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Mathematics

Curriculum GuideCurriculum Guide

Clovis Municipal Schools

Bridge to Algebra II

Created March 2017

MAT 221 2080

Integrated Pathway: Mathematics I

Created March 21, 2017

1st Nine WeeksReason quantitatively and use units to solve problems

N-Q.1 Reason quantitatively and use units to solve problems. 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.N-Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of descriptive modeling.N-Q.3 Reason quantitatively and use units to solve problems. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Interpret the structure of expressionsA-SSE.1 Interpret the structure of expressions. 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 entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.

Create equations that describe numbers or relationshipsA-CED.1 Create equations that describe numbers relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions.A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Understand solving equations as a process of reasoning and explain the reasoningA-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.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

Construct and compare linear, quadratic, and exponential models and solve problemsF-LE.2 Construct and compare linear functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading thesefrom a table)F-LE.3 Construct and compare linear models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.F-LE.5 Construct and compare linear models and solve problems. Interpret the parameters in a linear function in terms of a context.

Understand the concept of a function and use function notationF-IF.1 Understand the concept of a function and use funtion notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to eachelement 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 off is the graph of the equation y=f(x).F-IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use functionnotation in terms of a context.F-IF.3 Understand the concept of a function and use function notation. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Forexample, the Fibona I sequence is defined recursively by f(0) = f(1) =1, f(n+1) = f(n) + f(n-1) for n is greater than or equal to 1.

Interpret functions that arise in applications in terms of the contextF-IF.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of thequantities, 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;F-IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of a change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Build new functions from existing functionsF.BF.3 Build new functions from existing functions. 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.

Bridge to Algebra II Common Core Standards


1st Nine Weeks, con't.Summarize, represent, and interpret data on two categorical and quantitative variables

S-ID.6 Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe howthe variables are related.S-ID.6c Fit a linear function for a scatter plot that suggests a linear association.S.ID.7 Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.S.ID.8 Interpret linear models. Compute (using technology) and interpret the correlation coefficent iof a linear fit.S.ID.9 Interpret linear models. Distinguish between correlation and causation.

Prove geometric theorems G-CO.9 Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior

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%).



2nd Nine WeeksCreate equations that describe numbers or relationships

A-CED.2 Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A-CED.3 Create equations that describe numbers or relationship. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods

Solve systems of equationsA-REI.5 Solve systems of equations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a mutiple of the other produces a system with the same solutions.A-REI.12 Represent and solve equations and iinequalities graphically. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strictinequality), and graph the solution set to a system of linear inequalities in two variables as the intersections of the corresponding half-planes.A-REI.10 Represent and solve equations and inequalities graphically. 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).

Interpret linear modelsS.1D.1 Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots). S.1D.2 Summarize, represent, and interpret data on a single count or measurement variable. Use statistics apporopriate to the shape of the data distribution to compare center(median, mean) and spread (interquartile range, standard deviateion) of two or more different data sets.S.1D.3 Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, a outing for possible effects of extreme data points (outliers).S.ID.5 Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in two-way frequency tables.Interpretrelative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.S.ID.6a 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 funciton suggested by the context. Emphasize linear, quadratic, and exponential models.

Interpret functions that arise in applications in terms of the contextF-IF.5 Interpret functions that arise in applications in terms of the context. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.For exanple, 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.F.BF.1a Determine an explicit expression, a recursive processs, or steps for calculation from a context.

Experiment with transformations in the planeG-CO.1 Experiment with transformations in the plane. Know precise definitions of an 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.G-CO.4 Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in terms of angles, ircles, perpendicular lines, parallel lines, and line segments.G-CO.10 Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parrallel to the third side and half the length; the medians of a triangle meet at a point.




3rd Nine WeeksRepresent and solve equations and inequalities graphically

A.REI.11 Represent and solve equations and inequalities graphically. 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 equatioin f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find sucessive approximations. Include cases where f(x) and/or g(x) are linear.

Analyze functions using different representationsF-IF.7a Graph linear functions and show intercepts.F-IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal description).

Build a function that models a relationship between two quantitiesF.BF.1b 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 adecaying exponential, and relate these functions to the model.F.BF.2 Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Construct and campare linear, quadratic, and exponential models and solve problemsF.LE.2 Construct exponential models and solve problems. Construct 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).F.LE.5 Construct and compare exponential models and solve problems. Interpret the parameters in an exponential function in terms of a context.F.LE.3 Construct and compare exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,quadratically, or (more generally) as a polynomial function.

Experiment with transformations in the planeG.CO. 2 Experiment with transformations in the plane. Represent transformations in the plane using e.g., transparencies and geometry software; describe that take points in thetransformations as functions plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translationversus horizontal stretch)G.CO.3 Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.G.CO.5 Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, orgeometry software. Specify a sequence of transformations that will carry a given figure onto another.

Understand congruence in terms of rigid motionsG.CO.6 Understand conngruence in terms of rigid motions. 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.G.CO.7 Understand congruence in terms of rigid motions. 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 coresponding pairs of angles are congruent.G.CO.8 Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid terms.

Prove geometric theoremsG.CO.11 Prove geometric theorems. 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.




4th Nine WeeksCreate 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 functions.Extend the properties of exponents to rational exponents

N-RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.N-RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Analyze functions using different representationsF-IF.7a Graph quadratic functions and show intercepts, maxima, and minima.F.lF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functionsF-IF.8a 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.

Solve equations and inequalitites in on variableA-REI.4 Solve equations and inequalities in one variable. 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 thequadratic 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 theequation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers "a" and "b".A-REI.7 Solve systems of 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 x^2+y^2=3A.REI.8 Solve systems of equations. Represent a system of linear equations as a single matrix equation in a vector variable.

Construct and compare linear, quadratic, and exponential models and solve problemsF.LE.1 Construct and compare quadratic models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.2 Construct and compare quadratic models and solve problems. Construct 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).F.LE.3 Construct and compare quadratic models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,quadratically, or (more generally) as a polynomial function.F.LE.5 Construct and compare quadratic models and solve problems. Interpret the parameters in an exponential function in terms of a context.

Interpret the stucture of expressionsA.SSE.2 Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. For example, see x^4-y-4 as (x^2)^2-(y^2)^2, thus recognizing it as a differenceof squares that can be factored as (x^2-y^2)(x^2+y^2)A-SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines. A-SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be written as [1.15^(1/12]^(12t) ≈1.012^(12t) to reveal theapproximate equivalent monthly interest rate if the annual rate is 15%.

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.



Common Core State Standards-Mathematics

Q- Quantities

Reason quantitatively and use units to solve problemsCluster:

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Performance Standards

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Grade: Page # : 01-02March 2017Revision Date:

Tier 2- Academic VocabularyTier 3- Domain Specific WordsVerbs- Level of Learning

Standard ResourcesMathematical Practices Explanations/Assessments

Key :

Include word problems where quantities are given in differentunits, which must be converted to make sense of the problem.For example, a problem might have an object moving 12 feetper second and another at 5 miles per hour. To comparespeeds, students convert 12 feet per second to miles per hour:

Graphical representations and data displays include, but arenot limited to: line graphs, circle graphs, histograms, multi-line graphs, scatterplots, and multi-bar graphs.

www.shmoop.com-sample assignments > drills > # 1-10www.orglib.com- High school > HS.N-Q.1 #4

N-Q.1Use units as a way to understand problemsand to guide the solution of multi-step problems; choose and interpret unitsconsistently in formulas; choose andinterpret the scale and the origin in graphsand data displays.

MP.2 Reason abstractly andquantitatively.

MP.4 ّ Model withmathematics.

MP.5 Use appropriate toolsstrategically.

MP.6 Attend to precision.

www.engageny.orgwww.shmoop.comwww.orglib.comwww.solar4schools.org-7 lessonswww.illustrativemathematics.org-traffic jamwww.achieve.com-Yogurt Packaging

Hands-On Algebra by Frances M. Thompson (1998)

Examples:• What type of measurements would one use to determine their income and expenses for one month?• How could one express the number of accidents in Arizona?

