FUSD Instructional Plan Algebra Grade 8- Unit: 4- Polynomial Expressions and Equations Modules: 14, 15 & 16 Days: 30 Module/ Standards Lesson Progressions Content and Language Objective Supporting Resources Lesson MP Focus Including Khan Academy Days Module 14 Polynomial and Operations Essential Question: How are polynomials like other number systems, such as whole numbers and integers? Module 14 A.APR.1 Combining Polynomials Adding, Subtracting, and Multiplying CCSS Module 14 A.SSE.1A Polynomials A.CED.1 CAASP INTERIM ASSESSMENT A.SSE.2 BLOCK (IAB) MP.4 MP.6 MP.8 14.1 A.APR.1 Understanding Polynomials Students will explore polynomial Khan Academy: Intro to A.SSE.1a A monomial is a number, variable, or expressions and how to simplify polynomials 2 days A.CED.1 product of numbers and variables that have them. whole number exponents. MP.8 A polynomial is a monomial or a sum or Students will explain how to classify Look for and difference of monomials. polynomial expressions and show express The degree of a polynomial is the greatest how to simplify them. regularity in of the sum of the degrees in the monomial repeated terms making up the polynomial. reasoning. 14.2 A.APR.1 Adding and Subtracting Polynomials Students will add and subtract Khan Academy: Adding and A.SSE.2 The Commutative and Associative polynomials. Subtracting Polynomials 2 days A.CED.1 properties of addition are often used when adding polynomials. Students will demonstrate how to MP.6 The Distributive Property is used to simplify add and subtract polynomials. Attend to some polynomials containing parentheses. precision. The Distributive Property is used to subtract a polynomial in parentheses. Page | 1 Updated 3/19 FUSD Instructional Plan Algebra Grade 8- Unit: 4- Polynomial Expressions and Equations Modules: 14, 15 & 16 Days: 30 14.3 A.APR.1 Multiplying Polynomials by Monomials Students will multiply polynomials Khan Academy: Multiplying A.SSE.2 The Commutative and Associative by monomials. Monomials 2 days A.CED.1 properties of multiplication are used when multiplying polynomials. Students will explain how to MP.4 The Distributive Property is used to simplify multiply polynomials by monomials. Model with some polynomials containing parentheses. mathematics. The Laws of Exponents may be used when multiplying polynomials. 14.4 A.APR.1 Multiplying Polynomials Students will multiply binomials and Animated Math Lesson 14.4 A.SSE.2 The method of using algebra tiles is similar polynomials. 2 days A.CED.1 to the method of multiplying a monomial by Module 14 Conceptual Video a polynomial. Students will show how to multiply – Polynomial and Operations MP.8 Look for The FOIL method can be used to multiply binomials and polynomials. (Lesson 14.4 Multiplying and express any two binomials, even ones containing Polynomials. Similar to regularity in multiple variables. Explore Activity, pg. 509) repeated The Distributive Property can be used with reasoning. any size or degree polynomial. Khan Academy: Multiplying monomials by polynomials Khan Academy: Multiplying binomials Khan Academy: Multiplying binomials by polynomials Module 15 Factoring Polynomials Essential Question: How can you factor expressions of the form 푎푥2 + 푏푥 + 푐 ? Module 15 Factor Polynomials Students will learn how to factor CCSS Module 15 various forms of polynomials 15.1 A.SSE.2 Factoring Polynomials Students will use the greatest Module 15 Conceptual Video A.SSE.3 Factors that are shared by two or more common factor to factor – Factoring Polynomials 1 day numbers are called common factors. polynomials. (Lesson 15.1 x2 + bx + c MP.7 Factoring. Explore Activity #1, pg. 533) Page | 2 Updated 3/19 FUSD Instructional Plan Algebra Grade 8- Unit: 4- Polynomial Expressions and Equations Modules: 14, 15 & 16 Days: 30 Look for and The greatest common factor (GCF) and the Students will show how to use the make use of Distributive Property may used to factor greatest common factor to factor Khan Academy: Factor structure. two or more monomials. polynomials. polynomials by common The GCF of an expression may be a binomial factor 15.2 A.SSE.2 Factoring 풙ퟐ + 풃풙 + 풄 Students will factor expressions of Khan Academy: Factoring A.SSE.3 Factoring a trinomial is “undoing FOIL ”or the form 푥2 + 푏푥 + 푐. Quadratics 2 days working FOIL in reverse. To factor a trinomial of the form Students will explain how to factor MP.4 푥2 + 푏푥 + 푐, list factor pairs of c and see expressions of the form Model with which ones add to b. 푥2 + 푏푥 + 푐. mathematics. Use the factor pair whose sum is equal to b to factor the trinomial. 