Ratios and Proportional Relationships. The Number System

Transcription

1 A Crrelin f n i ig e v In re C n m wih Cm y d u S f e r u C m b l he A grde 6 Ri nd Prprinl Relinhip Undernd ri cncep nd ue ri rening lve prblem. 1. Undernd he cncep f ri nd ue ri lnguge decribe ri relinhip beween w quniie. [6.RP.1] 2. Undernd he cncep f uni re /b cied wih ri :b wih b 0, nd ue re lnguge in he cnex f ri relinhip. [6.RP.2] 3. Ue ri nd re rening lve rel-wrld nd mhemicl prblem, e.g., by rening bu ble f equivlen ri, pe digrm, duble number line digrm, r equin. [6.RP.3] Inv. 2: ACE Hw Likely I I? Inv. 1: A Fir Lk Chnce Inv. 2: Experimenl nd Thereicl Prbbiliy Inv. 3: Mking Deciin wih Prbbiliy Inv. 4: Prbbiliy, Geneic, nd Gme. Mke ble f equivlen ri reling quniie wih whle number meuremen, find miing vlue in he ble, nd pl he pir f vlue n he crdine plne. Ue ble cmpre ri. [6.RP.3.] b. Slve uni re prblem including he invlving uni pricing nd cnn peed. [6.RP.3.b] c. Find percen f quniy re per 100 (e.g., 30% f quniy men 30/100 ime he quniy); lve prblem invlving finding he whle, given pr nd he percen. [6.RP.3.c] I Inv. 5: Mre Abu Percen d. Ue ri rening cnver meuremen uni; mnipule nd rnfrm uni pprpriely when muliplying r dividing quniie. [6.RP.3.d] The Number Syem Apply nd exend previu undernding f muliplicin nd diviin divide frcin by frcin. 4. Inerpre nd cmpue quien f frcin, nd lve wrd prblem invlving diviin f frcin by frcin, e.g., by uing viul frcin mdel nd equin repreen he prblem. [6.NS.1] Cmpue fluenly wih muli-digi number nd find cmmn fcr nd muliple. 5. Fluenly divide muli-digi number uing he ndrd lgrihm. [6.NS.2] I Inv. 2: ACE 2, 29, 34, 35

2 6. Fluenly dd, ubrc, muliply, nd divide muli-digi deciml uing he ndrd lgrihm fr ech perin. [6.NS.3] I 7. Find he gree cmmn fcr f w whle number le hn r equl 100 nd he le cmmn muliple f w whle number le hn r equl 12. Ue he diribuive prpery expre um f w whle number wih cmmn fcr muliple f um f w whle number wih n cmmn fcr. [6.NS.4] Inv. 2: Whle-Number Pern nd Relinhip Inv. 3: Cmmn Muliple nd Cmmn Fcr Apply nd exend previu undernding f number he yem f rinl number. 8. Undernd h piive nd negive number re ued geher decribe quniie hving ppie direcin r vlue (e.g., emperure bve/belw zer, elevin bve/belw e level, credi/debi, piive/negive elecric chrge); ue piive nd negive number repreen quniie in rel-wrld cnex, explining he mening f 0 in ech iuin. [6.NS.5] 9. Undernd rinl number pin n he number line. Exend number line digrm nd crdine xe fmilir frm previu grde repreen pin n he line nd in he plne wih negive number crdine. [6.NS.6] Inv. 1: Fundriing Frcin Inv. 2: Shring nd Cmpring wih Frcin Inv. 1: Eiming wih Frcin I. Recgnize ppie ign f number indicing lcin n ppie ide f 0 n he number line; recgnize h he ppie f he ppie f number i he number ielf, e.g., ( 3) = 3, nd h 0 i i wn ppie. [6.NS.6.] b. Undernd ign f number in rdered pir indicing lcin in qudrn f he crdine plne; recgnize h when w rdered pir differ nly by ign, he lcin f he pin re reled by reflecin cr ne r bh xe. [6.NS.6.b] c. Find nd piin ineger nd her rinl number n hriznl r vericl number line digrm; find nd piin pir f ineger nd her rinl number n crdine plne. [6.NS.6.c] 10. Undernd rdering nd blue vlue f rinl number. [6.NS.7] Inv. 1: Fundriing Frcin Inv. 2: Shring nd Cmpring wih Frcin. Inerpre emen f inequliy emen bu he relive piin f w number n number line digrm. [6.NS.7.] Inv. 1: Fundriing Frcin Inv. 2: Shring nd Cmpring wih Frcin b. Wrie, inerpre, nd explin emen f rder fr rinl number in rel-wrld cnex. [6.NS.7.b] I Inv. 1: ACE 58 c. Undernd he blue vlue f rinl number i dince frm 0 n he number line; inerpre blue vlue mgniude fr piive r negive quniy in rel-wrld iuin. [6.NS.7.c]