Question: Flooding in Europe from excessive rainfall hasbeen on the rise in recent year. Which of the following is aquantity for describing rainfall in this context?-mm/hr-m/s-km/hr-g/cm

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


MP.4 Model withmathematics.


ww.solar4schools.org- 7 lessonswww.opened.comwww.illustrativemathematics.org- traffic jam



Q- Quantities

Reason quantitatively and use units to solve problemsCluster:

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Domain:




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The margin of error and tolerance limit varies according tothe measure, tool used, and context.

Example:• Determining price of gas by estimating to the nearest cent is appropriate because you will not pay in fractions of a cent but the cost of gas is $3.479/gallon.

www.parcc.org (released items)Algebra II PARCC Unit 2 computer-based, #6Algebra I PARCC Unit 1 paper-based, # 11C & #11D

N-Q.3Choose a level of accuracy appropriate tolimitations on measurement when reportingquantities.


MP.3 Construct viablearguments and critique thereasoning of others.




www.achieve.org- Yogurt Packagingwww.orglib.comwww.illustrativemathematics.org- Bus and Car- Calories in a sports drink- Weed killer



SSE- Seeing Structure in Expressions

Interpret the structure of expressions

★ Modeling Standard

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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, theexpression $10,000(1.055)5 represents the amount of money Ihave in an account. My account has a starting value of$10,000 with a 5.5% interest rate every 5 years, where 10,000and (1+.055) are factors, and the $10,000 does not depend onthe amount the account is increased by.

Students should understand the vocabulary for the parts thatmake up the whole expression and be able to identify thoseparts and interpret their meaning in terms of a context.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 11 #13, pg. 17 #5 and p. 35 #15 - Algebra Practice and Problem Solving Workbook p. 5 #6-8

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

MP.1 Make sense ofproblems and persevere insolving them.



MP.7 Look for and make useof structure.

Algebra 1 Common Core, Pearson 2012 - Chapter 1, Sections 1-2 - Chapter 3, Section 7 - Chapter 4, Sections 5 and 7 - Chapter 5, Sections 3-5 - Chapter 7, Sections 6-8 - Chapter 8, Sections 7-8 - Chapter 9, Sections 1-2 and 5-6

www.map.mathshell.org#16 Interpreting Algebraic Expression

www.engageny.orgAlgebra 1 Module 4www.illustrattivemathematics.org/illustrations/390Algebra 2 Common Core, Pearson 2012Chapter 5, Section 2Chapter 8, Section 4

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, theexpression $10,000 (1.055) 5 represents the amount of moneyI have in an account. My account has a starting value of$10,000 with a 5.5% interest rate every 5 years, where 10,000and (1+.055)are factors, and the $10,000 does not depend onthe amount the account is increased by.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 28 #14 - Algebra Practice and Problem Solving Workbook p. 5 #4-8, p. 7 #25, p. 29 #4-7, p. 129 #1-6 and p. 137 #5-6

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





Algebra 1 Common Core, Pearson 2012 - Chapter 1, Sections 1, 2 and 7 - Chapter 4, Sections 5 and 7 - Chapter 5, Sections 3 and 4 - Chapter 7, Sections 7 and 8 - Chapter 8, Sections 5-8 - Chapter 9, Section 5


www.engageny.orgAlgebra 1 Module 4www.illustrativemathematics.org/HSA-SSE-A1Algebra 2 Common Core, Pearson 2012Chapter 4, Section 5Chapter 5, Section 1Chapter 8, Section 4www.schmoop.comHigh School: Algebra-Seeing Structure in Expressions





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Students group together parts of an expression to revealunderlying structure.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 18 #7 - Algebra Practice and Problem Solving Workbook p. 233 #4 and #6

A.SSE.1bInterpret complicated expressions byviewing one or more of their parts as a single entity. For example, interpretP(1+r)n as the product of P and a factornot depending on P. ★





Algebra 1 Common Core, Pearson 2012 - Chapter 3, Section 7 - Chapter 4, Section 7 - Chapter 7, Section 7 - Chapter 8, Sections 6-8 - Chapter 9, Section 5Hands-On Algebra by Frances M. Thompson (1998)


www.engageny.orgAlgebra 1 Module 4

Algebra 2 Common Core, Pearson 2012Chapter 1, Section 6Chapter 7, Sections 1 - 3Chapter 8, Section 4www.schmoop.comHigh School: Algebra-Seeing Structure in Expressions

Students rewrite algebraic expressions by combining liketerms or factoring to reveal equivalent forms of the sameexpression.

Students should extract the greatest common factor (whethera constant, a variable, or a combination of each). If theremaining expression is quadratic, students should factor theexpression further.

Example: Factor x3 -2x2 -35xAlgebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 26 #6, p. 28 #16, p. 37 #30 and p. 38 #35 - Algebra Practice and Problem Solving Workbook p. 253 #1, 6

A.SSE.2Use the structure of an expression toidentify ways to rewrite it. For example,see x4 - y4 as (x2)2 - (y2)2, thus recognizing itas a difference of squares that can befactored as (x2 - y2)(x2 + y2).



Algebra 1 Common Core, Pearson 2012 - Chapter 5, Sections 3-5 - Chapter 8, Sections 7-8Hands-On Algebra by Frances M. Thompson (1998)

www.map.mathshell.org#16 Interpreting Algebraic Expression#66 Pythagorean Theorem: Square Areas#46 Manipulating Polynomials

www.engageny.orgAlgebra 1 Module 4Algebra 2 Common Core, Pearson 2012Chapter 4, Section 4Chapter 5, Section 3Chapter 6, Sections 1 - 3Chapter 8, Section 4www.schmoop.comHigh School: Algebra-Seeing Structure in Expressions





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Students factor quadratic expressions and find the zeros ofthe quadratic function it represents. Zeroes are the x valuesthat yield a y value of 0. They should also explain themeaning of the zeros as they relate to the problem.Example:. If (3m2−15m) is the income gathered at a rockconcert, what values of m would produce an income of 0?

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 43 #16 - Algebra Practice and Problem Solving Workbook p. 273 #1-5

A-SSE.3aFactor a quadratic expression to reveal thezeros of the function it defines. ★





Algebra 1 Common Core, Pearson 2012 - Chapter 9, Sections 4

www.shmoop.comHigh School: AlgebraSeeing Structure in Expressionswww.sophia.org/ccss-math-standard-9-12asse3a-pathwaywww.khanacademy/commoncore/grade-HSA-A-SSE


Students will use the properties of operations to createequivalent expressions.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 42 #10 and p. 45 #27 - Algebra Practice and Problem Solving Workbook p. 277

www.parcc.org (released items)Algebra 1 PARCC Unit 1, #6A, #7 Unit 3, #36

A-SSE.3bComplete the square in a quadraticexpression to reveal the maximum orminimum value of the function it defines.★


MP.2 ٘ Reason abstractly andquantitatively.




www.illustrativemathematics.orgtask - rewriting a quadratic expressiongreatminds.netLesson 11hcpss.cominstructional resources (Skate Park)






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Key :

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.

Algebra 1 Common Core , Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 33 #2-6 - Algebra Practice and Problem Solving Workbook p. 221 #6

www.parcc.org (released items)Algebra I EOY PARCC #31

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 to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. ★

MP.1 ٘ Make sense ofproblems and persevere insolving them.





www.shmoop.comHigh School: AlgebraSeeing Structure in ExpressionsAlgebra II PARCC Unit 3, #37www.sophia.orgwww.learnzillion.comwww.achieve.orgSpread of Disease



CED- Creating Equations

Create equations that describe numbers or relationships


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Key :

Equations can represent real world and mathematicalproblems. Include equations and inequalities that arise whencomparing the values of two different functions, such as onedescribing linear growth and one describing exponentialgrowth.

