Algebra

Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
A.SSE.1 Interpret expressions that represent a quantity in terms of its context.*	How do context clues assist in developing an appropriate expression or equation to solve?	-Write an expression or equation based on the information provided in a problem.	-Expression -Equation -Sum -Difference -Quantity -Quotient	3 days
A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.	How do numbers and symbols relate to each other in a given problem?	-Distinguish between the various parts of an expression or an equation.	-Term -Factor -Coefficient -Variable	3 days
A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.	Why is it important to consider every aspect of a given problem or scenario before attempting to solve the problem? How do terms in an expression or equation relate to each other?	-Manipulate quantities in an equation to demonstrate the relationship between terms -Evaluate the necessity and use of information provided in a word problem. -When given a word problem, determine which information is needed to solve the problem and which information is extraneous.	-Inverse Operation -Extraneous Information	3 days
A.SSE.2Use the structure of an expression to identify ways to rewrite it. For example, see x4-y4as (x2)2-(y2)2, thus recognizing it as a difference of squares that can be factored as (x2-y2) (x2+y2).	What qualities of a given function signify the possibility the function could be simplified using difference of squares?	-Develop a visual demonstrating the steps needed to factor a function of a degree higher than 2	-Structure of an expression -Factoring	3 days
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*	When is an understanding of equivalent expressions beneficial?	-Create a visual with samples of two equivalent expressions and two expressions which are not equivalent; Explain your findings	-Equivalent -Expression	3 days
A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.	What is the relationship between the zeros of a function and its corresponding graph?	-Examine a set of graphs and a list of equations to determine which equations match each graph by first determining the zeros	-Factor -Zeros	3 days
A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.	What is the correlation between maximum and minimum and a roller coaster?	-Design your own rollercoaster using an online rollercoaster tycoon game and four quadratic equations of your creation	-Complete the square -Maximum -Minimum	3 days
A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ≈1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.	How does monthly interest rate affect the overall cost of an item?	-Choose an item you would like to buy with a credit card; then use an online calculator to determine what the overall cost of the item would be based on the minimum payments you would pay and the interest rate	-Exponents -Exponential functions -Interest -Annual rate	3 days
A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ration is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*	Would you rather have $1 million or the sum of a penny doubled every day for a month?	-Create a collage or visual of the items you would purchase with your new found wealth	-Geometric series -Finite	3 days
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
A.APR.1Understand 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.	What is the difference between an open and a closed system?	--Design a graphic, including examples, which demonstrates the difference between an open and closed system -Create a worksheet of no less than six problems involving completing arithmetic operations on polynomials	-Polynomial -Analogous -Open System -Closed System -Like terms	3 days
A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x-a is p(a), so p(a) = 0 if and only if (x-a) is a factor of p(x)	How does use of synthetic division assist in solving for the solution of a polynomial with a given x-value?	-Experiment with different coefficients to create a 5th degree polynomial with -3 as a factor.	-Remainder -Division -Polynomial division -Synthetic division -Remainder Theorem	3 days
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.	What is the relationship between the zeros of a polynomial and the x-axis?	-Given a 4th degree polynomial, determine the zeros and (from Common Core) construct a rough graph of the function defined by the polynomial.	-Zeros -Polynomials -Concavity -Increasing -Decreasing -Factor	3 days
A.APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2+y2) 2 = (x2-y2) 2+ (2xy)2 can be used to generate Pythagorean triples.	When an identity is proven valid, what may be said about it?	-Choose a polynomial identity and prove its truth in a visual to be displayed in the classroom; use at least three examples (+/-/0)	-Polynomial identities	1 day
A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)	In what fields is knowledge of Pascal’s Triangle useful? Why?	-Research Pascal’s Triangle; create a brief (approximately 5 minute) presentation on one area of study in which Pascal’s Triangle is useful. Present your research to the class and other educators in the building.	-Binomial Theorem -Expansion -Pascal’s Triangle	1 day
A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.	With the accessibility of the internet, how is higher level mathematics more reachable to high school learners than 20 years ago?	-Experiment with three different computer algebra systems available at http://www.sai.msu.su/sal/A/1/ and recommend a system which most assists in completing polynomial division	-Rational expression -Long division	1 day
A.APR.7 (+)Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.	What does it mean for a system to be closed?	-Create a worksheet and answer key with no less than seven problems  which require the addition, subtraction, multiplication and/or division of rational expressions	-Rational expressions -Analogous	1 day
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
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 simple rational and exponential functions.	How does the use of the inverse operation assist in solving algebraic word problems?	-Explain the relationship between inverse operations and both sides of the equation or inequality. -Select the appropriate sequence of operations to complete the problem.	-Inequality -Order of Operations	3 days
