Middle School Mathematics Parent Guide

Transcription

1 Middle Schl Mathematics Parent Guide Curriculum Aligned t NJ CCSS: August 2012 Revised July 2015 District Missin The Suth Brunswick Schl District will prepare students t be lifelng learners, critical thinkers, effective cmmunicatrs and wise decisin makers. This will be accmplished thrugh the use f the New Jersey Cre Curriculum Cntent Standards (NJCCCS) and/r the Cmmn Cre State Standards (CCSS) at all grade levels. The schls will maintain an envirnment that prmtes intellectual challenge, creativity, scial and emtinal grwth and the healthy physical develpment f each student. ~Adpted Annual Bard Apprval f Mathematics Curriculum August 2016 This curriculum is apprved fr all regular educatin prgrams as specified and fr adptin r adaptatin by all prgrams including thse fr Special Educatin, English Language Learners, At- Risk Students and Gifted and Talented Students in accrdance with Bard f Educatin Plicy.

2 Nte t Parents The curriculum guide yu are abut t enter is just that, a guide. Teachers use this dcument t steer their instructin and t ensure cntinuity between classes and acrss levels. It prvides guidance t the teachers n what students need t knw and able t d with regard t the learning f a particular cntent area. The curriculum is intentinally written with sme spaces in it s that teachers can add their wn ideas and activities s that the wrld language classrm is persnalized t the students. Hw t Read the Curriculum Dcument Curriculum Tpic Grade Level Summary Ratinale Interdisciplinary Cnnectins 21 st Century Cnnectins Terminlgy Standards Enduring Understandings Essential Questins Objectives Assessments Lessn Plans & Pacing Resurces Area f cntent (e.g. Science) Curse r Unit f Study (e.g. Bilgy) Grade Level Cluster (e.g. High Schl) r specific grade level (e.g. Kindergarten) A brief verview f the curse r unit f study. A statement as t why we are teaching this curse r unit. Which ther areas f cntent t which there is majr linkage. Fr example, a health educatin unit might link t science, language arts, scial studies, art, physical educatin, etc. Hw this curse r unit is preparing students t be cllege and career ready. Referred t as S.A.L.T., each curse r unit indicates which f the fllwing it is building: Skills such as critical r creative thinking, cllabratin, cmmunicatin, r cre values Awareness such as glbal, crss- cultural r career. Literacy such as infrmatin, media, technlgy, etc. Traits necessary fr success in life and careers such as prductivity. Key vcabulary and terms Here yu will find the standards that this curse r unit f study is addressing. Our curriculum is standards- based. The standards are the fundatin f the unit. Yu can get mre infrmatin n state standards by ging t the NJ Department f Educatin at The big ideas, cncepts r life lessns that students walk away with at the end f a unit f study. Open ended questins that are cnsidered thrughut the unit f study. These are big, wrthy f wnder questins ften with multiple respnses. The discrete skills and knwledge that students will gain during the unit f study. Assessments (tests, quizzes, prjects, activities) that tell us if the students grasped the enduring understandings f the unit. Scpe and sequence f lessns: hw many, hw lng & apprximately in what rder. Majr resurces assciated with the curse r unit.

3 Mathematics Acknwledgments We are appreciative f the leadership prvided by ur curriculum specialists and the knwledge, skills, wrk and effrt f the teachers wh served n ur curriculum writing teams. In many cases, ur units are hme- grwn. While aligning with state and natinal standards, they are designed with the needs f the Suth Brunswick student ppulatin in mind. Articulatin The Supervisrs, Specialists, Curriculum Chairpersns, Technlgy Staff Develpers, Directrs and the Assistant Superintendent fr Curriculum and Instructin meet fr articulatin at rundtables and nging administrative and cntent meetings thrughut the year. Amng the tpics f discussin are the fllwing: curriculum review cycle, curriculum mapping, resurces (rdering, budgeting, inventry), lessn plans, bservatin lk- frs, prfessinal develpment, NJ Quality Single Accuntability Cntinuum and academic achievement, placement, acceleratin, enrichment, basic skills, instructinal supprt, technlgy prficiencies and cntent- specific technlgies, frmative and summative assessments, and varius curriculum tasks. Mathematics Curriculum Develpment Teams cmprised f teachers at every grade level alng with representative special educatin meet tgether thrughut the year as needed. In a time perid f majr revisin, the teams will meet with greater frequency. G dwn deep enugh int anything and yu will find mathematics. ~Dean Schlicter

4 TABLE OF CONTENTS Preamble Missin K-12 Suth Brunswick Beliefs K-12 Prgram Delivery K-12 Resurces K-12 Assessment K-12 Cre Cntent Curriculum Standards K-12 Curriculum by Curse Middle Schl Curriculum Map Curriculum fr Grade 6 Big Idea/Enduring Understandings/Essential Questins Desired Results: Standards Objectives: Knwledge and Skills Assessments Resurces/Cnnectins Pacing Charts Curriculum fr Grades 7-8 Big Idea/Enduring Understandings/Essential Questins Desired Results: Standards Objectives: Knwledge and Skills Assessments Resurces/Cnnectins Pacing Charts Appendix Nte: The elementary math curriculum can be fund in the K-2 and 3-5 Mathematics Curriculum Guides. The 9-12 mathematics curriculum can be fund in the SBHS Mathematics Curriculum Guides: Cre Math and Elective Math.

5 PREAMBLE TO THE MATHEMATICS CURRICULUM Missin Statement The Suth Brunswick Mathematics Prgram will be based n a well-articulated curriculum that is aligned with standards, has interwven technlgy, is cnnected in meaningful ways t ther curriculum and real life, that prvides fr differentiated needs f students, that is taught by teachers wh are well-grunded in and cmfrtable with bth cntent and methdlgy, and that leads t equity and excellence in math achievement fr all children. Suth Brunswick s Beliefs 1. Develp cncepts cncretely, pictrially, and then abstractly. Students use manipulatives t mdel abstract ideas, t represent the mdels as pictures, and finally t translate the mdel and/r picture int symblic ntatin. Smetimes the transitin frm cncrete t abstract takes years, as in the case f multi-digit additin cmputatin; ther times the transitin may take a few class sessins, as in the case f multiplying fractins. 2. Require students t justify their answers. During class discussins and in written wrk students shuld always be asked why. Students shuld be able t verbalize, mdel, and t write the reasn an answer has been given. 3. Prvide time fr students t write and talk mathematics. Students keep a math jurnal and discuss mathematical ideas as part f cperative grups and as part f the whle class. Writing and talking mathematics allws students t clarify and explain thinking, justify answers, explain strategies, ask questins, listen t thers, and react t ideas. 4. Develp prblem situatins frm ther cntent areas and frm everyday experiences. Science, scial studies, and language cntent are integrated int mathematics lessns. Fr example, when intrducing 2-digit additin, the initial cncrete mdel might be develped ut f a scial studies unit n Cmmunity Helpers. If the class has graphed the number f peple ging int different municipal buildings, finding the number f peple ging int 2 r 3 f the buildings tgether can begin the develpment f a 2-digit additin algrithm. 5. Give attentin t cnnectins amng tpics in math, between math and ther cntent areas, and between math and daily life. Students shuld recgnize, fr example, that the array mdel f multiplicatin, the area f a rectangle, and paper flding t multiply fractins are all based n the same idea. Students shuld use strategies develped in math lessns in their wrk with ther cntent and in their daily lives 6. Always encurage use f multiple strategies. Fr example, a large number f bjects can be cunted in several ways: by nes, by tws, by gruping int tens r by matching with a hundrednumber bard. Alng with traditinal algrithms, students shuld explre alternate methds f cmputatin, including cmputatinal strategies develped by the students themselves. 7. Have students estimate quantities. Students then use that estimate t check reasnableness f answers. Estimate lengths, weights, and s n befre measuring. Put ut a handful f cubes and estimate the quantity. 8. Make mental math a part f any cmputatin. Encurage students t calculate mentally. Help them t take the risk f giving an answer withut using pencil and paper first. Mental math

6 strategies are treated as just anther way, tgether with pencil and paper, calculatrs, cncrete mdels, and pictrial mdels t calculate an answer. 9. Urge students t chse their tls and methds. Students are encuraged t chse amng many different methds fr prblem slving (draw a picture, guess and check, write an equatin, and s n), fr calculating answers (mental math, paper and pencil, estimatin, calculatr), and fr mdeling (base ten blcks, mney, ge-bards, cunters, and s n). 10. Integrate cmputers and calculatrs int mathematics lessns. Students need t begin t chse technlgy as a tl. Graphing prgrams are ne way t display data; spreadsheet prgrams are used t slve prblems; calculatrs allw students t deal with mre cmplicated numbers. Students shuld be ffered the pprtunity t use nline virtual manipulatives, Internet resurces and interactive whitebards when available. Calculatrs allw students t deal with mre cmplex prblem slving. 11. Have students wrk in a variety f settings. The chice f settings - cperative grups, pairs f students, individuals, and whle grups - depends n the teacher's bjective and the specific cntent f the lessn. Students shuld be expsed t each kind f setting thrughut the schl year. 12. Design, develp, implement and evaluate digital-age learning experiences and assessments. Fr example, use f classrm technlgies such as interactive whitebards, prjectin devices, digital hardware and sftware. Prgram Delivery Our math classrms are effective standards-based envirnments that fster understanding f big mathematical ideas, help students make cnnectins between learning experiences, and enable students t see themselves as mathematicians. There are varied math paths that students fllw during their curse f study in Suth Brunswick. Elementary Schl: Grade Level Math & Differentiatin Accelerated Math K-5 Middle Schl: 6 th Grade Unit Math 6 th Grade Transitins (accelerated math) Pre-Algebra Cncepts f Algebra Algebra I Gemetry Algebra II (taken n the HS campus) High Schl: Cre Curses (3-Year Sequence): Algebra I 1, Gemetry, Algebra II Illustrative Math Electives: Pre-Calculus, Calculus, Statistics, Discrete Math, Cmputer Science 2 1 Algebra I is a graduatin requirement. 2 Cmputer Science fr the 21 st Century als meets the mandate fr 21 st Century.

