Targeted Cntent Standard(s): A.SSE.1 Interpret expressins that represent a quantity in terms f its cntext. a)interpret cmplicated expressins by viewing ne r mre f their parts as a single entity. Fr example, interpret P(1+r)n as the prduct f P and a factr nt depending n P.* A.SSE.2 Use the structure f an expressin t identify ways t rewrite it. Fr example, see x 4 -y 4 as (x 2 ) 2 -(y 2 ) 2, thus recgnizing it as a difference f squares that can be factred as (x 2 y 2 )(x 2 + y 2 ). APR.1 Understand that plynmials frm a system analgus t the integers, namely, they are clsed under the peratins f additin, subtractin, and multiplicatin; add, subtract, and multiply plynmials. Targeted Mathematical Practice(s): 1 Make sense f prblems and persevere in slving them. 2 Reasn abstractly and quantitatively. 3 Cnstruct viable arguments and critique the reasning f thers. 4 Mdel with mathematics. 5 Use apprpriate tls strategically. 6 Attend t precisin. 7 Lk fr and make use f structure. 8 Lk fr an express regularity in repeated reasning. Supprting Cntent Standard(s): (ptinal) Student Friendly Learning Targets I can Add, subtract, and multiply plynmials Interpret expressins. View cmplicated expressins by its parts. Identify ways t rewrite quadratic expressins. A.CED.1 Create equatins and inequalities in ne variable and use them t slve prblems. Include equatins arising frm linear and quadratic functins, and simple ratinal and expnential functins. Explanatin f Rigr: (Fill in thse that are apprpriate.) Cnceptual: Students will interpret cmplicated expressins by viewing ne r mre f their parts. Prcedural: Students will add, subtract, and multiply plynmials, identify ways t rewrite quadratic expressins, and factr and cmplete the square n quadratic functins. Applicatin: Vcabulary: Plynmial Mnmial Binmial Trinmial Degree f a plynmial Standard frm f a plynmial Leading cefficient Cmbine like terms Distributive prperty (distributin)
Evidence f Learning (Assessment): Pre-Assessment: n pre-assessment fr this unit Frmative Assessment(s): Operatins n Plynmials, Tiling the Flr Summative Assessment: This lessn will be assessed at the end f the unit Self-Assessment: Lessn Prcedures: Segment 1 Apprximate Time Frame: 45-50 minutes Lessn Frmat: Whle Grup Small Grup Independent Resurces: Fcus: Intrducing plynmials with an emphasis n imprtant vcabulary Math Practice Lk Fr(s): Mdeled Guided Cllabrative Assessment MP#2: Reasn abstractly and quantitatively. Students will extend the prperties f real numbers t plynmial expressins. Ptential Pitfall(s) Differentiatin fr Remediatin: Mdalities Represented: Cncrete/Manipulative Picture/Graph Table/Chart Symblic Oral/Written Language Real-Life Situatin Differentiatin fr English Language Learners: Pre-teach vcabulary Differentiatin fr Enrichment: Independent Practice (Hmewrk): Practice prblems invlving cmbining like terms and identifying different degree plynmials using apprpriate vcabulary Steps: - Present students with a variety f plynmial expressins (including expressins with different numbers f terms, different degrees and different leading cefficients). Withut discussing lessn vcabulary, ask students t individually grup the expressins in any manner they see fit. - Once students have srted their expressins, grup them tgether and ask students t explain their chices in srting the plynmial expressins. Sme may have srt them based n Teacher Ntes/Reflectins:
the number f terms while thers srt them by degree and thers srt them based n the leading cefficient. Hld class discussin n the different assrtments which leads t the discvery f the need fr the lessn s vcabulary. - Define plynmial, mnmial, binmial, trinmial (tie t the vcabulary term nn-linear ). - Discuss prefixes mn, bi, and ply and cnnect t prir knwledge. - Define degree and discuss briefly hw t determine degree f a plynmial. - Shw students hw t manipulate a plynmial int standard frm. Fr example, - Define leading cefficient. - Use given plynmials mdeling real-wrld situatins t estimate values between tw pints and have students talk with their partners abut each prblem. Fr example: Cmpanies verseas prduce many f the electrnic devices that we use every day. The number P (in thusands) f devices prduced by a particular cmpany between 2006 and 2012 can be mdeled by the fllwing equatin where t is the number f years since 2006: Hw many electrnic devices were prduced in 2008? If the cmpany cntinues t prduce at this rate, hw many devices will they prduce in 2020?