Example:

• Lava coming from the eruption of a volcano follows aparabolic path. The height h in feet of a piece of lavat seconds after it is ejected from the volcano is given by h(t)= -t2 +16t +936. After how many seconds does the lavareach its maximum height of 1000 feet?

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 11-14 #12, 14, 20, 21, 24, 26, 29; p. 22 #29 - Algebra Practice and Problem Solving Workbook p. 41 #6-7; p. 45 #3-5; p. 49 #6; p. 53 #6; p. 85 #7; p. 89 #6; p. 93 #7; p. 105 #6; p. 269 #8; p. 277 #6 and p. 281 #7

A-CED.1Create equations and inequalities in onevariable and use them to solve problems.Include equations arising from linear andquadratic functions, and simple rationaland exponential functions. ★





Algebra 1 Common Core, Pearson 2012 - Chapter 1, Section 8 - Chapter 2, Sections 1-5, 7-8 - Chapter 3, Sections 2-4, 6-8 - Chapter 9, Sections 3-6 - Chapter 11, Section 5

www.map.mathshell.org#13 Sorting Equations & Identities

www.illustrativemathematics.org/content-standards/HSA/CED/A/1www.engageny.orgAlgebra I Module 1, Topic D, Lesson 25 (#1-7)www.khanacademy.org/commoncore/grade-HSA-A-CED


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.

Example: The height of a ball t seconds after it is kickedvertically depends upon the initial height and velocity of theball and on the downward pull of gravity. Suppose the ballleaves the kicker’s foot at an initial height of 0.7 m with initial upward velocity of 22m/sec. Write an algebraicequation relating flight time t in seconds and height h inmeters for this punt.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 9-10 #1-2 and 8; p. 12 #15; p. 19 #17; p. 20-21 #23-25; and p. 34 #7. - Algebra Practice and Problem Solving Workbook p. 265 #1

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





Algebra 1 Common Core, Pearson 2012 - Chapter 1, Section 9 - Chapter 4, Section 5 - Chapter 5, Sections 2-5 - Chapter 7, Sections 6-7 - Chapter 9, Sections 1-2 - Chapter 10, Section 5 - Chapter 11, Sections 6-7 - Concept Bytes Chapter 9, Section 4 and - Chapter 11, Section 7

www.map.mathshell.org#3 Solving Linear Equations in Two Variables#1 Optimization Problems: Boomerangs

www.illustrativemathematics.org/HSA-CED.A.2www.shmoop.com/common-core-standards/ccss-hs-a-ced-2.html



CED- Creating Equations

Create equations that describe numbers or relationships


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Key :

When given a problem situation involving limits or restrictions, represent thesituation symbolically using an equation or inequality. Interpret the solution(s)in the context of the problem. When given a real world situation involvingmultiple restrictions, develop a system of equations and/or inequalities thatmodels the situation.

Example: A club is selling hats and jackets as a fundraiser. Their budget is$1500 and they want to order at least 250 items. They must buy at least asmany hats as they buy jackets. Each hat costs $5 and each jacket costs $8.• Write a system of inequalities to represent the situation.• Graph the inequalities.• If the club buys 150 hats and 100 jackets, will the conditions be satisfied?• What is the maximum number of jackets they can buy and still meet the conditions?

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 29 #24 and p. 44 #19 - Algebra Practice and Problem Solving Workbook p. 189 #6; p. 289 #5 and p. 287 #13-14

A-CED.3Represent constraints by equations orinequalities, and by systems of equationsand/or inequalities, and interpret solutionsas viable or nonviable options in amodeling context. For example, representinequalities describing nutritional and costconstraints on combinations of differentfoods.★





Algebra 1 Common Core, Pearson 2012 - Chapter 6, Sections 4-5 - Chapter 9, Section 8

www.map.mathshell.org#3 Solving Linear Equations in Two Variables#1 Optimization Problems: Boomerangs

www.shmoop.com/common-core-standards/ccss-hs-a-ced-3.htmlwww.illustrativemathematics.org/HSA-CEDwww.engageny.orgAlgebra I Module 1, Topic C, Lesson 24


Examples:The Pythagorean Theorem expresses the relation between thelegs a and b of a right triangle and its hypotenuse c with theequation 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.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 10 #6; p. 13 #25; p. 42 #8 and p. 43 #13 - Algebra Practice and Problem Solving Workbook p. 57 #3 and #6

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.★






Algebra 1 Common Core, Pearson 2012 - Chapter 2, Section 5 - Chapter 9, Section 3

www.map.mathshell.org#5 Modeling Situations with Linear Equations

www.engageny.orgAlgebra 1 Module 1, Topic C, Lesson 19www.illustrativemathematics.org/content-standards/HSA/CED/A/4/tasks/1828www.shmoop.com/common-core-standards/ccss-hs-a-ced-4.html



IF- Interpreting Functions

Understand the concept of a function and use function notation Cluster:

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11


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 afunction should be developed through an understanding thateach input has exactly one output. If a specific rule can bewritten which models the relation between the input and oneunique output, then it is a function. When this relationship isestablished,the variable y becomes f(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 theequation using function notation, f(x)=3x+5. The domain of afunction given by an algebraic expression, unless otherwisespecified, is the largest possible domain.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 20 #19-21; p. 21 #27 - Algebra Practice and Problem Solving Workbook p. 133 #1-5

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).




Algebra 1 Common Core, Pearson 2012 - Chapter 4, Section 6


www.engageny.orgwww.betterlesson.comwww.pblpathways.comwww.sharemylesson.com

The domain of a function given by an algebraic expression,unless otherwise specified, is the largest possible domain.

Examples:•If f(x) = x2 = 4x -12, find f(2)•Let f(x) = 2(x + 3)2. Find f(3), f (-1/2), f(a) and f(a-h)•If P(t) is the population of Tucson t years after 2000,interpret the statementsP(0) = 487,000 and P(10)-P(9) = 5,900.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 20 #22; p. 22 #28 and 30-31 - Algebra Practice and Problem Solving Workbook p. 133 #1-5; p. 132 #13-14

F-IF.2Use function notation, evaluate functionsfor inputs in their domains, and interpretstatements that use function notation interms of a context.






www.map.mathshell.org#62 Lines and Linear Equations



Understand the concept of a function and use function notationCluster:

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11


Domain:


Tier 2- Academic Vocabulary Tier 3- Domain Specific WordsVerbs- Level of Learning


Key :


F-IF.3Recognize that sequences are functions,sometimes defined recursively, whosedomain is a subset of the integers. Forexample, the Fibonacci sequence is definedrecursively by f(0) = f(1) = 1, f(n+1) = f(n)+ f(n-1) for n ≥ 1.



MP.8 Look for and expressregularity in repeatedreasoning.



www.engageny.orgwww.betterlesson.comwww.pblpathways.comwww.sharemylesson.com

Students may be given graphs to interpret or produce graphsgiven an expression or table for the function, by hand orusing technology. Examples:• A rocket is launched from 180 feet above the ground at timet = 0. The function that models this situation is given by h = –16t2 + 96t + 180, where t is measured in seconds and h isheight above the ground measured in feet.• What is a reasonable domain restriction for t in this context?• Determine the height of the rocket two seconds after it waslaunched.• Determine the maximum height obtained by the rocket. • Determine the time when the rocket is 100 feet above theground.• Determine the time at which the rocket hits the ground.• How would you refine your answer to the first questionbased on your response to the second and fifth questions.Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 18 #9 - Algebra Practice and Problem Solving Workbook p. 117 #5; p. 157 #5; p. 221 #3; p. 261 #1-2; p. 265 # 1-3

F-IF.4For a function that models a relationshipbetween two quantities, interpret keyfeatures of graphs and tables in terms of thequantities, and sketch graphs showing keyfeatures given a verbal description of therelationship. Key features include:intercepts; intervals where the function is increasing, decreasing, positive, ornegative; relative maximums andminimums; symmetries; end behavior; andperiodicity. ★

MP.2 Reason abstractly and quantitatively.






