8 th Grade Math: Pre-Algebra

Transcription

1 Hardin Cunty Middle Schl ( ) 1 8 th Grade Math: Pre-Algebra Curse Descriptin The purpse f this curse is t enhance student understanding, participatin, and real-life applicatin f middle-schl mathematics thrugh the use f a pre-algebra curriculum, student-supprt prgrams, and technlgy-advanced classrms. The gals f the curse are t empwer students with a brad usability f mathematics as well as t prvide a smther transitin int a high schl algebra curse. Within the curse, students will increase their awareness f the real number system t include the irratinal numbers. Students will extend their knwledge f algebraic expressins and equatins that invlve slving a system f equatins as well as graphing linear functins. Students will cntinue the use f scientific ntatin and extend the cncept f square rts in the develpment f the Pythagrean Therem t slve real-wrld prblems. The verall design f this curse encmpasses an active-learning envirnment with a strict attentin t building student reasning, cmmunicatin, mdeling, and prblem-slving abilities with in real-wrld applicatins. Curse Objectives By the end f this curse, yu shuld be able t: 1. Reasn, cmmunicate, represent, and prblem-slve effectively while develping mathematical prficiency. 2. Describe the differences between the ratinal and irratinal number systems by peratins and prperties. Use accurate cmputing strategies t develp number sense, and cmputatinal fluency when perating with numbers in scientific ntatin.

2 Hardin Cunty Middle Schl ( ) 2 Effectively use rates t determine apprpriate distances, speed, and time (D = rt) relatinships as well as unit rates t cmpare best buys. 3. Describe the algebraic relatinships presented by tables, graphs, and symbls assciated with patterns, equatins, and functins. Create mdels f real-wrld mathematical phenmena using apprpriate technlgy. Represent, analyze, and slve prblems assciated with linear and nn-linear equatins and functins. 4. Use technlgy t develp cnvincing arguments, prfs, and prperties t supprt cnjectures in gemetric reasning assciated with parallel lines cut by a transversal. Extend the cncept f square rts t find distances algebraically using the Pythagrean Therem. 5. Create and interpret statistical data assciated with scatterplts and lines f best fit t make cnjectures and identify misrepresentatins f published data. Textbk This curse uses the Glence Pre-Algebra textbk published by Glence/McGraw-Hill 2012 and its assciated nline textbk resurces frm Cnnect-ED as well as teacher supplemented instructinal resurces. Each student will be assigned a student textbk in additin t a username and passwrd t access the Cnnect-Ed site. Each student is respnsible fr the cnditin f the textbk as well as the security f their username and passwrd. Curse Outline Belw is a tentative utline f the units and lessns fr each nine-week perid thrughut the curse. Please nte sme skills maybe shifted peridically r verlapped in a 9-week perid based n the level f student understanding.

3 Hardin Cunty Middle Schl ( ) 3 1 st 9-weeks Unit 1: Expressins, Integers, and Equatins This unit builds upn students understanding and fluency with algebraic expressins and equatins. Students will be able t represent real-wrld situatins with algebraic expressins and slve cntextual prblems that invlve peratins with integers. In additin students will be able t analyze and slve tw-step/multi-step equatins using the distributive prperty and by cmbining like terms. Standards Areas f Fcus Tasks Perfrmance 8.EE.7 Represent algebraic relatinships with expressins and equatins. Mdel algebraic expressins and equatins symblically. Simplify expressins and equatins by cmbining like terms. Mdel and use the distributive prperty t slve equatins. 8.EE.7 Slve real-wrld prblems using symblic algebra. Slve ne, tw, and multi-step equatins. Slve equatins where f(x)=g(x). 8.EE.7 Develp strng number sense when perating with integers. Develp the rules fr adding, subtracting, multiplying, and dividing integers. Parent Review Date

