curriculum map algebra i quarter 1 -...

Curriculum Map Algebra I Quarter 1

Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.1 * Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (A) linear equations (B) linear inequalities (G) absolute value equations (H) absolute value inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will solve problems by creating equations and inequalities in one variable.

References: Algebra 1

Section 1.2 - 1.9 Section 2.3 - 2.7

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs

MAP Assessment Tasks A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks

Essential Vocabulary: Inequality


Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's Law V=IR to highlight resistance R. [Limit to formulas that are linear in the variable of interest or formulas involving squared variables.] Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will rearrange formulas to solve for a specified variable. References: Algebra 1

Section 1.6 Review this standard with the different types of equations (linear, exponential, and quadratic).



Essential Vocabulary: Formula Laws of Equality


Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.3 * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Include simple

exponential equations that rely only on application of the laws of exponents such as 5x=125 or 2x=

]

(A) linear and literal equations (B) linear inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will solve linear equations and inequalities, including coefficients represent by letters. References: Algebra 1

Section 1.1 Lab Section 1.2 Section 1.4 Lab Section 1.6 - 1.9 Section 2.1 – 2.7 Section 2.6 Lab Section 5.1 Lab

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Boomerangs

Solving Quadratic Equations: Cutting Corners

MAP Assessment Tasks A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Essential Vocabulary:

Exponent


Essential Question: In what ways can the choice of units, quantities, and levels of accuracy impact a solution? Number - Quantities AI.N.Q.1 * Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (A) units (B) scale and origin Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Supporting Objective: I will use units to understand problems and to interpret solutions. References: Algebra 1

Section 1.1 Section 1.6 Section 1.8 - 1.9 Section 3.5

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Modeling: Having Kittens MAP Assessment Tasks A19 Leaky Faucet A24 Yogurt Essential Vocabulary:

Formula Literal equation Origin Scale


Essential Question: How does the knowledge of integers help when working with rational and irrational numbers? Number – The Real Number System AI.N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [Connect to physical situations, e.g., finding the perimeter of a square of area 2.] Mathematical Practices: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. PARCC Priority: Algebra I Additional Objective: I will understand the properties of adding and multiplying rational and irrational numbers. References: Algebra 1

Section 6.5 Extension CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Equations of Circles 2 Rational and Irrational Numbers 1 Rational and Irrational Numbers 2 MAP Assessment Tasks N01 The Real Number System Essential Vocabulary:

Closure Element Set Subset


Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.10 * Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [Focus on linear and exponential equations.] (A) linear equations Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. PARCC Priority: Algebra I Major Objective: I will understand that a graph represents all possible solutions to a two variable function. References: Algebra 1

Section 3.4 Section 4.1 Section 8.1 Section 8.10 Extension




Linear function Linear equation


Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.12 * Graph the solutions to a linear inequality in two variables as 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. (A) linear inequality (B) system of linear inequalities Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will graph linear inequalities and systems of linear inequalities. References: Algebra 1

Section 5.5 – 5.6 Section 5.6 Lab




Boundary Half plane Strict inequality


Essential Question: How can the relationship between quantities best be represented? Functions – Interpreting Functions AI.F.IF.7 * Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] a*. Graph linear and quadratic functions and show intercepts, maxima, and minima. (A) linear functions Mathematical Practices: 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Supporting Objective: I will graph functions by hand or using technology. References: Algebra 1

Section 3.4 Section 4.1 – 4.2 Section 4.5 – 4.7 Section 4.7 Lab Section 4.9 – 4.10 Section 4.10 Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions

Essential Vocabulary: Linear equation Linear function x intercept y intercept


Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (A) linear equations Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will represent relationships between quantities by creating equations in two or more variables. References: Algebra 1

Section 4.1 - 4.2 Section 4.5 - 4.7 Section 5.1 Section 5.4



Essential Vocabulary: Axis Direct variation Slope Constant of variation Quadratic equations Slope intercept form Coordinate plane Scale


Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.3 * Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. [Limit to linear equations and inequalities.] (A) linear equations (B) linear inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will understand constraints as they apply to real world problems. References: Algebra 1

Section 3.3 Section 4.2 Section 4.5 - 4.7



Essential Vocabulary: Constraint Non-viable Viable


Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.3 * Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. [Limit to linear equations and inequalities.] (C) system of linear equations (D) system of linear inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will understand constraints as they apply to real world problems. References: Algebra 1

Section 5.1 - 5.6 Section 8.7



Essential Vocabulary: Constraint Non-viable Viable


Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [Include systems of equations that yield infinitely many solutions and no solutions.] Mathematical Practices: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. PARCC Priority: Algebra I Additional Objective: I will prove the elimination method of solving a system of equations is valid. References: Algebra 1

Section 5.3 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org

Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Boomerangs



Elimination method Infinitely many solutions No solution System of equations


Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.6 Solve systems of linear. equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Mathematical Practices:

2. Reason abstractly and quantitatively 6. Attend to precision. 4. Model with mathematics. 7. Look for and make use of structure. 5. Use appropriate tools strategically 8. Look for and express regularity in repeated reasoning.

PARCC Priority: Algebra I Additional Objective: I will solve systems of linear equations in a variety of methods. References: Algebra 1

Section 5.1 - 5.4 Section 5.1 Lab




Substitution method


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of y=f(x). [Focus on linear and exponential functions] Mathematical Practices: 2. Reason abstractly and quantitatively. PARCC Priority: Algebra I Major Objective: I will understand the meaning of a function. References: Algebra 1

Section 3.2 – 3.4 Section 3.2 Lab Section 3.4 Lab

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions Essential Vocabulary:

Domain Function Range


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [Focus on linear and exponential functions] Mathematical Practices: 2. Reason abstractly and quantitatively. PARCC Priority: Algebra I Major Objective: I will use function notation to evaluate functions for a given domain. I will identify independent and dependent variables. I will write an equation in function notation. I will interpret functions in context. References: Algebra 1



Dependent variable Function rule Inputs Function notation Independent variable Outputs


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f (0) = f (1) = 1, f (n+1) = f (n) + f (n-1) for n is greater than or equal to 1. [Emphasize arithmetic and geometric sequences as examples of linear and exponential functions.] Mathematical Practices: 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will recognize that sequences are functions. References: Algebra 1

Section 3.6 Section 9.1


Arithmetic sequence Geometric sequence Range Common difference Negative correlation Relation Common ratio No correlation Sequence Correlation Positive correlation Term Domain


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.4 * For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (A) linear functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will interpret the key features of a function graph. References: Algebra 1



Decreasing Maximum Vertex End behavior Minimum Zeros Increasing Symmetry


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (A) linear functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will relate the domain of a function to its graph and apply appropriate constants. References: Algebra 1

Section 3.2 – 3.4 Section 4.1 – 4.2 Section 4.5


Constraints


Essential Question: How can the relationship between quantities best be represented? Functions – Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (A) linear functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will calculate and interpret the average rate of change for a function. I will compare rates of change from a graph. References: Algebra 1

Section 4.3 – 4.4 Section 4.3 Lab Section 4.6


Average rate of change Slope


Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (A) linear functions Mathematical Practices: 6. Attend to precision. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting Objective: I will compare the properties of two functions when they are represented different ways, for instance comparing graphs to tables or to equations. References: Algebra 1

Section 4.1 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions Essential Vocabulary:

Average rate of change


Essential Question: In what ways can functions be built? Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (A) linear functions Mathematical Practices : 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when a linear equation is changed. I will find the value of k given the graphs. References: Algebra 1

Section 4.10 Section 4.9 Lab Section 4.10 Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Ferris Wheel Medical Testing Modeling: Rolling Cups Generalizing Patterns: Table Tiles Modeling Conditional Probabilities 2 Representing Polynomials