Segment 2 Apprximate Time Frame: 90 100 minutes Fcus: Adding, subtracting, and multiplying plynmials (including mnmial x plynmial and binmial x binmial). Lessn Frmat: Whle Grup Small Grup Independent Mdeled Guided Cllabrative Assessment Resurces: Algebra tiles (if desired) Mdalities Represented: Cncrete/Manipulative Picture/Graph Table/Chart Symblic Oral/Written Language Real-Life Situatin Math Practice Lk Fr(s): MP#2: Reasn abstractly and quantitatively. Students will extend the prperties f real numbers t plynmial expressins. Differentiatin fr Remediatin: Differentiatin fr English Language Learners: Differentiatin fr Enrichment: Ptential Pitfall(s): Students may make mistakes when a -1 needs t be distributed t a plynmial r make sign errrs. Students may struggle with cnnecting knwledge f finding area t plynmials. Students may distribute the expnent when a binmial is squared instead f expanding first. Independent Practice (Hmewrk): Practice prblems fr all cmbinatins f plynmials t reinfrce crrect prcedures when using the distributive prperty.
Steps: - Give students an example f cmbining like terms (n terms). Fr example, - Ask students t recall the apprpriate methd fr simplifying this expressin. - Then use the same expressin frm abve, but add sme terms Ask students t give suggestins fr simplifying this expressin. The gal is t have students arrive at the cnclusin that the same rules f additin and subtractin apply t plynmials f degree 2. - Prvide students several examples t wrk n with a partner, including additin and subtractin. Include an example like this ne, paying clse attentin t hw the subtractin affects the secnd plynmials: - Multiplying a mnmial by a plynmial (Brief distributive prperty review) Give students an example f a cnstant multiplied by a plynmial f degree 1. Fllw up with a mnmial multiplied by a plynmial f degree 2. Cntinue prviding examples as needed, including pprtunities fr students t use distributin and cmbining f like-terms. Fr example: Teacher Ntes/Reflectins: - Multiplying tw binmials using the distributive prperty. Using distributive prperty as a fundatin, demnstrate the prcedure fr multiplying tw binmials. Emphasize the distributive prperty and shw multiple ways t apprach the prcedure. Prvide several examples fr students t practice with a partner including nes similar t these: (x + 3)(x + 4) (x 3)(x 2) (x 1)(x + 6) (x + 2) 2 Make sure that yu cver perfect squares and difference f squares t prepare fr use in factring and cmpleting the square in Unit 3. - Apply the cncepts and prcedures f multiplying tw binmials t a real-wrld situatin. Fr example, An artist needs t frame a picture using a matte. Using the dimensins in the diagram belw, write an expressin that represents the area f the
picture and matte.
Segment 3 Apprximate Time Frame: 100-120 minutes Lessn Frmat: Whle Grup Small Grup Independent Resurces: Fcus: Multiplying tw plynmials with degree > 1. Math Practice Lk Fr(s): Mdeled Guided Cllabrative Assessment MP#2: Reasn abstractly and quantitatively. Students will extend the prperties f real numbers t plynmial expressins. Mdalities Represented: Cncrete/Manipulative Picture/Graph Table/Chart Symblic Oral/Written Language Real-Life Situatin Differentiatin fr Remediatin: Differentiatin fr English Language Learners: Differentiatin fr Enrichment: Ptential Pitfall(s): Students may attempt t d these prblems in their heads instead f thrughly writing ut each step in the distributin prcedure, which wuld cause students t lse terms. Students may neglect negative cefficients when multiplying tw terms and when cmbining like terms. Steps: - Review multiplying tw binmials and use this as a bridge t multiplying plynmials with larger degree. - As a large grup, wrk thrugh ne example like this ne belw: Be sure t use the term distributin t cnnect with previus learning. - Create a set f practice prblems fr students t wrk n with a partner. - Have students share their wrk in sme way (n the bard, paper pass, etc.) t generate discussin abut prper prcedures and cmmn errrs when multiplying plynmials. - Take a Chance n Plynmials Activity Pre-cut the ply-cards and enrichment set f plycards. Pre-cut the dice ut f cardstck (nt regular paper) and then assemble them. If yu chse, yu can use regular 6-sided dice and assign the numbers t the necessary peratins. Independent Practice (Hmewrk): Teacher Ntes/Reflectins:
Divide yur class int grups f 2 students and give each grup ne activity packet. If desired, the number f cards and trials can be reduced. Segment 4 Apprximate Time Frame: 45-50 minutes Lessn Frmat: Whle Grup Small Grup Independent Resurces: Operatins f Plynmials Assessment Fcus: Assessing student understanding f the peratins n plynmials as they relate t peratins n real numbers. Math Practice Lk Fr(s): Mdeled Guided Cllabrative Assessment MP#2: Reasn abstractly and quantitatively. Students will extend the prperties f real numbers t plynmial expressins. Differentiatin fr Remediatin: Mdalities Represented: Cncrete/Manipulative Picture/Graph Table/Chart Symblic Oral/Written Language Real-Life Situatin Differentiatin fr English Language Learners: Differentiatin fr Enrichment: Ptential Pitfall(s): Independent Practice (Hmewrk): Steps: - Use assessment Operatins n Plynmials Teacher Ntes/Reflectins: