates include SSS, SAS, and AA.Congruence postulates include SSS, SAS, ASA, AAS,and H-L.Students may use geometric simulation software to modeltransformations and demonstrate a sequence oftransformations to show congruence or similarity of figures.

Connect with G.CO.8 and G.CO.11 and use trianglecongruency criteria to determine all of the properties ofparallelograms and special parallelograms.

Geometry Common Core, Pearson, 2012 - p. 277 #3-14 - p. 342 #4-13, 21-23 - p. 421 #5-36


G-SRT.5Use congruence and similarity criteria fortriangles to solve problems and to proverelationships in geometric figures.


MP.4 Model withmathematicsMP.6 Attend to precision.


Geometry Common Core, Pearson, 2012 - Chapter 4, Section 2-7 - Chapter 5, Section 1, 2, 4 - Chapter 6, Section 1-6 - Chapter 7, Section 2-4



SRT- Similarity, Right Triangles, and Trigonometry

Define trigonometric ratios and solve problems involving right triangles


Cluster:

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1


Domain:




Key :

Using SOHCOHTOA, solve for one side of a right triangleusing a side and an angle.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p.498 #29-34

Geometry Common Core, Pearson, 2012 - p. 519 #19-24


G-SRT.8Use trigonometric ratios and PythagoreanTheorem to solve right triangles in appliedproblems. ★

MP.1Make sense of problems andpersevere in solving them.

MP.4Model with mathematics.

MP.5Use appropriate toolsstrategically.


Geometry Common Core, Pearson, 2012 - Chapter 8, Section 1-4



C-Circles

Understand and apply theorems about circles.Cluster:

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1


Domain:




Key :

An archeologist dug up an edge piece of a circular plate. Hewants to know what the original diameter of the plate wasbefore it broke. However, the piece of pottery does notdisplay the center of the plate. How could he find theoriginal dimensions? Apply what you know about chordsin circles. You are given two circles of diameters 24cm and10cm. Locate two chords of equal length, 8 cm for eachcircle. Compare their distances from the centers of thecircles. Using Interactive Geometry Software, investigatemeasurements of central angles and inscribed angles thatintercept the same arc. What is the relationship of these anglemeasures? Then, explain why inscribed angles on adiameter are always 90°. Also, make an argument for whythe opposite angles in a quadrilateral inscribed in a circle aresupplementary.Geometry Common Core, Pearson, 2012 - p. 679 #35-42 - p. 915 #14-21ACTCoachMathematics,TriumphLearning,2014 - p. 258 #1-3

G-C.2Identify and describe relationships amonginscribed angles, radii, and chords. Includethe relationship between central, inscribed,and circumscribed angles; inscribed angleson a diameter are right angles; the radiusof a circle is perpendicular to the tangentwhere the radius intersects the circle.




Geometry Common Core, Pearson, 2012 - Chapter 10, Section 6 - Chapter 12, Section 2-3



GPE- Expressing Geometric Properties with Equations

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

(+) For advanced course: calculus, advanced statistics, etc.

Cluster:

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Key :

Use the Pythagorean Theorem to derive the equation of acircle, given the center and the radius.Given an equation of a circle, complete the square to find thecenter and radius of a circle.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 250 #1-10


G-GPE.1Derive the equation of a circle of givencenter and radius using PythagoreanTheorem; complete the square to find thecenter and radius of a circle given by anequation.








GPE- Expressing Geometric Properties with Equations

Use coordinates to prove simple geometric theorems algebraically


Cluster:

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Domain:




Key :

Lines can be horizontal, vertical, or neither.Students may use a variety of different methods to construct aparallel or perpendicular line to a given line and calculate theslopes to compare the relationships.

Blitzer PreCalculus, 4th Edition, Pearson, 2010 - p. 200 #5-12

Geometry Common Core, Pearson, 2012 - p. 210 #41-46 - p. 482 #24-28


G-GPE.5Prove the slope criteria for parallel andperpendicular lines and use them to solvegeometric problems (e.g., find the equationof a line parallel or perpendicular to a givenline that passes through a given point).




Geometry Common Core, Pearson, 2012 - Chapter 3, Section 8 - Chapter 6, Section 3-4



MG-Modeling with Geometry

Apply geometric concepts in modeling situations.Cluster:

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1


Domain:




Key :

Solve design problems by designing an object or structurethat satisfies certain constraints, such as minimizing cost orworking with a grid system based on ratios (i.e., Theenlargement of a picture using a grid and ratios andproportions) Use example from G-MG.1.

Geometry Common Core, Pearson, 2012 - p. 208, Question 24


G-MG.3Apply geometric methods to solve designproblems (e.g., designing an object orstructure to satisfy physical constraints orminimize cost; working with typographicgrid systems based on ratios). ★

MP.1Make sense of problems andpersevere in solving them.

MP.4Model with mathematics.

MP.5Use appropriate toolsstrategically.

Geometry Common Core, Pearson, 2012 - Chapter 3, Section 4


Online resources for secondary math curriculum revision – Spring 2013

www.illustrativemathematics.org

http://illuminations.nctm.org/

www.insidemathematics.org

www.ccsstoolbox.com

map.mathshell.org

http://aaamath.com/

www.veccnj.org

www.thirteen.org/get-‐the-‐math/teachers/overview-‐of-‐the-‐lessons/26/

http://algebra1teachers.com/unit%204.html

http://ccssmath.org/?page_id=1303

https://sites.google.com/site/rpsccss

Documents

Math - Clovis Municipal School District - COLLEGE … · COLLEGE PREP MATH COMMON CORE STANDARDS 1st Nine Weeks Extend the properties of exponents to rational exponents. N-RN.1 Explain