F-IF Interpret functions that arise in applications in terms of the context F-IF Analyze functions using different representations function notation in terms of a context. 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ 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.★ 7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including 9-2: Concept Byte Collecting Quadratic Data Journal Prompt(s): Provide an example of a real-world situation that is best represented by a nonlinear function. Describe the features that are common to the graphs of all quadratic functions. Explain how to approximate the roots of a quadratic equation when the roots are not integers. Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking.
Glencoe 9-5: Solving Quadratic Equations by Using the Quadratic formula Pearson Algebra II 4-8: Complex Numbers Pearson Algebra I Book Page 572 #22, #41, & #42 Use KNWS, SQRQCQ, or UPS√ Strategy √ Explain the difference between the additive inverse of a complex number and a complex conjugate. Pearson Algebra I Book Page 588 1 & 2 Use KNWS, SQRQCQ, or UPS√ Strategy √ Utilize Tasks to include the Standards for Mathematical Practice where students have to reason, justify, explain, construct & model their thinking. (See Lesson 6-1) Solve systems of equations 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. Pearson 9-8: Systems of Linear and Quadratic Equations Vocabulary: Systems of linear equations, systems of quadratic equations, elimination, substitution Compare & Contrast How are solving systems of linear equations and solving systems of linear and quadratic equations alike? How are they different? Journal Prompt(s): Pearson Algebra I Book Page 586 #31 & #32 Use KNWS, SQRQCQ, or UPS√ Strategy √
Pearson Algebra I Book Page 588 Tasks 1 - 3 Use KNWS, SQRQCQ, or UPS√ Strategy √ Rational Expressions & Functions ( 4.5 weeks) A-CED Create equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Pearson 11-1: Simplifying Rational Expressions Glencoe 11-3: Simplifying Rational Expressions Extra Practice Vocabulary: Rational expression, excluded value Journal Prompt(s): When simplifying rational expressions, why may it be necessary to exclude values? Explain. Suppose neither the numerator not the denominator of a rational expression can be factored Is the expression necessarily in simplified form? Explain. Pearson Algebra I Book Page 656 #40 Use KNWS, SQRQCQ, or UPS√ Strategy √ A‐APR Rewrite rational expressions. 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. Pearson 11-2: Multiplying & Dividing Rational Expressions Glencoe 11-4: Multiplying & Dividing Rational Vocabulary: Complex fraction, rational expression Compare & Contrast How are multiplying rational expressions and multiplying numerical fractions similar? How are they different? Journal Prompts):