Essential Vocabulary: Dilation Horizontal stretch Vertical compression Horizontal compression Parameter Vertical shift Horizontal shift Reflection Vertical stretch


August 2014 Quarter 2 Page 1 of 18

Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.3 * Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. [Include quadratic and exponential expressions] (B) exponential expressions c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.15(1/12))(12t) = 1.012(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. PARCC Priority: Algebra I Supporting Objective: I will use properties of exponents to transform expression s for exponential functions. References: Algebra 1

Section 9.2 Supplement CLAROOM CHALLENGE ACTIVITES: map.mathshell.org

Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials

MAP Assessment Tasks A04 Circle Pattern N02 Seeing Structure in Expressions Essential Vocabulary:

Exponential function

http://map.mathshell.org/materials/lessons.php?taskid=437&subpage=concept






Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (B) exponential expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r)n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (B) exponential expressions Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will interpret expressions that represent a quantity. References: Algebra 1




Coefficients Factors Square Cube roots Quadratic expressions Terms







Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.1 * Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (E) exponential equations (F) exponential inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will create exponential equations and inequalities. References: Algebra 1

Section 9.2 Supplement



Essential Vocabulary: Exponential function



Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (B) exponential equations Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will create exponential system of equations. References: Algebra 1

Section 9.2 Supplement



Essential Vocabulary: Exponential function



Essential Question: When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.1 * Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Mathematical Practices: 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will distinguish between situations which can be modeled with linear and exponential functions. References: Algebra 1


CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens MAP Assessment Tasks E11 Table Tiling N08 Linear and Exponential Models Essential Vocabulary:

Equal differences Equal intervals Exponential functions Exponential growth Geometric sequences



Essential Question: When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.2 * Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (A) linear functions (B) exponential functions Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will construct linear and exponential functions from arithmetic and geometric sequences given:

Graph Description of a relationship Two input – outputs pairs.

References: Algebra 1

Section 3.6 Section 4.5 – 4.7 Section 9.3 – 9.4 Section 4.1 – 4.2 Section 9.1 Section 9.3 Lab - Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens MAP Assessment Tasks E11 Table Tiling N08 Linear and Exponential Models Essential Vocabulary:

Arithmetic sequence Exponential function Sequence Constant of variation Geometric sequence Term



Essential Question: When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.3 * Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [Include comparison between linear and exponential models as well as compare linear and exponential growth to quadratic growth.] (A) compare linear and exponential models (B) compare linear and exponential growth to quadratic growth Mathematical Practices: 2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically and as a polynomial function using tables and graphs. References: Algebra 1

Section 9.5 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens MAP Assessment Tasks E11 Table Tiling N08 Linear and Exponential Models Essential Vocabulary:

Average rate of change Exponential models Polynomial function Exponential growth Linear models Quadratic growth



Essential Question: When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.5 * Interpret the parameters in a linear or exponential function in terms of a context. [Limit exponential functions to those of the form f(x) =bx+k.] (A) linear functions (B) exponential functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. PARCC Priority: Algebra I Supporting Objective: I will interpret the parameters of a function in terms of a context. References: Algebra 1


Slope intercept form



Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.3 * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Include simple

exponential equations that rely only on application of the laws of exponents such as 5x=125 or 2x=

]

(C) exponential equations Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will solve exponential equations and inequalities. References:

Supplement CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org






Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.10 * Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [Focus on linear and exponential equations.] (B) exponential equations Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. PARCC Priority: Algebra I Major Objective: Objective: I will understand that a graph represents all possible solutions to a two variable function. References:





Exponential function Exponential graph



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.4 * For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (B) exponential functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will interpret the key features of an exponential function graph. References: Algebra 1


Decreasing Maximum Symmetry End behavior Minimum Vertex Increasing



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (B) exponential functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will relate the domain of a function to its graph and the quantative relationship. References: Algebra 1