7 Nte: Many students begin the cre sequence during their middle schl years, which allws fr them t take up t three Advanced Placement level curses. Althugh nly three years f mathematics is required fr graduatin, the majrity f Suth Brunswick students take fur years f math. Recgnizing the differing needs f ur students, all f the curses ffered have several levels, including Elements, Regular, Advanced, and Hnrs/AP Resurces The fllwing are resurces used in ur mathematics prgrams. Elementary Schl Investigatins in Data, Number, and Space Sctt Fresman-Addisn Wesley Mathematics On Cre Mathematics (Hughtn Mifflin Harcurt) Manipulatives: Hands-n and virtual Technlgies: Sctt Fresman and Calculatrs (Grades K-1: Calc-U-Vue; Grades 2-5: TI- 108) SMART Bards (interactive whitebards) Mdel classrm technlgies: prjectrs, DVD players, speakers Study Island (Grades 3-5) Accelerated 5 th Grade Math- MathScape, Cnnected Math Middle Schl 6 th Grade Unit Math- Big Ideas Accelerated 6 th Grade Math- Big Ideas Advanced I 7th-8 th McDugal Littell Pre-Algebra, Grade 7 Big Ideas Math, Grade 8 Big Ideas Math, Hlt McDugal Algebra I, Jurgeusn Gemetry Manipulatives; Hands-n equatins, cmmunicatrs (mini-whitebards), integer tiles, and 3-D prisms and cubes Technlgies: SMARTBards (interactive whitebards); dcument camera; Texts Web sites & Hmewrk Helplines; Calculatrs (TI 30SX II, TI-84); Study Island High Schl Anchr Texts: Hlt McDugal Texts, Hughtn Mifflin Texts Technlgies: Graphing Calculatrs (TI 84 and TI 89); Gemeter Sketchpad SMART Bard (interactive whitebards) Assessments There are multiple and varied frms f assessment at each grade level. What fllws is a list f the key assessment tls used at each level. Assessments at the Elementary Level District-made Beginning f Year Math Assessment fr Kindergarten Mid-Year Check In fr Kindergarten District-made End f Year Cmpetency Tests K-5 District-made End f Year Math Acceleratin Tests K-5 District-made Pre and Psttests fr grades 1-5 State Assessments (PARCC 3-5) Mad Minute Drills/Otter Creek Drills

8 Teacher-Made Tests, Prjects Assessments at the Middle Level: Teacher-made Tests, Quizzes & Prjects District-made Pre and Pst Assessments Mid Terms and Final exams fr Algebra and Gemetry (advanced math) Crssrads (District Placement) Test Algebra Predictive Test fr placement State Assessments (PARCC 6-8) Assessments at the High Schl Level Teacher-made tests, quizzes and prjects District-made Pre and Pst Assessments Midterms and final exams (upper level curses) Final exams (cre curses) State Assessments (PARCC 9-11) SAT, PSAT, ACT, Accuplacer, ASVAB AP exams Curriculum Cntent Standards fr Mathematics The Suth Brunswick mathematics curriculum was develped t meet the bjectives as stated in the NJ State Department f Educatin Cre Curriculum Cntent Standards 2009 and/r the Cmmn Cre State Standards Technlgy Educatin, 21 st Century Life and Career Educatin, and Character Educatin lessns are embedded where meaningful. Crss-curricular cnnectins are purpsely and explicitly nted. The curriculum is written in the Understanding by Design frmat and is based n enduring understandings (brad cncepts) with essential questins and bth frmative and summative assessments. Cmplete cpies f the standards fr mathematics may be fund at: Cmmn Cre State Standards Initiative (CCSSI)

9 MIDDLE SCHOOL CURRICULUM

10 CURRICULUM MAP: MIDDLE SCHOOL Standards 6 th Grade Math Middle Schl Cre Curse Offerings Transitins Math Pre Algebra Cncepts f Algebra Algebra I Mathematical Practices are encmpassed in every curse thrughut middle schl: 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 and express regularity in repeated reasning. Ratis and Prprtinal Relatinships The Number System Expressins and Equatins Gemetry Statistics and Prbability 6.RP.1 6.RP.2 6.RP.3 6.NS.1 6.NS.2 6.NS.3 6.NS.4 6.NS.5 6.NS.6 6.NS.7 6.NS.8 6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9 6.G.1 6.G.2 6.G.3 6.G.4 6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5 6.RP.1 7.RP.1 6.RP.2 7.RP.2 6.RP.3 7.RP.3 6.NS.1 7.NS.1 6.NS.2 7.NS.2 6.NS.3 7.NS.3 6.NS.4 6.NS 5 6.NS.6 6.NS.7 6.NS.8 6.EE.1 7.EE.1 6.EE.2 7.EE.2 6.EE.3 7.EE.3 6.EE.4 7.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9 6.G.1 7.G.1 6.G.2 7.G.2 6.G.3 7.G.3 6.G.4 6.SP.5 7.SP.5 7.SP.6 7.SP.7 7.SP.8 7.RP.1 7.RP.2 7.RP.3 7.NS.1 7.NS.2 7.NS.3 7.EE.1 7.EE.2 7.EE.3 7.EE.4 7.G.1 7.G.2 7.G.3 7.G.4 7.G.5 7.G.6 7.SP.1 7.SP.2 7.SP.3 7.SP.4 7.SP.5 7.SP.6 7.SP.7 7.SP.8 7.RP.1 7.RP.2 7.RP.3 7.NS.1 8.NS.1 7.NS.2 8.NS.2 7.NS.3 7.EE.1 8.EE.1 7.EE.2 8.EE.2 7.EE.3 8.EE.3 7.EE.4 8.EE.4 8.EE.4 8.EE.5 8.EE.6 8.EE.7 7.G.1 8.G.1 7.G.2 8.G.2 7.G.3 8.G.3 7.G.4 8.G.4 7.G.5 8.G.5 7.G.6 8.G.6 8.G.7 7.SP.1 8.SP.1 7.SP.2 8.SP.4 7.SP.3 7.SP.4 7.SP.5 7.SP.6 7.SP.7 7.SP.8 Geme try See High Schl curriculum guides, as these are curses taught at the middle schl level, but are cnsidered high schl curses.

11 Functins 8.F.1 8.F.2 8.F.3

12 Middle Schl Math Curses Sixth Grade Unit Math Transitins Math (Accelerated Math) Pre Algebra Cncepts f Algebra Algebra I Gemetry Algebra II

13 CURRICULUM OVERVIEW: SIXTH GRADE UNIT MATH Cntent Area: Mathematics Curse Title: 6 th Grade Unit Math Curse Descriptin: Unit Math cvers 6 th grade math standards. Curse Ratinale: This prgram is a 6th grade, n-level curse ffered thrugh bth a cnceptual and skill-based apprach. It als addresses the Natinal Cuncil f Teacher f Mathematics (NCTM) standards and is funded n the Twelve Effective Instructinal Practices f the Suth Brunswick Schl District. Technlgy is embedded where meaningful and crss-curricular cnnectins are purpsely and explicitly nted. Primary Interdisciplinary Cnnectins: Language Arts, Science, Scial Studies, Physical Educatin, Art, Astrnmy, Architecture and Technlgy. 21 st Century Cnnectins S= Skills; A= Awareness; L= Literacy; T= Traits S Critical Thinking & Prblem Slving, Creativity & Innvatin, Cmmunicatin & Cllabratin, Cre Ethical Values A L T Glbal, Crss Cultural, Career Cntent, Financial, Civic, Health, Infrmatin, Technlgy, Media Initiative, Prductivity, Accuntability, Self Directin, Humr, Resilience, Perseverance, Respnding with wnderment and awe, Kindness, Respect, Service t Others, Respnsible risktaking, Manners, Respnsibility, Empathy Standards: The curriculum is written in the Understanding by Design frmat and is based n enduring understandings, essential questins and bth frmative and summative assessments. The math standards are brken int tw categries: Cntent and Prcess. Cntent Standards indicate what we want students t knw: EXPRESSIONS AND EQUATIONS 6.EE.1 write and evaluate numerical expressins invlving whle-number peratins, pwers, expnents and rder f peratins 6.EE.2 write expressins and identify parts f an expressin using mathematical terms