3 d. Diinguih cmprin f blue vlue frm emen bu rder. [6.NS.7.d] 11. Slve rel-wrld nd mhemicl prblem by grphing pin in ll fur qudrn f he crdine plne. Include ue f crdine nd blue vlue find dince beween pin wih he me fir crdine r he me ecnd crdine. [6.NS.8] Exprein nd Equin Apply nd exend previu undernding f rihmeic lgebric exprein. 12. W rie nd evlue numericl exprein invlving whle-number expnen. [6.EE.1] Inv. 4: Fcrizin: Serching fr Fcr Sring 13. W rie, red, nd evlue exprein in which leer nd fr number. [6.EE.2] I. Wrie exprein h recrd perin wih number nd wih leer nding fr number. [6.EE.2.] I b. Idenify pr f n exprein uing mhemicl erm (um, erm, prduc, fcr, quien, cefficien); view ne r mre pr f n exprein ingle eniy. [6.EE.2.b] Inv. 1: Fcr nd Prduc Inv. 4: Fcrizin: Serching fr Fcr Sring Inv. 5: Puing I All Tgeher I c. Evlue exprein pecific vlue f heir vrible. Include exprein h rie frm frmul ued in rel-wrld prblem. Perfrm rihmeic perin, including he invlving whle number expnen, in he cnveninl rder when here re n prenhee pecify priculr rder (Order f Operin). [6.EE.2.c] Inv. 1: Deigning Bumper Cr Inv. 3: Meuring Tringle Inv. 4: Meuring Prllelgrm Inv. 5: Meuring Irregulr Shpe nd Circle CC Inv. 2: Number Prperie ndalgebric Equin 14. Apply he prperie f perin genere equivlen exprein. [6.EE.3] 15. I denify when w exprein re equivlen (i.e., when he w exprein nme he me number regrdle f which vlue i ubiued in hem). [6.EE.4]

