ࡱ>   kz_ bjbj +bbvB FFFFFZZZ8&Zp"""$q#ކiF'%!""'%'%ކFFXG+++'%FF+'%++.kHr%nn@]0NnT5(rrb F} ""|+*#d#"""ކކK+"""'%'%'%'%""""""""" : Rigorous Curriculum Design Unit Planning Organizer Subject(s)High School MathematicsGrade/CourseHonors Math IIUnit of StudyUnit 1: Functions, Equations and SystemsUnit Type(s)Q'Topical Q'X Skills-based Q' Thematic Pacing14 Days (Block and A-Day/B-Day) Unit Abstract This first algebra and functions unit of Math II builds on the units of Math I that developed student understanding of functions and their representation in table, graphs, and symbolic rules and the particular properties of linear, exponential, and quadratic functions. This unit reviews and extends student ability to recognize, describe, and use functional relationships among quantitative variables, with special emphasis on relationships that involve two or more variables. Students begin with a review of patterns of change that are modeled well by single-variable functionswith special attention to Students develop an understanding of a wide range of models, including power models of the forms EMBED Equation.3 , EMBED Equation.3 , and EMBED Equation.3 . Emphasis for honors students will be placed on higher order thinking skills that impact practical and increasingly complex applications in a problem-centered, connected approach. Students will also develop a good understanding of the shapes of the graphs and the numerical patterns in the tables generated by the new models, how these models compare to each other and linear and exponential models, and possible real-world situations that can be represented by each model. Students will also simplify radical expressions and apply properties of exponents. Honors students will learn how to use the substitution and elimination methods to solve systems involving three equations and three variables. Honors students will also complete projects throughout the course. Common Core Essential State Standards Conceptual Category: Number and Quantity; Algebra; and Functions Domain: 1) The Real Number System (N-RN) 2) Quantities (N-Q) 3) Creating Equations (A-CED) 4) Reasoning with Equations and Inequalities (A-REI) 5) Interpreting Functions (F-IF) 6) Building Functions (F-BF) Clusters: 1) Extend the properties of exponents to rational exponents. (N-RN) 2) Reason quantitatively and use units to solve problems. (N-Q) 3) Create equations that describe numbers or relationships. (A-CED) 4) Represent and solve equations and inequalities graphically. (A-REI) 5) Understand the concept of a function and use function notation. Interpret functions that arise in applications in terms of the context. Analyze functions using different representations. (F-IF) 6) Build a function that models a relationship between two quantities. Build new functions from existing functions. (F-BF) Standards: N-RN.2 REWRITE expressions involving radicals and rational exponents using the properties of exponents. 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.  HYPERLINK "http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/wiki/9d087/NQ2.html" N-Q.2 DEFINE appropriate quantities for the purpose of descriptive modeling.  HYPERLINK "http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/wiki/c729c/NQ3.html" N-Q.3 CHOOSE a level of accuracy appropriate to limitations on measurement when reporting quantities. 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. Note: Extend to linear-quadratic and linear-inverse variation (simplest rational) systems of equations. HN: SOLVE systems of three equations and three variables. A-CED.4 REARRANGE formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Note: At this level, extend to compound variation relationships. 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). Note: At this level, extend to quadratics. 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. Note: At this level, extend to quadratic functions.  HYPERLINK "http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/wiki/4b98a/FIF2.html" 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. Note: At this level extend to quadratic, simple power, and inverse variation functions. 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. Note: At this level, extend to quadratic, right triangle trigonometry, and inverse variation functions. 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. b. GRAPH square root, cube root, and piece-wise defined functions, including step functions and absolute value functions. F-IF.9 COMPARE properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Note: At this level, extend to quadratic, simple power, and inverse variation functions. F-BF.1 WRITE a function that describes a relationship between two quantities. a. DETERMINE an explicit expression, a recursive process, or steps for calculation from a context. Note: Continue to allow informal recursive notation through this level. 