14 6.EE.3 6.EE.4 6.EE.5 apply prperties f peratins t general equivalent expressins identify when tw expressins are equivalent understand slving an equatin r inequality and use substitutin THE NUMBER SYSTEM 6.NS.1 interpret and cmpute prducts and qutients f fractins and mixed numbers and slve wrd prblems 6.NS.2 fluently divide multi-digit numbers using the standard algrithm 6.NS.3 fluently add, subtract, multiply and divide multi-digit decimals using standard algrithm 6.NS.4 greatest cmmn factr, least cmmn multiple and distribute prperty, prime factrizatin, adding and subtracting fractins and factring expressins 6.NS.5 understand psitive and negative numbers as having ppsite directins r values, and the meaning f 0 using integers, decimals and fractins 6.NS.6 ratinal numbers as a pint n a number line and in a plane line with negative crdinates a) recgnize ppsite signs f numbers as lcatins and relatin t 0 using integers, fractins and decimals b) rdered pairs in quadrants and reflectins in the crdinate plane c) find and psitin integers and ratinal numbers n a vertical and hrizntal number line and pairs f integers n the crdinate plane 6.NS.7 understand rdering and abslute value f ratinal numbers a) interpret statements f inequality b) write, interpret and explain statements f rder c) abslute value f ratinal numbers; interpret abslute value d) cmparisns f abslute value 6.NS.8 slve real wrld and mathematical prblems by graphing pint in all fur quadrants and find distance between pints RATIOS & PROPORTIONAL RELATIONSHIPS 6.RP.1 rati and rati language 6.RP.2 rate, unit rate and ratis 6.RP.3 rati and rate reasning a) tables r equivalent ratis, find missing values and plt values, tables t cmpare ratis b) unit rate invlving unit pricing and cnstant speed c) percent f a quantity, slve finding the whle, part and percent d) rati reasning t cnvert measurements units GEOMETRY 6.G.1 area f triangles, special quadrilaterals and plygns by cmpsing and decmpsing int ther shapes 6.G.2 vlume f right rectangular prism with fractinal edge lengths and packing with unit cubes 6.G.3 draw plygns in crdinate plane, use crdinates t find length 6.G.4 #-D figures using nets f rectangles and triangles, use nets t find surface area STATISTICS & PROBABILITY 6.SP.1 statistical questins 6.SP.2 distributin f data: center, spread and verall shape 6.SP.3 measures f center vs. measures f variatin 6.SP.4. dt plts, histgrams and bx and whisker plts 6.SP.5 summarize numerical data sets a) reprt number f bservatins and describe measurement and units f measurement

15 b) describe patterns using measures f center and variability: mean, median, interquartile range and mean abslute deviatin c) relate measures f center and variability t shape f data TECHNOLOGY A.5 Determine the benefits f a wide range f digital tls by using them t slve prblems A.5 Select and use apprpriate tls and digital resurces t accmplish a variety f tasks and t slve prblems. 21 st CENTURY THEMES A Critical thinking and prblem slving B Creativity and innvatin C Cllabratin, teamwrk and leadership D Crss-cultural understanding and interpersnal cmmunicatin E Cmmunicatin and Media Fluency F Accuntability, Prductivity and Ethics A Career awareness Prcess Standards indicate hw we want students t learn: Mathematical Practice: 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. A cmplete cpy f the standards fr 7 th GRADE may als be fund at: Cmmn Cre State Standards Initiative (CCSSI) Overview f Tpics fr Grade Six Ratis and Prprtinal Relatinships Understand rati cncepts and use rati reasning t slve prblems. The Number System Apply and extend previus understandings f multiplicatin and divisin t divide fractins by fractins. Multiply and divide multi-digit numbers and find cmmn factrs and multiples. Apply and extend previus understandings f numbers t the system f ratinal numbers. Expressins and Equatins Apply and extend previus understandings f arithmetic t algebraic expressins. Reasn abut and slve ne-variable equatins and inequalities. Represent and analyze quantitative relatinships between dependent and independent variables. Gemetry Slve real-wrld and mathematical prblems invlving area, surface area, and vlume. Statistics and Prbability Develp understanding f statistical variability. Summarize and describe distributins.

16 Enduring Understandings: Thrugh prblem slving, students experience the usefulness f mathematics in the real wrld. Number System Apply and extend previus understandings f multiplicatin and divisin t divide fractins by fractins. Cmpute fluently with multi-digit numbers and find cmmn factrs and multiples. Apply and extend previus understanding f numbers t the system f ratinal numbers. Expressins and Equatins Apply and extend previus understandings f arithmetic t algebraic expressins. Reasn abut and slve ne-variable equatins and inequalities. Represent and analyze quantitative relatinships between dependent and independent variables. Ratis and Prprtins Understand rati cncepts and use rati reasning t slve prblems. Statistics and Prbability Develp understanding f statistical variability. Summarize and describe distributins. Gemetry Slve real-wrld and mathematical prblems invlving area, surface area and vlume. Essential Questins: Number System Hw d yu knw which peratin t chse when slving a real-life prblem? Hw can yu use repeated factrs in re-life prblems? What is the effect f inserting parentheses int a numerical expressin? Withut dividing, hw can yu tell when a number is divisible by anther number? Hw can yu find the greatest cmmn factr f tw numbers? Hw can yu find the least cmmn multiple f tw numbers? What des it mean t multiply fractins? Hw can yu divide by a fractin? Hw can yu mdel divisin by a mixed number? Hw can yu add and subtract decimals? Hw can yu multiply decimals? Hw can yu base-ten blcks t mdel decimal divisin? Hw d yu mental math t multiply tw numbers? Hw can yu represent numbers that are less than zer? Hw can yu use a number line t rder real-life events? Hw can yu use a number line t cmpare psitive fractins and decimals? Hw can yu describe hw far an bject is frm zer? Hw can yu graph and lcate pints that cntain negative numbers in a crdinate plane? Expressins and Equatins Hw can yu write and evaluate an expressin that represents a real-life prblem? Hw can yu write an expressin that represents an unknwn quantity? Des the rder in which yu perfrm an peratin matter?

17 Hw des rewriting a wrd prblem help yu slve a wrd prblem? Hw can yu use additin, subtractin, multiplicatin r divisin t slve an equatin? Hw can yu write an equatin in tw variables? Hw can yu use a number line t represent slutins f an inequality? Hw can yu use additin, subtractin, multiplicatin and divisin t slve an inequality? Ratis and Prprtins Hw can yu represent a relatinship between tw quantities? Hw can yu find tw ratis that describe the same relatinship? Hw can yu use rates t describe changes in real-life prblems? Hw can yu cmpare tw ratis? What is the cnnectin between ratis, fractins and percents? Hw can yu use mental math t find the percent f a number? Statistics and Prbability Hw can yu tell whether a questin is a statistical questin? Hw can yu find an average value f a data set? In what ther ways can yu describe an average f a data set? Hw can yu describe the spread f a data set? Hw can yu use the distances between each data value and the mean f a data set t measure the spread f a data set? Hw can yu use place values t represent data graphically? Hw can yu use intervals, tables and graphs t analyze data? Hw can yu describe the shape f the distributin f a data set? Hw can yu use the quartiles t represent data graphically? Gemetry Hw can yu derive the frmula fr area f a triangle, trapezid and parallelgram? Hw can yu find the lengths f line segments in a crdinate plane? Hw can yu draw 3-D figures? Hw can yu find the area f the entire surface f a prism? Hw can yu use a net t find the surface area f a pyramid? Hw can yu find the vlume f a rectangular prism with fractinal edge lengths? Unit Objectives Number System Students will be divide tw fractins and understand relatinship between multiplicatin and divisin. Students will be able t divide multi-digit numbers using standard algrithm Students will use knwledge f whle number peratins t perfrm the same peratins with decimals. Students will determine factrs and multiples f numbers t determine greatest cmmn factr and least cmmn multiple and slve real-wrld prblems. Students will represent psitive and negative numbers n a number line and use t describe situatins in the real wrld. Students will learn numbers with ppsites, lcatin n a number line and relatinship t zer.

18 Students will learn t graph psitive and negative numbers in the crdinate place and identify quadrants. Students will use the number line t rder sets f psitive and negative numbers and graph rdered pairs in all quadrants and slve real-wrld prblems. Students will learn statements f inequalities. Students will use knwledge f ratinal numbers t describe real-wrld situatins. Students will apply abslute value t real situatins. Expressins and Equatins Students will expnents t shw repeated multiplicatin Students will write algebraic expressins, describe expressins and their parts, and identify variables. Students will learn rder f peratins. Students will write and identify equivalent expressins in real-wrld mathematical prblems. Students will learn t use substitutin whether a number is a slutin f an equatin f inequality. Students will write expressins t represent real-wrld r mathematical prblems. Students will use yur knwledge f peratins t slve equatins. Students will understand that an inequality has many slutins and graph them n a number line. Students will write equatins and analyze relatinships between tw variables. Ratis and Prprtins Students will be able t write ratis fr varius situatins Students will be able t determine if ratis are equivalent as well hw t determine and unknwn in an equivalent rati Students will be able t write and calculate unit rates t slve wrd prblems Students will use prprtins t slve prblems Students will use prprtins t determine the relatinship in a table and graph, determine the cnstant f prprtinality, write equatins and understand graphs r prprtins Students will use prprtins t slve prblems invlving scale drawings and similar figures. Students will be able t relate fractins, decimals, and percents t each ther. Students will slve three different types f percent prblems. Students will represent percent equatins in an algebraic cntext. Students will use their knwledge f percents t help them slve real wrld prblems. Statistics and Prbability Students will identify statistical and nn-statistical questins. Students will display data in histgrams, dt plts, bx plts and calculate the mean, median, interquartile range and mean abslute deviatin in a data set. Students will cunt the number f values in a data set identify the type f data and its unit f measurement. Students will cmpare mean and median and use t describe a value f a data set. Gemetry Students will find the areas f triangle, special quadrilaterals, and plygns t slve bth real-wrld and mathematical prblems.

