Unit 1 Operations with Rational Numbers Math 7

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1 Number f Days: 34 9/5/17 10/20/17 Unit Gals Stage 1 Unit Descriptin: Students cntinue t build an understanding f the number line frm their wrk in 6th grade. Students cnvert between the fractin frm t decimal frm f a ratinal number using lng divisin. They learn t add, subtract, multiply, and divide integers, while maintaining the prperties f peratins and the relatinships between additin and subtractin, and multiplicatin and divisin. Students will then apply their understanding t perfrm the fur peratins n psitive and negative ratinal numbers in the cntext f real-wrld situatins. Materials: number lines, 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 SMP 5 SMP 6 SMP 7 SMP 8 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.NS.A Apply and extend previus understandings f peratins with fractins t add, subtract, multiply, and divide ratinal numbers. [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 Integer peratins can be represented in multiple ways using manipulatives, number lines, and real-wrld situatins. Adding any tw ratinal numbers, p + q, can be represented as the number lcated a distance q frm p, in the psitive r negative directin depending n whether q is psitive r negative. The distance between tw ratinal numbers n a number line is the abslute value f their difference. Ratinal numbers can be divided as lng as the divisr is nt zer; every qutient f ratinal numbers is a ratinal number. Applying previus understandings f prperties f peratins as strategies t add, subtract, multiply, and divide psitive and negative ratinal numbers will help slve real-wrld and mathematical prblems. KNOWLEDGE Students will knw The definitin f academic vcabulary wrds, such as additive inverse, integers, ppsites, and ratinal number. The sum f ppsite numbers is zer. Any subtractin prblem can be written as an equivalent additin prblem. The decimal frm f a ratinal number terminates in 0s r eventually repeats. Acquisitin ESSENTIAL QUESTIONS Students will keep cnsidering Hw are adding and subtracting integers related? Hw are multiplying and dividing integers related? When in the real-wrld wuld yu add, subtract, multiply, r divide ratinal numbers? SKILLS Students will be skilled at and/r be able t Add, subtract, multiply, and divide psitive and negative ratinal numbers t slve real-wrld and mathematical prblems. Interpret ratinal numbers n a number line, including representing additin and subtractin expressins. Apply prperties f peratins as strategies t add, subtract, multiply, and divide ratinal numbers. Cnvert a fractin t a decimal using lng divisin. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Psted 9/13/17

2 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.NS.A Apply and extend previus understandings f peratins with fractins t add, subtract, multiply, and divide ratinal numbers. 7.NS.1 Apply and extend previus understandings f additin and subtractin t add and subtract ratinal numbers; represent additin and subtractin n a hrizntal r vertical number line diagram. a. Describe situatins in which ppsite quantities cmbine t make 0. Fr example, a hydrgen atm has 0 charge because its tw cnstituents are ppsitely charged. b. Understand p + q as the number lcated a distance q frm p, in the psitive r negative directin depending n whether q is psitive r negative. Shw that a number and its ppsite have a sum f 0 (are additive inverses). Interpret sums f ratinal numbers by describing real wrld cntexts. c. Understand subtractin f ratinal numbers as adding the additive inverse, p q = p + ( q). Shw that the distance between tw ratinal numbers n the number line is the abslute value f their difference, and apply this principle in real wrld cntexts. d. Apply prperties f peratins as strategies t add and subtract ratinal numbers. 7.NS.2 Apply and extend previus understandings f multiplicatin and divisin and f fractins t multiply and divide ratinal numbers. a. Understand that multiplicatin is extended frm fractins t ratinal numbers by requiring that peratins cntinue t satisfy the prperties f peratins, particularly the distributive prperty, leading t prducts such as ( 1)( 1) = 1 and the rules fr multiplying signed numbers. Interpret prducts f ratinal numbers by describing real-wrld cntexts. b. Understand that integers can be divided, prvided that the divisr is nt zer, and every qutient f integers (with nn-zer divisr) is a ratinal number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret qutients f ratinal numbers by describing real-wrld cntexts. c. Apply prperties f peratins as strategies t multiply and divide ratinal numbers. d. Cnvert a ratinal number t a decimal using lng divisin; knw that the decimal frm f a ratinal number terminates in 0s r eventually repeats. 7.NS.3 Slve real-wrld and mathematical prblems invlving the fur peratins with ratinal numbers. [m] 7.EE.B Slve real life and mathematical prblems using numerical and algebraic expressins and equatins. 7.EE.3 Slve multi step real life and mathematical prblems psed with psitive and negative ratinal numbers in any frm (whle numbers, fractins, and decimals), using tls strategically. Apply prperties f peratins t calculate with numbers in any frm; cnvert between frms as apprpriate; and assess the reasnableness f answers using mental cmputatin and estimatin strategies. Fr example: If a wman making $25 an hur gets a 10% raise, she will make an additinal 1/10 f her salary an hur, r $2.50, fr a new salary f $ If yu want t place a twel bar 9 3/4 inches lng in the center f a dr that is 27 1/2 inches wide, yu will need t place the bar abut 9 inches frm each edge; this estimate can be used as a check n the exact cmputatin. Key: [m] = majr clusters; [s] = supprting clusters; [a] = additinal clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Psted 9/13/17