Algebra 1 Common Core, Pearson 2012 - Chapter 4, Sections 2-3 - Chapter 5, Sections 3-5 - Chapter 7, Sections 6-7 - Chapter 9, Sections 1-2 and 7 - Chapter 11, Section 7




Understand the concept of a function and use function notation Cluster:

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


11


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. Students may explain orally, or in written format, theexisting relationships.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 19 #12; p. 38 #33; p. 41 #4; p. 46-47 #29, 33 and 35 - Algebra Practice and Problem Solving Workbook p. 215 #14-16; p. 261 #5

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. ★




Algebra 1 Common Core, Pearson 2012 - Chapter 4, Section 4 - Chapter 7, Section 6 - Chapter 9, Section 1 - Chapter 11, Section 6


www.illuminations.nctm.org-Barbie Bungee-Domain: Representations

Students should be able to describe patterns of changes from tables 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.

Algebra 1 Common Core , Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 25 #1 - Algebra Practice and Problem Solving Workbook p. 141 #1-6

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. ★




Algebra 1 Common Core, Pearson 2012 - Chapter 5, Section 1 - Concept Byte Chapter 9, Section 2


www.illuminations.nctm.org-Cardiac Output, Rate of Change, Accumulation-Pedal Power




* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


11


Domain:




Key :

Key characteristics include but are not limited to maxima,minima, intercepts, symmetry, end behavior, and asymptotes.Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to graphfunctions.

Examples:•Describe key characteristics of the graph off(x) = │x – 3│ + 5.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 34 #10 - Algebra Practice and Problem Solving Workbook p. 149 #1; p. 153 #4; p. 157 #3; p. 169 #5

F-IF.7Graph functions expressed symbolicallyand show key features of the graph, byhand in simple cases and using technologyfor more complicated cases. ★



Algebra 1 Common Core, Pearson 2012 - Chapter 5, Sections 3-5 and 8 - Chapter 7, Sections 6-7 - Chapter 9, Sections 1-2


Key characteristics include but are not limited to maxima,minima, intercepts, symmetry, end behavior, and asymptotes.Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to graphfunctions.Examples:•Describe key characteristics of the graph off(x) = │x – 3│ + 5.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 25 #3; p. 27 #10 - Algebra Practice and Problem Solving Workbook p. 149 #6; p. 153 #6; p.157 #3; p. 217 #4; p. 261 #1; p. 265 #6

F-IF.7aGraph linear and quadratic functions andshow intercepts, maxima, and minima.



Algebra 1 Common Core, Pearson 2012 - Chapter 5, Sections 3-5 and 8 - Chapter 7, Sections 6-7 - Chapter 9, Sections 1-2


www.illuminations.nctm.org-Light It Upwww.khanacademy.org




* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


11


Domain:




Key :

Key characteristics include but are not limited to maxima,minima, intercepts, symmetry, end behavior, and asymptotes.Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to graphfunctions.Examples:•Describe key characteristics of the graph off(x) = │x – 3│ + 5.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 28 #15 - Algebra Practice and Problem Solving Workbook p. 169 #5; p. 309 #4 and 6

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



Algebra 1 Common Core, Pearson 2012 - Chapter 5, Section 8 - Chapter 9, Section 1 - Chapter 10, Section 5 - Concept Byte Chapter 5, Section 8


www.illuminations.nctm.org-Light It Upwww.khanacademy.org

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 41 #1-2; p. 42 #7 - Algebra Practice and Problem Solving Workbook p. 273 #4; p. 277 #5-7

F-IF.8aUse the process of factoring and completingthe square in a quadratic function to showzeros, extreme values, and symmetry of thegraph, and interpret these in terms of acontext.



Algebra 1 Common Core, Pearson 2012 - Chapter 9, Sections 4-5





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11


Domain:




Key :

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 30 #28; p. 36 #23 - Algebra Practice and Problem Solving Workbook p. 157 #1; p. 265 #1-3

F-IF.9Compare properties of two functions eachrepresented in a different way(algebraically, graphically, numerically intables, or by verbal descriptions).



Algebra 1 Common Core, Pearson 2012 - Chapter 5, Section 5 - Chapter 7, Section 6 - Chapter 9, Section 2



BF- Building Functions

Build a function that models a relationship between two quantities


Cluster:

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


5


Domain:




Key :

Students will analyze a given problem to determine the function expressed by identifying patterns in the function’srate of change. They will specify intervals of increase,decrease, constancy, and, if possible, relate them to thefunction’s description in words or graphically. Students mayuse graphing calculators or programs, spreadsheets, orcomputer algebra systems to model functions.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 38 #36; p. 36 #19; p. 42 #6; p. 46 #30 - Algebra Practice and Problem Solving Workbook p. 149 #5; p.157 #4; p. 219 #15

F-BF.1Write a function that describes arelationship between two quantities. ★

MP.1 Make sense ofproblems and persevere insolving them.MP.2 Reason abstractly andquantitatively.MP.3 Construct viablearguments and critique thereasoning of others.MP.4 Model withmathematics.MP.5 Use appropriate toolsstrategically.MP.6 Attend to precision.MP.7 Look for and make useof structure.MP.8 Look for and expressregularity in repeatedreasoning.

Algebra 1 Common Core, Pearson 2012 - Chapter 4, Section 7 - Chapter 5, Sections 3-5 - Chapter 7, Section 7 - Chapter 9, Section 2


www.map.mathshell.org#9 Generalizing Patterns: Table Tiles

Examples from above:• You buy a $10,000 car with an annual interest rate of 6percent compounded annually and make monthly paymentsof $250. Express the amount remaining to be paid off as afunction of the number of months, using a recursion equation.• A cup of coffee is initially at a temperature of 93º F. Thedifference between its temperature and the room temperature of 68º F decreases by 9% each minute. Write a functiondescribing the temperature of the coffee as a function of time.• The radius of a circular oil slick after t hours is given in feetby r=10t2 - 0.5t, for 0 ≤ t ≤ 10. Find the area of the oil slickas a function of time.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 19 #14; p. 29 #25 - Algebra Practice and Problem Solving Workbook p. 137 #6; p. 157 #5; p. 225 #6

F-BF.1aDetermine an explicit expression, arecursive process, or steps for calculationfrom a context.


Algebra 1 Common Core, Pearson 2012 - Chapter 4, Section 7 - Chapter 5, Sections 3-5 - Chapter 7, Section 8



www.illustrativemathematic.org-Intro to Recursion and Sequences.





Cluster:

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


5


Domain:




Key :

Students will analyze a given problem to determine the function expressed by identifying patterns in the function’srate of change. They will specify intervals of increase,decrease, constancy, and, if possible, relate them to thefunction’s description in words or graphically. Students mayuse graphing calculators or programs, spreadsheets, orcomputer algebra systems to model functions.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 46 #31 - Algebra Practice and Problem Solving Workbook p. 285 #4

F-BF.1bCombine standard function types usingarithmetic operations. For example, build afunction that models the temperature of acooling body by adding a constant functionto a decaying exponential, and relate thesefunctions to the model.





www.mathisfun.com-tutorial and practice: operations with functions

An explicit rule for the nth term of a sequence gives an as anexpression in the term’s position n; a recursive rule gives thefirst term of a sequence, and a recursive equation relates an tothe preceding term(s). Both methods of presenting a sequencedescribe an as a function of n.Examples:•Generate the 5th-11th terms of a sequence if A1= 2 and•Use the formula: An= A1 + d(n - 1) where d is the commondifference to generate a sequence whose first three terms are:-7, -4, and -1.•There are 2,500 fish in a pond. Each year the population decreases by 25 percent, but 1,000 fish are added to the pondat the end of the year. Find the population in five years. Also,find the long-term population.Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 19 #15; p. 36 #22 - Algebra Practice and Problem Solving Workbook p. 137 #5-6; p. 225 #2-3 and 6

F-BF.2Write arithmetic and geometric sequencesboth recursively and with an explicitformula, use them to model situations, andtranslate between the two forms. ★






www.engageny.org-Lesson-Math: F.BF.2

www.opened.com-Resource Library F.BF.2





Cluster:

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5


Domain:




Key :

Students will apply transformations to functions andrecognize functions as even and odd. Students may usegraphing calculators or programs, spreadsheets, or computeralgebra systems to graph functions.Examples:•Is f(x) = x3 - 3x2 + 2x + 1 even, odd, or neither? Explain youranswer orally or in written format.