19 Students will graph plygns in the crdinate plane and find the length f a side Students will find the vlume f right rectangular prisms with fractinal edge lengths. Students will use nets t find surface area f 3-D figures. Terminlgy: Abslute value, algebraic expressin, base, bx and whisker plt, cefficient, cmmn multiples, cmpsite figure, cnstant, cnversin factr, crdinate plane, dependent variable, edge, equatin, equatin in tw variables, equivalent expressins, equivalent rates, equivalent ratis, evaluate, expnent, face, factr pair, factr tree, factring and expressins, first quartile. Five-number summary, frequency, frequency table, graph f an inequality, GCF, LCM, histgram, independent variable, inequality, integers, interquartile range, inverse peratins, leaf, LCD, like terms, mean, MAD, measure f center and variatin, median, mde, negative and psitive numbers, net, numerical expressin, ppsites, rder f peratins, rigin, utlier, percent, perfect square, plygn, plyhedrn, pwer, prime factrizatin, prism, pyramid, quadrants, quartiles, range, rate, rati, rati tables, reciprcals, slid, slutin, slutin f an equatin in tw variables, slutin f an inequality, slutin set, statistical questin, statistics, stem stem-and-leaf plt, surface area, terms, third quartile, unit analysis, unit rate, variable, vertex vlume Frmative Assessments Onging and thrughut unit f study; assessments may include: Infrmal assessments Teacher-based assessments Specific interim assessments; frmats may vary: Pre-test Benchmark Assessment Pst-test Benchmark Assessment Curse Resurces: Technlgies: COWS, Chrmebks, SMART Bards, Ntebk sftware, CCSS website, PwerSchl Text: Larsn & Bswell, Big Ideas Math Green Hughtn Mifflin Harcurt, On Cre Mathematics, Grade 6 Other: Study Island, Teacher made/wrkbk resurces

20 CURRICULUM OVERVIEW: TRANSITIONS MATH Cntent Area: Mathematics Curse Title: Transitins Curse Descriptin: Accelerated 6 th grade Mathematics Curse Ratinale: This prgram is an accelerated 6 th grade curse ffered thrugh bth a cnceptual and skill-based apprach. It als addresses the Cmmn Cre Standards and math practices. Technlgy is embedded where meaningful and crss-curricular cnnectins are purpsely and explicitly nted. Primary Interdisciplinary Cnnectins: Language Arts, Science, Scial Studies, Physical Educatin, Art, Astrnmy, Architecture and Technlgy. 21 st Century Cnnectins S= Skills; A= Awareness; L= Literacy; T= Traits S Critical Thinking & Prblem Slving, Creativity & Innvatin, Cmmunicatin & Cllabratin, Cre Ethical Values A L Glbal, Crss Cultural, Career Cntent, Financial, Civic, Health, Infrmatin, Technlgy, Media T Initiative, Prductivity, Accuntability, Self Directin, Humr, Resilience, Perseverance, Respnding with wnderment and awe, Kindness, Respect, Service t Others, Respnsible risk-taking, Manners, Respnsibility, Empathy Standards: The curriculum is written in the Understanding by Design frmat and is based n enduring understandings and brad cncepts, essential questins, and bth frmative and summative assessments. The math standards are brken int tw categries: Cntent and Prcess. Cntent Standards indicate what we want students t knw: EXPRESSIONS AND EQUATIONS 6.EE.1 - write and evaluate numerical expressins invlving whle-number peratins, pwers, expnents and rder f peratins 6.EE.2 - write expressins and identify parts f an expressin using mathematical terms 6.EE.3 apply prperties f peratins t general equivalent expressins 6.EE.4 identify when tw expressins are equivalent

21 6.EE.5 understand slving an equatin r inequality and use substitutin 7.EE.1 - add, subtract, factr, and expand linear expressins with ratinal cefficients 7.EE.2 - expressins in different frms 7.EE.3 - multi-step psitive and negative ratinal numbers in any frm and apply prperties f peratins. 7.EE.4 variables, cnstructing simple equatins and inequalities THE NUMBER SYSTEM 6.NS.4 distributive prperty and factring expressins 6.NS.5 understand psitive and negative numbers as having ppsite directins r values, and the meaning f 0 using integers, decimals and fractins 6.NS.6 ratinal numbers as a pint n a number line and in a plane line with negative crdinates a) Recgnize ppsite signs f numbers as lcatins and relatin t 0 using integers, fractins and decimals b) rdered pairs in quadrants and reflectins in the crdinate plane c) find and psitin integers and ratinal numbers n a vertical and hrizntal number line and pairs f integers n the crdinate plane 6.NS.7 understand rdering and abslute value f ratinal numbers a) interpret statements f inequality b) write, interpret and explain statements f rder c) abslute value f ratinal numbers; interpret abslute value d) cmparisns f abslute value 6.NS.8 slve real wrd and mathematical prblems by graphing pint in all fur quadrants and find distance between pints 7.NS.1 - add and subtract ratinal numbers; represent n a hrizntal r vertical number line diagram. a) ppsite quantities cmbine t make 0 b) abslute value f integers and additive inverse prperty c) subtractin f ratinal numbers and shw n number line d) prperties f peratins as strategies t add and subtract ratinal numbers 7.NS.2 - multiplicatin and divisin f fractins t multiply and divide ratinal numbers a) multiplicatin f integers b) divisin f integers c) multiply and divide ratinal numbers d) lng divisin resulting in terminating and repeating decimals 7.NS.3 - real-wrld prblems using fur peratins with ratinal numbers RATIOS & PROPORTIONAL RELATIONSHIPS 6.RP.1- rati and rati language 6.RP.2 - rate, unit rate and ratis 6.RP.3 rati and rate reasning a) tables r equivalent ratis, find missing values and plt values, tables t cmpare ratis b) unit rate invlving unit pricing and cnstant speed c) percent f a quantity, slve finding the whle, part and percent d) rati reasning t cnvert measurements units 7.RP.1- unit rates and ratis measured in like r different units 7.RP.2 - prprtinal relatinships between quantities. a) prprtinal relatinships b) cnstant f prprtinality (unit rate) c) prprtinal relatinships by equatins. 7.RP.3 - prprtinal relatinships t slve multistep rati and percent prblems

22 GEOMETRY 6.G.1 Area f triangles, special quadrilaterals and plygns by cmpsing and decmpsing. 6.G.2 Vlume f right rectangular prism with fractinal edge lengths. 6.G.3 draw plygns in crdinate plane, use crdinates t find length 7.G.6 - area, vlume and surface area f tw- and three-dimensinal bjects cmpsed f triangles, quadrilaterals, plygns, cubes, and right prisms STATISTICS & PROBABILITY 6.SP.1 statistical questins 6.SP.2 distributin f data: center, spread and verall shape 6.SP.3 measures f center vs. measures f variatin 6.SP.4. dt plts, histgrams and bx and whisker plts 6.SP.5 summarize numerical data sets a) reprt number f bservatins b) describe attributes: measurement and units f measurement c) describe patterns using measures f center and variability: mean, median, interquartile range and mean abslute deviatin d) relate measures f center and variability t shape f data TECHNOLOGY A.5 Determine the benefits f a wide range f digital tls by using them t slve prblems A.5 Select and use apprpriate tls and digital resurces t accmplish a variety f tasks and t slve prblems. 21 st CENTURY THEMES A Critical thinking and prblem slving B Creativity and innvatin C Cllabratin, teamwrk and leadership D Crss-cultural understanding and interpersnal cmmunicatin E Cmmunicatin and Media Fluency F Accuntability, Prductivity and Ethics A Career awareness Prcess Standards indicate hw we want students t learn: Mathematical Practice: 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. A cmplete cpy f the standards fr 6 th /7th GRADE may als be fund at: Cmmn Cre State Standards Initiative (CCSSI) Enduring Understandings: Number System

23 Apply and extend previus understandings f multiplicatin and divisin t divide fractins by fractins. Cmpute fluently with multi-digit numbers and find cmmn factrs and multiples. Apply and extend previus understanding f numbers t the system f ratinal numbers. Previus understanding f number and the rdering f numbers t the full systems f ratinal number peratins f numbers can be directly applied t ratinal numbers. Ratinal numbers can be used t slve real wrld prblems. Expressins and Equatins Apply and extend previus understandings f arithmetic t algebraic expressins. Reasn abut and slve ne-variable equatins and inequalities. Represent and analyze quantitative relatinships between dependent and independent variables. Smetimes there is mre than ne step t slve an equatin. Inequalities are used when slving real life applicatin prblems. Equatins can be slved using different prperties. Ratis and Prprtins Apply and understand ratis, rates, and unit rates when slving real life prblems. Understand rati cncepts and use rati reasning t slve prblems. Utilize prprtinal relatinships t slve real wrld prblems Percents are used in real wrld prblems Percents can be applied t prblems in different ways Statistics and Prbability Statistical measures f center and measures f variatin are used t help slve real wrld prblems. Understand that data can be used t use statistical questins. Gemetry Slve real-wrld and mathematical prblems invlving area, surface area and vlume. Frmulas can be determined and used t calculate the area f bth regular and irregular shapes 3D figures have unique characteristics and prperties Perimeter and area f 2D figures are useful when finding vlume and surface area f 3D figures. Essential Questins: Number System Hw d peratins affect ratinal numbers? Hw can we use ratinal numbers t slve real wrld applicatin prblems? Hw can yu represent numbers that are less than zer? Hw can yu use a number line t rder real-life events? Hw can yu use a number line t cmpare psitive fractins and decimals? Hw can yu describe hw far an bject is frm zer? Hw can yu graph and lcate pints that cntain negative numbers in a crdinate plane? Expressins and Equatins