4 Hardin Cunty Middle Schl ( ) 4 1 st 9-weeks Unit 2: Rates, Functins, and Graphing This unit builds upn student knwledge f ratis, rates, and linear functins. Students will be able t calculate unit rates in rder t determine best buy and use rates t slve distance (D=rt) prblems. In additin, students will be able t graph linear functins, use slpe t analyze situatins cmparing linear and nnlinear functins, and find slutins t a system f equatins. Standards Areas f Fcus Tasks Perfrmance 8.EE.5 SPI Use real-wrld applicatins t determine the best buy using unit rates. Calculate and cmpare unit rates t determine the best buy. 8.EE.5, Slve prblems invlving distance (D = rt). SPI Using the distance equatin (D = rt), determine distance/rate/time. Parent Review Date

5 Hardin Cunty Middle Schl ( ) 5 2 nd 9-weeks Unit 2: Rates, Functins, and Graphing (cnt.) This unit builds upn student knwledge f ratis, rates, and linear functins. Students will be able t calculate unit rates in rder t determine best buy and use rates t slve distance (D=rt) prblems. In additin, students will be able t graph linear functins, use slpe t analyze situatins cmparing linear and nnlinear functins, and find slutins t a system f equatins. Standards Areas f Fcus Tasks Perfrmance 8.EE.5, 8.EE.7, 8.EE.8, 8.F.1-5, SPI , SPI /3.2 SPI SPI EE.6, SPI Parent Review Graph prprtinal and linear relatinships. Interpret the unit rate as the slpe f a graph f a prprtinal relatinship. Define and translate between the varius representatins f a linear functin. Analyze the graph f a linear functin t find its slutins. Cmpare functins as linear r nnlinear. Find the slutin t systems f equatins. Use similar triangles t interpret the meaning f slpe. Develp the slpe frmula. Find the slpe frm a table, set f pints, graph, r equatin. Derive the equatin f a line thrugh the rigin as y = mx and the equatin f line intersecting the y-axis as y = mx + b. Date

6 Hardin Cunty Middle Schl ( ) 6 3 rd 9-weeks Unit 3: Scientific Ntatin, the Real Number System, and the Pythagrean Therem. This unit extends students peratins f real-wrld prblems with numbers in scientific ntatin, numbers within the real number system and the use f the Pythagrean Therem. Students will be able t perate fluently with numbers in scientific ntatin. In additin, students will be able t classify and cmpare ratinal and irratinal numbers within the real number system. Lastly, students will be able t derive the Pythagrean Therem and implement its use t slve real-wrld prblems. Standards Areas f Fcus Tasks Perfrmance 8.EE.3, 8.EE.4, Slve real-wrld prblems in scientific ntatin. SPI Cnvert numbers t and frm scientific SPI ntatin. Cmpute sums, differences, prducts, and qutients f numbers in scientific ntatin. 8.NS.1, 8.NS.2, SPI Classify, rder, and cmpare ratinal and irratinal numbers n the number line. Identify numbers and square rts as ratinal/irratinal. 8.G.6, 8.G.7, 8.G.8, Use the Pythagrean Therem t slve cntextual prblems. SPI , SPI Mdel and derive the Pythagrean Therem Find the missing values f the hyptenuse r legs f a right triangle. Find the distance between tw pints in the crdinate plane. Parent Review Date

7 Hardin Cunty Middle Schl ( ) 7 4 th 9-weeks Unit 4: Angle Relatinships and Data Analysis This unit intrduces the prperties f angles frmed by parallel lines cut by a transversal and uses graphical representatins t determine relatinships between tw sets f data. Students will be able t identify and measure the angles frmed when parallel lines are cut by a transversal. In additin students will be able t interpret graphical representatins f data and identify misleading infrmatin published in graphs and ther media. Standards Areas f Fcus Tasks Perfrmance 8.G.1, 8.G.5, SPI SP.1, 8.SP.2, 8.SP.3, 8.SP.4, SPI SPI Understand the angle relatinships frmed frm parallel lines cut by a transversal. Determine cmplementary/supplementary angles. Analyze cngruent angle pairs (alternate interir/exterir, crrespnding, adjacent). Find missing angle values. Represent real-wrld data with scatterplts t make and test cnjectures. Generalize the relatinship between tw sets f data with scatterplts and lines f best fit. Determine the equatin fr a line f best fit. Analyze misrepresentatins f published data in the media. Cnsider the surce, design, and display in the misrepresentatin f data. Parent Review Date

