Rigorous Curriculum Design



Rigorous Curriculum Design

Unit Planning Organizer

|Subject(s) |High School Mathematics |

|Grade/Course |Honors Math II |

|Unit of Study |Unit 1: Functions, Equations and Systems |

|Unit Type(s) |❑Topical ❑X Skills-based ❑ Thematic |

|Pacing |14 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 functions—with special attention to |

|Students develop an understanding of a wide range of models, including power models of the forms[pic],[pic], and[pic]. 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. |

| |

|N-Q.2 DEFINE appropriate quantities for the purpose of descriptive |

|modeling. |

| |

|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. |

| |

| |

| |

|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 STANDARDS” |

|N-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 [pic] can be written as ( [pic])2 or as [pic]. |

|Write these expressions in radical form. How would you confirm that these forms are |

|equivalent? |

|Considering that [pic], which form would be easier to simplify without a |

|calculator? Why? |

| |

|Ex. When calculating[pic] , Kyle entered 9^3/2 into his calculator. Karen entered it |

|as[pic]. 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: [pic] (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 [pic]. |

| |

|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 |

|company’s profit from calculator sales. |

|c. How many of each type of calculator should the company produce to maximize profit using the stock on hand? |

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| |

| |

|HN.1 Solve systems involving three equations and three variables. |

|Solve this system of equations using elimination. |

|[pic] |

| |

|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[pic], 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. |

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|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. John’s earnings are represented by the equation, p(x) = 2x and Jerry’s 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. |

|[pic] |

|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 [pic] for the function[pic]. |

| |

|Ex. The function [pic] 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 [pic] and interpret the meaning of the point in the context of the problem. |

|Ex. Let[pic]. Find[pic], [pic], [pic], and [pic]. |

|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. |

|[pic] |

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| |

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|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. [pic] |

| |

|Ex. Compare the patterns of (x, y) values when produced by these functions: [pic]and [pic] 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 diver’s 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 [pic]and [pic], and explain the differences in terms of the algebraic expressions for the |

|functions |

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|[pic] |

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|“Unpacked” Concepts |“Unwrapped” Skills |COGNITION |

|(students need to know) |(students need to be able to do) |DOK |

| |N-RN.2 | |

| | | |

|Operations and properties of integers can be extended to |I can apply the properties of exponents to simplify |3 |

|situations involving rational and irrational numbers. |algebraic expressions with integer exponents. | |

| | | |

| |I can apply the properties of exponents to simplify |3 |

| |algebraic expressions with rational exponents. | |

| | |3 |

| |I can write radical expressions as expressions with | |

| |rational exponents. |3 |

| | | |

| |I can write expressions with rational exponents as radical| |

| |expressions. | |

| | | |

| |N-Q.1 | |

| | |1 |

|Interpreting numbers as quantities with appropriate units, |I can label units through multiple steps of a problem. | |

|scales, and levels of accuracy allows one to effectively | | |

|model and make sense of real world problems. |I can use and interpret units when solving formulas. |2 |

| | | |

| |N-Q.2 | |

| | | |

| |I can identify the variables or quantities of significance| |

| |from the data provided. |3 |

| | | |

| |I can identify or choose the appropriate unit of measure | |

| |for each variable or quantity. | |

| | | |

| |N-Q.3 |3 |

| | | |

| |I can report calculated quantities using the same level of| |

| |accuracy as used in the problem statement. | |

| | | |

| | | |

| | |2 |

| |A-CED.3 | |

|Relationships between numbers can be represented by |I can identify the variables and quantities represented in|1 |

|equations, inequalities, and systems. |a real-world problem. | |

| | |2 |

| |I can determine the best models for the real-world problem| |

| |(e.g., linear equation, linear inequality, quadratic | |

| |equation, quadratic inequality). |3 |

| | | |

| |I can write the system of equations and/or inequalities | |

| |that best models the problem. |3 |

| | | |

| |I can graph the system on coordinate axes with appropriate|2 |

| |labels and scales. | |

| | |4 |

| |I can interpret solutions in the context of the situation | |

| |modeled and decide if they are reasonable. |3 |

| | | |

| |I can solve a system involving three equations and three | |

| |variables. | |

| | | |

| |A-CED.4 | |

| |I can solve formulas for a specified variable. | |

| | | |

| |A-REI.10 | |

|There is often an optimal method of manipulating equations |I can explain that every point (x, y) on the graph of an |1 |

|and inequalities to solve a mathematical problem; however, |equation represents values x and y that make the equation | |

|other methods, which may not be as efficient, can still |true. | |

|provide insight into the problem. | |1 |

| |I can verify that any point on a graph will result in a | |

| |true equation when their coordinates are substituted into | |

| |the equation. |1 |

| | | |

| |A-REI.11 | |

| |I can explain that a point of intersection on the graph of|2 |

| |a system of equations, y = f(x) and | |

| |y = g(x), represents a solution to both equations. | |

| | |2 |

| |I can infer that since y = f(x) and | |

| |y = g(x), f(x) = g(x) by the substitution property. |3 |

| | | |

| |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). | |

| |F-IF.2 | |

|Equations, verbal descriptions, graphs and tables provide |I can decode function notation and explain how the output | |

|insight into the relationship between quantities. |of a function is matched to its input (e.g., the function | |