24 Hw can yu write and evaluate an expressin that represents a real-life prblem? Hw can yu write and expressin that represents an unknwn quantity? Des the rder in which yu perfrm an peratin matter? Hw des rewriting a wrd prblem help yu slve a wrd prblem? Hw can yu use additin, subtractin, multiplicatin r divisin t slve an equatin? Hw can yu write and equatin in tw variables? Hw can yu use a number line t represent slutins f an inequality? Hw can yu use additin, subtractin, multiplicatin and divisin t slve an inequality? Hw are equatins slved? What are different prperties f equatins and hw can they help slve them? What happens when tw sides f an equatin are nt equal? Ratis and Prprtins Hw can yu represent a relatinship between tw quantities? Hw can yu find tw ratis that describe the same relatinship? Hw can yu use rates t describe changes in real-life prblems? Hw can yu cmpare tw ratis? What is the cnnectin between ratis, fractins and percents? Hw can yu use mental math t find the percent f a number? Hw can yu cmpare lengths between custmary metric systems? Hw can yu rder numbers that can be written as fractins, decimals, and percents? Hw d yu recgnize and represent prprtinal relatinships between quantities? Hw d yu apply prprtins? What is percent f increase and decrease? Hw d yu find discunts, selling prices, and interest? Hw are percents used t help slve real wrld prblems? What are the different ways percent prblems are represented? Statistics and Prbability Hw can yu tell whether a questin is a statistical questin? Hw can yu find an average value f a data set? In what ther ways can yu describe an average f a data set? Hw can yu describe the spread f a data set? Hw can yu use the distances between each data value and the mean f a data set t measure the spread f a data set? Gemetry Hw can yu derive the frmula fr area f a triangle, trapezid and parallelgram? Hw can yu find the lengths f line segments in a crdinate plane? Hw can yu draw 3-D figures? Hw can yu find the area f the entire surface f a prism? Hw can yu use a net t find the surface area f a pyramid? Hw can yu find the vlume f a rectangular prism with fractinal edge lengths? Unit Objectives Number System Students will be applying their prir knwledge f the number system t prblems invlving ratinal numbers. Students will be able t add, subtract, multiply and divide ratinal numbers.

25 Students will transfrm ratinal numbers int decimals. Students will slve real wrld prblems using ratinal numbers. Expressins and Equatins Students will examine cmmutative and assciative prperties f different equatins. Students will cmbine like terms within an equatin and learn t use the distributive prperty t slve equatins. Students will slve multi-step equatins invlving different techniques Students will graph and slve inequalities invlving additin, subtractin, multiplicatin, and divisin. Ratis and Prprtins Students will be able t write ratis fr varius situatins. Students will be able t determine if ratis are equivalent as well hw t determine and unknwn in an equivalent rati. Students will be able t calculate unit rates t slve wrd prblems. Students will use prprtins t slve prblems. Students will use prprtins t determine the relatinship in a table and graph, determine the cnstant f prprtinality, write equatins and understand graphs r prprtins. Students will be able t relate fractins, decimals, and percents t each ther. Students will slve three different types f percent prblems. Students will represent percent equatins in an algebraic cntext. Students will apply percent f increase and percent f decrease when slving prblems. Students will use their knwledge f percents t help them slve real wrld prblems. Statistics and Prbability Students will identify statistical and nn-statistical questins. Students will display data in histgrams, dt plts, bx plts and calculate the mean, median, interquartile range and mean abslute deviatin in a data set. Students will cunt the number f values in a data set identify the type f data and its unit f measurement. Students will cmpare mean and median and use t describe a value f a data set. Gemetry Students will calculate the perimeter f different 2D gemetrical figures. Students will calculate the area f rectangles, parallelgrams, triangles and trapezids. Students will use previus knwledge f area frmulas t calculate the area f irregular and shaded figures. Students will learn hw t cmpute the vlume f different 3D figures. Students will cmpute surface area f different 3D figures. Terminlgy: simplify, cnjecture, evaluate, slve, equivalent, numerical expressin, variable expressin, evaluate, pwers, expnent, perfect square, base, rder f peratins, integers, abslute value, crdinate plane, quadrants, rdered pair, rigin, like terms, variable, cefficients, cnstants, equatins, inverse peratins, slutin, equatins, linear, inequality, slutin set, independent, dependent, prime number, cmpsite number, prime factrizatin, equivalent fractins, cmplex fractins, reciprcals, simplest frm, ratinal number, real numbers, multiplicative inverse, rati, rate, unit rate, prprtin, crss

26 prduct, prprtinal relatinship, similar figures, cngruent figures, scale drawings, scale mdels, percent, percent f change, markup, discunt, interest, simple interest, cmpund interest, relatin, dmain, mean, median, mde, range, input, utput, cnversin factr, MAD, quartile, frequency table, bx and whisker plts, stem-and-leaf plt, histgram, plygn, cmpsite figure, prism, pyramid, net, edge, surface area, vertex vlume Assessments Frmative: Summative: Onging and thrughut unit f study; assessments may include- Infrmal assessments Teacher-based assessments Specific interim assessments; frmats may vary- Pre-test Benchmark Assessment Pst-test Benchmark Assessment Curse Resurces: Technlgies: COWS, Chrme Bks SMART Bards, Ntebk sftware, CCSS website, Pwer Schl Text: Big Ideas Math Advanced 1 Big Ideas Math Red (Supplementary) OnCre Mathematics Middle Schl 6 and 7 Hughtn Mifflin Harcurt Other: Study Island, Teacher made/wrkbk resurces

27 CURRICULUM OVERVIEW: PRE ALGEBRA Cntent Area: Mathematics Curse Title: Pre-Algebra Curse Descriptin r Cntent Overview: Pre-Algebra which cvers 7 th and 8 th grade math standards. Curse Ratinale: This prgram is an 8th grade, n-level curse, and 7 th grade accelerated curse, ffered thrugh bth a cnceptual and skill-based apprach. It als addresses the Natinal Cuncil f Teacher f Mathematics (NCTM) standards and is funded n the Twelve Effective Instructinal Practices f the Suth Brunswick Schl District. Technlgy is embedded where meaningful and crss-curricular cnnectins are purpsely and explicitly nted. Primary Interdisciplinary Cnnectins: Language Arts, Science, Scial Studies, Physical Educatin, Art, Astrnmy, Architecture and Technlgy. 21 st Century Cnnectins S= Skills; A= Awareness; L= Literacy; T= Traits S Critical Thinking & Prblem Slving, Creativity & Innvatin, Cmmunicatin & Cllabratin, Cre Ethical Values A L T Glbal, Crss Cultural, Career Cntent, Financial, Civic, Health, Infrmatin, Technlgy, Media Initiative, Prductivity, Accuntability, Self Directin, Humr, Resilience, Perseverance, Respnding with wnderment and awe, Kindness, Respect, Service t Others, Respnsible risk-taking, Manners, Respnsibility, Empathy Standards: The curriculum is written in the Understanding by Design frmat and is based n enduring understandings, essential questins and bth frmative and summative assessments. The math standards are brken int tw categries: Cntent and Prcess. Cntent Standards n what we want students t knw: EXPRESSIONS AND EQUATIONS 7.EE.1 add, subtract, factr, and expand linear expressins with ratinal cefficients 7.EE.2 expressins in different frms 7.EE.3 multi-step psitive and negative ratinal numbers in any frm and apply prperties f peratins. 7.EE.4 variables, cnstructing simple equatins and inequalities

