Unit 1 Equatins and Inequalities Number f Days: 29 9/5/17 10/13/17 Unit Gals Stage 1 Unit Descriptin: Students extend their understanding f slving linear equatins in ne variable t slving equatins with variables n bth sides f the equal sign. Students will analyze and interpret the slutin f an equatin t determine if the equatin has ne slutin, infinitely many slutins, r n slutins. Students will extend their knwledge f equatins int slving tw-step inequalities. Materials: algebra tiles, magnetic algebra tiles (teacher mdel), prtractr, tw clr cunters Standards fr Mathematical Practice SMP 1 Make sense f prblems and persevere in slving them. SMP 2 Reasn abstractly and quantitatively. SMP 3 Cnstruct viable arguments and critique the reasning f thers. SMP 4 Mdel with mathematics. SMP 5 Use apprpriate tls strategically. SMP 6 Attend t precisin. SMP 7 Lk fr and make use f structure. SMP 8 Lk fr and express regularity in repeated reasning. Transfer Gals Students will be able t independently use their learning t Make sense f never-befre-seen prblems and persevere in slving them. Cnstruct viable arguments and critique the reasning f thers. Making Meaning UNDERSTANDINGS Students will understand that Equatins can be used t mdel and slve real-wrld situatins. Slving an equatin is the prcess f answering a questin: which value(s), if any, make the equatin true? Equatins can have ne slutin, n slutin, r infinitely many slutins. Slving an inequality is the prcess f answering a questin: Which values frm a specified set, if any, make the inequality true? ESSENTIAL QUESTIONS Students will keep cnsidering Hw can equatins be used t mdel and slve real-wrld and mathematical prblems? Hw can yu use the structure f an equatin t determine if it has ne slutin, infinitely many slutins, r n slutins? What are the similarities and differences between equatins and inequalities? Standards fr Mathematical Cntent Clusters Addressed [m] 7.EE.A Use prperties f peratins t generate equivalent expressins. [m] 7.EE.B Slve real life and mathematical prblems using numerical and algebraic expressins and equatins. [m] 8.EE.C Analyze and slve linear equatins and pairs f simultaneus linear equatins. KNOWLEDGE Students will knw An equatin is a mathematical sentence that shws tw equal expressins. Yu can add, subtract, multiply, r divide bth sides f an equatin by the same nnzer number and the tw sides will remain equal. The slutin set f an inequality represents multiple slutins that make the inequality statement true. Acquisitin SKILLS Students will be skilled at and/r be able t Slve linear equatins in ne variable with ratinal number cefficients, including equatins that use the distributive prperty and cmbine like terms. Write and slve linear equatins in ne variable t represent real-wrld situatins. Identify and write examples f linear equatins in ne variable with ne slutin, infinitely many slutins, r n slutins. Slve wrd prblems leading t inequalities f the frm px + q > r and px + q < r, where p, q, and r are specific ratinal numbers and graph the slutin set n a number line. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Psted 10/9/17
Unit 1 Equatins and Inequalities Assessed Grade Level Standards Standards fr Mathematical Practice SMP 1 Make sense f prblems and persevere in slving them. SMP 2 Reasn abstractly and quantitatively. SMP 3 Cnstruct viable arguments and critique the reasning f thers. SMP 4 Mdel with mathematics. SMP 5 Use apprpriate tls strategically. SMP 6 Attend t precisin. SMP 7 Lk fr and make use f structure. SMP 8 Lk fr and express regularity in repeated reasning. Standards fr Mathematical Cntent [m] 7.EE.A Use prperties f peratins t generate equivalent expressins. 7.EE.1 Apply prperties f peratins as strategies t add, subtract, factr, and expand linear expressins with ratinal cefficients. [m] 7.EE.B Slve real life and mathematical prblems using numerical and algebraic expressins and equatins. 7.EE.4 Use variables t represent quantities in a real wrld r mathematical prblem, and cnstruct simple equatins and inequalities t slve prblems by reasning abut the quantities. a. Slve wrd prblems leading t equatins f the frm px + q = r and p(x + q) = r, where p, q, and r are specific ratinal numbers. Slve equatins f these frms fluently. Cmpare an algebraic slutin t an arithmetic slutin, identifying the sequence f the peratins used in each apprach. Fr example, the perimeter f a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Slve wrd prblems leading t inequalities f the frm px + q > r r px + q < r, where p, q, and r are specific ratinal numbers. Graph the slutin set f the inequality and interpret it in the cntext f the prblem. Fr example: As a salespersn, yu are paid $50 per week plus $3 per sale. This week yu want yur pay t be at least $100. Write an inequality fr the number f sales yu need t make, and describe the slutins. [m] 8.EE.C Analyze and slve linear equatins and pairs f simultaneus linear equatins. 8.EE.7 Slve linear equatins in ne variable. a. Give examples f linear equatins in ne variable with ne slutin, infinitely many slutins, r n slutins. Shw which f these pssibilities is the case by successively transfrming the given equatin int simpler frms, until an equivalent equatin f the frm x = a, a = a, r a = b results (where a and b are different numbers). b. Slve linear equatins with ratinal number cefficients, including equatins whse slutins require expanding expressins using the distributive prperty and cllecting like terms. Key: [m] = majr clusters; [s] = supprting clusters; [a] = additinal clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Psted 10/9/17
