Mathematics Scope & Sequence Geometry

Transcription

1 Mathematic Scope & Sequece Geometry Revied: Augut 2018 Firt Gradig Period (42 ) Readie Stadard() G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) Ivetigate the egmet additio ad agle additio potulate through cotructio (G.5A) Compare ad cotrat udefied term ad defiitio(g.4a) Cotruct cogruet egmet uig a compa ad a traightedge (G.5B) Cotruct cogruet agle uig a compa ad a traightedge (G.5B) Cotruct a egmet biector uig a compa ad a traightedge (G.5B) Cotruct a agle biector uig a compa ad a traightedge (G.5B) Co tru ctio G.4A ditiguih betwee udefied term, defiitio, potulate, cojecture, ad theorem G.5B cotruct cogruet egmet, cogruet agle, a egmet biector, a agle biector, perpedicular lie, the perpedicular biector of a lie egmet, ad a lie parallel to a give lie through a poit ot o a lie uig a compa ad a traightedge G.5C ue the cotructio of cogruet egmet, cogruet agle, agle biector, ad perpedicular biector to make cojecture about geometric relatiohip Cotruct perpedicular lie uig a compa ad a traightedge (G.5B) Cotruct the perpedicular biector of a lie egmet uig a compa ad a traightedge (G.5B) Ivetigate agle biector ad perpedicular biector potulate through cotructio (G.5A) Cotruct a lie parallel to a give lie through a poit ot o the lie uig a compa ad a traightedge (G.5B) Create variou polygo or figure uig combiatio of cotructio of egmet, agle, ad agle ad egmet biector icludig parallel ad perpedicular egmet ad make cojecture about the geometric relatiohip withi the figure (G.5C)* Make cojecture about geometric relatiohip uig cotructio of cogruet egmet, cogruet agle, agle biector, ad perpedicular biector uig a variety of tool uch a a compa ad traight edge, paper foldig, ad dyamic geometric oftware (G.5C) 8-10 Defie the udefied term baed o their characteritic (G.4A) Textbook Sectio : 1.1, 1.2, 4.3, 4.4 Firt Gradig Period curriculum cotiued o ext page.

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3 Readie Stadard() A gl e a d S eg m e t G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.4A ditiguih betwee udefied term, defiitio, potulate, cojecture, ad theorem Ivetigate the Agle Additio ad Segmet Additio Potulate to make cojecture (G.5A) Compare the cotructio of the Agle Additio Potulate ad Segmet Additio Potulate to the algebraic repreetatio (G.5C) Compare ad cotrat defiitio, potulate, ad cojecture (G.4A) Idetify the udefied ad defied term of Geometry i a 3D model (G.4A) Explore real world example of the Agle Additio ad Segmet Additio Potulate uig a variety of tool uch a a compa ad traight edge, paper foldig, ad dyamic geometric oftware to make cojecture about geometric relatiohip (G.5C)* 9-10 G.5C ue the cotructio of cogruet egmet, cogruet agle, agle biector, ad perpedicular biector to make cojecture about geometric relatiohip Textbook Sectio : 1.1, 1.2, 4.4 Firt Gradig Period curriculum cotiued o ext page.