28 8.EE.1 prperties f integer expnents, generating equivalent numerical expressins 8.EE.2 square and cube rt symbls represent slutins t equatins, evaluate square rts f small perfect squares and cube rts f small perfect cubes. 8.EE.3 pwers f 10, estimating very large r small quantities 8.EE.4 peratins with numbers expressed in scientific ntatin. Use scientific ntatin and chse units f apprpriate size measurement 8.EE.5 graph prprtinal relatinships, interpret unit rate as slpe, cmpare prprtinal relatinships. 8.EE.6 using similar triangles t explain why slpe is the same between any tw pints, derive equatin f a line 8.EE.7 slve linear equatins in ne variable a. give examples f linear equatins with a different number f slutins, shw which number f slutins is true in each case b. slve linear equatins with ratinal number cefficients, cmbining like terms, distributive prperty THE NUMBER SYSTEM 7.NS.1 add and subtract ratinal numbers; represent n a hrizntal r vertical number line diagram. a) ppsite quantities cmbine t make 0 b) abslute value f integers and additive inverse prperty c) subtractin f ratinal numbers and shw n number line d) prperties f peratins as strategies t add and subtract ratinal numbers 7.NS.2 multiplicatin and divisin f fractins t multiply and divide ratinal numbers a) multiplicatin f integers b) divisin f integers c) multiply and divide ratinal numbers d) lng divisin resulting in terminating and repeating decimals 7.NS.3 real-wrld prblems using fur peratins with ratinal numbers 8. NS.1 decimal expansin, difference between ratinal and irratinal numbers 8.NS.2 ratinal numbers apprximate irratinal t cmpare size and find n number line. RATIOS & PROPORTIONAL RELATIONSHIPS 7.RP.1 unit rates and ratis measured in like r different units 7.RP.2 prprtinal relatinships between quantities. a) prprtinal relatinships b) cnstant f prprtinality (unit rate) c) prprtinal relatinships by equatins. 7.RP.3 prprtinal relatinships t slve multi-step rati and percent prblems GEOMETRY 7.G.1 scale drawings f gemetric figures. 7.G.2 gemetric shapes with given cnditins: triangle fcus. 7.G.3 tw-dimensinal figures resulting frm three-dimensinal figures: rectangular prisms and right rectangular pyramids 7.G.4 frmulas fr the area and circumference f a circle 7.G.5 - supplementary, cmplementary, vertical, and adjacent angles in a multi-step prblem t write and slve simple equatins fr an unknwn angle in a figure 7.G.6 area, vlume and surface area f tw- and three-dimensinal bjects cmpsed f triangles, quadrilaterals, plygns, cubes, and right prisms 8.G.1 rtatin, reflectin and translatin

29 8.G.2 8.G.3 8.G.4 8.G.5 8.G.6 8.G.7 8.G.9 cngruence f tw-dimensinal figures with transfrmatins, describing transfrmatins describe effect f transfrmatin n a figure using crdinates similarity f tw-dimensinal figures after transfrmatin(s) dne t the first, describe sequence that exhibits similarity between them parallel lines cut by transversal, angle sum and exterir angles, angle-angle criterin fr similar triangles. explain Pythagrean Therem and its cnverse apply the Pythagrean Therem t determine unknwn sides knw the frmulas fr vlumes f cnes, cylinders and spheres and use them t slve prblems STATISTICS & PROBABILITY 7.SP.1 statistics, sample ppulatins and randm sampling 7.SP.2 randm sampling and ppulatin, and infrmal cmparative ppulatin inferences 7.SP.3 degree f visual verlap f tw numerical data distributins and measure f variability 7.SP.4. measures f center and measures f variability frm randm samples and prbability mdel 7.SP.5 chance events and likelihd f events 7.SP.6 prbability f a chance events and lng-run relative frequency 7.SP.7 prbability mdels a) unifrm prbability mdel with equal prbability b) prbability mdel (which may nt be unifrm) 7.SP.8 prbabilities f cmpund events a) prbability f a cmpund event is the fractin f utcmes b) represent sample spaces fr cmpund events c) simulatins t generate frequencies fr cmpund events 8.SP.1 cnstruct and interpret scatter plts, describe patterns and analyze data 8.SP.4 lk fr patterns, cmpare categrical data and their displays, relative frequencies FUNCTIONS 8.F.1 each input has exactly ne utput, graph f a functin is a set f rdered pairs with an input and crrespnding utput. 8.F.2 cmpare prperties f tw functins represented in different ways 8.F.3 Interpret the equatin f a line as defining a linear functin whse graph is a straight line TECHNOLOGY A.5 Determine the benefits f a wide range f digital tls by using them t slve prblems A.5 Select and use apprpriate tls and digital resurces t accmplish a variety f tasks and t slve prblems. 21 st CENTURY THEMES A Critical thinking and prblem slving B Creativity and innvatin C Cllabratin, teamwrk and leadership D Crss-cultural understanding and interpersnal cmmunicatin E Cmmunicatin and Media Fluency F Accuntability, Prductivity and Ethics A Career awareness Prcess Standards n hw we want students t learn.

30 Mathematical Practice: 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. A cmplete cpy f the standards fr 7 th and 8 th GRADE may als be fund at: Cmmn Cre State Standards Initiative (CCSSI) Enduring Understandings: Number System Previus understanding f peratins f numbers can be directly applied t ratinal numbers Ratinal numbers can be used t slve real wrld prblems Expressins and Equatins Equatins can be slved using different prperties Smetimes there is mre than ne step t slve in an equatin Inequalities are used when slving fr real life applicatin prblems Ratis and Prprtins Utilize prprtinal relatinships t slve real wrld prblems Percents are used in real wrld prblems Percents can be applied t prblems in different ways Statistics and Prbability Events are classified int different types. This determines the rute t slving the prblem Prbability, measures f center, and measures f variatin all are used t help slve real wrld applicatin prblems Gemetry Frmulas can be determined and used t calculate the area f bth regular and irregular shapes 3D figures have unique characteristics and prperties Perimeter and area f 2D figures are useful when finding vlume and surface area f 3D figures Essential Questins: Number System Hw d peratins affect ratinal numbers? Hw can we use ratinal numbers t slve real wrld applicatin prblems? Expressins and Equatins Hw are equatins slved? What are different prperties f equatins and hw can they help slve them? What happens when tw sides f an equatin are nt equal? Ratis and Prprtins Hw d yu recgnize and represent prprtinal relatinships between quantities? Hw d yu apply prprtins?

31 Hw are percents used t help slve real wrld prblems? What are the different ways percent prblems are represented? Statistics and Prbability Hw des prbability relate t real wrld applicatin prblems? Hw can measures f center and variatin be used t cmpare tw sets f data? Hw are different events classified and what can I use t slve them? Gemetry Can we determine if three side lengths wuld create a triangle? What is the difference between area and perimeter? Hw are 3D figures different frm 2D figures? What is a crss sectin f a figure and hw will that help cmpute prperties f the figure? Hw are surface area and vlume fund fr a 3D figure? Unit Objectives Number System Students will be applying their prir knwledge f the number system t prblems invlving ratinal numbers. Students will be able t add, subtract, multiply and divide ratinal numbers Students will transfrm ratinal numbers int decimals Students will slve real wrld prblems using ratinal numbers Expressins and Equatins Students will examine cmmutative and assciative prperties f different equatins Students will cmbine like terms within an equatin and learn t use the distributive prperty t slve equatins Students will slve multi-step equatins invlving different techniques Students will graph and slve inequalities invlving additin, subtractin, multiplicatin, and divisin Ratis and Prprtins Students will be able t write ratis fr varius situatins Students will be able t determine if ratis are equivalent as well hw t determine and unknwn in an equivalent rati Students will be able t calculate unit rates t slve wrd prblems Students will use prprtins t slve prblems Students will use prprtins t determine the relatinship in a table and graph, determine the cnstant f prprtinality, write equatins and understand graphs r prprtins Students will use prprtins t slve prblems invlving scale drawings and similar figures Students will be able t relate fractins, decimals, and percents t each ther Students will slve three different types f percent prblems Students will represent percent equatins in an algebraic cntext Students will apply percent f increase and percent f decrease when slving prblems Students will use their knwledge f percents t help them slve real wrld prblems Statistics and Prbability Students will be intrduced t the cncept f sampling Students will be able t draw inferences abut a ppulatin based ff a sample Students will be able t cmpare tw ppulatins and slve real wrld applicatin prblems with them

32 Students will be able t measure the difference between the centers by expressing it as a multiple f a measure f variability Students will understand that the prbability f a chance event is a number between 0 and 1 that expresses the likelihd f the event ccurring Students will be able t use experimental and theretical prbability t determine the likelihd f an event ccurring Students will use the fundamental cunting principle t slve prblems Find prbabilities f cmpund events using rganized lists, tables, tree diagrams, and simulatin Gemetry Students will calculate the perimeter f different 2D gemetrical figures Students will calculate the circumference and area f different circles Students will be able t determine whether a triangle is pssible r nt Students will discver special pairs f triangles and the relatinships they yield Students will calculate the area f rectangles, parallelgrams, triangles and trapezids Students will use previus knwledge f area frmulas t calculate the area f irregular and shaded figures Students will be intrduced t 3D slids and crss sectins f 3D figures Students will learn hw t cmpute the vlume f different 3D figures Students will cmpute surface area f different 3D figures Terminlgy: Numerical expressin, variable, variable expressin, evaluate, pwers, expnent, base, rder f peratins, integers, abslute value, crdinate plane, rdered pair, like terms, equatins, inverse peratins, equatins, linear inequality, prime number, cmpsite number, prime factrizatin, equivalent fractins, simplest frm, ratinal number, multiplicative inverse, rati, rate, unit rate, prprtin, crss prduct, prprtin, similar figures, cngruent figures, scale drawings, scale mdels, utcmes, event, prbability, dds in favr, dds against, theretical prbability experimental prbability, cunting principles, percent, percent f change, markup, discunt, interest, simple interest, cmpund interest, relatin, dmain, range, input, utput, linear, square rt, perfect square, Pythagrean Therem, plygn, regular, slant height, lateral area, net, surface area, cmbinatin, permutatin, n factrial, disjint, cmplementary, independent, dependent, transversal, angles Assessments Onging and thrughut unit f study; assessments may include: Infrmal assessments Teacher-based assessments Suggested assessments Specific interim assessments; frmats may vary. Standardized End f Unit Assessments Standardized Mid Term Assessments Curse Resurces: Technlgies: Text: Other: COWS, Chrme Bks SMART Bards, Ntebk sftware, NJCTL website, Pwer Schl McDugal Littell Pre-Algebra Big Ideas Math Red (Supplementary) Study Island, Teacher made/wrkbk resurces