Section 9.4 – 9.5 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions Essential Vocabulary:

Domain Exponential functions Function Quantative relationship



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (B) exponential functions Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will calculate and interpret average rate of change (slope) of a function. I will compare rates of change from a graph. References: Algebra 1

Section 8.2 – 8.3 Section 9.4 Extension Section 9.5


Exponential function Rate of change Run Linear function Rise Slope Quadratic function



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (B) exponential functions Mathematical Practices: 6. Attend to precision. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting Objective: I will compare properties of two functions each represented in a different way. References: Algebra 1





Essential Question: In what ways can functions be built? Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (B) exponential functions Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when the quadratic and exponential equation is changed. I will find the value of k given the graphs. References: Algebra 1

Section 8.3 Lab Section 8.4


MAP Assessment Tasks A02 Patchwork A12 Printing Tickets E11 Table Tiling A06 Sidewalk Patterns E07 Skeleton Tower E13 Sidewalk Stones

Essential Vocabulary: Quadratic functions Translation Vertical intercept Vertical transformation



Essential Question: In what ways can functions be built? Functions - Building Functions AI.F.BF.1 * Write a function that describes a relationship between two quantities. [Focus on linear, exponential, and quadratic functions.] a*. Determine an explicit expression, a recursive process, or steps for calculation from a context. (A) linear functions (B) exponential functions Mathematical Practices:

1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 4. Model with mathematics. 8. Look for and express regularity in repeated reasoning. 5. Use appropriate tools strategically.

PARCC Priority: Algebra I Supporting Objective: I will write a function describing the relationship between two quantities. References: Algebra 1

Section 8.4 Section 8.7 Section 9.3 – 9.4 Section 9.3 Extension



Essential Vocabulary: Compound interest Exponential growth Half –life Dependent variable Function notation Independent variable Exponential decay Function rule



Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (A) linear expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r)n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (A) linear expressions Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will understand the parts of an expression, such as terms, factors and coefficients. References: Algebra 1




Coefficients Factors

Equations Linear expressions







Essential Question: How can the properties of the real number system be useful when working with polynomials and rational expressions? Algebra - Arithmetic with Polynomials and Rational Expressions AI.A.APR.1 * Understand that polynomials form a system analogous to the integers namely; they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x.] (A) addition and subtraction (B) multiplication Mathematical Practices: 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will understand that polynomials represent quantities and therefore can be added, subtracted and multiplied. References: Algebra 1

Section 6.4 – 6.6 Section 6.3 - 6.4 Lab Section 6.5 Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Algebraic Expressions Manipulating Polynomials Representing Polynomials MAP Assessment Tasks N03 Arithmetic with Polynomials and Rational Expressions Essential Vocabulary:

Polynomial


Page 1 of 82

Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (C) quadratic expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r)n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (C) quadratic expressions Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will interpret expressions that represent a quantity. References: Algebra 1



Essential Vocabulary: Coefficients Factors Square Cube roots Quadratic expressions Terms






Page 2 of 82

Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2) (x2 + y2). Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will write equivalent expressions. References: Algebra 1

Section 7.2 – 7.4 Section 7.1 and 7.2 Lab Section 7.5 – 7.6

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials o


Exponents Factor Squares






Page 3 of 82

Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [Tasks are limited to quadratic equations.] Mathematical Practices: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. PARCC Priority: Algebra I Major Objective: I will solve one step equations by using addition and subtraction. I will solve one step equations by using multiplication and division. I will solve equations with variables on both sides. References: Algebra 1

Section 1.1 and 1.4 Lab Section 1.2 - 1.5




Linear function Linear equation


Page 4 of 82

Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.4 * Solve quadratic equations in one variable. a*. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2=q that has the same solutions. Derive the quadratic formula from this form. (A) process of completing the square (B) derive quadratic formula b*. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a± bi for real numbers a and b. [Include existence of complex number system, but do not solve quadratics with complex solutions until Algebra 2.] (A) real roots (B) quadratic formula yields complex roots Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will solve quadratic equations by completing the square. I will solve quadratic equations by the quadratic formula. I will derive the quadratic formula. I will recognize the types of roots from quadratic equation including real and complex roots. References: Algebra 1

