Overarching Big Ideas, Enduring Understandings, and Essential Questions (These spiral throughout the entire curriculum.)

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1 Course: Graphing Grade: Designer(s): Alex Skroupa Overview of Course (Briefly describe what students should understand and be able to do as a result of engaging in this course): This course will cover a wide range of mathematical topics that will prepare students for collegiate mathematics. The course is targeted towards students who are sophomores, juniors, or seniors. The course will illustrate how mathematics can be applied to the daily lives of students in interesting and practical ways. The course will enable students to develop problem solving skills and foster critical thinking skills. The course will use technology, in particular, the TI 83 Plus graphing calculator. Students will be expected to master specific mathematical skills both algebraically and on the TI 83 Plus graphing calculator. Overarching Big Ideas, Enduring Understandings, and Essential Questions (These spiral throughout the entire curriculum.) Big Idea (A Big Idea is typically a noun and always transferable within and among content areas.) Standard(s) Addressed (What Common Core Standard(s) and/or PA Standard(s) addresses this Big Idea?) Enduring Understanding(s) (SAS refers to Enduring Understandings as Big Ideas. EUs are the understandings we want students to carry with them after they graduate. EUs will link Big Ideas together. Consider having only one or two EUs per Big Idea.) Essential Question(s) (Essential Questions are broad and open ended. Sometimes, EQs can be debated. A student s answer to an EQ will help teachers determine if he/she truly understands. Consider having only one or two EQs per Enduring Understanding.) ity CC.2.1.HS.F.3 Apply reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. Parentheses reinforce the order of operations. Complex numbers are used when there is a negative under the square root. The TABLE functionality on the graphing calculator allows the user to display information in a more simplified manner. The TBLSET button determines the boundaries of the table. How do parentheses determine how a calculator solves a problem? When is a number not real? How is the TABLE function helpful when dealing with multiple values affecting one equation? How can the x-intercept(s) and y-intercept be determined of a function without doing any algebra?

2 CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. An intersection point is not only where the two lines cross in a graph. The intersection point is where the two graphs are equal. A matrix is an arrangement of data in rows and columns. The solution to a matrix is where the equations are equivalent. It is the intersection point of two or more equations. What does intersection point truly mean for a What daily applicational purposes are there for matrices? How do different views of graphs alter the view of the graph that is seen? How is a program written on the graphing calculator? The graphing calculator s ZOOM feature allows different views of a graph to be visible. The TRACE feature traverses up-and-down a line allowing precise values to be found. Algebra CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.4.HS.B.1 Summarize, represent, and interpret data on two categorical and variables. CC.2.4.HS.B.3 Analyze linear models to make A quadratic function is in the form ax 2 +bx+c. It is possible to write programs in the graphing calculator to solve quadratic equations. The graphing calculator s graph is used to determine the domain and range of a function. It is possible to have a function within another function. Inverse functions have the data reversed from their original functions. Exponential functions must have an exponent in the equation. What makes a function a What is the difference in an absolute value equation if the addition or subtraction occurs inside or outside of the absolute value brackets? What are the differences between a oneto-one function and a many-to-one Must y always be the equation that is solved for in a Do exponential functions have a slope? How do exponents affect a graph? How are logarithms and natural logarithms related?

3 interpretations based on the data. Big Ideas, Enduring Understandings, and Essential Questions Per Unit of Study (These do NOT spiral throughout the entire curriculum, but are specific to each unit.) Month of Instruction (In what month(s) will you teach this unit?) Title of Unit Big Idea(s) (A Big Idea is typically a noun and always transferable within and among content areas.) Standard(s) Addressed (What Common Core Standard(s) and/or PA Standard(s) addresses this Big Idea?) Enduring Understanding(s) (SAS refers to Enduring Understandings as Big Ideas. EUs are the understandings we want students to carry with them after they graduate. EUs will link Big Ideas together. Consider having only one or two EUs per Big Idea.) Essential Question(s) (Essential Questions are broad and open ended. Sometimes, EQs can be debated. A student s answer to an EQ will help teachers determine if he/she truly understands. Consider having only one or two EQs per Enduring Understanding.) Common Assessment(s)* (What assessments will all teachers of this unit use to determine if students have answered the Essential Questions?) Common Resource(s)* Used (What resources will all teachers of this unit use to help students understand the Big Ideas?) August Numerics Order of Operations CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.1.HS.F.2 Apply properties of rational and irrational to solve real world or mathematical problems. Parentheses reinforce the order of operations. Does order matter when solving math problems? How do parentheses determine how a calculator solves a problem? Graphing Scavenger Hunt September Numerics Sets and Lists CC.2.1.HS.F.3 Apply reasoning to choose and interpret units The list on the graphing calculator is where values are entered into when What are easy methods to use when entering data into a graphing calculator?