4 Ren bu nd lve ne-vrible equin nd inequliie. 16. U ndernd lving n equin r inequliy prce f nwering quein: which vlue frm pecified e, if ny, mke he equin r inequliy rue? Ue ubiuin deermine wheher given number in pecified e mke n equin r inequliy rue. [6.EE.5] I Inv. 2: ACE U e vrible repreen number nd wrie exprein when lving rel-wrld r mhemicl prblem; undernd h vrible cn repreen n unknwn number, r, depending n he purpe hnd, ny number in pecified e. [6.EE.6] Inv. 3: Plygn Prperie nd Tiling Inv. 4: Building Plygn Inv. 5: Mking Irregulr Shpe nd Circle 18. S lve rel-wrld nd mhemicl prblem by wriing nd lving equin f he frm x + p = q nd px = q fr ce in which p, q, nd x re ll nnnegive rinl number. [6.EE.7] Inv. 3: Plygn Prperie nd Tiling Inv. 4: Building Plygn Inv. 5: Mking Irregulr Shpe nd Circle 19. W rie n inequliy f he frm x > c r x < c repreen cnrin r cndiin in rel-wrld r mhemicl prblem. Recgnize h inequliie f he frm x > c r x < c hve infiniely mny luin; repreen luin f uch inequliie n number line digrm. [6.EE.8] Repreen nd nlyze quniive relinhip beween dependen nd independen vrible. 20. U e vrible repreen w quniie in rel-wrld prblem h chnge in relinhip ne nher; wrie n equin expre ne quniy, hugh f he dependen vrible, in erm f he her quniy, hugh f he independen vrible. Anlyze he relinhip beween he dependen nd independen vrible uing grph nd ble, nd rele hee he equin. [6.EE.9] Gemery Slve rel-wrld nd mhemicl prblem invlving re, urfce re, nd vlume. 21. F ind he re f righ ringle, her ringle, pecil qudrilerl, nd plygn by cmping in recngle r decmping in ringle nd her hpe; pply hee echnique in he cnex f lving rel-wrld nd mhemicl prblem. [6.G.1] Inv. 1: Deigning Bumper Cr Inv. 3: Meuring Tringle Inv. 4: Meuring Prllelgrm Inv. 5: Meuring Irregulr Shpe nd Circle 22. F ind he vlume f righ recngulr prim wih frcinl edge lengh by pcking i wih uni cube f he pprprie uni frcin edge lengh, nd hw h he vlume i he me wuld be fund by muliplying he edge lengh f he prim. Apply he frmul V = l w h nd V = b h find vlume f righ recngulr prim wih frcinl edge lengh in he cnex f lving rel-wrld nd mhemicl prblem. [6.G.2] CC Inv. 4: Meuremen 23. D rw plygn in he crdine plne given crdine fr he verice; ue crdine find he lengh f ide jining pin wih he me fir crdine r he me ecnd crdine. Apply hee echnique in he cnex f lving rel-wrld nd mhemicl prblem. [6.G.3] Inv. 2: ACE 39

5 24. R epreen hree-dimeninl figure uing ne mde up f recngle nd ringle, nd ue he ne find he urfce re f hee figure. Apply hee echnique in he cnex f lving rel-wrld nd mhemicl prblem. [6.G.4] Inv. 3: ACE 39 CC Inv. 4: Meuremen Siic nd Prbbiliy Develp undernding f iicl vribiliy. 25. R ecgnize iicl quein ne h nicipe vribiliy in he d reled he quein nd ccun fr i in he nwer. [6.SP.1] 26. U ndernd h e f d clleced nwer iicl quein h diribuin which cn be decribed by i cener, pred, nd verll hpe. [6.SP.2] 27. R ecgnize h meure f cener fr numericl d e ummrize ll f i vlue wih ingle number, while meure f vriin decribe hw i vlue vry wih ingle number. [6.SP.3] Summrize nd decribe diribuin. 28. D iply numericl d in pl n number line, including d pl, higrm, nd bx pl. [6.SP.4] CC Inv. 5: Higrm nd Bx Pl 29. Summrize numericl d e in relin heir cnex, uch by: [6.SP.5]. Repring he number f bervin. [6.SP.5.] Hw Likely I I? Inv. 1: A Fir Lk Chnce Inv. 2: Experimenl nd Thereicl Prbbiliy Inv. 3: Mking Deciin wih Prbbiliy Inv. 4: Prbbiliy, Geneic, nd Gme b. Decribing he nure f he ribue under inveigin, including hw i w meured nd i uni f meuremen. [6.SP.5.b] c. Giving quniive meure f cener (medin nd/r men) nd vribiliy (inerqurile rnge nd/r men blue deviin), well decribing ny verll pern nd ny riking deviin frm he verll pern wih reference he cnex in which he d were ghered. [6.SP.5.c] d. Reling he chice f meure f cener nd vribiliy he hpe f he d diribuin nd he cnex in which he d were ghered. [6.SP.5.d] Inerninl cumer: vii PernGlblSchl.cm Cpyrigh Pern Educin, Inc., r i ffilie. All righ reerved. PDF.0511.AV.LS M PernSchl.cm CC Inv. 5: Higrm nd Bx Pl