3 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.NS.A The student interprets ratinal number values n a number line, including representatins f additin and subtractin expressins. The student applies prperties f peratins as strategies t add and subtract ratinal numbers. The student applies prperties f peratins as strategies t multiply and divide ratinal numbers. The student cnverts frm a fractinal frm f ratinal numbers t a decimal frm f ratinal numbers. The student slve real-wrld and mathematical prblems invlving the fur peratins with ratinal numbers. 7.EE.B The student applies prperties f peratins t evaluate numeric expressins, including cnverting between different frms f numbers. 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.NS.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.NS.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.NS.A 7.EE.B Other Evidence Frmative Assessment Opprtunities Infrmal teacher bservatins Checking fr understanding using active participatin strategies Exit slips/summaries s 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 9/13/17

4 Days Learning Target Expectatins 1 day I will explre peratins with ratinal numbers by participating in the Opening. Suggested Sequence f Key Learning Events and Instructin OPENING TASK Number Line Reasning This Opening is a Sl-Team-Teach activity. Pass ut the activity, Number Line Reasning, and have students wrk independently. If students are struggling, yu may play the interactive vide The Number Line. Next, have students wrk as a grup t cme t a cnsensus and then have a class discussin abut students slutins utilizing Talk Mves t share the different methds used. This task is a gateway int the entire unit. Big Ideas Math Curse 2 (Activities and Lessns) Supplemental Resurces Cnceptual Understanding: Number Line Reasning The Number Line Interactive Vide 4-5 I will add integers by Using manipulatives t create cnjectures abut the rules fr adding integers. (SMP 5, 7, 8) Using a hrizntal and vertical number line diagram. Shwing that a number and its ppsite have a sum f zer (called additive inverses). Explaining p + q as the number lcated a distance q frm p, in the psitive r negative directin depending n whether q is psitive r negative. (SMP 3) Interpreting sums f integers by describing realwrld cntexts. (SMP 2) Answering questins such as Why d additive inverses have a sum f zer? Hw can yu add integers using multiple methds? Hw is adding integers similar t adding whle numbers? Hw is it different? (SMP 7) Synergy Item Bank: Item ID 53043, 53059, 53334, Sectin 1.1 (Activities 2 and 3; Sectin 1.2 (Activities 1, 2, 3, and 4; Examples 1, 2, and 3) STEM Vide: Freezing Slid Cnceptual Understanding: Adding Integers with Number Lines Adding Tw-Digit Numbers Additive Inverse Vide mypd Curse #2572: Adding Integers With Tw Clr Cunters Prcedural Skills and Integer Additin Beat the Cmputer Drill Adding Integers Tic-Tac- Te Khan Academy: Intr t adding negative numbers Applicatin: NBC Learn Vide Science f Glf: Math f Glf Scring STEM Vide Perfrmance : Melting Matters LONG BEACH UNIFIED SCHOOL DISTRICT 4 Psted 9/13/17

5 4-5 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins Big Ideas Math Curse 2 (Activities and Lessns) I will subtract integers by Using manipulatives t create cnjectures abut the rules fr subtracting integers. (SMP 5, 7, 8) Shwing that the distance between tw integers n a number line is the abslute value f their difference. Explaining subtractin f integers as adding the additive inverse, p q = p + ( q). (SMP 3) Interpreting differences f integers by describing real-wrld cntexts. (SMP 2) Answering questins such as Why d yu add the inverse when subtracting? Hw can yu subtract integers using multiple methds? Hw is subtracting integers similar t subtracting whle numbers? Hw is it different? (SMP 7) Synergy Item Bank: Item ID 53316, 57151, 64844, Sectin 1.3 (Activities 1, 2, 3, and 4; Examples 1, 2, and 3) Supplemental Resurces Cnceptual Understanding: Subtracting Integers Using Tw-Clr Cunters PwerPint Subtracting Tw-Digit Numbers Integer Operatins n the Number Line Which One Desn t Belng? Prcedural Skills and Adding and Subtracting Integers Cmic Strip Activity Tp This Game Adding and Subtracting Integers Math-O Adding and Subtracting Integers Tic-Tac-Te Khan Academy: Intr t subtracting negative numbers Khan Academy: Adding & subtracting with negatives n the number line Applicatin: Cliff Diving Differences f Integers Mdeling: Hw Much Did the Temperature Drp? (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 5 Psted 9/13/17