Unit 1 Equatins and Inequalities Assessment Evidence Unit Assessment Evidence f Learning Stage 2 Claim 1: Students can explain and apply mathematical cncepts and carry ut mathematical prcedures with precisin and fluency. Cncepts and skills that may be assessed in Claim1: 7.EE.A The student generates equivalent linear expressins using a cmbinatin f additin and subtractin, factring, and expansin. 7.EE.B The student slves wrd prblems leading t inequalities f the frm px + q > r and px + q < r, where p, q, and r are specific ratinal numbers. The student graphs the slutin set f an inequality n a number line. 8.EE.C The student slves linear equatins in ne variable with ratinal number cefficients, including equatins that require expanding expressins using the distributive prperty and cllecting like terms. The student identifies and writes examples f linear equatins in ne variable with ne slutin, infinitely many slutins, r n slutins. Claim 2: Students can slve a range f wellpsed prblems in pure and applied mathematics, making prductive use f knwledge and prblem-slving strategies. Standard clusters that may be assessed in Claim 2: 7.EE.A 7.EE.B 8.EE.C Claim 3: The student can clearly and precisely cnstruct viable arguments t supprt their wn reasning and critique the reasning f thers. Standard clusters that may be assessed in Claim 3: 7.EE.A 8.EE.C Claim 4: The student can analyze cmplex, real-wrld scenaris and can cnstruct and use mathematical mdels t interpret and slve prblems. Standard clusters that may be assessed in Claim 4: 7.EE.B 8.EE.C Other Evidence Frmative Assessment Opprtunities Infrmal teacher bservatins Checking fr understanding using active participatin strategies Exit slips/summaries Tasks Mdeling Lessns (SMP 4) Frmative Assessment Lessns (FAL) Quizzes / Chapter Tests SBAC Interim Assessment Blcks Access Using Frmative Assessment fr Differentiatin fr suggestins. Lcated n the LBUSD website M Mathematics Curriculum Dcuments LONG BEACH UNIFIED SCHOOL DISTRICT 3 Psted 10/9/17
Unit 1 Equatins and Inequalities Days Learning Target Expectatins 1 day 4-5 I will explre slving equatins by participating in the Opening Task. I will review skills that will help me slve multi-step equatins by Suggested Sequence f Key Learning Events and Instructin OPENING TASK (chse ne) Secret Number has students create expressins and then equatins based n their secret number. First, have students wrk independently and then with a partner. Then, facilitate a class discussin abut students strategies and appraches utilizing Talk Mves. The Magician Mark the Magnificent is an animated clip where Mark the Magnificent has students start with different numbers and end up with the same answer after perfrming sme calculatins. An Educatr s Guide is available n the site. (SMP 1, 2) Adding, subtracting, multiplying, and dividing integers. (SMP 7, 8) Generating equivalent expressins using the distributive prperty and by cmbining like terms. Slving ne-step and tw-step equatins. Answering questins such as Explain why sme terms are like terms and thers are nt. (SMP 3) Hw d yu simplify algebraic expressins? Describe hw t slve a ne-step and tw-step equatin. What des it mean t be a slutin t an equatin? Synergy Item Bank: Item ID 53043, 53053, 53055, 53266, 53314, 53334, 51044, 52652, 53080 (Activities and Lessns) What Yu Learned Befre (p. 1) Sectin 1.1 (Activities 1, 2, and 3; Examples 1, 2, 3, and 4) Supplemental Resurces Cnceptual Understanding: Secret Number The Magician Mark the Magnificent Cnceptual Understanding: mypd Curse #2582: Tw Clr Cunters fr Integer Operatins Desms: Central Park mypd Curse #2463: Algebra Tiles Build, Draw, Write Explring Equatins Task Tw-Step Equatins Task Prcedural Skills and Fluency: Distributive Prperty Hw D They Fit? Mixed Operatins with Integers Math-O Khan Academy: Cmbining like terms Applicatin: Mdeling: What Des 2000 Calries Lk Like? (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 4 Psted 10/9/17