Section 8.6 - 8.9 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org

Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Boomerangs Solving Quadratic Equations: Cutting Corners

Essential Vocabulary: Complex roots Quadratic equations Quadratic formula

Real roots


Page 5 of 82

Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.3 * Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. [Include quadratic and exponential expressions] (A) quadratic expressions a*. Factor a quadratic expression to reveal the zeros of the function it defines. (A) factor a quadratic expression (B) reveal the zeros by factoring b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. PARCC Priority: Algebra I Supporting Objective: I will factor an expression and find the zeros of the function. References: Algebra 1

Section 7.3 – 7.6 Section 7.4 Section 8.5 Lab

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials

Essential Vocabulary: Factor Zero






Page 6 of 82

Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.1 * Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (C) quadratic equations (D) quadratic inequalities Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will create quadratic equations and inequalities to solve problems. References: Algebra 1

Section 8.6 - 8.9 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org

Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs


Essential Vocabulary: Quadratic functions Quadratic inequalities


Page 7 of 82

Essential Question: How can algebra describe the relationship between sets of numbers? Algebra – Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (C) quadratic equations Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will represent relationships between quantities by creating equations in two or more variables. References: Algebra 1




Essential Vocabulary: Axis Quadratic equations Slope Coordinate plane Scale Slope intercept form Direct variation


Page 8 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.4 * For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (C) quadratic functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will match graphs to their verbal descriptions. I will recognize key features of a quadratic function. References: Algebra 1

Section 8.2 – 8.3 Section 8.5 Section 8.10 Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials Essential Vocabulary:

Continuous graph Discrete graph


Page 9 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (C) quadratic functions Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will graph functions given a limited domain. I will graph functions given the domain of all real numbers. References: Algebra 1


Domain


Page 10 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (C) quadratic functions Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will calculate and interpret average rate of change (slope) of a function. I will compare rates of change from a graph. References: Algebra 1

Section 8.2 – 8.3 Section 9.4 Extension Section 9.5


Exponential function Rate of change Run Linear function Rise Slope Quadratic function


Page 11 of 82

Essential Question: How can the properties of the real number system be useful when working with polynomials and rational expressions? Algebra - Arithmetic with Polynomials and Rational Expressions AI.A.APR.3* Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (A) quadratic polynomials Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Supporting Objective: I will identify zeros of polynomials by factoring. I will use the zeros to construct a rough graph of the function. References: Algebra 1

Section 8.6 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Algebraic Expressions Manipulating Polynomials Representing Polynomials MAP Assessment Tasks N03 Arithmetic with Polynomials and Rational Expressions Essential Vocabulary:


Page 12 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.7 * Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] a*. Graph linear and quadratic functions and show intercepts, maxima, and minima. (B) quadratic functions Mathematical Practices: 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Supporting Objective: I will identify quadratic functions and determine whether they have minimums or maximums. I will graph functions and give the domain and range. References: Algebra 1

Section 8.1 – 8.5 Section 8.1 - 8.3 Lab Section 8.10 Extension


Minimum Maximum Parabola Quadratic function


Page 13 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.8 * Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Mathematical Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting Objective: I will find the zeros of a quadratic function. I will find the axis of symmetry and vertex. References: Algebra 1

Section 8.1 - 8.3 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions Essential Vocabulary:

Axis of symmetry Zeros of a function


Page 14 of 82

Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (C) quadratic functions Mathematical Practices: 6. Attend to precision. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting Objective: I will compare functions in different representations. References: Algebra 1

Section 8.2 – 8.3 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Forming Quadratics Functions and Everyday Situations Representing Polynomials MAP Assessment Tasks A16 Sorting Functions N06 Interpreting Functions Essential Vocabulary:



