01-013 Enhance Instructional Transition Guie Unit 08: Exponents an Polynomial Operations (18 ays) Possible Lesson 01 (4 ays) Possible Lesson 0 (7 ays) Possible Lesson 03 (7 ays) POSSIBLE LESSON 0 (7 ays) Lesson Synopsis: Stuents simplify polynomials using the laws of exponents. Stuents a, subtract, an multiply polynomials. Stuents recognize the similarity in multiplying real numbers versus multiplying polynomials using algebra tiles. TEKS: A.4 Founations for functions. The stuent unerstans the importance of the skills require to manipulate symbols in orer to solve problems an uses the necessary algebraic skills require to simplify algebraic expressions an solve equations an inequalities in problem situations. The stuent is expecte to: A.4A A.4B Fin specific function values, simplify polynomial expressions, transform an solve equations, an factor as necessary in problem situations. Reainess Stanar Use the commutative, associative, an istributive properties to simplify algebraic expressions. Supporting Stanar A.11 Quaratic an other nonlinear functions. The stuent unerstans there are situations moele by functions that are neither linear nor quaratic an moels the situations. The stuent is expecte to: A.11A Use patterns to generate the laws of exponents an apply them in problem-solving situations. Supporting Stanar Performance Inicator(s): Combine an simplify polynomial expressions to solve problem situations such as the following: The perimeter of a quarilateral garen is x + 3x 4. The first sie is represente by x + x. The secon sie is represente by 5x 3. The thir sie is represente by x 6x 10. What expression represents the fourth sie? The base of a right triangle is ( x 5). The height of the triangle is ( x + 1). The perimeter of the triangle is ( 7x + 5). Fin the area of the triangle an the length of the thir sie. Create a graphic organizer for each problem that inclues a iagram of the problem situation, a polynomial expression to represent the problem situation, an a solution process to the problem situation. (A.4A, A.4B; A.11A) 1C; 5B Key Unerstaning(s): Polynomial expressions have specific characteristics an can be simplifie using the properties of algebra an laws of exponents an applie in problem situations. Vocabulary of Instruction: 01, TESCCC 04/1/13 page 1 of 7
01-013 Enhance Instructional Transition Guie algebraic expression associative property binomial commutative property istributive property exponents factor factoring monomial polynomial term trinomial Suggeste 1 Topics: Laws of exponents Engage 1 Stuents apply laws of exponents to simplify monomials in orer to assess unerstaning of exponents an operations with exponents. 1. Prior to instruction, create car set: Expo-Match by copying on carstock, laminating, cutting apart, an placing each set in a plastic zip bag. One set of cars will be neee for each pair of stuents.. Place stuents in pairs. Distribute car set: Expo-Match to each pair. Distribute hanout: Expo- Match Recoring Sheet to each stuent. Instruct stuents to work with their partner to match problems on the recoring sheet with the simplifie polynomials on the cars an recor their results. Allow stuents 5 10 minutes to complete the activity. Monitor an assess stuents to check for unerstaning. Facilitate a class iscussion of stuent results, clarifying any misconceptions. Ask: What metho i you use to match problems to simplifie monomials? Answers may vary. What rules of exponents i you use to simplify the problems? Answers may vary. Multiplication, ivision, an power rules were applie; etc. 3 Topics: Types of polynomials (monomial, binomial, trinomial) Simplification of polynomials Operations with polynomials Car Set: Expo-Match (1 per stuents) Expo- Match Recoring Sheet KEY Hanout: Expo-Match Recoring Sheet (1 per isplay carstock (3 sheets per stuents) scissors plastic zip bag (sanwich size) (1 per stuents) Hanout: Algebra Tile Templates (carstock 1 per Monomials 01, TESCCC 04/1/13 page of 7
01-013 Enhance Instructional Transition Guie Suggeste Explore/Explain 1 Stuents explore the characteristics of polynomials. Stuents simplify polynomial expressions an perform operations of aition an subtraction with polynomial expressions. 1. Distribute hanout: Algebra Tile Templates, scissors, an a plastic zip bag to each stuent. Instruct stuents to create a set of algebra tiles by cutting apart the tiles an placing them in a plastic zip bag. One teacher set of algebra tiles will also nee to be create.. Place stuents in pairs. Display teacher resource: Monomials. Instruct stuents to work with their partner to buil each representation using algebra tiles, an evelop a efinition of monomial. Facilitate a class iscussion of stuent responses, clarifying any misconceptions. Emphasize that a monomial consists of one term; either a constant (number), or the prouct of a constant, an one or more variables with whole number exponents. Explain that the prefix mono- means one. 3. Display teacher resource: Binomials. Instruct stuents to work with their partner to buil each representation using algebra tiles, an evelop a efinition of binomial. Facilitate a class iscussion of stuent responses, clarifying any misconceptions. Emphasize that a binomial consists of two monomial terms. Explain that the prefix bi- means two. 4. Prior to isplaying trinomials, ask stuents what they think a trinomial woul look like an how they woul justify their reasoning. (A trinomial woul have 3 terms because the prefix tri- means three.) Instruct stuents to use the algebra tiles an work with their partner to create a moel of what they think a trinomial woul look like. Display teacher resource: Trinomials. Instruct stuents to verify if their representation coul be inclue on the sie that moels These are trinomials. Facilitate a class iscussion of stuent responses, clarifying any misconceptions. Emphasize that a trinomial consists of three monomial terms. Explain that the prefix tri- means three. 