33 CURRICULUM OVERVIEW: CONCEPTS OF ALGEBRA Cntent Area: Mathematics Curse Title: Cncepts f Algebra Curse Descriptin r Cntent Overview: Cncepts f Algebra Curse which cvers 8 th grade math standards. Curse Ratinale: This prgram is an 8 th grade n level curse, and a 7 th grade accelerated curse, ffered thrugh bth a cnceptual and skill-based apprach. The fundatin f the prgram is the Cmmn Cre Standards fr Mathematical Cntent and Standards fr Mathematical Practice. The apprach encurages abstract thught, reasning, and inquiry as students persevere t answer Essential Questins. Primary Interdisciplinary Cnnectins: Language Arts, Science, Scial Studies, Physical Educatin, Art, Astrnmy, Architecture and Technlgy. 21 st Century Cnnectins S= Skills; A= Awareness; L= Literacy; T= Traits S Critical Thinking & Prblem Slving, Creativity & Innvatin, Cmmunicatin & Cllabratin, Cre Ethical Values A L T Glbal, Crss Cultural, Career Cntent, Financial, Civic, Health, Infrmatin, Technlgy, Media Initiative, Prductivity, Accuntability, Self Directin, Humr, Resilience, Perseverance, Respnding with wnderment and awe, Kindness, Respect, Service t Others, Respnsible risk-taking, Manners, Respnsibility, Empathy Standards: The curriculum is written in the Understanding by Design frmat and is based n enduring understandings, essential questins and bth frmative and summative assessments. The math standards are brken int tw categries: Cntent and Prcess. Cntent Standards n what we want students t knw: THE NUMBER SYSTEM 8.NS.1 Knw that numbers that are nt ratinal are called irratinal. Understand infrmally that every number has a decimal expansin; fr ratinal numbers shw that the decimal expansin

34 repeats eventually and cnvert a decimal expansin which repeats eventually int a ratinal number 8.NS.2 Use ratinal apprximatins f irratinal numbers t cmpare the size f irratinal numbers, lcate them apprximately n a number line diagram, and estimate the value f expressins EXPRESSIONS AND EQUATIONS 8.EE.1 Knw and apply the prperties f integer expnents t generate equivalent numerical expressins 8.EE.2 Use square rt and cube rt symbls t represent slutins t equatins f the frm x^2 = p and x^3 = p, where p is a psitive ratinal number. Evaluate square rts f small perfect squares and cube rts f small perfect cubes. Knw that the square rt f 2 is irratinal 8.EE.3 - Use numbers expressed in the frm f a single digit times an integer pwer f 10 t estimate very large r very small quantities, and t express hw many times as much ne is than the ther 8.EE.4 Perfrm peratins with numbers expressed in scientific ntatin, including prblems where bth decimal and scientific ntatin are used. Use scientific ntatin and chse units f apprpriate size fr measurements f very large r very small quantities 8.EE.5 Graph prprtinal relatinships, interpreting the unit rate as the slpe f the graph. Cmpare tw different prprtinal relatinships represented in different ways 8.EE.6 Use similar triangles t explain why the slpe m is the same between any tw distinct pints n a nn-vertical line in the crdinate plane; derive the equatin y = mx fr a line thrugh the rigin and the equatin y = mx + b fr a line intercepting the vertical axis at b. 8.EE.7 Slve linear equatins in ne variable 8.EE.8 Analyze and slve pairs f simultaneus equatins FUNCTIONS 8.F.1 Understand that a functin is a rule that assigns t each input exactly ne utput. The graph f a functin is the set f rdered pairs cnsisting f an input and the crrespnding utput 8.F.2 Cmpare prperties f tw functins each represented in a different way 8.F.3 Interpret the equatin Interpret the equatin y = ms + b as defining a linear functin, whse graph is a straight line; give examples f functins that are nt linear. 8.F.4 Cnstruct a functin t mdel a linear relatinship between tw quantities. Determine the rate f change and initial value f the functin frm a descriptin f a relatinship r frm tw (x,y) values 8.F.5 Describe qualitatively the functinal relatinship between tw quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features f a functin that has been described verbally. GEOMETRY 8.G.1 Verify experimentally the prperties f rtatins, reflectins, and translatins 8.G.2 Understand that a tw-dimensinal figure is cngruent t anther if the secnd can be btained frm the first by a sequence f rtatins, reflectins, and translatins; given tw cngruent figures describe a sequence that exhibits the cngruence between them 8.G.3 Describe the effect f dilatins, translatins, rtatins, and reflectins n 2D figures using crdinates 8.G.4 - Understand that a 2D figure is similar t anther if the secnd can be btained frm the first by a sequence f rtatins, reflectins, translatins, and dilatins; given tw similar 2D figures, describe a sequence that exhibits the similarity f triangles

35 8.G.5 Use infrmal arguments t establish facts abut the angle sum and exterir angle f triangles, abut the angles created when parallel lines are cut by a transversal, and the angle-angle criterin fr similarity f triangles 8.G.6 Explain a prf f the Pythagrean Therem and its cnverse 8.G.7 Apply the Pythagrean Therem t determine unknwn side lengths in right triangles in realwrld and mathematical prblems in tw and three dimensins. 8.G.8 Apply the Pythagrean Therem t find the distance between tw pints in a crdinate system 8.G.9 Knw the frmulas fr the vlumes f cnes, cylinders, and spheres and use them t slve real-wrld mathematical prblems STATISTICS AND PROBABILITY 8.SP.1 Cnstruct and interpret scatter plts fr bivariate measurement data t investigate patterns f assciatin between tw quantities. Describe patterns such as clustering, utliers, psitive r negative assciatin, linear assciatin, and nnlinear assciatin. 8.SP.2 Knw that straight lines are widely used t mdel relatinships between tw quantitative variables. Fr scatter plts that suggest a linear assciatin, infrmally fit a straight line, and infrmally assess the mdel fit by judging the clseness f the data pints t the line 8.SP.3 Use the equatin f a linear mdel t slve prblems in the cntext f bivariate measurement data, interpreting the slp and intercept 8.SP.4 Understand that patterns f assciatin can als be seen in bivariate categrical data by displaying frequencies and relative frequencies in a tw-way table. Cnstruct and interpret a tw-way table summarizing data n tw categrical variables cllected frm the same subjects. Use relative frequencies calculated fr rws r clumns t describe an assciatin between the tw variables. TECHNOLOGY A.5 Determine the benefits f a wide range f digital tls by using them t slve prblems A.5 Select and use apprpriate tls and digital resurces t accmplish a variety f tasks and t slve prblems. 21 st CENTURY THEMES A Critical thinking and prblem slving B Creativity and innvatin C Cllabratin, teamwrk and leadership D Crss-cultural understanding and interpersnal cmmunicatin E Cmmunicatin and Media Fluency F Accuntability, Prductivity and Ethics A Career awareness Prcess Standards indicate hw we want students t learn: Mathematical Practice: 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.

36 Lk fr and express regularity in repeated reasning. A cmplete cpy f the standards fr Grade 8 may als be fund at: Cmmn Cre State Standards Initiative (CCSSI) Enduring Understandings: Number System Squares and radicals can help slve real wrld prblems Squares and radicals affect the numbers that are being used within an peratin The rules fr radicals can be applied t variable expressins Expressins and Equatins Hw t slve an equatin in ne variable be slved fr that variable Hw t slve an equatin fr a variable in the equatin Varius methds can be used t slve equatins and the slutin t an equatin can be checked by substituting int the riginal equatin Functins The definitin f a functin and what it s graph represents Prperties f functins and their graphs are similar but nt identical Slpe-intercept frm is an easy way f graphing functins The ability t graph a functin and write a functin frm a graph Gemetry Cngruent figures can be frmed by a series f transfrmatins Similar figures can be frmed by a series f transfrmatins Understand angle relatinships in ne and tw-dimensinal figures The Pythagrean Therem can be used t slve real wrld prblems The Pythagrean Therem aids in slving prblems invlving right triangles There are different frmulas that can be used when slving fr the vlume f a 3D figure Statistics and Prbability Scatter plts, line f best fit, and frequencies all help interpret data within a prblem Patterns can be mdeled using different graphs Straight lines are widely used t mdel relatinships Essential Questins Number System What is the difference between ratinal and irratinal numbers? Hw d radicals and squares help slve real wrld prblems? Hw are radicals and squares useful fr slving equatins and manipulating numbers? Expressins and Equatins Hw will scientific ntatin help when writing numbers and equatins? Hw is scientific ntatin used in real wrld applicatin prblems? Hw are numbers cmpared and manipulated using scientific ntatin? Hw can the value f an unknwn variable be fund? What is meant by the slpe f a line, and hw can knwing a line s slpe help t graph a line and find parallel and perpendicular lines? Hw can real wrld situatins be mdeled by systems? Hw can slutins be fund t a system? Functins What is a functin? Hw are functins represented?