| |f(x) = 2x2 + 4 squares the input, doubles the square, and |2 |

| |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|3 |

| |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. |3 |

| |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 |2 |

| |[pic]). | |

| |I can choose inputs that make sense based on a problem | |

| |situation. |2 |

| |I can analyze the input and output values of a function | |

| |based on a problem situation. |2 |

| |F-IF.5 | |

| |I can explain how the domain of a function is represented |2 |

| |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. |2 |

| |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 |

| |F-BF.1a | |

|Functions can be created by identifying the pattern of a |Explicit & Recursive Expressions: | |

|relationship or by applying geometric transformations to an |I can define explicit and recursive expressions of a |1 |

|existing function. |function. | |

| |I can identify the quantities being compared in a |1 |

| |real-world problem. | |

| |F-BF.3 | |

| |I can identify the effects of k (positive and negative) on| |

| |a given function. |2 |

| |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 |2 |

| |functions with different k values. | |

| |I can experiment using technology to illustrate the |2 |

| |effects of k on a graph. | |

| | |3 |

|Essential Questions |Corresponding Big Ideas |

|How does knowledge of integers help when working with rational and |Operations and properties of integers can be extended to situations |

|irrational numbers? (N-RN) |involving rational and irrational numbers. |

|In what ways can the choice of units, quantities, and levels of |The choice of appropriate units, scales, and levels of accuracy allows|

|accuracy impact a solution? (N-Q) |one to effectively model and make sense of real world problems. |

|How can I use algebra to describe the relationship between sets of |Algebra can be used to describe relationships between numbers by using|

|numbers? |equations, inequalities, and systems. |

|(A-CED) | |

|In what ways can the problem be solved, and why should one method be |Even though there may be an optimal method of solving a problem, other|

|chosen over another? (A-REI) |methods, which may not be as efficient, can still provide insight into|

| |the problem. |

|How can the relationship between quantities best be represented? |The relationship between quantities can be represented by equations, |

|(F-IF) |verbal descriptions, graphs and tables. |

|In what ways can functions be built? |Functions can be built by identifying the pattern of a relationship or|

|(F-BF) |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 Objectives |

|Key Vocabulary |

|N-RN.2 |SWBAT explain the meaning of the key vocabulary specific to the standards: |

|N-Q.1 |exponent laws of exponents simplify |

|N-Q.2 |expression integer rational |

|N-Q.3 |units scale function |

|A-CED.3 |origin x- coordinate intersection |

|A-CED.4 |solution linear function quadratic function |

|A-REI.10 |domain intercepts |

|A-REI.11 | |

|F-IF.2 |absolute value function system of equations |

|F-IF.5 |exponential function substitution property |

|F-IF.7b |piecewise-defined function |

|F-IF.9 | |

|F-BF.1a | |

|F-BF.3 | |

|Language Function |

|F-IF.2 |SWBAT explain how to determine if the solution of a quadratic equation is correct. |

|N-RN.2 |SWBAT describe the meaning of square and cube roots. |

|F-BF.3 |SWBAT use visuals to explain effects on a graph when adding or subtracting a value to the function. |

|A-CED.3 |SWBAT give a step-by-step process in writing systems of linear equations to match given problem conditions. |

|A-REI.11 |SWBAT use visuals to name the function that a particular graph represents. |

|F-IF.7b | |

|Language Structure |

|F-IF.5 |SWBAT understand and explain the types of situations that could be modeled by quadratic equations. |

|Lesson Tasks |

|F-IF.9 |SWBAT explore simple power models through tables, graphs and symbolic rules. |

|A-REI.10 |SWBAT to estimate the solution of a quadratic equation using a table of values and a graph. |

|F-IF.2 | |

|F-BF.3 |SWBAT summarize fundamental properties for transforming exponential expressions into alternative equivalent |

| |forms. |

|A-CED.4 |SWBAT solve linear equations for one variable in terms of the other. |

|Language Learning Strategies |

|F-IF.2 |SWBAT identify and interpret language that provides information in matching a function rule with its graph, |

|F-IF.5 |without using a calculator. |

|F-IF.9 |SWBAT 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 Materials |

|Physical |Technology-Based |

|Glencoe Algebra 2 (very |Honors Resources |

|minimal) |Core Plus Contemporary Mathematics in Context (1st Edition) |

| |Course 2, Part A Assessment Resources: |

|Core Plus Contemporary |Unit 4 Take-Home Assessment |

|Mathematics in Context, Course |Unit 4 Project: The Quadratic Formula |

|2 (2nd ed.) – Unit 1 |HN Solving Systems of Three Equations and Three Variables: |

| |Core Plus Contemporary Mathematics in Context (2nd Edition): Unit 1, Lesson 3, page 67, #25 |

|Core Plus Contemporary |Solving Systems in Three Variables Tutorials: |

|Mathematics in Context, Course |1) |

|3 (1st ed.) |2) |

| |3) |

|COMAP |4) |

|Dana Center Assessment Items |5) |

| |Solving Systems in Three Variables Worksheets: |

| |1)

| |f |

| |2) |

| |3)

| |df |

| | |

| | |

| |CPMP-Tools Software |

| | |

| |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​ ([pic] ) |

| |Function Matching: |

| | |

| |What’s the Function? |

| | |

| | |

| | |

| |Movement with Functions: |

| | |

| | |

| | |

| | |

| |Domain Representations: |

| | |

| | |

| | |

| |Math Assessment Project |

| | |

| | |

| |MAP Lesson Units: |

| |1) Functions and Everyday Situations |

| | |

| | |

| |Tasks |

| |1) A16: Sorting Functions |

| | |

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