•Describe effect of varying the parameters a, h, and k have onthe shape and position of the graph of f(x) = a(x-h)2 + k.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 26 #5; p. 37 #25 - Algebra Practice and Problem Solving Workbook p. 169 #2, 4 and 7; p. 261 #2

F-BF.3Identify the effect on the graph of replacingf(x) by f(x) + k, k f(x), f(kx), and f(x + k)for specific values of k (both positive andnegative); find the value of k given thegraphs. Experiment with cases and illustratean explanation of the effects on the graphusing technology. Include recognizing evenand odd functions from their graphs andalgebraic expressions for them.




Algebra 1 Common Core, Pearson 2012 - Chapter 5, Sections 3-4 and 8 - Chapter 7, Section 7 - Chapter 9, Sections 1-2 - Concept Byte Chapter 5, Section 3



REI- Reasoning with Equations and Inequalities

Solve equations and inequalities in one variableCluster:

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4


Domain:




Key :

Examples:Solve, Ax + B = C for x. What are the specific restrictions on A?

What is the difference between solving an equation and simplifying an expression?

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 11 #10-11; pg. 12 #16-19; p. 13 #22-23; p. 17 #2 and 4; and p. 18 #6 and 11 - Algebra Practice and Problem Solving Workbook p. 45 #1-2; p. 49 #1-2; p. 53 #6; p. 57 #6; p. 85 #7; p. 89 #1-3; p. 93 #7 and p. 97 #1-2

A-REI.3Solve linear equations and inequalities inone variable, including equations withcoefficients represented by letters.

Per Evidence Statement:Tasks do not include absolute valueequations or compound inequalities.




Algebra 1 Common Core, Pearson 2012 - Chapter 2, Sections 1-5, 7-8 - Chapter 3, Sections 2-6


www.map.mathshell.org#13 Sorting Equations and Identities#14 Defining Regions using Inequalities

www.khanacademy.orgAlgebra: Reasoning with Equations and Inequalitieswww.shmoop.comwww.illustrativemathematics.org

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 .

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 43 #11; p. 44 #18; and p. 46 #32 - Algebra Practice and Problem Solving Workbook p. 269 #1-3; p. 273 #1-4; p. 277 #2 and 7; and p. 281 #2-3

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






www.khanacademy.orgAlgebra: Reasoning with Equations and Inequalitieswww.shmoop.comwww.illustrativemathmatics.org



Solve equations and inequalities in one variable Cluster:

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


4


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 of y = ax2 + bx + c .

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 43 #12 and 14; p. 44 #17 and 20 - Algebra Practice and Problem Solving Workbook p. 277 #1-7 and p. 281 #1 and 4

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






www.khanacademy.orgAlgebra: Reasoning with Equations and Inequalities

map.mathshell.orgLessonsSolving Quadratic Equations

www.shmoop.comHigh School: AlgebraReasoning with Equations and Inequalities

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 .

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 43 #15; p. 44 #21-22 - Algebra Practice and Problem Solving Workbook p. 281 #4; p. 269 #5 and 8; and p. 273 #2

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.






www.khanacademy.orgAlgebra: Reasoning with Equations and Inequalities

www.shmoop.comHigh School: AlgebraReasoning with Equations and Inequalities



Solve systems of equationsCluster:

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6


Domain:




Key :

Example:

Given that the sum of two numbers is 10 and their differenceis 4, what are the numbers? Explain how your answer can bededuced from the fact that they two numbers, x and y, satisfythe equations x + y = 10 and x – y = 4.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 29 #23 - Algebra Practice and Problem Solving Workbook p. 181 #6

A-REI.5Prove that, given a system of two equationsin two variables, replacing one equation bythe sum of that equation and a multiple ofthe other produces a system with the same solutions.



Algebra 1 Common Core, Pearson 2012 - Chapter 6, Section 3Algebra 2 Common Core, Pearson 2012 - Chapter 3, Section 2

www.map.mathshell.org#3 Solving Linear Equations in Two Variables#68 Classifying Solutions to Systems of Equations

www.shmoop.comwww.kahnacademy.org

The system solution methods can include but are not limitedto graphical, elimination/linear combination, substitution, andmodeling. Systems can be written algebraically or can berepresented in context. Students may use graphingcalculators, programs, or applets to model and findapproximate solutions for systems of equations.Examples:• José had 4 times as many trading cards as Phillipe. AfterJosé gave away 50 cards to his little brother and Phillipe gave5 cards to his friend for this birthday, they each had an equalamount of cards. Write a system to describe the situation andsolve the system. • Solve the system of equations: x+ y = 11 and 3x – y = 5.Use a second method to check your answer.

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 29 #21; p. 30 #27 - Algebra Practice and Problem Solving Workbook p. 173 #1-5; p. 177 #4; p. 181 #6; p. 185 #4

A-REI.6Solve systems of linear equations exactlyand approximately (e.g., with graphs),focusing on pairs of linear equations in twovariables.







Algebra 1 Common Core, Pearson 2012 - Chapter 6, Sections 1-4Algebra 2 Common Core, Pearson 2012 - Chapter 3, Section 1-3

www.map.mathshell.org#3 Solving Linear Equations in Two Variables#1 Optimization Problems: Boomerangs#68 Classifying Solutions to Systems

www.shmoop.comwww.kahnacademy.org




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6


Domain:




Key :

Example:Two friends are driving to the Grand Canyon in separate cars. Suzette has been there before and knows the way but Andreadoes not. During the trip Andrea gets ahead of Suzette andpulls over to wait for her. Suzette is traveling at a constantrate of 65 miles per hour. Andrea sees Suzette drive past. Tocatch up, Andrea accelerates at a constant rate. The distancein miles (d) that her car travels as a function of time in hours(t) since Suzette’s car passed is given by d = 3500t2.

Write and solve a system of equations to determine how longit takes for Andrea to catch up with Suzette.


A-REI.7Solve a simple system consisting of a linearequation and a quadratic equation in twovariables algebraically and graphically. Forexample, find the points of intersectionbetween the line y = –3x and the circle x2 +y2 = 3.







Algebra 1 Common Core, Pearson 2012 - Chapter 9, Section 8Algebra 2 Common Core, Pearson 2012 - Chapter 4, Section 9

www.map.mathshell.org#3 Solving Linear Equations in Two Variables #1 Optimization Problems: Boomerangs#68 Classifying Solutions to Systems

www.kahnacademy.orgwww.engageny.orgAlgebra II Module 1, Topic C, Lesson 31

Example:

Which of the following points is on the circle with equation(x-1)2 + (y+2)2 = 5?

(a) (1, -2) (b) (2, 2) (c) (3, -1) (d) (3, 4)

Algebra 1 Common Core , Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 9 #3; p. 18 #10 - Algebra Practice and Problem Solving Workbook p. 37 #6; p. 117 #4-5; p. 125 #5

A-REI.10Understand that the graph of an equation intwo variables is the set of all its solutionsplotted in the coordinate plane, oftenforming a curve (which could be a line).