Page 15 of 82

Essential Question: In what ways can functions be built? Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (C) quadratic functions Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when the quadratic and exponential equation is changed. I will find the value of k given the graphs. References: Algebra 1

Section 8.3 Lab Section 8.4



Essential Vocabulary: Quadratic functions Translation Vertical intercept Vertical transformation


Page 16 of 82

Essential Question: When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.3 * Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [Include comparison between linear and exponential models as well as compare linear and exponential growth to quadratic growth.] (B) compare linear and exponential growth to quadratic growth Mathematical Practices: 2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically and as a polynomial function using tables and graphs. References: Algebra 1


Average rate of change Exponential models Polynomial function Exponential growth Linear models Quadratic growth



quarter 4 Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.4 * For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (D) square root and cube root function Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will graph and identify key features of a function that model a relationship between quantities. References: Algebra 1

Section 9.3 Extension Section 9.4





Essential Question: Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r)n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (D) square and cube root expressions Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Major Objective: I will interpret expressions that represent a quantity in terms of its context. References:

Supplement CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org



Cube root expressions Square root expressions




Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (D) square root and cube root functions Mathematical Practices: 4. Model with mathematics. PARCC Priority: Algebra I Supporting Objective: I will relate the domain of a function to its graph and apply appropriate constants. References: Algebra 1



Axis of symmetry Parabola Vertex Maximum Quadratic equation Zero of a function Minimum Quadratic function



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (D) square root and cube root function Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will calculate and interpret the average rate of change of a function. I will compare rates of change from a graph. I will identify linear and nonlinear rates of change. References: Algebra 1



Rate of change Rise Run Slope



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.7 * Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] b*. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [Compare and contrast absolute value, step and piecewise-defined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range, and usefulness when examining piecewise-defined functions.]" (A) square root and cube root Mathematical Practices: 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will graph various functions and identify their characteristics. References: Algebra 1






Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (D) square root and cube root function Mathematical Practices: 6. Attend to precision. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting

Objective: I will compare properties of square root and cube root functions. I will compare properties of step and piecewise defined functions to include absolute value. References: Algebra 1

Section 4.1 Section 8.2 – 8.3 Section 9.2 Section 4.10 Extension Section 8.10 Extension Section 9.5


Essential Vocabulary: Absolute value function Step and piece wise function



Essential Question: In what ways can functions be built?

Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (E) Square root and cube root functions Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when a step, piecewise, or root equation is changed. I will find the value of k given the graphs. References: Algebra 1

Section 4.9 Lab Section 4.10 Extension Section 8.4 Section 4.10 Section 8.3 Lab



Essential Vocabulary: Family of functions Reflection Transformation

Parent function Rotation Translation



Essential Question: In what ways can the problem be solved, and why should one method be chosen over another? Algebra – Reasoning with Equations and Inequalities AI.A.REI.11 * Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Mathematical Practices: 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will explain the relationship between x coordinates and the intersection of the graph y = f(x) and y = g(x). References: Algebra 1

Section 1.5 Lab Section 8.5 Section 8.5 Lab




Quadratic equation



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.4 * For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (E) step and piecewise-defined functions including absolute value Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will graph and identify key features of a function that model a relationship between quantities. References: Algebra 1






Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (E) piece-wise defined functions (including step functions and absolute functions) Mathematical Practices: 4. Model with mathematics. PARCC Priority: Algebra I Supporting Objective: I will relate the domain of a function to its graph and apply appropriate constants. References: Algebra 1






Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (E) step and piecewise-defined functions including absolute value Mathematical Practices: 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will calculate and interpret the average rate of change of a function. I will compare rates of change from a graph. I will identify linear and nonlinear rates of change. References: Algebra 1



Rate of change Rise Run Slope



Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.7 * Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] b*. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [Compare and contrast absolute value, step and piecewise-defined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range, and usefulness when examining piecewise-defined functions.]" (B) step and piecewise-defined functions including absolute value Mathematical Practices: 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Supporting Objective: I will graph various functions and identify their characteristics. References: Algebra 1