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. Note: At this level, extend to quadratic functions and k f(x).  Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.  UNPACKED STANDARDSN-RN.2 Students should be able to use the properties of exponents to rewrite expressions involving rational exponents as expressions using radicals. Ex. The expression EMBED Equation.DSMT4 can be written as ( EMBED Equation.DSMT4)2 or as EMBED Equation.DSMT4. Write these expressions in radical form. How would you confirm that these forms are equivalent? Considering that EMBED Equation.DSMT4, which form would be easier to simplify without a calculator? Why? Ex. When calculatingEMBED Equation.DSMT4 , Kyle entered 9^3/2 into his calculator. Karen entered it asEMBED Equation.DSMT4. They came out with different results. Which was right and how could the other student modify their input? N-Q.1 Use units as a tool to help solve multi-step problems. For example, students should use the units assigned to quantities in a problem to help identify which variable they correspond to in a formula. Students should also analyze units to determine which operations to use when solving a problem. Given the speed in mph and time traveled in hours, what is the distance traveled? From looking at the units, we can determine that we must multiply mph times hours to get an answer expressed in miles:  QUOTE   (Note that knowledge of the distance formula is not required to determine the need to multiply in this case.) N-Q.1 Based on the type of quantities represented by variables in a formula, choose the appropriate units to express the variables and interpret the meaning of the units in the context of the relationships that the formula describes. N-Q.1 When given a graph or data display, read and interpret the scale and origin. When creating a graph or data display, choose a scale that is appropriate for viewing the features of a graph or data display. Understand that using larger values for the tick marks on the scale effectively zooms out from the graph and choosing smaller values zooms in. Understand that the viewing window does not necessarily show the x- or y-axis, but the apparent axes are parallel to the x- and y-axes. Hence, the intersection of the apparent axes in the viewing window may not be the origin. Also be aware that apparent intercepts may not correspond to the actual x- or y-intercepts of the graph of a function. Ex. A group of students organized a local concert to raise awareness for The American Diabetes Foundation. They have several expenses for promoting and operating the concert and will be making money through selling tickets. Their profit can be modeled by the formula P = x(4,000 250x) 7500. Graph the profit model using an appropriate scale and explain your reasoning. N-Q.2 Define the appropriate quantities to describe the characteristics of interest for a population. For example, if you want to describe how dangerous the roads are, you may choose to report the number of accidents per year on a particular stretch of interstate. Generally speaking, it would not be appropriate to report the number of exits on that stretch of interstate to describe the level of danger. Ex. What quantities could you use to describe the best city in North Carolina? Ex. What quantities could you use to describe how good a basketball player is? N-Q.3 Understand that the tool used determines the level of accuracy that can be reported for a measurement. Ex. Determining price of gas by estimating to the nearest cent is appropriate because you will not pay in fractions of a cent but the cost of gas is  EMBED Equation.3 . A-CED.3 Use constraints which are situations that are restricted to develop equations and inequalities and systems of equations or inequalities. Describe the solutions in context and explain why any particular one would be the optimal solution. Extend to linear-quadratic and linear-inverse variation (simplest rational) systems of equations. A-CED.3 When given a problem situation involving limits or restrictions, represent the situation symbolically using an equation or inequality. Interpret the solution(s) in the context of the problem. When given a real world situation involving multiple restrictions, develop a system of equations and/or inequalities that models the situation. In the case of linear programming, use the Objective Equation and the Corner Principle to determine the solution to the problem. Ex. Imagine that you are a production manager at a calculator company. Your company makes two types of calculators, a scientific calculator and a graphing calculator. a. Each model uses the same plastic case and the same circuits. However, the graphing calculator requires 20 circuits and the scientific calculator requires only 10. The company has 240 plastic cases and 3200 circuits in stock. Graph the system of inequalities that represents these constraints. b. The profit on a scientific calculator is $8.00, while the profit on a graphing calculator is $16.00. Write an equation that describes the companys profit from calculator sales. c. How many of each type of calculator should the company produce to maximize profit using the stock on hand? HN.1 Solve systems involving three equations and three variables. Solve this system of equations using elimination.  