Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results


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1 Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results Unit Title: Quadratic Expressions & Equations Course: Algebra I Unit 8  Quadratic Expressions & Equations Brief Summary of Unit: At the end of this unit, students will be able to work with quadratic expressions and equations. Students will be able to add, subtract and multiply polynomials. Students will also be able to solve quadratic equations by factoring. Textbook Correlation: Glencoe Algebra I Chapter 8 Sections 19 Time Frame: 4 weeks Note It is recommended that this unit have two assessments. WSD Overarching Essential Question Students will consider WSD Overarching Enduring Understandings Students will understand that How do I use the language of math (i.e. symbols, words) to make sense of/solve a problem? How does the math I am learning in the classroom relate to the realworld? What does a good problem solver do? What should I do if I get stuck solving a problem? How do I effectively communicate about math with others in verbal form? In written form? How do I explain my thinking to others, in written form? In verbal form? How do I construct an effective (mathematical) argument? How reliable are predictions? Why are patterns important to discover, use, and generalize in math? How do I create a mathematical model? How do I decide which is the best mathematical tool to use to solve a problem? Mathematical skills and understandings are used to solve realworld problems. Problem solvers examine and critique arguments of others to determine validity. Mathematical models can be used to interpret and predict the behavior of real world phenomena. Recognizing the predictable patterns in mathematics allows the creation of functional relationships. Varieties of mathematical tools are used to analyze and solve problems and explore concepts. Estimating the answer to a problem helps predict and evaluate the reasonableness of a solution. Clear and precise notation and mathematical vocabulary enables effective communication and comprehension. Level of accuracy is determined based on the context/situation.
2 How do I effectively represent quantities and relationships through mathematical notation? How accurate do I need to be? When is estimating the best solution to a problem? Using prior knowledge of mathematical ideas can help discover more efficient problem solving strategies. Concrete understandings in math lead to more abstract understanding of math. Students will be able to independently use their learning to Transfer know that a quadratic equation can be written to model a real world situation. Meaning Essential Questions Students will consider questions such as... Understandings Students will understand that... Why is it important to simplify and evaluate polynomial expressions? What operation on a set of polynomials would best create a useful expression for a given situation? What does a solution mean in terms of a given situation? Is a solution a viable solution to a problem? When is it necessary to use polynomials? What is the best way to factor an expression? Why is it possible for a quadratic equation to have one solution, two solutions or no solutions? How is it possible for a quadratic equation to have two solutions, but in a realworld context only have one solution? When is factoring useful? Monomials can be used to form larger expressions called polynomials Polynomials can be added, subtracted and multiplied to form equivalent expressions and those forms have different purposes for the ease of application to real world situations. Simplifying like terms is useful when working with polynomials. Just because an equation has a solution, does not necessarily mean the solution is a viable option in a realworld context. Factoring polynomials follows the same rules as factoring a number. There are multiple strategies that can be used to attempt factoring polynomials. Factoring can be used to simplify a larger polynomial expression. Factoring is one strategy that can be used to solve quadratic equations. Some solutions to a quadratic equation are not feasible in a real world context. Acquisition Key Knowledge Key Skills
3 Zeroes of a function Factoring Polynomials Formulas (area and volume) Monomials Binomials Trinomials Degree of a Polynomial Leading Coefficient Like Terms Constant Distributive Property (multiplying polynomials) Zero Product Property Identify the terms, factors and coefficients of an expression and relate them to real world situations Rewrite a quadratic expression into an equivalent form and identify the usefulness of the equivalent form in context Expand and condense expressions, relating multiplying and factoring Add and subtract polynomials Multiply a polynomial by a monomial Multiply a polynomial by a polynomial using the distributive property Use special patterns to determine the square of a sum or a difference and to determine the product of a sum and a difference Factor to identify and interpret the meaning of the zeroes of a quadratic expression Factor a polynomial expression using the distributive property and greatest common factor Factor a polynomial expression using factoring by grouping Solve quadratic equations of the form ax 2 + bx = 0 Factor expressions of the form x 2 + bx + c and ax 2 + bx + c Solve quadratic equations of the form x 2 + bx + c and ax 2 + bx + c by factoring Factor binomial expressions that are differences of squares Use the differences of squares factoring to solve equations Factor perfect square trinomials Solve perfect square trinomial equations Solve realworld problems involving quadratic equations using multiple strategies. Determine if two expressions are equivalent Interpret solutions of equations based on the problem Determine whether a solution is reasonable Standards Alignment MISSOURI LEARNING STANDARDS A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeroes of the function it defines.
4 A.SSE.1 1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A.REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A.CED 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. Goals: 1.1, 1.4, 1.5, 1.6, 1.7, , 2.3, , 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, , 4.4, 4.5, 4.6 Performance: Math 1, 4, 5 SHOWME STANDARDS
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