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.	What strategies may be used to effectively create equations with two or more variables? How do the elements of an equation assist in accurately graphing the equation on coordinate axes?	-Based on a given word problem, create and solve an equation which results in an accurate response to the question. -Construct an accurate geometric response to a given word problem or set of equations.	-Slope -Intercept -Coordinate Plane -Graph -Graphing Calculator	3 days
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.	What limitations exist when solving problems algebraically and/or graphically? Why is flipping the inequality necessary when multiplying or dividing by a negative number?	-Distinguish between rational and irrational responses when solving equations. -Examine the reasons why a solution is viable or non-viable.	-Viable -Inequality -Constraint -Systems of Equations	3 days
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.	How are inverse operations used to highlight a quantity of interest?	-Explain how knowledge of inverse operations allow for the rearrangement of variables and terms to solve for a requested quantity of interest	-Quantity of Interest -Reasoning	3 days
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
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.	Why is it important to complete a step to both sides of the equation?	-Create a diagram outlining the steps to solve an equation; provide multiple examples of the process. -Explain each step of the process outlined in the diagram.	-Solving equations -Inverse operation	3 days
A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise	How do the fundamental rules of order of operations assist in solving rational and radical equations?	-Create a 2-minute video teaching how to solve either rational or radical equations; post your video on the class webpage or YouTube	-Rational equations -Radical equations -Variables	3 days
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.	Why is knowledge of the inverse operation necessary in solving equations?	-Support the relationship between inverse operations and solving equations by providing both linear examples and those including inequalities.	-Equation -Inequality -Coefficient -Variable	3 days
A.REI.4 Solve quadratic equations in one variable.	What is the relationship between driving a car and quadratic equations?	-Given an equation and its derivative, experiment with different values of x to determine the distance a car travels and it’s speed	-Variable -Factor -Quadratic equation	3 days
A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2 = q that has the same solutions. Derive the quadratic formula from this form.	How does knowledge of completing the square assist in the derivation  of the quadratic formula?	-Create a poster for display of 1) an example of completing the square on an equation of your choosing and 2) the creation of the quadratic formula from the equation ax2+bx+c=0	-Completing the square -Quadratic formula	3 days
A.REI.4b Solve quadratic equations by inspection (e.g., for x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and writing them as a±bi for real numbers a and b.	What aspects of an equation should be considered when determining which method to utilize to solve the equation?	-Evaluate a given problem to determine the best method to solve the equation and then support your selection in three to five sentences	-Square roots -Completing the square -Quadratic formula -Factoring	3 days
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.	Why is it acceptable to increase or decrease an equation by a chosen factor when solving systems of equations with two variables?	-Defend that increasing or decreasing an equation by a chosen factor does not affect the solutions to the equation.	-System of equations -Substitution	2 days
A.REI.6 Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables.	How can the graph of a system of equations assist in determining the solutions?	-Examine a system of equations and develop a strategy to determine the exact and graphical approximation of the result.	-Pairs of equations	2 days
A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2+y2=3.	How is the solution to a system of equations determined by looking at their graphs?	-Design a  simple systems of a linear equation and a quadratic equation in two variables and solve 1) By hand, 2) Using a TI Graphing Calculator (Take a picture), AND 3) using Microsoft Mathematics (Print out); Display your work by	-System of equation -Linear equation -Quadratic equation -Circle formula	2 days
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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).	How do the solutions of a two-variable equation relate to its graph? How do the qualities of an equation dictate what the graph looks like it?	-Construct an accurate coordinate plan and graph when given a two-variable equation. -Formulate the equation of a given graph. -Contrast the differences between linear and quadratic graphs and equations.	-Graph -Linear -Quadratic -Polynomial -Function -Origin -Solution	3 days
A.REI.11 Explain why the x-coordinate of the points where the graphs of the equations y=f(x) and y=g(x) intersect are 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.*	How does the intersection of a graph to the x-axis relate to the solution of the equation? How does the intersection of two functions relate to solutions of the functions? How can technology be utilized to solve geometric problems?	-Support how the intersection of two functions is a common solution of the functions. -Experiment with various modes on a graphing calculator to contrast changes in the graph based on mode selected (e.g. how does a trigonometric graph look in radian versus degree mode)	-Absolute Value -Exponential -Logarithmic -Approximate -Radian -Degree	3 days
A.REI.12 Graph the solutions to a linear inequality in two variables as a 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.	When is the structure of a line significant in considering inequalities? What is significant about the shading of inequalities on a coordinate plane?	-Compare the solutions of two inequalities based on the shading of a graph. -When given two inequalities, construct a coordinate plane and accurate graph the equations to determine the appropriate solution through shading.	-Inequalities -Shade -Equal to -Linear Inequality -Graph the Solution	3 days