Algebra 1 Common Core, Pearson 2012 - Chapter 1, Section 9 - Chapter 4, Sections 2-4

www.engageny.orgAlgebra I Module 1, Topic C, Lesson 24 www.shmoop.com




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6


Domain:




Key :

Students need to understand that numerical solution methods(data in a table used to approximate an algebraic function)and graphical solution methods may produce approximatesolutions, and algebraic solution methods produce precisesolutions that can be represented graphically or numerically.Students may use graphing calculators or programs togenerate tables of values, graph, or solve a variety offunctions.Example:Given the following equations determine the x value thatresults in an equal output for both functions.

f(x) - 3x - 2 g(x) = (x+3)2 -1

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 28 #19; p. 35 #12 - Algebra Practice and Problem Solving Workbook p. 287 #13-14

A-REI.11Explain why the x-coordinates of the pointswhere the graphs of the equations y = f(x)and y = g(x) intersect are the solutions ofthe equation f(x) = g(x); find the solutionsapproximately, e.g., using technology tograph the functions, make tables of values,or find successive approximations. Includecases where f(x) and/or g(x) are linear,polynomial, rational, absolute value,exponential, and logarithmic functions. ★





Algebra 1 Common Core, Pearson 2012 - Chapter 7, Section 6 - Chapter 9, Section 8 - Concept Bytes Chapter 4, Section 4 and Chapter 6, Section 1

www.map.mathshell.org#68 Classifying Solutions to Systems

www.engageny.orgAlgebra I Module 3, Topic C, Lesson 16Algebra II Module 3, Topic D, Lesson 24 (Logs)

www.khanacademy.orgwww.shmoop.com

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 than 100magazines every year. At least 30 of these are women’s magazines, but the company always publishes at least asmany women’s magazines as men’s magazines. Find a system 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 solution.

Algebra 1 Common Core , Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 29 #20; p.30 #29-30 - Algebra Practice and Problem Solving Workbook p. 189 #1-6; p. 193 #4-5

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.



Algebra 1 Common Core, Pearson 2012 - Chapter 6, Sections 5-6 - Concept Byte Chapter 6, Section 6Algebra 2 Common Core, Pearson 2012 - Chapter 3, Section 3

www.map.mathshell.org#14 Defining Regions using Inequalities

www.khanacademy.orgwww.shmoop.comwww.engageny.orgAlgebra 1 Module 1, Topic C, Lesson 21Algebra 1 Module 1, Topic C, Lesson 22


APR- Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomialsCluster:

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1


Domain:

Grade: Page # : 23March 2017Revision Date:



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 (16x 4+9)

Algebra 1 Common Core, Pearson 2012 - Algebra 1 Progress Monitoring Assessments p. 35 #14,;p. 36 #16-18, 20-21, 24; p. 37 #26, 28-29; and p. 38 #34 - Algebra Practice and Problem Solving Workbook p. 229 #4-6; p. 233 #1, 4-5; p. 237 #1-6; and p. 241 #1 and 3

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.





www.map.mathshell.org#46 Manipulating Polynomials

www.engageny.orgAlgebra I Module 4, Topic A, Lesson 2www.shmoop.comwww.khanacademy.org


RN- Real Number System

Extend the properties of exponents to rational exponentsCluster:

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2


Domain:

Grade: Page # : 24March 2017Revision Date:



Key :

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

www.parcc.org (released items)Algebra II PARCC Unit 1, # 2, # 5Algebra II PARCC Unit 2, # 23

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(51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal5.




www.shmoop.com-HSN-RN.A.1 -sample assignments -aligned resources

www.engageny.org- N.RN.1 -Algebra II Module 3, Topic A, Lesson 4

www.google.com-”hcpss.com n.rn.1” -N.RN.1 & N.RN.2 -instructional resources

Students should be able to use the properties of exponents torewrite expressions involving radicals as expressions usingrational exponents.

www.parcc.org (released items)Algebra II PARCC Unit 1, # 2, # 5Algebra II PARCC Unit 2, # 23

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


www.shmoop.com-HSN-RN.A.1 -sample assignments -aligned resources

www.engageny.org- N.RN.1 -Algebra II Module 3, Topic A, Lesson 4

www.google.com-”hcpss.com n.rn.1” -N.RN.1 & N.RN.2 -instructional resources


ID- Interpreting Categorical and Quantitative Data

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

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11


Domain:




Key :

Construct dot plots, histograms and box plots for dataon a real number line.

Algebra 1 Common Core, Pearson 2012- Algebra Practice and Problem Solving Workbookp. 356 #18-19

www.parcc.org (released items)Algebra II PARCC paper-based, unit 2, #22

S-ID.1Represent data with plots on the realnumber line (dot plots, histograms, and boxplots).




www.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-speed trapwww.orglib.com-assessment questions, examples, practice sheets

www.parcc.org (released items)Algebra II PARCC paper-based, unit 2, #26Algebra I PARCC paper-based, unit 1, #12

S-ID.2Use statistics appropriate to the shape of thedata distribution to compare center(median, mean) and spread (interquartilerange, standard deviation) of two or moredifferent data sets.







www.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-speed trapwww.orglib.com-assessment questions, examples, practice sheets



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

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11


Domain:




Key :

Students may use spreadsheets, graphing calculators andstatistical software to statistically identify outliers and analyze data sets with and without outliers as appropriate.

Algebra 1 Common Core, Pearson 2012- Algebra Practice and Problems Solving Workbookp. 353 #25-28

S-ID.3Interpret differences in shape, center, andspread in the context of the data sets,accounting for possible effects of extremedata points (outliers) .







www.google.com- “troup.com s.id.1” > unit 6 www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-speed trapwww.orglib.com-assessment questions, examples, practice sheets

www.parcc.org (released items)Algebra I PARCC, unit 2, #1

S-ID.5Summarize categorical data for twocategories in two-way frequency tables .Interpret relative frequencies in the contextof the data (including joint, marginal, andconditional relative frequencies). Recognizepossible associations and trends in the data.







www.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.orgwww.orglib.com-assessment questions, examples, practice sheets



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

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11


Domain:




Key :

The residual in a regression model is the difference betweenthe observed and the predicted Y for some x (y thedependent variable) and the independent variable). So if wehave a model y=ax+b , and a data point (x i,yi) the residual isfor this point is: ri=yi-(axi+b). Students may use spreadsheets,graphing calculators, and statistical software to represent data, describe how the variables are related, fit functions todata, perform regressions, and calculate residuals.www.parcc.org (released items)Algebra II PARCC paper-based, unit 3, #6

S-ID.6Represent data on two quantitativevariables on a scatter plot , and describehow the variables are related.







www.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.orgwww.orglib.com-assessment questions, examples, practice sheets

www.parcc.org (released items)Algebra II PARCC, paper-based unit 3, #36

S-ID.6aFit a function to the data; use functionsfitted to data to solve problems in thecontext of the data. Use given functions orchoose a function suggested by the context.Emphasize linear, quadratic, andexponential models.



MP.4 Model with mathematics.




www.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org- Olympic Men’s 100 meter dashwww.orglib.com-assessment questions, examples, practice sheets




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11


Domain:




Key :

www.sophia.org-”s.id.6b” > Residuals -Quiz after tutorialwww.holland.wnyric.org-”s.id.6b” > Residuals Name: Date: 1.