INCLUDEPICTURE "http://media.wiley.com/Lux/29/255429.eq04001.png" \* MERGEFORMATINET  A-CED.4 Solve multi-variable formulas or literal equations, for a specific variable. Explicitly connect this to the process of solving equations using inverse operations. At this level, extend to compound variation relationships. Ex. If, solve for T2. A-REI.10 Understand that all points on the graph of a two-variable equation are solutions because when substituted into the equation, they make the equation true. At this level, extend to quadratics. A-REI.11 Construct an argument to demonstrate understanding that the solution to every equation can be found by treating each side of the equation as separate functions that are set equal to each other, f(x) = g(x). Allow y1=f (x) and y2= g(x) and find their intersection(s). The x-coordinate of the point of intersection is the value at which these two functions are equivalent, therefore the solution(s) to the original equation. Students should understand that this can be treated as a system of equations and should also include the use of technology to justify their argument using graphs, tables of values, or successive approximations. At this level, extend to quadratic functions. A-REI.11 Understand that solving a one-variable equation of the form f(x) = g(x) is the same as solving the two-variable system y = f(x) and y = g(x). When solving by graphing, the x-value(s) of the intersection point(s) of y = f(x) and y = g(x) is the solution of f(x) = g(x) for any combination of linear and exponential functions. Use technology, entering f(x) in y1 and g(x) in y2, graphing the equations to find their point of equality. At this level, extend to quadratic functions. Ex. How do you find the solution to an equation graphically? A-REI.11 Solve graphically, finding approximate solutions using technology. At this level, extend to quadratic functions. A-REI.11 Solve by making tables for each side of the equation. Use the results from substituting previous values of x to decide whether to try a larger or smaller value of x to find where the two sides are equal. The x-value that makes the two sides equal is the solution to the equation. At this level, extend to quadratic functions. Ex. John and Jerry both have jobs working at the town carnival. They have different employers, so their daily wages are calculated differently. Johns earnings are represented by the equation, p(x) = 2x and Jerrys by g(x) = 10 + 0.25x. a. What does the variable x represent? b. If they begin work next Monday, Michelle told them that Friday would be the only day they made the same amount of money. Is she correct in her assumption? Explain your reasoning. c. When will Jerry earn more money than John? When will John earn more money than Jerry? During what day will their earnings be the same? Justify your conclusions. F-IF.2 Students should continue to use function notation throughout high school mathematics, understanding f(input) = output, f(x)=y. F-IF.2 Students should be comfortable finding output given input (i.e. f(3) = ?) and finding inputs given outputs (f(x) = 10) and describe their meanings in the context in which they are used. At this level, extend to quadratic, simple power and inverse variation functions. Ex.  a. Solve h(5) and explain the meaning of the solution. b. Solve h(t) = 0 and explain the meaning of the solution. Using function notation, evaluate functions and explain values based on the context in which they are in. At this level, extend to quadratic, simple power, and inverse variation functions. Ex. Evaluate  QUOTE   for the function QUOTE  . Ex. The function  QUOTE   describes the height h in feet of a tennis ball x seconds after it is shot straight up into the air from a pitching machine. Evaluate  QUOTE   and interpret the meaning of the point in the context of the problem. Ex. Let EMBED Equation.3 . Find EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3 . Ex. If P(t) is the population of Tucson t years after 2000, interpret the statements P(0) = 487,000 and P(10) - P(9) = 5,900. F-IF.7b Students should graph functions given by an equation and show characteristics such as, but not limited to intercepts, maximums, minimums, and intervals of increase or decrease. Students may use calculators for more difficult cases. Ex. Describe key characteristics of the graph of f(x) = %x  3% + 5. Ex. Sketch the graph and identify the key characteristics of the function described below.  