8 Hardin Cunty Middle Schl ( ) 8 4th 9-weeks Unit 5: Cmmn Cre Readiness This unit is t strengthen prerequisite skills necessary fr implementing cmmn cre standards. Students will build upn current knwledge f gemetric prperties and extend it int 2-D and 3-D figures. Standards Areas f Fcus Tasks Perfrmance 8.G.1, 8.G.2, 8.G.3, 8.G.4, Verify the gemetric prperties f rtatins, reflectins, and translatins. Understand the meaning f cngruence as it applies t 2-D figures. Cnstruct cngruent mdels f 2-D figures and describe the sequence that exhibits the similarity between them. 8.G.9 Slve prblems invlving the vlume f cylinders, cnes, and spheres. Knw hw t use the frmulas fr the vlumes invlving 3-D bjects t slve mathematical prblems. Parent Review Date

9 Hardin Cunty Middle Schl ( ) 9 Assignments and Literacy Initiative The Different Kinds f Assignments The assignments thrughut the curse are used nt nly t assess student understanding but they are als intended t make learning math meaningful. In additin t implementing exercises and prjects t prmte skill and practice, several literacy cmpnents have been added t increase critical-thinking skills and supprt the HCMS Literacy Initiative. A variety f assignments include: Online Readings-- Online reading assignments are included in the curse. They may cme frm Wikipedia definitins, bk excerpts, etc., t prvide an intrductin t a lessn, prvide infrmatin, r be articles r papers that have been authred by experts in the field. Readings frm E-Bks-- Yu may have t read and present n any required readings frm the textbk which incrprate, histrical facts, inventins, statistics assciated with the lessn cntent. Web Quests Web Quests teach yu hw t use the Internet as a resurce tl. Yu may be given links t websites that either enhance the cntent f readings r shw yu where infrmatin and resurces can be fund. Sme prvide nline stries r articles. Mst als have Discussin Questins relating t the cntent f the internet resurce. Exercises-- may cnsist f cmpleting skill and practices prblems, slving applicatin prblems, r prviding respnses t Higher-Order Thinking (HOT) questins. Exercises are usually perfrmed ffline with pencil and paper. Prjects-- are individual assignments that require yu cnduct research and design a platfrm fr presenting the infrmatin. Mst prjects are assignments that assess yur ability t extend yur learning f the subject utside f the classrm. Discussin Questins-- are answered in the class discussin frum, either grup discussin r via psting, and frm the cre f class cmmunicatin. Discussin Questins may ask yu t apply mathematics cncepts t yur wn circumstances, prvide

10 Hardin Cunty Middle Schl ( ) 10 yur pinin abut the cntent, r share yur experiences cmpleting exercises r activities. Participatin in discussins is required. Reflective Activities-- Reflective activities such as analyzing student wrk, writing up test crrectins, r critiquing an assignment may be used as a methd fr yu t analyze, synthesize, and evaluate math cntent. Cllabrative Prjects-- Cllabrative prjects can invlve teams f students wrking tgether t participate in study grups, write research papers, make presentatins, and take part in simulatin activities. The prjects allw interactins with fellw students and build n facilitatin and planning skills. Tutring and RTI There are several frms f tutring and Respnse t Interventin (RTI) prgrams created t meet yur needs in the curse. The nline textbk cmes with a vide-based persnal tutr that recvers the material previusly learned in class. Tutring is als available afterschl twice a week fr additinal help in math. Here yu can cmplete assignments r ask fr help as needed n any subject area. Additinal remediatin and enrichment activities are prvided during SPI Lab time. Remember at HCMS we are here t help yu. All yu have t d is ask!