Unit 2 Expressions, Equations, and Inequalities Math 7

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1 Unit 2 Expressins, Equatins, and Inequalities Math 7 Number f Days: 24 10/23/17 12/1/17 Unit Gals Stage 1 Unit Descriptin: Students cnslidate and expand previus wrk with generating equivalent expressins and slving equatins. They apply the prperties f peratins as strategies t factr and expand linear expressins with ratinal cefficients. They slve real-life and mathematical prblems using numerical and algebraic expressins, equatins, and inequalities. Materials: algebra tiles, calculatrs Standards fr Mathematical Practice SMP 1 SMP 2 SMP 3 SMP 4 SMP 5 SMP 6 SMP 7 SMP 8 Make sense f prblems and persevere in slving them. Reasn abstractly and quantitatively. Cnstruct viable arguments and critique the reasning f thers. Mdel with mathematics. Use apprpriate tls strategically. Attend t precisin. Lk fr and make use f structure. Lk fr and express regularity in repeated reasning. 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. 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 and inequalities can be used t represent real life situatins. Slving an equatin is the prcess f answering a questin: Which values frm a specified set, if any, make the equatin true? Slving an inequality is the prcess f answering a questin: Which values frm a specified set, if any, make the inequality true? Acquisitin KNOWLEDGE Students will knw The definitin f academic vcabulary wrds, such as Additin Prperty f Inequality, Divisin Prperty f Inequality, factr, Multiplicatin Prperty f Inequality, and Subtractin Prperty f Inequality. Algebraic expressins and equatins can be translated int wrds. There may be mre than ne way t write an algebraic expressin t represent a given situatin. 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. Slving inequalities is very similar t slving equatins, except yu must reverse the inequality symbl when multiplying r dividing bth sides f an inequality by a negative number. ESSENTIAL QUESTIONS Students will keep cnsidering Hw can yu generate equivalent algebraic expressins? Hw can equatins and inequalities be used t help slve real-wrld prblems? Cmpare and cntrast slving equatins and inequalities. SKILLS Students will be skilled at and/r be able t Add, subtract, factr, and expand linear expressins with ratinal cefficients. Generate equivalent linear expressins using a cmbinatin f additin and subtractin, factring, and expansin. Slve linear equatins in ne variable with ratinal number cefficients, including equatins with the distributive prperty. Slve tw-step inequalities in ne variable with ratinal number cefficients and graph the slutin set n a number line. Create and slve equatins and inequalities in ne variable t represent a situatin. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Psted 9/28/17

2 Unit 2 Expressins, Equatins, and Inequalities Math 7 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. 7.EE.2 Understand that rewriting an expressin in different frms in a prblem cntext can shed light n the prblem and hw the quantities in it are related. Fr example, a a = 1.05a means that increase by 5% is the same as multiply by [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. Key: [m] = majr clusters; [s] = supprting clusters; [a] = additinal clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Psted 9/28/17

3 Unit 2 Expressins, Equatins, and Inequalities Math 7 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 adds and subtracts linear expressins with ratinal cefficients. The student factrs linear expressins with ratinal cefficients. The student expands linear expressins with ratinal cefficients. 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 equatins f the frm px + q = r and p ( x + q) = r, where p, q, and r are specific ratinal numbers. 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. 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 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 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 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 9/28/17

4 Unit 2 Expressins, Equatins, and Inequalities Math 7 Days Learning Target Expectatins 1 day 4-5 I will explre expressins, equatins, and inequalities by participating in the Opening Task. I will generate equivalent expressins with ratinal cefficients by Suggested Sequence f Key Learning Events and Instructin OPENING TASK Creating Expressins Students will wrk with a partner t d this Opening Task. Befre cncluding the activity, facilitate a class discussin abut students varius expressins utilizing Talk Mves t share their ideas. This task is a gateway int the unit n expressins, equatins, and inequalities. (SMP 2, 8) Using algebra tiles t represent equivalent expressins. (SMP 5) Using prperties f peratins t cmbine like terms. Factring linear expressins. Using the distributive prperty t expand linear expressins. Using substitutin as a methd t check if the expressins are equivalent. Answering questins such as What is the difference between a linear and nnlinear expressin? Hw can yu prve if tw expressins are equivalent? Explain hw t factr a linear expressin. (SMP 3) Hw can yu use the distributive prperty t check yur factring? Synergy Item Bank: Item ID 51044, 51706, 53757, 53792, 54402, 54405, Big Ideas Math Curse 2 (Activities and Lessns) Sectin 3.1 (Activity 1; Sectin 3.2 (Activities 2 and 3; Extensin 3.2 ( Supplemental Resurces Cnceptual Understanding: Creating Expressins mypd Curse #2579: Opening Tasks in Math Classrms Cnceptual Understanding: EngageNY: Writing Sums as Prducts Factring Equivalent Expressins 2 Task Prduct f Distributive Prperty Task Desms: Central Park Prcedural Skills and Expressins Mix-Freeze- Match Distributive Prperty Hw D They Fit? Desms: Expressins Mash-Up Khan Academy: Cmbining like terms Khan Academy: The distributive prperty & equivalent expressins Applicatin: Ticket t Ride Task Ty Trains Task Expense Reprt Task Desms: Pl Brder Prblem LONG BEACH UNIFIED SCHOOL DISTRICT 4 Psted 9/28/17