5. Facilitate a class iscussion of polynomial. Define the prefix poly (many) for the stuents, an ask them to iscuss what the term polynomial might mean. Some stuents might suggest a polynomial woul contain more than three terms; explain that it is the name we use for many nomials so that monomials, binomials, an trinomials, as well as expressions that have more than three terms, are calle polynomials. 6. Distribute hanout: Ponering Polynomials to each stuent. Refer stuents to page 1. Display teacher resource: Ponering Polynomials, an facilitate a class iscussion of characteristics of polynomials. Instruct stuents to work with their partner to complete the table at the bottom of page 1. Allow stuents time to complete the table. Monitor an assess stuents to check for unerstaning. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of stuent results, clarifying any misconceptions. 7. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of simplifying Binomials Trinomials Ponering Polynomials KEY Ponering Polynomials (1 per teacher) Hanout: Ponering Polynomials (1 per isplay carstock (3 sheets per stuent, 3 sheets per teacher) scissors (1 per stuent, 1 per teacher) plastic zip bag (sanwich size) (1 per stuent, 1 per teacher) It is important for the stuents to moel using the algebra tiles. By builing the moels stuents see that a monomial is mae up of only one type of tile an binomials have two types of tiles. The algebra tile sets will be use again in 01, TESCCC 04/1/13 page 3 of 7
01-013 Enhance Instructional Transition Guie polynomials, moeling problems 1. Instruct stuents to work with their partner to complete problems 3 5 on hanout: Ponering Polynomials. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of stuent results, clarifying any misconceptions. 8. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of combining polynomials, moeling problems 6 7. Instruct stuents to work with their partner to complete problems 8 10 on hanout: Ponering Polynomials. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of stuent results, clarifying any misconceptions. 9. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of applying polynomials, moeling problem 11. Instruct stuents to work with their partner to complete problems 1 13 on hanout: Ponering Polynomials. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Ponering Polynomials, facilitate a class iscussion of stuent results, clarifying any misconceptions. 10. Instruct stuents to work inepenently to complete the Practice Problems on hanout: Ponering Polynomials. This may be complete as homework, if necessary. Explore/Explain of this lesson. On hanout: Ponering Polynomials, the concepts on pages 3 4 are a review from Unit 0 (combining like terms) an Unit 08 Lesson 01 (Laws of Exponents). However, struggling stuents may benefit from class iscussion an moeling, instea of group work exploration. 4 Topics: Arrays an area moel representations of multiplication Concrete moel representation of multiplication of polynomials Explore/Explain Stuents investigate the connections between arrays or area moels, whole-number multiplication, binomial multiplication, an concrete moels of binomial multiplication. 1. Place stuents in pairs. Distribute hanout: Binomial Rectangles, 1 set of map pencils, an 1 ruler to each stuent. Distribute sheets of hanout: Gri Paper (1 centimeter) to each stuent.. Refer stuents to problem 1 on hanout: Binomial Rectangles. Display teacher resource: Binomial Rectangles Problem 1 KEY, an facilitate a class iscussion to moel problem 1. Ask: What will be the shape of the multiplication array? (rectangular) How woul the numbers 1 an 13 be represente as imensions on the gri paper? (The 1 woul be represente by shaing ten gris horizontally with one color to represent the tens Binomial Rectangles Problem 1 KEY Binomial Rectangles Problem KEY Binomial Rectangles KEY (1 per teacher) Binomial Rectangles Hanout: Binomial Rectangles (1 per Hanout: Gri Paper (1 centimeter) ( sheets per Algebra 01, TESCCC 04/1/13 page 4 of 7