S-ID.6bInformally assess the fit of a function byplotting and analyzing residuals.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique thereasoning of others.





www.illustrativemathematics.com- Restaurant Bill & Party Sizewww.sophia.org- “s.id.6b” > Residualswww.shmoop.com- aligned resources -videoswww.engageny.org

Given a table of scatter plot data, write a linear function.

www.parcc.org (released items)Algebra I PARCC paper-based unit 2, #21

S-ID.6cFit a linear function for a scatter plot thatsuggests a linear association.







www.sophia.orgwww.google.com- “troup.com s.id.1” > unit 6www.thirteen.org- math in restaurantswww.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.orgwww.orglib.com-assessment questions, examples, practice sheets




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Key :

www.parcc.org (released items)Algebra II PARCC paper-based unit 3, #33

S-ID.7Interpret the slope (rate of change) and theintercept (constant term) of a linear modelin the context of the data.






www.google.com- “troup.com s.id.1” > unit 6www.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-Coffee & Crime-Olympic-Texting & Gradeswww.orglib.com-assessment questions, examples, practice sheets

Calculate the correlation coefficient for the following data.x y12 18 75 43 62 40 2(in a table)a. r = -.012b. r = -.2c. r = -.022d. r = -.32

S-ID.8Compute (using technology) and interpretthe correlation coefficient of a linear fit.




www.google.com- “troup.com s.id.1” > unit 6www.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-Coffee & Crime-Olympic-Texting & Gradeswww.orglib.com-assessment questions, examples, practice sheets




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11


Domain:




Key :

Some data leads observers to believe that there is a cause andeffect relationship when a strong relationship is observed.Students should be careful not to assume that correlationimplies causation. The determination that one thing causesanother requires a controlled randomized experiment. Example:•Diane did a study for a health class about the effects of astudent’s end-of-year math test scores on height. Based on agraph of her data, she found that there was a directrelationship between students’ math scores and height. Sheconcluded that “doing well on your end-of-course math testsmakes you tall.” Is this conclusion justified? Explain anyflaws in Diane’s reasoning.

www.parcc.org (released items)Algebra II PARCC paper-based unit 2, #20B

S-ID.9Distinguish between correlation andcausation.




www.google.com- “troup.com s.id.1” > unit 6www.engageny.orgwww.shmoop.com- aligned resources -videoswww.illustrativemathematics.org-Coffee & Crime-High Blood Pressure-Math Test Gradeswww.orglib.com-assessment questions, examples, practice sheets


CO- Congruence

Experiment with transformations in the plane Cluster:

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11


Domain:




Key :

Definitions are used to begin building blocks for proof. Infuse thesedefinitions into proofs and other problems. Pay attention toMathematical practice 3 “Construct viable arguments and critique thereasoning of others:Understand and use stated assumptions,definitions and previously established results in constructingarguments.” Also mathematical practice number six says, “ Attend toprecision: Communicate precisely to others and use clear definitionsin discussion with others and in their own reasoning.” Know that apoint has position, no thickness or distance. A line is made of infinitely many points, and a line segment is a subset of the points ona line with endpoints. A ray is defined as having a point on one endand a continuing line on the other. An angle is determined by theintersection of two rays. A circle is the set of infinitely many pointsthat are the same distance from the center forming a circular are,measuring 360 degrees. Perpendicular lines are lines in the interest ata point to form right angles. Parallel lines that lie in the same planeand are lines in which every point is equidistant from thecorresponding point on the other line.

-Chapter 8:section 3 #1-30section 4 # 9-22section 6 #3-35PARCC (2015) EOY #22

G-CO.1Know precise definitions of angle, circle,perpendicular line, parallel line, and linesegment, based on the undefined notions ofpoint, line, distance along a line, anddistance around a circular arc.

MP.6 Attend to precision. Integrated Mathematics 1, Houghton, Mifflin, Harcourt 2016

-Chapter 8, section 3-Chapter 8, section 4-Chapter 8, section 6

Describe and compare geometric and algebraictransformations on a set of points as inputs to produceanother set of points as outputs, to include translations andhorizontal and vertical stretching. Using InteractiveGeometry Software perform the following dilations(x,y)→(4x,4y) (x,y)→(x,4y) (x,y)→(4x, y) on the triangledefined by the points (1,1) (6,3) (2,13). Compare and contrastthe following from each dilation: angle measure, side length,perimeter.

-Chapter 11 # 7-10

G-CO.2Represent transformations in the planeusing, e.g., transparencies and geometrysoftware; describe transformations asfunctions that take points in the plane asinputs and give other points as outputs.Compare transformations that preservedistance and angle to those that do not (e.g.,translation versus horizontal stretch).



Integrated Mathematics 1, Houghton, Mifflin, Harcourt 2016

-Chapter 11, section 4


CO- Congruence

Experiment with transformations in the planeCluster:

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11


Domain:




Key :

Describe the rotations and reflections of a rectangle,parallelogram, trapezoid, or regular polygon that maps each figure onto itself, beginning and ending with thesame geometric shape. Given combinations of rotations and reflections, illustrate each combination with a diagram.Where a combination is not possible, give examples toillustrate why that will not work (coordinate arguments).

-Chapter 11section 2 #1-16section 3 #7-16

www.parcc.org (released items)PARCC (2015) EOY #3

G-CO.3Given a rectangle, parallelogram, trapezoid,or regular polygon, describe the rotationsand reflections that carry it onto itself.





-Chapter 11, section 2-Chapter 11, section 3

Refer to 8.G where students have already experimented withthe properties of rigid transformations and dilations. Studentsshould understand and be able to explain that when a figure isreflected about a line, the segment that joins the preimage point to its corresponding image point is perpendicularlybisected by the line of reflection. When figures are rotated,the points travel in a circular path over some specified angleof rotation. When figures are translated, the segments of thepreimage are parallel to the corresponding segments of theimage.

Students may use geometry software and/or manipulatives tomodel transformations. Students may observe patterns anddevelop definitions of rotations, reflections, and translations.

-Chapter 11section 1 #9-24section 2 #1-16section 3 #7-16

G-CO.4Develop definitions of rotations,reflections, and translations in terms ofangles, circles, perpendicular lines, parallellines, and line segments.




Integrated Mathematics 1, Houghton, Mifflin,Harcourt 2016



CO- Congruence


* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


11


Domain:




Key :

Using Interactive Geometry Software or graph paper,perform the following transformations on the triangle ABCwith coordinates A(4,5), B(8,7) and C(7,9). First, reflect thetriangle over the line y=x. Then rotatethe figure 180° about the origin. Finally, translate the figure up 4 units and to theleft 2 units. Write the algebraic rule in the form (x,y)→(x’,y’)that represents this composite transformation Students mayuse geometry software and/or manipulatives to modeltransformations and demonstrate a sequence oftransformations that will carry a given figure onto another.

-Chapter 11:section 3 #35section 4 #35, 36

www.parcc.org (released items)PARCC (2015) EOY#4,18,21

G-CO.5Given a geometric figure and a rotation,reflection, or translation, draw thetransformed figure using, e.g., graph paper,tracing paper, or geometry software.Specify a sequence of transformations thatwill carry a given figure onto another.





-Chapter 11, section 3-Chapter 11, section 4

A rigid motion is a transformation of points in spaceconsisting of a sequence of one or more translations,reflections, and/or rotations. Rigid motions are assumed topreserve distances and angle measures. Use descriptions ofrigid motions to move figures in a coordinate plane, andpredict the effects rigid motion has on figures in the coordinate plane. Use this fact knowing rigid transformationspreserve size and shape or distance and angle measure, to connect the idea of congruency and to develop the definitionof congruent.

Students may use geometric software to explore the effects ofrigid motion on a figure(s).

-Chapter 11section 2, #1-16section 3, #7-16section 4 #7-10www.parcc.org (released items)PARCC (2015) EOY #19, 24

G-CO.6Use geometric descriptions of rigid motionsto transform figures and to predict theeffect of a given rigid motion on a givenfigure; given two figures, use the definitionof congruence in terms of rigid motions todecide if they are congruent.







CO- Congruence


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11


Domain:




Key :

Use the definition of congruence, based on rigid motion, to show twotriangles are congruent if and only if their corresponding sides andcorresponding angles are congruent. This standard connects with GSRT.3. Students should connect that two triangles are congruent if and only if theyare similar with a scale factor of one. Building on their definition ofsimilarity, this means that a rigidtransformation will preserve the angle measures and the sideswill change (or not change) by a scale factor of one. A rigid motionis a transformation of points in space consisting of a sequence of oneor more translations, reflections, and/or rotations. Rigid motions areassumed to preserve distances and angle measures.Congruence of trianglesTwo triangles are said to be congruent if one can be exactlysuperimposed on the other by a rigid motion, and the congruencetheorems specify the conditions under which this can occur.