EMBED Equation.DSMT4  Ex. Graph the function f(x) = 2x by creating a table of values. Identify the key characteristics of the graph. F-IF.9 Students should compare the properties of two functions represented by verbal descriptions, tables, graphs, and equations. For example, compare the growth of two linear functions, two exponential functions, or one of each. At this level, extend to quadratic, simple power, and inverse variation functions. Ex. Compare the functions represented below. Which has the lowest minimum? a. f(x) = 3x2 +13x +4 b.  Ex. Compare the patterns of (x, y) values when produced by these functions:  QUOTE  and  QUOTE   by completing these tasks. Write a NOW- NEXT equation that would provide the same pattern of (x, y) values for each function. How would you describe the similarities and differences in the relationships of x and y in terms of their graphs, tables, and equations? F-BF.1a Recognize when a relationship exists between two quantities and write a function to describe them. Use steps, the recursive process, to make the calculations from context in order to write the explicit expression that represents the relationship. Note: Continue to allow informal recursive notation through this level. Ex. A single bacterium is placed in a test tube and splits in two after one minute. After two minutes, the resulting two bacteria split in two, creating four bacteria. This process continues for one hour until test tube is filled up. How many bacteria are in the test tube after 5 minutes? 15 minutes? Write a recursive rule to find the number of bacteria in the test tube after n minutes. Convert this rule into explicit form. How many bacteria are in the test tube after one hour? F-BF.3 Know that when adding a constant, k, to a function, it moves the graph of the function vertically. If k is positive, it translates the graph up, and if k is negative, it translates the graph down. If k is either added or subtracted from the x-value, it translates the graph of the function horizontally. If we add k, the graph shifts left and if we subtract k, the graph shifts right. The expression (x + k) shifts the graphs k units to the left because when x + k = 0, x = -k. Us the calculator to explore the effects these values have when applied to a function and explain why the values affect the function the way it does. The calculator visually displays the function and its translation making it simple for every student to describe and understand translations. At this level, extend to quadratic functions and, k f(x). Ex. If f(x) represents a divers position from the edge of a pool as he dives from a 5ft. long board 25ft. above the water. If his second dive was from a 10ft. long board that is 10ft above the water, what happens to my equation of f(x) to model the second dive? Compare the shape and position of the graphs of  EMBED Equation.3 and  EMBED Equation.3 , and explain the differences in terms of the algebraic expressions for the functions  Unpacked Concepts (students need to know)Unwrapped Skills (students need to be able to do)COGNITION DOK Operations and properties of integers can be extended to situations involving rational and irrational numbers.N-RN.2 I can apply the properties of exponents to simplify algebraic expressions with integer exponents. I can apply the properties of exponents to simplify algebraic expressions with rational exponents. I can write radical expressions as expressions with rational exponents. I can write expressions with rational exponents as radical expressions.  3 3 3 3  Interpreting numbers as quantities with appropriate units, scales, and levels of accuracy allows one to effectively model and make sense of real world problems.N-Q.1 I can label units through multiple steps of a problem. I can use and interpret units when solving formulas. N-Q.2 I can identify the variables or quantities of significance from the data provided. I can identify or choose the appropriate unit of measure for each variable or quantity. N-Q.3 I can report calculated quantities using the same level of accuracy as used in the problem statement.  1 2 3 3 2 Relationships between numbers can be represented by equations, inequalities, and systems.A-CED.3 I can identify the variables and quantities represented in a real-world problem. I can determine the best models for the real-world problem (e.g., linear equation, linear inequality, quadratic equation, quadratic inequality). I can write the system of equations and/or inequalities that best models the problem. I can graph the system on coordinate axes with appropriate labels and scales. I can interpret solutions in the context of the situation modeled and decide if they are reasonable. I can solve a system involving three equations and three variables. A-CED.4 I can solve formulas for a specified variable.  