37 What can a relatinship between numbers tell abut a prblem? Are prperties f functins and graphs the same fr all functins? Gemetry Hw can yu use mdels f ne and tw-dimensinal figures t shw cngruent figures? Hw can yu use mdels f ne and tw-dimensinal figures t shw similar figures? Hw des the Pythagrean Therem help slve real wrld prblems? Hw d we cmpute the distance and midpint within prblems? What is a 3-dimensinal figure? Hw can I find the vlume f a 3D figure? Hw can the vlume f a 3D figures help me slve real wrld prblems? Statistics and Prbability Hw can infrmatin frm a prblem be represented in a way t see a pattern r a frequency? What is a line f best fit and hw can it supply a cnclusin? Are interpretatin and predicatin an accurate cnclusin fr a prblem? Unit Objectives Number System Students will be able t find the squares and square rts f bth ratinal and irratinal numbers Students will knw the perfect squares. They will als be able t simplify perfect square radical expressins as well as nn-perfect square radicands Students will use the perfect squares t apprximate square rts Students will be use their understanding f square rts t simplify rts f variables Students will understand the prperties f expnents and will use them t slve equatins with perfect square and cube rts Expressins and Equatins Students will be able t slve equatins Students will be able t transfrm a frmula t a different frm f that equatin Students will express numbers using scientific ntatin Students will recgnize the difference between scientific ntatin and standard frm Students will distinguish the difference between different numbers written in scientific ntatin Students will slve equatins with additin, subtractin, multiplicatin, and divisin using numbers in scientific ntatin Students will be able t graph a line given different frms f the equatin Students will be able t identify parallel and perpendicular lines frm their slpes Students will be able t describe hw slpe relates t hrizntal and vertical lines Students will be able t graph systems f linear equatins r t find a slutin Students will be able t translate real wrld prblem int a system Students will be able t slve a system f equatins by using substitutin and eliminatin Functins Students will understand what a functin is and its crrespnding graph Students will cmpare prperties f different functins and relate the infrmatin t real wrld situatins Students will graph slpe-intercept frm f a line

38 Students will cnstruct a functin and determine the rate f change and initial value Students will describe a functinal relatinship by examining a graph Gemetry Students will be able t transfrm figures n a crdinate plane Students will be able t use their understanding f angle relatinships t find unknwn angles Students will be able t describe a sequence f transfrmatins that will result in cngruent figures Students will be able t describe a sequence f transfrmatins and dilatins that will result in similar figures Students will be able t explain the prf f the Pythagrean Therem Students will find unknwn side lengths using the Pythagrean Therem Students will use the Pythagrean Therem t slve prblems invlving distance and midpints Students will slve real wrld applicatin prblems using the Pythagrean Therem Students will identify what a 3-dimensinal figure is Students will use a frmula t find the vlume f a prism and cylinder Students will use a frmula t find the vlume f pyramids, cnes, and spheres Statistics and Prbability Students will be able t graph scatter plts Students will interpret and examine data t cme t a cnclusin Students will knw abut line f best fit and tw variable data relatinships Students will understand patterns f assciatin in bivariate categrical data Students will use frequency t slve real life prblems and make predictins fr future nes Terminlgy: Numerical expressin, variable, variable expressin, evaluate, pwers, expnent, base, squared, square rt, cube, cube rt, rder f peratins, integers, abslute value, crdinate plane, rdered pair, like terms, equatins, inverse peratins, equatins, linear inequality, equivalent fractins, simplest frm, ratinal number, irratinal numbers, multiplicative inverse, rati, rate, unit rate, prprtin, crss prduct, similar figures, cngruent figures, scale drawings, scale mdels, functin, relatin, mapping, dmain, range, input, utput, linear, perfect square, Pythagrean Therem, legs, hyptenuse, distance, plygn, regular, surface area, vlume, cmplementary, supplementary, crrespnding, alternate interir, alternate exterir, transversal, angles, translatin, reflectin, rtatin, symmetry, dilatin, scale factr, slpe, intercepts, rise ver run, standard frm, parallel, perpendicular, scatter plts, frequency, crrelatin Assessments Onging and thrughut unit f study; assessments may include: Infrmal assessments Teacher-based assessments Suggested assessments Specific interim assessments; frmats may vary. Standardized End f Unit Assessments Standardized Quarterly Assessments Standardized Mid Term Assessments

39 Curse Resurces: Technlgies: Text: Other: COWs, SMART Bards, Ntebk Sftware, Pwer Schl, Perfrmance Matters, Chrmebks, wikis, nline vides McDugal Littell Algebra Big Ideas Math Blue (Supplementary) Study Island; Teacher made wrksheets and prjects

40 CURRICULUM OVERVIEW: ALGEBRA I Textbk: Algebra I Hlt McDugal Cmmn Cre Editin 2012 Curriculum: This is lcated in the Cre Curse Curriculum fr the High Schl. The Pacing Chart that fllws is the ne used in the middle schl fr delivery f Algebra I curriculum. Trimester I Cncepts fund in: Chapters 1, 2, 3, 4, and Sectins *Tw-week review f Chapters 1 and 2 Chapter Variables In Algebra 1.2 Slving Equatins with +, Slving Equatins with *, / 1.4 Slving Multi-Step Equatins 1.5 Slving Equatins with Variables n Bth Sides 1.6 Slving fr a Variable 1.7 Slving Abslute Value Equatins 1.8 Rates, Ratis & Prprtins 1.9 Applicatins f Prprtins 1.10 Precisin & Accuracy Chapter Graphing & Writing Inequalities 2.2 Slving Inequalities with +, Slving Inequalities with *, / 2.4 Slving Multi-Step Inequalities Trimester II Cncepts fund in: Sectins 5.5 and 5.6, Chapters 6, 7, and Sectins Chapter Slving Linear Inequalities 5.6 Slving Systems f Linear Inequalities Chapter Integer Expnents 6.2 Ratinal Expnents 6.3 Plynmials 6.4 +, - Plynmials 6.5 Multiplying Plynmials 6.6 Special Prducts f Plynmials Chapter Factrs & GCF 7.2 Factring by GCF 7.3 Factring x 2 + bx + c 7.4 Factring ax 2 + bx + c 7.5 Factring Special Prducts 7.6 Chsing a Factring Methd Chapter Identifying Quadratic Functins 8.2 Characteristics f Trimester III Cncepts fund in: Sectins , Chapters 9 and 10 Chapter Slving Quadratic Equatins by Graphing 8.6 Slving Quadratic Equatins by Factring 8.7 Slving Quadratic Equatins by Using Square Rts 8.8 Cmpleting the Square 8.9 The Quadratic Frmula & Discriminant Chapter Gemetric Sequences 9.2 Expnential Functins 9.3 Expnential Grwth & Decay 9.4 Linear, Quadratic, and Expnential Mdels 9.5 Cmparing Functins Chapter Organizing & Displaying Data 10.2 Frequency & Histgram 10.3 Data Distributins

41 2.5 Slving Inequalities with Variables n Bth Sides 2.6 Slving Cmpund Inequalities 2.7 Slving Abslute Value Inequalities *Summer Packet Quiz Chapter Graphing Relatinships 3.2 Relatins & Functins 3.3 Writing Functins 3.4 Graphing Functins 3.5 Scatter Plts & Trend Lines 3.6 Arithmetic Sequences Chapter 4 (Skip 4.10) 4.1 Identifying Linear Functins 4.2 Using Intercepts 4.3 Rate f Change & Slpe 4.4 The Slpe Frmula 4.5 Direct Variatin 4.6 Slpe Intercept Frm 4.7 Pint-Slpe Frm 4.8 Line f Best Fit 4.9 Slpes f Parallel & Perpendicular Lines Chapter Slving Systems by Graphing 5.2 Slving Systems by Substitutin 5.3 Slving Systems by Eliminatin 5.4 Slving Special Systems Quadratic Functins 8.3 Graphing Quadratic Functins 8.4 Transfrming Quadratic Functins 10.4 Misleading Graphs & Statistics 10.5 Experimental Prbability 10.6 Theretical Prbability 10.7 Independent & Dependent Events TRIMESTER GRADES will be determined using the belw categry weights: Tests 35% (50) Each Chapter r large prtins f data (always pre-annunced) Quizzes 30% (30) Each Chapter and small prtins f data (annunced and pp quizzes) Classwrk 20% (10) Classrm activities & labs (team wrk activities) Hmewrk 15% (10) Daily effrt & fllw up activities

42 CURRICULUM OVERVIEW: GEOMETRY AND ALGEBRA II Curriculum: This is lcated in the Cre Curse Curriculum fr the High Schl.

43 DISTRICT APPENDIX There are the varius strands that crss cntent. They have relevance t every curricular area and all grade levels. The strands are interwven int cntent and integrated int instructin. They d nt stand alne. A synpsis f each strand is included in this dcument. The full SBSD K-12 District Appendix, with detailed infrmatin abut each strand, can be fund as a separate dcument. Tpics Teaching fr the 21st Century Educatinal Technlgy Standards 21st Century Life and Career Educatin Skills Character Educatin Differentiatin Understanding by Design (UbD): Reader s Digest Versin