-Chapter 11section 4 #7-10

G-CO.7Use the definition of congruence in termsof rigid motions to show that two trianglesare congruent if and only if correspondingpairs of sides and corresponding pairs ofangles are congruent.




Use the definition of congruence, based on rigid motion, todevelop and explain the triangle congruencecriteria; ASA, SSS, SAS, AAS, and HL. Students shouldconnect that these triangle congruence criteria are specialcases of the similarity criteria in GSRT.3. ASA and AAS aremodified versions of the AA criteria for similarity. Studentsshould note that the “S” in ASA and AAS has to be present to include the scale factor of one, which is necessary toshow that it is a rigid transformation. Students should alsoinvestigate why SSA and AAA are not useful for determiningwhether triangles are congruent.Chapter 11section #7-10

G-CO.8Explain how the criteria for trianglecongruence (ASA, SAS, and SSS) followfrom the definition of congruence in termsof rigid motions.






CO- Congruence


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11


Domain:




Key :

Students may use geometric simulations (computer softwareor graphing calculator) to explore theorems about lines andangles. In 8 thgrade, students have already experimented with these angle/line properties (8.G.5). The focus at this level isto prove these properties, not just to use and know them.

Chapter 8:Section 3 #1-30Section 4 #9-22Section 6 #3-35

Chap 10:Section 2 #1-16,21,22Section 3 # 33-36Sectin 5 #3-20

www.parcc.org (released items)PARCC (2015)EOY #20

G-CO.9Prove theorems about lines and angles.Theorems include: vertical angles arecongruent; when a transversal crossesparallel lines, alternate interior angles arecongruent and corresponding angles arecongruent; points on a perpendicularbisector of a line segment are exactly thoseequidistant from the segment’s endpoints.





-Chapter 8, Section 3-Chapter 8, section 4-Chapter 8, section 6-Chapter 10, section 2-Chapter 10, section 3-Chapter 10, section 5

Using any method you choose, construct the medians of a triangle.Each median is divided up by the centroid. Investigate therelationships of the distances of these segments. Can you create adeductive argument to justifywhy these relationships are true? Can you prove why the medians allmeet at one point for all triangles? Extension: using coordinategeometry, how can you calculate the coordinate of the centroid? Canyou provide an algebraicargument for why this works for any triangle? Using InteractiveGeometry Software or tracing paper, investigate the relationships ofsides and angles when you connect the midpoints of the sides of atriangle. Using coordinates can you justify why the segment thatconnects the midpoints of two of the sides is parallel to the oppositeside. Using coordinates justify that the segment that connects themidpoints of two of the sides is half the length of the opposite side. Ifyou have not done so already, can you generalize your argument andshow that it works for all cases?

-Chapter 12: Section 1 # 1-26Section 4 # 1-16www.parcc.org (released items)PARCC (2015) EOY #23, 25

G-CO.10Prove theorems about triangles. Theoremsinclude: measures of interior angles of atriangle sum to 180°; base angles ofisosceles triangles are congruent; thesegment joining midpoints of two sides of atriangle is parallel to the third side andhalf the length; the medians of a trianglemeet at a point.





-Chapter 12, Section 4-Chapter 12, section 1


CO- Congruence


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11


Domain:




Key :

Jerry is laying out the foundation for a rectangular foundation for 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 is rectangular. 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.

-Chapter 7Section 2 #3-38

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.





-Chapter 7, Section 2


LE- Linear, Quadratic, and Exponential Models

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


Cluster:

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4


Domain:


Tier 2- Academic Vocabulary Tier 3- Domain Specific WordsVerbs- Level of Learning


Key :

Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to model andcompare linear and exponential functions.Examples:•A cell phone company has three plans. Graph the equationfor each plan, and analyze the change as the number ofminutes used increases. When is it beneficial to enroll in Plan1? Plan 2? Plan 3?1.$59.95/month for 700 minutes and $0.25 for eachadditional minute,2.$39.95/month for 400 minutes and $0.15 for eachadditional minute, and3.$89.95/month for 1,400 minutes and $0.05 for eachadditional minute.•A computer store sells about 200 computers at the price of$1,000 per computer. For each $50 increase in price, aboutten fewer computers are sold. How much should thecomputer store charge per computer in order to maximizetheir profit?Algebra 1 Common Core, Pearson 2012- Student Edition p. 595 #4

F-LE.1Distinguish between situations that can bemodeled with linear functions and withexponential functions.★






Algebra 1 Common Core, Pearson 2012- Concept Byte Chapter 9, Section 7

www.map.mathshell.org#39 Modeling: Having Kittens

www.orgLib.comwww.EngageNY.orgwww.learnzillion.comwww.IllustrativeMathematics.comwww.tapintoteenminds.com


Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to construct linearand exponential functions.Examples:•Determine an exponential function of the form f(x) = ab2

using data points from the table. Graph the function andidentify the key characteristics of the graph.

x f(x)0 11 33 27•Sara’s starting salary is $32,500. Each year she receives a$700 raise. Write a sequence in explicit form to describe thesituation.Algebra 1 Common Core, Pearson 2012- Algebra 1 Progress Monitoring Assessmentsp. 21 #26; p. 35 #11; p. 41 #3; p. 42 #5; p. 45 #26; p. 47 #37- Algebra Practice and Problem Solving Workbook

p. 149 #1 and 4; p. 153 #4 and 6; p. 157 #5; p. 215 #1-2

F-LE.2Construct linear and exponential functions,including arithmetic and geometricsequences, given a graph, a description of arelationship, or two input-output pairs(include reading these from a table). ★




Algebra 1 Common Core, Pearson 2012- Chapter 4, Section 7- Chapter 5, Sections 3-5- Chapter 7, Sections 6 and 8- Chapter 9, Section 7

www.map.mathshell.org#37 Comparing Investments#62 Lines and Linear Equations

tapintoteenminds.com: Domino SkyscraperShmoop: aligned resources, assignmentHCPSS.com: instructional resources; tasks



LE- Linear, Quadratic, and Exponential Models

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


Cluster:

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4


Domain:




Key :

Example:Contrast the growth of the f(x)=x3 and f(x)=3x.

F-LE.3Observe using graphs and tables that aquantity increasing exponentiallyeventually exceeds a quantity increasinglinearly, quadratically, or (more generally)as a polynomial function. ★



Algebra 1 Common Core, Pearson 2012- Chapter 9, Section 7- Concept Byte Chapter 9, Section 2

www.IllustrativeMathematics.com-Population and Food Supply-Exponential versus Linear Growth

www.betterlesson.com-Compare/Contrast Linear vs. Exponential Functions-Task Lessons


Students may use graphing calculators or programs,spreadsheets, or computer algebra systems to model andinterpret parameters in linear, quadratic or exponentialfunctions.

Example:•A function of the form f(n) = P(1 + r)n is used to model theamount of money in a savings account that earns 5% interest,compounded annually, where n is the number of years sincethe initial deposit. What is the value of r? What is themeaning of the constant P in terms of the savings account?Explain either orally or in written format.

Algebra 1 Common Core, Pearson 2012- Algebra 1 Progress Monitoring Assessments

p. 35 #13- Algebra Practice and Problem Solving Workbook

p. 157 #5; p. 165 #6; p. 221 #2

F-LE.5Interpret the parameters in a linear orexponential function in terms of a context.★



Algebra 1 Common Core, Pearson 2012- Chapter 5, Sections 3-5 and 7- Chapter 7, Section 7

www.Opened.com--videos; lesson plans; assessmentswww.HCPSS.comwww.Orglib.com


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