6 Days Learning Target Expectatins 2-3 I will check my understanding f peratins with ratinal numbers by participating in the FAL. Suggested Sequence f Key Learning Events and Instructin FORMATIVE ASSESSMENT LESSON (chse ne) Adding and Subtracting Directed Numbers (SMP 1, 2, 3, 5, 6, 7, 8) Using Psitive and Negative Numbers in Cntext (SMP 1, 2, 3, 4, 6, 7, 8) Big Ideas Math Curse 2 (Activities and Lessns) Supplemental Resurces 4-5 I will multiply integers by Using manipulatives t create cnjectures abut the rules fr multiplying integers. (SMP 5, 7, 8) Explaining why the prduct f tw negative numbers must be psitive using prperties, i.e. ( 1)( 1) = 1. (SMP 3) Interpreting prducts f integers in real-wrld cntexts. (SMP 2) Answering questins such as Hw can yu multiply integers using multiple methds? Hw is multiplying integers similar t multiplying whle numbers? Hw is it different? (SMP 7) Synergy Item Bank: Item ID 53058, 53339, 53354, 53444, 53449, Sectin 1.4 (Activities 1, 2, 3, and 4; Sectin 2.4 (Only Activity 1) Cnceptual Understanding: mypd Curse #2574: Multiplying Integers with Tw Clr Cunters Multiplying Tw-Digit Numbers Why is a Negative Times a Negative Always Psitive? Prcedural Skills and Integer Multiplicatin Beat the Cmputer Drill Right n Target Game Add, Subtract, Multiply Integer Operatins Hw D They Fit? Integers Prduct Game Khan Academy: Multiply & divide negative numbers Khan Academy: Expnents with negative bases Applicatin: Multiply t Make 64 The Running Vides LONG BEACH UNIFIED SCHOOL DISTRICT 6 Psted 9/13/17

7 4-5 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins Big Ideas Math Curse 2 (Activities and Lessns) I will divide integers by Using manipulatives t create cnjectures abut the rules fr dividing integers. (SMP 5, 7, 8) Explaining that integers can be divided as lng as the divisr is nt zer and knw that every qutient f integers is a ratinal number. (SMP 3) Interpreting qutients f integers in real-wrld cntexts. (SMP 2) Answering questins such as Cmpare and cntrast multiplying and dividing integers. Hw can yu divide integers using multiple methds? Hw is dividing integers similar t dividing whle numbers? Hw is it different? (SMP 7) Synergy Item Bank: Item ID 53315, 53442, 53446, 53448, Sectin 1.5 (Activities 1, 2, 3, and 4; Supplemental Resurces Cnceptual Understanding: Dividing Psitive and Negative Numbers Vide Dividing Tw-Digit Numbers Missing Factr Mdel fr Dividing Integers mypd Curse #2467: Dividing Integers with Tw Clr Cunters Prcedural Skills and Integer Divisin Beat the Cmputer Drill Multiplying and Dividing Integers Cnnect 4 Mixed Operatins with Integers Math-O Substituting Negative Values int Algebraic Expressins Khan Academy: Multiply & divide negative numbers Khan Academy: Negative signs in fractins LONG BEACH UNIFIED SCHOOL DISTRICT 7 Psted 9/13/17

8 9-10 Suggested Sequence f Key Learning Events and Instructin Days Learning Target Expectatins Big Ideas Math Curse 2 (Activities and Lessns) I will apply peratins f ratinal numbers by Cnverting a fractin int a decimal using lng divisin. Adding, subtracting, multiplying, and dividing psitive and negative decimals, fractins, and mixed numbers. Slving real-wrld and mathematical prblems invlving the fur peratins with psitive and negative ratinal numbers. Applying prperties and rder f peratins as strategies t add, subtract, multiply, and divide psitive and negative ratinal numbers. Answering questins such as When wuld yu need t add, subtract, multiply, r divide ratinal numbers in a realwrld cntext? Hw is adding ratinal numbers similar t adding integers? Hw is it different? (SMP 7) Synergy Item Bank: Item ID 70785, 53053, 53268, 53332, 53475, 67819, Sectin 2.1 (Examples 1 and 2) Sectin 2.2 (Activities 1, 2, and 3; Sectin 2.3 (Activities 1 and 2; Sectin 2.4 (Activities 2, 3, and 4; STEM Vide: Carpenter r Jiner Supplemental Resurces Cnceptual Understanding: Cnverting Ratinal Numbers Vide Decimal Expansins f Fractins Operatins n the Number Line Ratinal Numbers Which One Desn t Belng? Multiplying Fractins 3 Prcedural Skills and Cnverting Between Fractins and Decimals Decimal Maze Multiplying Ratinal Numbers Prduct Game Khan Academy: Adding & subtracting negative fractins Khan Academy: Multiply & divide negative fractins Applicatin: Differences and Distances Wh is the Better Batter? STEM Vide Perfrmance : Precisely Perfect LONG BEACH UNIFIED SCHOOL DISTRICT 8 Psted 9/13/17

9 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 Ch. 1 Study Help (p. 20) unit assessment n Practice (SMPs) alng with the cntent standards Ch. 1 Review (p ) peratins with t review the unit. Ch. 2 Study Help (p. 56) 1-2 ratinal numbers Ch. 2 Review (p ) by Supplemental Resurces Applicatin: Bttling Dwnlads Htel Elevatr 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 Number System have been cvered. This blck may nw be administered. LONG BEACH UNIFIED SCHOOL DISTRICT 9 Psted 9/13/17

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