Essential Question: How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (E) step and piecewise-defined functions including absolute value Mathematical Practices: 6. Attend to precision. 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting

Objective: I will compare properties of square root and cube root functions. I will compare properties of step and piecewise defined functions to include absolute value. References: Algebra 1

Section 4.1 Section 8.2 – 8.3 Section 9.2 Section 4.10 Extension Section 8.10 Extension Section 9.5


Essential Vocabulary: Absolute value function Step and piece wise function



Essential Question: In what ways can functions be built?

Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (D) step and piecewise defined functions including absolute value functions. Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when a step, piecewise, or root equation is changed. I will find the value of k given the graphs. References: Algebra 1

Section 4.9 Lab Section 4.10 Extension Section 8.4 Section 4.10 Section 8.3 Lab



Essential Vocabulary: Family of functions Reflection Transformation

Parent function Rotation Translation



Essential Question: How can the properties of the real number system be useful when working with polynomials and rational expressions? Algebra - Arithmetic with Polynomials and Rational Expressions AI.A.APR.3* Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (B) cubic polynomials Mathematical Practices: 7. Look for and make use of structure. PARCC Priority: Algebra I Supporting Objective: I will identify zeros of polynomials and construct a graph. References: Algebra 1

Section 8.6 Section 8.10 Extension

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Algebraic Expressions Manipulating Polynomials Representing Polynomials MAP Assessment Tasks N03 Arithmetic with Polynomials and Rational Expressions Essential Vocabulary:

Nonlinear systems of equations



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Major Objective: I will interpret slope and intercept in the context of data. References: Algebra 1

Section 4.8 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Statistics: A Case of Muddying the Waters Representing Data 1: Using Frequency Graphs Representing Data 2: Using Box Plots MAP Assessment Tasks N11 Quantitative Essential Vocabulary:

Intercept (constant term)

Rate of change Slope



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. 8. Look for and express regularity in repeated reasoning. PARCC Priority: Algebra I Major Objective: I will compute and interpret the correlation coefficient. References: Algebra 1


Correlation coefficient



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.9 Distinguish between correlation and causation. Mathematical Practices: 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. PARCC Priority: Algebra I Major Objective: I will distinguish between correlation and causation. References: Algebra 1


Causation Correlation



Essential Question: In what ways can functions be built? Functions - Building Functions AI.F.BF.1 * Write a function that describes a relationship between two quantities. [Focus on linear, exponential, and quadratic functions.] a*. Determine an explicit expression, a recursive process, or steps for calculation from a context. (B) exponential functions (C) quadratic functions Mathematical Practices:

1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 4. Model with mathematics. 8. Look for and express regularity in repeated reasoning. 5. Use appropriate tools strategically.

PARCC Priority: Algebra I Supporting Objective: I will write a function describing the relationship between two quantities. References: Algebra 1

Section 8.4 Section 8.7 Section 9.3 – 9.4 Section 9.3 Extension



Essential Vocabulary: Compound interest Exponential growth Half –life Dependent variable Function notation Independent variable Exponential decay Function rule



Essential Question: In what ways can the choice of units, quantities, and levels of accuracy impact a solution? Number - Quantities AI.N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. Mathematical Practices: 4. Model with mathematics. 6. Attend to precision. PARCC Priority: Algebra I Supporting Objective: I will use units that are appropriate when modeling a problem. References: Algebra 1


CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Modeling: Having Kittens MAP Assessment Tasks A19 Leaky Faucet A24 Yogurt Essential Vocabulary:

Model



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data Mathematical Practices:

1. Make sense of problems and persevere in solving them. 5. Use appropriate tools strategically. 2. Reason abstractly and quantitatively. 6. Attend to precision. 3. Construct viable arguments and critique the reasoning of others.