5 Unit 2 Expressins, Equatins, and Inequalities Math Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins Big Ideas Math Curse 2 (Activities and Lessns) I will fluently slve Using algebra tiles t understand the prcess f Sectin 3.3 equatins f the slving tw-step equatins and equatins (Activities 1 and 2; frm px + q = r cntaining the distributive prperty. (SMP 5) and p ( x + q) = r, Cnstructing equatins t slve real-wrld and Sectin 3.4 mathematical prblems. (SMP 2) (Activities 1 and 3; where p, q, and r Cmparing an algebraic slutin t an arithmetic Examples 1 and 2) are specific ratinal slutin by identifying the sequence f peratins Sectin 3.5 numbers by used in each apprach. (Activities 1, 2, and 3; Answering questins such as Why d yu use inverse peratins t slve STEM Vide: Rck equatins? Climbing Why might yu slve sme prblems algebraically, but ther prblems yu may slve arithmetically? Hw can yu check yur slutin when slving an equatin? What des yur slutin mean when slving equatins? Synergy Item Bank: Item ID 52992, 53380, 53752, 53080, 53791, 53758, Supplemental Resurces Cnceptual Understanding: Slving Equatins with Algebra Tiles Algebra Tiles Equatin Mat and Recrding Sheet EngageNY: Understanding Equatins EngageNY: Slving Equatins with Algebra Tw-Step Equatins Task mypd Curse #2864: Clthesline Math: Slving Equatins Prcedural Skills and EngageNY: Equatins with Distributive Prperty One- and Tw-Step Equatins Math-O Khan Academy: Tw-step equatin intr Khan Academy: Tw-step equatins with decimals and fractins Applicatin: STEM Vide Perfrmance Task: Planning the Climb Mdeling: What Des 2000 Calries Lk Like? (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 5 Psted 9/28/17

6 Unit 2 Expressins, Equatins, and Inequalities Math 7 Days Learning Target Expectatins 2-3 I will check my understanding f equatins by participating in the FAL. Suggested Sequence f Key Learning Events and Instructin FORMATIVE ASSESSMENT LESSON Slving Linear Equatins (SMP 1, 2, 3, 4, 6, 7, 8) Big Ideas Math Curse 2 (Activities and Lessns) Supplemental Resurces 5-6 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. (SMP 2) 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? What des a clsed r pen circle represent in the graph? Cmpare and cntrast slving inequalities with slving equatins. When and why d yu reverse the inequality symbl when slving an inequality? Why can t yu replace an inequality sign with an equal sign when slving inequalities? Hw d yu check yur slutin when slving an inequality? When d yu use an inequality instead f an equatin t slve a prblem? Synergy Item Bank: Item ID 53082, 53340, 53751, 53753, Sectin 4.1 (Activities 1 and 3; Sectin 4.2 (Activities 1 and 2; Sectin 4.3 (Activities 1 and 3; Sectin 4.4 (Activity 1; STEM Vide: Space Cadets Cnceptual Understanding: Desms: Inequalities n the Number Line Creating Inequalities Task Prcedural Skills and Slving One-Step Inequalities Cncentratin Slving Inequalities by Adding r Subtracting Sl-Team-Teach Khan Academy: Tw-step inequalities Applicatin: Building Financial Literacy: Darla s Mnthly Financial Obligatins Fishing Adventures Task Sprts Equipment Set Task Mdeling: Wdy s Raise (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 6 Psted 9/28/17

7 Unit 2 Expressins, Equatins, and Inequalities Math 7 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins Big Ideas Math Curse 2 (Activities and Lessns) I will prepare fr the Incrprating the Standards fr Mathematical unit assessment n Practice (SMPs) alng with the cntent standards expressins, t review the unit. equatins, and inequalities by 1-2 Ch. 3 Study Help (p. 94) Ch. 3 Review (p ) Ch. 4 Study Help (p. 136) Ch. 4 Review (p ) Supplemental Resurces Prcedural Skills and A Trick fr Yu Game Tic-Tac-Te Game 2-Step Equatins and Inequalities Carusel Applicatin: Car Dealership Task 1 day 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 Expressins and Equatins have been cvered. This blck may nw be administered. LONG BEACH UNIFIED SCHOOL DISTRICT 7 Psted 9/28/17