1 2 3 3 2 4 3 There is often an optimal method of manipulating equations and inequalities to solve a mathematical problem; however, other methods, which may not be as efficient, can still provide insight into the problem.A-REI.10 I can explain that every point (x, y) on the graph of an equation represents values x and y that make the equation true. I can verify that any point on a graph will result in a true equation when their coordinates are substituted into the equation. A-REI.11 I can explain that a point of intersection on the graph of a system of equations, y = f(x) and y = g(x), represents a solution to both equations. I can infer that since y = f(x) and y = g(x), f(x) = g(x) by the substitution property. I can infer that the x-coordinate of the points of intersection for y = f(x) and y = g(x) are also solutions for f(x) = g(x). I can use a graphing calculator to determine the approximate solutions to a system of equation, f(x) and g(x).  1 1 1 2 2 3 Equations, verbal descriptions, graphs and tables provide insight into the relationship between quantities. F-IF.2 I can decode function notation and explain how the output of a function is matched to its input (e.g., the function f(x) = 2x2 + 4 squares the input, doubles the square, and adds four to produce the output). I can convert a table, graph, set of ordered pairs, or description into function notation by identifying the rule used to turn inputs into outputs and writing the rule. I can use order of operations to evaluate a function for a given domain (input) value. I can identify the numbers that are not in the domain of a function (e.g., 0 is not in the domain of g(x) =1/x and negative numbers are not in the domain of  EMBED Equation.3 ). I can choose inputs that make sense based on a problem situation. I can analyze the input and output values of a function based on a problem situation. F-IF.5 I can explain how the domain of a function is represented in its graph. I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain. F-IF.7b I can analyze functions using different representations: F-IF.9 I can compare properties of two functions when represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions). 2 3 3 2 2 2 2 2 2  Functions can be created by identifying the pattern of a relationship or by applying geometric transformations to an existing function. F-BF.1a Explicit & Recursive Expressions: I can define explicit and recursive expressions of a function. I can identify the quantities being compared in a real-world problem. F-BF.3 I can identify the effects of k (positive and negative) on a given function. f(x) + k f(x + k) k f(x) f(kx) I can find the value of k given a graph. I can analyze the similarities and differences between functions with different k values. I can experiment using technology to illustrate the effects of k on a graph. 1 1 2 2 2 3 Essential QuestionsCorresponding Big IdeasHow does knowledge of integers help when working with rational and irrational numbers? (N-RN)Operations and properties of integers can be extended to situations involving rational and irrational numbers.In what ways can the choice of units, quantities, and levels of accuracy impact a solution? (N-Q)The choice of appropriate units, scales, and levels of accuracy allows one to effectively model and make sense of real world problems.How can I use algebra to describe the relationship between sets of numbers? (A-CED)Algebra can be used to describe relationships between numbers by using equations, inequalities, and systems.In what ways can the problem be solved, and why should one method be chosen over another? (A-REI)Even though there may be an optimal method of solving a problem, other methods, which may not be as efficient, can still provide insight into the problem.How can the relationship between quantities best be represented? (F-IF) The relationship between quantities can be represented by equations, verbal descriptions, graphs and tables.In what ways can functions be built? (F-BF) Functions can be built by identifying the pattern of a relationship or by applying geometric transformations to an existing function. Vocabulary Exponent, laws of exponents, simplify, expression, integer, rational, units, scale, function, origin, x- coordinate, intersection, solution, linear function, quadratic function, absolute value function, exponential function, system of equations, substitution property, domain, piecewise-defined function, intercepts, function notation [ f(x) ]  Language ObjectivesKey Vocabulary N-RN.2 N-Q.1 N-Q.2 N-Q.3 A-CED.3 A-CED.4 A-REI.10 A-REI.11 F-IF.2 F-IF.5 F-IF.7b F-IF.9 F-BF.1a F-BF.3SWBAT explain the