01-013 Enhance Instructional Transition Guie followe by two gris shae in another color to represent the ones. The same woul be one vertically to represent the thirteen but shae three gris to represent the ones.) How will the partial proucts be represente on the gri paper? (The partial rectangular areas forme using the horizontal imension by the vertical imension.) 3. Instruct stuents to work with their partner to complete problem on hanout: Binomial Rectangles. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Display teacher resource: Binomial Rectangles Problem KEY, an facilitate a class iscussion of stuent results, clarifying any misconceptions. 4. Distribute hanout: Algebra Tile Table an a set of algebra tiles to each stuent. Refer stuents to problem 3 on hanout: Binomial Rectangles. Using algebra tiles an teacher resource: Algebra Tile Table, facilitate a class iscussion to moel problem 3, introucing binomial multiplication with variables. 5. Instruct stuents to work with their partner to complete problems 4 5 on hanout: Binomial Rectangles. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Binomial Rectangles, facilitate a class iscussion of stuent results, clarifying any misconceptions. 6. Instruct stuents to work inepenently to complete problems 6 7 on hanout: Binomial Rectangles. This may be complete as homework, if necessary. Tile Table Hanout: Algebra Tile Table (1 per isplay algebra tiles (1 set per stuent, 1 set per teacher) (previously create) map pencils (1 set per ruler (1 per Stuents will nee their algebra tile sets an Algebra Tile Table again in Unit 08 Lesson 03. 5 Topics: Multiplication of polynomials Applications of polynomial multiplication Explore/Explain 3 Stuents transition from multiplying polynomials concretely an pictorially to mathematical processes. Stuents apply the rectangle moel an istributive moel for performing polynomial multiplication. Multiplying Polynomials KEY Multiplying Polynomials (1 per teacher) Hanout: Multiplying Polynomials (1 per 1. Distribute hanout: Multiplying Polynomials to each stuent. Refer stuents to page 1. Display teacher resource: Multiplying Polynomials, an facilitate a class iscussion on multiplying polynomials, moeling Investigation 1 problems 1. Instruct stuents to work with their partner to complete problems 3 4. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Multiplying Polynomials, facilitate a class iscussion of stuent graphing calculator (1 per graphing calculator with isplay 01, TESCCC 04/1/13 page 5 of 7
01-013 Enhance Instructional Transition Guie results, clarifying any misconceptions.. Refer stuents to page of hanout: Multiplying Polynomials. Using teacher resource: Multiplying Polynomials, facilitate a class iscussion of multiplication patterns, moeling problems 5 7. Instruct stuents to work with their partner to complete problems 8 9. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Multiplying Polynomials, facilitate a class iscussion of stuent results. 3. Refer stuents to page 3 of hanout: Multiplying Polynomials. Using teacher resource: Multiplying Polynomials, facilitate a class iscussion of istribution, moeling Investigation problem 10. Instruct stuents to work with their partner to complete problems 11 15. Allow stuents time to complete the problems. Monitor an assess stuents to check for unerstaning. Using teacher resource: Multiplying Polynomials, facilitate a class iscussion of stuent results. 4. Instruct stuents to work inepenently to complete problems 16 18 on hanout: Multiplying Polynomials. This may be complete as homework, if necessary. Encourage all stuents to verbalize the steps as they work through this stage. As stuents work through the istributive moel, tell them to cover up the secon term in the first parentheses as they are multiplying by the first term, either with their finger or a small piece of paper. 6 Topics: Simplification of polynomials Operations with polynomials Elaborate 1 Stuents simplify polynomial expressions an perform operations with polynomial expressions. 1. Facilitate a class iscussion to ebrief problems 16 18 on hanout: Multiplying Polynomials to check for unerstaning.. Place stuents in pairs. Distribute hanout: Express Yourself to each stuent. 3. Instruct stuents to work with their partner to complete the hanout. This may be complete as homework, if necessary. Express Yourself KEY Hanout: Express Yourself (1 per isplay 7 Evaluate 1 Teacher Resource (optional): Evaluating Polynomials KEY 1. Assess stuent unerstaning of relate concepts an processes by using the Performance Inicator(s) aligne to this lesson. Hanout (optional): Evaluating Polynomials PI (1 01, TESCCC 04/1/13 page 6 of 7
01-013 Enhance Instructional Transition Guie Performance Inicator(s): Combine an simplify polynomial expressions to solve problem situations such as the following: The perimeter of a quarilateral garen is x + 3x 4. The first sie is represente by x + x. The secon sie is represente by 5x 3 represents the fourth sie? 5. The thir sie is represente by The base of a right triangle is ( x ). The height of the triangle is ( x + 1) triangle is ( 7x + 5) x 6x 10. What expression. The perimeter of the. Fin the area of the triangle an the length of the thir sie. Create a graphic organizer for each problem that inclues a iagram of the problem situation, a polynomial expression to represent the problem situation, an a solution process to the problem situation. (A.4A, A.4B; A.11A) 1C; 5B per As an optional assessment tool, use hanout (optional): Evaluating Polynomials PI. 01, TESCCC 04/1/13 page 7 of 7