4 and scales in formulas, graphs, and data displays. determining maximum, minimum, mean, median, standard deviation, etc. September Numerics Complex Numbers CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers. CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic expressions to solve problems Complex numbers are used when there is a negative under the square root. i is equivalent to 1. i can be used the same as a variable when performing addition, subtraction, multiplication, and division problems. When is a number not real? What is the purpose of complex numbers? What happens to i when it is raised to powers other than 1? Complex Number September October Table and Graph CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about The TABLE functionality on the graphing calculator allows the user to display information in a more simplified manner. The TBLSET button determines the boundaries of the table. It is possible to graph multiple translations on one line of the graphing calculator. The x-intercept and y- intercept can be found by looking at the graph How does the data display on a calculator help to interpret data? How is the TABLE function helpful when dealing with multiple values affecting one equation? How can the table be user-generated instead of calculatorgenerated? How can the x- intercept(s) and y- intercept be determined for a

5 functions and their graphs. and using the ZERO functionality. function without doing any algebra? October Intersections CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.1.HS.F.3 Apply reasoning to choose and interpret units and scales in formulas, graphs, and data displays. An intersection point is not only where the two lines cross in a graph. The intersection point is where the two graphs are equal. What does intersection point truly mean for a How are intersection points used in the real world? October Matrix Operations CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials. A matrix is an arrangement of data in rows and columns. The solution to a matrix is where the equations are equivalent. It is the intersection point of two or more equations. What daily applicational purposes are there for matrices? What do matrix solutions suggest about the number of dimensions of the original problem? tail?id=e6d135d FAA56B2D5728 B51C79 Matrix Operating on Matrices Lab CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalitie

6 s and systems of equations/inequalitie s algebraically and graphically. October November Box-and- Whisker Plots CC.2.1.HS.F.3 Apply reasoning to choose and interpret units and scales in formulas, graphs, and data displays. Box-and-whisker plots use the 5 critical values for the min, max, first quartile, third quartile, and median. How do the median and the mean differ in some graphical representations? tail?id=d91d0c06bd 6C4133BD2F E400&ref=/en/us /activity/search/key words?key=box+and +whisker&colle ction=3e3fb303e38f4 d1da8352d2ccc5254 5c Box and Whisker Lab October November Random Numbers CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. The calculator can produce random numbers, just like a statistical random number table found in all statistics textbooks. How truly random is the random number generator on the graphing calculator? How do random numbers help with probability? Random Number Random Numbers Lab November Graphs CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. The graphing calculator s ZOOM feature allows different views of a graph to be visible. The TRACE feature How do different views of graphs alter the view of the graph that is seen? How are exact values on a graph Translations of Graphs Lab

7 CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. traverses up-anddown a line allowing precise values to be found. determined without the use of algebra? November Algebra Solver Function CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. The Solver ity in the graphing calculator allows basic algebra problems to be solved. Can the graphing calculator solve for the variable x? Is it easier to solve equations by hand or on the graphing calculator? tail?id=8acbaf3a92 1D4D27A6BDBA3C7 580B2E4&ref=/en/u s/activity/search/ke ywords?key=solver& amp;collection=3e3f b303e38f4d1da8352 d2ccc52545c Writing a Program on the TI 83 Plus calculator November December Algebra Quadratic Functions CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. A quadratic function is in the form ax 2 +bx+c. It is possible to find the axis of symmetry, vertex, etc. of a quadratic function. It is possible to write programs in the graphing calculator to solve quadratic equations. How does the vertex relate to the minimum or maximum of a How is a program written on the graphing calculator? Quadratic Function Parabola Axis of Symmetry Vertex Quadratic Equation December Algebra Functions CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply The graphing calculator s graph is used to determine the domain and range of a What makes a function a What prohibits a tail?id=f235e1546a

8 them in terms of their context. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. function. Absolute value functions can be transformed. value from being allowed in a What is the difference in an absolute value equation if the addition or subtraction occurs inside or outside of the absolute value brackets? 094DF0A80FF5A709 EED6E9 Domain Range Function Zeros December Algebra Combining Functions CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. It is possible to have a function within another function. A one-to-one function has one y-value for each x value. What is the difference between f(g(x)) and g(f(x))? Does f( x) = f(x) or does f( x) = f(x)? What is the difference between a one-to-one function and a many-to-one Polynomial Functions Degree Rational Function Even Function Odd Function Complex Numbers Conjugate Composite Function One-to-One Function December January Algebra Inverse Functions CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve Inverse functions have the data reversed from their original functions. Does x or y get solved for with an inverse Must y always be the equation that is solved for in a un.com/sets/functio n-inverse.html Inverse Functions Exponential

9 equations and justify the solution method. Function January Algebra Exponential Functions CC.2.2.HS.C.5 Construct and compare linear, quadratic and exponential models to solve problems. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. Exponential functions must have an exponent in the equation. Exponential functions have a unique graph. Where are exponential functions used in the real world? Do exponential functions have a slope? How do exponents affect a graph? How are logarithms and natural logarithms related? tail?id=a99ac1f511 BB4C97924D7A9B89 60F046 Probability Sample Space Event Fundamental Counting Rule Exponential Reflections Lab January Statistics Probability CC.2.4.HS.B.1 Summarize, represent, and interpret data on two categorical and variables. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. Probability is the study of random phenomena. Conditional probability involves one event preceding another event. Is the occurrence of an event totally random? How does one probability event affect another probability event? tail?id=3e8c6f5b70 FF477AA30383C05D 052D70 Quartiles Interquartile Range s Heads Up! Lab Probability Lab Activity

10 January Statistics Frequency Distributions CC.2.4.HS.B.1 Summarize, represent, and interpret data on two categorical and variables. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and variables. Frequency distributions are tables the shows intervals of data entries. A frequency histogram is a graphical way to represent a frequency distribution. How can data best be displayed to convey a point? How do class widths affect the frequency histogram? Frequency Distribution Frequency of a Class Midpoint of a Class Relative Frequency Cumulative Frequency Frequency Histogram CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.