Performance (Modeling)Task Introduction to Polynomials: College Fund A.REI.11, A.CED.1.a 1 Pair/group Yes Others Lesson Analysis Lesson 1: Polynomial Functions Objective Using standard form of a polynomial function, students will work individually/in pair/in group to classify polynomial, describe key features and end behavior of polynomial functions, ASB correctly answering ____ exit slip questions. Focused Mathematical Practices MP2: Reason abstractly and quantitatively MP 5: Use appropriate strategically MP 7: Look for and make use of structure Vocabulary: Monomial, degree of a monomial, polynomial, degree of a polynomial, polynomial function, standard form of a polynomial function, roots, zeros, turning point, end behavior Common Misconceptions: Classifying polynomial by degree – students choose degree based on first term, before putting function in standard form Describing end behavior of a polynomial – students may forget the rules of the table, then incorrectly plug values into the polynomial equation (specifically, plugging in a negative number. i.e. incorrectly stating that (-1)^2 = -1) Most relevant CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Point F.IF.7.c: Graph polynomial functions, identifying zeros when suitable factorizations Review Vocabulary (degree, standard form, monomial, polynomial, leading term, increasing Review Create a table for a pattern / write a pattern rule Lesson 5.1 / online textbook resources 2 days Lesson Check: pg. 285 (use as exit slip)
Reducing rational expressions by a common factor creates equivalent expressions numerator of a rational expression in order to possibly divide common factors A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Review Fractions cannot have zero as a denominator Dividing polynomials requires a common term Multiplying polynomials requires distribution New A rational expression cannot have 0 as a denominator; the zero creates a restriction to the domain. Dividing rational expressions requires a common term Multiplying rational expressions requires distribution Review Multiplication and division of fractions When multiplying fraction you multiply numerators and multiply denominators New Multiplication and division of rational expressions When multiplying rational expressions you need to multiply numerators and multiply denominators, distributive property when necessary
Lesson 8: Solving Rational Equations Objectives Using operations with rational expressions SWBAT work in _____________________ to solve equations including rational expressions and use these skills to solve real life problems correctly for 3 out of 4 problems on a daily exit slip. Focused Mathematical Practices MP 1: Make sense of problems and persevere in solving them MP 2: Reason abstractly and quantitatively MP 4: with mathematics MP 7: Look for and make use of structure Vocabulary: Rational equations Common Misconceptions: -mistakes with combining like terms - not checking for extraneous solutions - using cross multiplication incorrectly CCSS Concepts What students will know Skills What students will be able to do Material/ Resource Suggested Pacing Assessment Check Point 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 Review Creating fractions with common denominators uses equivalent fractions New Creating rational expressions with common denominators uses equivalent expressions Review Simplifying fractions by dividing common factors from the numerator and the denominator Factoring polynomials New Simplifying rational expression by dividing common factors from the numerator and denominator Text book- 8.6 Note: the standard A.REI.2 indicates solve SIMPLE rational equations, do not give 2 days Exit slip: pg. 545 and 5
examples, a computer algebra system. A.SSE.2: Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Factoring polynomials in rational expressions to simplify the expression students equations that has polynomial in higher than 2 degree A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Review Solving equations means isolating the variable that you are trying to solve for Denominators are cleared by finding a common denominator and multiplying both sides by that denominator or using cross multiplication if possible Any time you multiply each side of an equation by an algebraic expression, it is possible to produce an extraneous solution. New Rational expression contain at least one variable in the denominator so the denominators must be cleared in order to isolate the variable When denominators are cleared equations are solved using inverse operations Review Using inverse operations to solve equations, including reciprocal fractions Checking solutions for extraneous solutions New Multiply each side of the equation by the LCD or cross-multiply to eliminate the denominators Check solutions for extraneous solutions