meaning of the key vocabulary specific to the standards: exponent laws of exponents simplify expression integer rational units scale function origin x- coordinate intersection solution linear function quadratic function domain intercepts absolute value function system of equations exponential function substitution property piecewise-defined function  Language Function F-IF.2SWBAT explain how to determine if the solution of a quadratic equation is correct.N-RN.2SWBAT describe the meaning of square and cube roots.F-BF.3SWBAT use visuals to explain effects on a graph when adding or subtracting a value to the function.A-CED.3SWBAT give a step-by-step process in writing systems of linear equations to match given problem conditions.A-REI.11 F-IF.7bSWBAT use visuals to name the function that a particular graph represents.Language Structure F-IF.5SWBAT understand and explain the types of situations that could be modeled by quadratic equations.Lesson Tasks F-IF.9SWBAT explore simple power models through tables, graphs and symbolic rules. A-REI.10 F-IF.2SWBAT to estimate the solution of a quadratic equation using a table of values and a graph.F-BF.3SWBAT summarize fundamental properties for transforming exponential expressions into alternative equivalent forms.A-CED.4SWBAT solve linear equations for one variable in terms of the other.Language Learning Strategies F-IF.2 F-IF.5SWBAT identify and interpret language that provides information in matching a function rule with its graph, without using a calculator.F-IF.9SWBAT determine what type of function fits a real-world example and write a sentence describing the relationship in the language of direct and inverse variation. Information and Technology Standards HS.TT.1.1 Use appropriate technology tools and other resources to access information HS.TT.1.2 Use appropriate technology tools and other resources to organize information Instructional Resources and MaterialsPhysicalTechnology-BasedGlencoe Algebra 2 (very minimal) Core Plus Contemporary Mathematics in Context, Course 2 (2nd ed.) Unit 1 Core Plus Contemporary Mathematics in Context, Course 3 (1st ed.) COMAP Dana Center Assessment Items Honors Resources Core Plus Contemporary Mathematics in Context (1st Edition) Course 2, Part A Assessment Resources: Unit 4 Take-Home Assessment Unit 4 Project: The Quadratic Formula HN Solving Systems of Three Equations and Three Variables: Core Plus Contemporary Mathematics in Context (2nd Edition): Unit 1, Lesson 3, page 67, #25 Solving Systems in Three Variables Tutorials: 1) HYPERLINK "http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut50_systhree.htm" http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut50_systhree.htm 2) HYPERLINK "http://www.youtube.com/watch?v=g6FQBfIwf3w" http://www.youtube.com/watch?v=g6FQBfIwf3w 3)  HYPERLINK "http://www.sosmath.com/soe/SE3/SE3.html" http://www.sosmath.com/soe/SE3/SE3.html 4) HYPERLINK "http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/systems-of-three-variables" http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/v/systems-of-three-variables 5) HYPERLINK "http://tutorial.math.lamar.edu/Classes/Alg/SystemsThreeVrble.aspx" http://tutorial.math.lamar.edu/Classes/Alg/SystemsThreeVrble.aspx Solving Systems in Three Variables Worksheets: 1) HYPERLINK "http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Systems%20of%20Three%20Equations%20Elimination.pdf" http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Systems%20of%20Three%20Equations%20Elimination.pdf 2) HYPERLINK "http://deanashirk.wikispaces.com/file/view/2.2+worksheet+for+solving+systems+of+equations+pdf.pdf" http://deanashirk.wikispaces.com/file/view/2.2+worksheet+for+solving+systems+of+equations+pdf.pdf 3) HYPERLINK "http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Systems%20of%20Three%20Equations%20Substitution.pdf" http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Systems%20of%20Three%20Equations%20Substitution.pdf CPMP-Tools Software  HYPERLINK "http://www.wmich.edu/cpmp/CPMP-Tools/" http://www.wmich.edu/cpmp/CPMP-Tools/ CPMP-Tools is a suite of both general purpose and custom software tools designed to support student investigation and problem solving in the Core-Plus Mathematics texts. CPMP-Tools can be used free of charge, not just by CPMP users. It is a Java based system and Java must be installed on the computer before using. NCTM Illuminations (HYPERLINK "http://illuminations.nctm.org)" \t "_blank" INCLUDEPICTURE "http://oaklandk12-public.rubiconatlas.org/common_images/page_world.png?v=Atlas7.2.6.173" \* MERGEFORMATINET  http://illuminations.nctm.org) Function Matching:  HYPERLINK "http://illuminations.nctm.org/ActivityDetail.aspx?ID=215" http://illuminations.nctm.org/ActivityDetail.aspx?ID=215 Whats the Function?  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