8. Look for and express regularity in repeated reasoning.

4. Model with mathematics. PARCC Priority: Algebra I Supporting Objective: I will summarize data in a two way frequency table. I will interpret the relative frequencies of data and look for trends. References: Algebra 1

Supplement CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Statistics: A Case of Muddying the Waters Representing Data 1: Using Frequency Graphs Representing Data 2: Using Box Plots MAP Assessment Tasks N11 Quantitative Essential Vocabulary:

Conditional relative frequencies Joint relative frequencies Marginal relative frequencies



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.6 * Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a*. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use a given functions or choose a function suggested by the context. Emphasize linear and exponential models. (A) linear functions b. Informally assess the fit of a function by plotting and analyzing residuals. [Focus on linear models, but may be used to preview quadratic functions.] c. Fit a linear function for a scatter plot that suggests a linear association. Mathematical Practices:

2. Reason abstractly and quantitatively. 6. Attend to precision. 4. Model with mathematics. 7. Look for and make use of structure. 5. Use appropriate tools strategically 8. Look for and express regularity in repeated reasoning.

PARCC Priority: Algebra I Supporting Objective: I will represent data on a scatter plot and describe how the variables are related. I will fit and assess the fit of a function to the data. References: Algebra 1

Section 3.5 Section 4.3 - 4.4 Section 4.8 Section 3.5 Lab Section 4.3 Lab

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Statistics: A Case of Muddying the Waters Representing Data 1: Using Frequency Graphs Representing Data 2: Using Box Plots

Essential Vocabulary: Line of best fit Linear functions Residuals Scatter plot



Essential Question: In what ways can the choice of units, quantities, and levels of accuracy impact a solution? Number - Quantities AI.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Mathematical Practices: 5. Use appropriate tools strategically. 6. Attend to precision. PARCC Priority: Algebra I Supporting Objective: I will choose which level of accuracy, i.e. rounding, is best when reporting quantities. References: Algebra 1

Section 1.10 CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Modeling: Having Kittens MAP Assessment Tasks A19 Leaky Faucet A24 Yogurt Essential Vocabulary:

Accuracy Rounding



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). Mathematical Practices: 4. Model with mathematics. 5. Use appropriate tools strategically. PARCC Priority: Algebra I Additional Objective: I will represent data using dot plots, histograms and box plots. References: Algebra 1

Section 10.1 – 10.3 Section 10.3 Lab

CLASSROOM CHALLENGE ACTIVITES: map.mathshell.org Interpreting Statistics: A Case of Muddying the Waters Representing Data 1: Using Frequency Graphs Representing Data 2: Using Box Plots MAP Assessment Tasks N11 Quantitative Essential Vocabulary:

Box plots Cumulative frequency Histograms Dot plots Frequency table Stem and leaf plots Circle graphs



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Mathematical Practices: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will compare the center and spread of two or more different data sets. References: Algebra 1



Center Median Spread Interquartile range Range Standard deviation Mean



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.3 Interpret differences in shape, center, and spread in the context of data sets, accounting for possible effects of extreme data points (outliers). Mathematical Practices: 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 7. Look for and make use of structure. PARCC Priority: Algebra I Additional Objective: I will interpret the effects of outliers on shape, center and spread. References: Algebra 1



Outlier Skew



Essential Question: How can the properties of data be communicated to illuminate its important features? Statistics and Probability - Interpreting Categorical and Quantative Data AI.S.ID.6 * Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a*. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use a given functions or choose a function suggested by the context. Emphasize linear and exponential models. (B) exponential functions (C ) quadratic functions Mathematical Practices:

2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure. 4. Model with mathematics. 8. Look for and express regularity in repeated reasoning.

PARCC Priority: Algebra I Supporting Objective: I will compare linear, quadratic, and exponential models. References: Algebra 1


Exponential model Linear model Quadratic model

curriculum map algebra i quarter 1 -...

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