15.3 A.SSE.2 Factoring 풂풙ퟐ + 풃풙 + 풄 Students will factor expressions of Khan Academy: Factoring A.SSE.3 To factor 푎푥2 + 푏푥 + 푐, you must take into the form 푎푥2 + 푏푥 + 푐. Quadratics 2 days account the factors of a when determining MP.7 b. Students will demonstrate how to Look for and If c > 0, then the signs of the constants in factor expressions of the form make use of the binomials must be the same. If c < 0, 푎푥2 + 푏푥 + 푐. structure. then the signs of the constants must be different. Use FOIL to test the combination of factor pairs that will yield the correct value of b. 15.4 A.SSE.2 Factoring Special Products Students will use special products to Khan Academy: Difference of A.SSE.3 A perfect square trinomial of the form aid in factoring. Squares 1 day 푎2 + 2푎푏 + 푏2 factors into (푎 + 푏)2. MP.8 A perfect square trinomial of the form Students will demonstrate how to Khan Academy: Perfect Look for and 푎2 − 2푎푏 + 푏2 factors into (푎 − 푏)2.. use special products to aid in Squares express The difference of two squares, 푎2 − 푏2, factoring. regularity in factors into (a + b) (a - b). repeated “Factoring completely” may mean factoring reasoning. a common monomial factor first and then Page | 3 Updated 3/19 FUSD Instructional Plan Algebra Grade 8- Unit: 4- Polynomial Expressions and Equations Modules: 14, 15 & 16 Days: 30 using special products to factor the remaining polynomial. Module 16 Solving Quadratic Equations Essential Question: How do you determine the best method for solving a quadratic equation or a system of equations? Module 16 A.CED.1 Solve Quadratic Equations Students will learn various methods CCSS Module 16 A.REI.4 of solving quadratic equations. A.SSE.3 A.SSE.3a F.IF.8 MP.1 MP.7 MP.8 16.1 A.CED.1 Solve Quadratic Equations Using Square Roots Students will solve quadratic Khan Academy: Solving A.REI.4b When solving a quadratic equation of the equations using square roots. quadratics by taking square 2 days form 푥2 = a, you must take the square root roots MP.1 of each side to get an equivalent equation. Students will demonstrate how to Make sense of The Product Property of Radicals or the solve quadratic equations using problems and Quotient Property of Radicals may be used square roots. persevere in to find a square root. solving them. When solving a quadratic equation that requires more solution steps, the solutions may or may not be opposites and the equations may or may not have real number solutions. 16.2 A.CED.1 Solve 풙ퟐ + 풃풙 + 풄 = 0 by Factoring Students will use factoring to solve Animated Math Lesson 16.2 A.REI.4 The Zero Product Property applies if the quadratic equations in standard 2 days A.SSE.3 quadratic expression in 푥2 + 푏푥 + 푐 = 0 is form when a = 1. Khan Academy: Solve by A.SSE.3a factorable. Factoring F.IF.8 To factor 푥2 + 푏푥 + 푐, list factor pairs of c Students will show how to use and see which ones add to b. factoring to solve quadratic MP.7 Before using the Zero Product Property, one equations in standard form when side of the equation must equal zero, and a=1. the quadratic must be factored completely. Page | 4 Updated 3/19 FUSD Instructional Plan Algebra Grade 8- Unit: 4- Polynomial Expressions and Equations Modules: 14, 15 & 16 Days: 30 Look for and The Zero Product Property can also be used make use of to find the zeros of a quadratic function. structure. 16.3 A.CED.1 Solve 풂풙ퟐ + 풃풙 + 풄 = 0 by Factoring Students will use factoring to solve Khan Academy: Solve by A.REI.4 The Zero Product Property applies if the quadratic equations of the form Factoring 2 days A.REI.4b quadratic expression 푎푥2 + 푏푥 + 푐 = 0 is 푎푥2 + 푏푥 + 푐 = 0. A.SSE.3 factorable. F.IF.8 To factor 푎푥2 + 푏푥 + 푐, list factor pairs of a Students will demonstrate how to and of c, and then see which outer and use factoring to solve quadratic MP.1 inner products give the right value of b. equations of the form 푎푥2 + 푏푥 + 푐 Make sense of Special factoring patterns may also be used = 0. problems and to factor the quadratic expression before persevere in solving. solving them. 16.4 A.REI.4 Solve 풙ퟐ + 풃풙 + 풄 = ퟎ by Completing the Students will solve the quadratic Module 16 Conceptual Video A.REI.4a Square equation 푥2 + 푏푥 + 푐 = 0 without - Solving Quadratic Equations 푏 2 days A.REI.4b To solve 푥2 + 푏푥 = −푐, add ( )2 to each factoring. (Lesson 16.4 Solving 2 2 A.SSE.1 푏 푏 x + bx + c = 0 by Completing side to get 푥2+ bx + ( )2= -c + ( )2. A.SSE.2 2 2 Students will show how to solve the the Square. Explore Activity, 푏 푏 A.SSE.3b Factor 푥2+ bx + ( )2as (푥 + )2. 푥2 + 푏푥 + 푐 = 0 pg.