Unit 1 Equatins and Inequalities 6-7 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins (Activities and Lessns) I will slve equatins with ratinal number cefficients by Using algebra tiles t represent slving multi-step equatins. (SMP 5) Cmbining like terms. Using the distributive prperty. Writing and slving equatins t mdel real-wrld and mathematical prblems. (SMP 2) Answering questins such as Why is it helpful t simplify bth sides f an equatin befre yu slve? Describe different methds that yu can use t slve an equatin. Explain yur reasning. (SMP 3) Hw d yu check yur answer after slving an equatin? What des the answer represent? Synergy Item Bank: Item ID 53752, 53758, 53791 Sectin 1.2 (Activity 1; Examples 1, 2, 3, and 4) STEM Vide: Training fr a Half Marathn Supplemental Resurces Cnceptual Understanding: Slving Equatins with Algebra Tiles Prcedural Skills and Fluency: Slving Multi-Step Linear Equatins Tic-Tac-Te A Trick fr Yu Game Khan Academy: Tw-step equatins with decimals and fractins Applicatin: Hw Old Are They? Task Mystery Letters Task Mdeling: Styrfam Cups (SMP 4) Mdeling: Wall Pictures (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 5 Psted 10/9/17
Unit 1 Equatins and Inequalities 6-7 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins (Activities and Lessns) I will slve Using algebra tiles. (SMP 5) Sectin 1.3 equatins with Determining the number f slutins. (Activity 1; variables n bth Creating examples f equatins with ne slutin, Examples 1, 2, 3, and 4) sides f the equal infinitely many slutins, and n slutins. (SMP 7) sign by Transfrming the given equatin int simpler, equivalent frms until x = a, a = a, r a = b results (where a and b are different numbers). (SMP 7) Writing and slving equatins t represent realwrld and mathematical prblems. (SMP 2) Answering questins such as Hw can yu slve an equatin with variables n bth sides? Des every equatin have a slutin? Justify yur reasning. (SMP 3) Create an equatin with ne slutin; n slutins; and infinitely many slutins. Describe yur methd fr creating these equatins. Synergy Item Bank: Item ID 51256, 50533, 50637, 57919, 51166 Supplemental Resurces Cnceptual Understanding: Clearing Decimals and Fractins Befre Slving an Equatin Create an Equatin with a Given Slutin Task Desms: Least Slutin One Slutin, N Slutins, Infinite Slutins Task Slving Equatins Task The Signs f Slutins Task Prcedural Skills and Fluency: Equatins with Variables n Bth Sides Sl-Team- Teach Multi-Step Equatins Carusel 1 Multi-Step Equatins Carusel 2 Slving Multi-Step Equatins Whip Khan Academy: Equatins with variables n bth sides Khan Academy: Equatins with parentheses Khan Academy: Number f slutins t equatins Applicatin Cupn vs. Discunt Task LONG BEACH UNIFIED SCHOOL DISTRICT 6 Psted 10/9/17
Unit 1 Equatins and Inequalities Days Learning Target Expectatins 2-3 I will check my understanding f slving equatins by participating in the FAL. Suggested Sequence f Key Learning Events and Instructin FORMATIVE ASSESSMENT LESSON (chse ne) Building and Slving Linear Equatins (SMP 1, 3, 5, 7, 8) Slving Linear Equatins in One Variable (SMP 1, 3, 5, 6, 7, 8) (Activities and Lessns) Supplemental Resurces 4-5 I will slve inequalities f the frm px + q > r and px + q < r, where p, q, and r are specific ratinal numbers by Cnstructing inequalities t slve real-wrld and mathematical prblems. Graphing the slutin set f the inequality and interpret it in the cntext f the prblem. (SMP 2) Answering questins such as Describe the slutin set f an inequality. Hw d yu graph the slutin set f an inequality? Explain what a clsed and pen circle represents in the graph. When and why d yu reverse the inequality symbl when slving an inequality? Cmpare and cntrast slving inequalities with slving equatins. Why can t yu replace an inequality sign with an equal sign? Hw d yu check yur slutin when slving an inequality? Synergy Item Bank: Item ID 53082, 53340, 53751, 53753, 53754 Sectin 11.1 (Activities 1 and 3; Examples 2 and 3) Sectin 11.2 (Activities 1 and 2; Examples 1, 2, and 3) Sectin 11.3 (Activities 1 and 3; Examples 1, 2, 3, and 4) Sectin 11.4 (Activity 1; Examples 1, 2, and 3) STEM Vide: Space Cadets Prcedural Skills and Fluency: Slving One-Step Inequalities Cncentratin Slving Inequalities by Adding r Subtracting Sl-Team-Teach Tw-Step Equatins and Inequalities Carusel Khan Academy: Tw-step inequalities Applicatin: Building Financial Literacy: Darla s Mnthly Financial Obligatins Car Dealership Task Fishing Adventures Task Sprts Equipment Set Task STEM Vide Perfrmance Task: Distance and Brightness f the Stars Mdeling: Wdy s Raise (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 7 Psted 10/9/17
Unit 1 Equatins and Inequalities Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins (Activities and Lessns) I will prepare fr the Incrprating the Standards fr Mathematical Ch. 1 Study Help (p. 16) unit assessment n Practice (SMPs) alng with the cntent standards Ch. 1 Review (p. 33 34) 1-2 equatins and t review the unit. Ch. 11 Study Help inequalities by (p. 476) Ch. 11 Review (p. 493 495) 1 day Unit Assessment Unit Assessment Students will take the Synergy Online Unit Assessment. Unit Assessment Resurces (Wrd r PDF) can be used thrughut the unit. At this pint, all standards addressed in the Math 7 SBAC Interim Assessment Blck Number System and Math 7 SBAC Interim Assessment Blck Expressins and Equatins have been cvered. These blcks may nw be administered. Supplemental Resurces Applicatin: Kennel Fees Task LONG BEACH UNIFIED SCHOOL DISTRICT 8 Psted 10/9/17