4 Co or di a te G eo m et ry Readie Stadard() G.2B derive ad ue the ditace, lope, ad midpoit formula to verify geometric relatiohip, icludig cogruece of egmet ad parallelim or perpedicularity of pair of lie G.2C determie a equatio of a lie parallel or perpedicular to a give lie that pae through a give poit G.2A determie the coordiate of a poit that i a give fractioal ditace le tha oe from oe ed of a lie egmet to the other i oe- ad two-dimeioal coordiate ytem, icludig fidig the midpoit G.6D verify theorem about the relatiohip i triagle, icludig proof of the Pythagorea Theorem, the um of iterior agle, bae agle of iocele triagle, midegmet, ad media, ad apply thee relatiohip to olve problem Verify/Prove the Pythagorea Theorem (G.6.D) Relate lope to the hypoteue of imilar right triagle (G.2B) Derive the lope formula (G.2.B) Determie if pair of lie are parallel, perpedicular or either uig the lope formula i mathematical ad real world ituatio (G.2.B) Give the equatio of a lie i variou form, write the equatio of a lie parallel to the give lie that pae through a give poit (G.2.C) Give the equatio of a lie i variou form, write the equatio of a lie perpedicular to the give lie that pae through a give poit (G.2.C) Derive the ditace formula uig the Pythagorea Theorem (G.2.B) Determie if egmet are cogruet uig the ditace formula i mathematical ad real world ituatio (G.2.B) Derive the midpoit formula (G.2.B) Verify a poit i the midpoit of a egmet by provig the egmet are cogruet (G.2.B) Fid the midpoit of a lie egmet i mathematical ad real-world ituatio (G.2.B) Fid the equatio of a circle with ceter at the origi ad radiu r (G.12E) G.12E how that the equatio of a circle with ceter at the origi ad radiu r i x 2 + y 2 = r 2 ad determi e the equatio for the graph of a circle with radiu r ad ceter (h, k), (x - h) 2 + (y - k) 2 =r 2 (SAT) Fid the equatio of a circle with ceter at ( h,k ) ad radiu r (G.12E) Write the equatio of a circle give a poit o the circle ad the ceter (G.12E) Graph the circle give the equatio of a circle (G.12E) Fid the coordiate of a poit located betwee two edpoit that i ¼ the ditace from oe edpoit to the other (G.2.A) Fid the locatio of poit i betwee two edpoit that are 1/3, 2/3, ad 1/4 the ditace from oe edpoit to the other (G.2.A)* Fid the coordiate of a miig edpoit give oe edpoit ad the midpoit i mathematical ad real-world ituatio (G.2.B) Select from the ditace, lope, ad/or midpoit formula to verify geometric relatiohip (G.2.B)

5 Textbook Sectio : 1.1, 4.5 Firt Gradig Period curriculum cotiued o ext page. Readie Stadard() G.4C verify that a cojecture i fale uig a couterexample Compare ad cotrat defiitio, potulate, cojecture, ad theorem (G.4A) Provide a couterexample i the form of a writte tatemet, picture, or graph for a give cojecture (G.4C) Logi cal Rea oi g G.4A ditiguih betwee udefied term, defiitio, potulate, cojecture, ad theorem G.4B idetify ad determie the validity of the covere, ivere, ad cotrapoitive of a coditioal tatemet ad recogize the coectio betwee a bicoditioal tatemet ad a true coditioal tatemet with a true covere Idetify covere, ivere, ad cotrapoitive tatemet of a coditioal tatemet (G.4B) Determie the validity of covere, ivere, ad cotrapoitive tatemet of a coditioal tatemet (G.4B) Idetify bicoditioal tatemet (G.4B) Recogize a correct bicoditioal tatemet related to a give true coditioal tatemet ad it true covere (G.4B) Apply the Law of Syllogim ad Detachmet to write proof (G.4B)* Textbook Sectio : 1.4, 1.5

6 Secod Gradig Period (39 ) Para llel Lie Readie Stadard() G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.6A verify theorem about agle formed by the iterectio of lie ad lie egmet, icludig vertical agle, ad agle formed by parallel lie cut by a traveral ad prove equiditace betwee the edpoit of a egmet ad poit o it perpedicular biector ad apply thee relatiohip to olve problem Verify theorem about vertical agle ad liear pair of agle (G.6A) Solve problem utilizig theorem about vertical agle ad liear pair of agle (G.6A) Make cojecture baed o patter of agle formed by parallel lie cut by a traveral utilizig a variety of tool, icludig real object, patty paper, compa, techology a appropriate (G.5A) Verify theorem about agle formed by parallel lie cut by a traveral (G.6A) Solve problem utilizig theorem about agle formed by parallel lie cut by a traveral (G.6A) Dicover ad apply the Parallel Lie Proportioality Theorem ad other ituatio ivolvig more tha oe traveral (G.6A)* Write proof about parallel lie cut by a traveral chooig from flow-chart ad two-colum proof (G.6A) 6-7 Textbook Sectio : 4.1, 4.2, 4.3

7 Readie Stadard() Tria gle Co grue ce G.2B derive ad ue the ditace, lope, ad midpoit formula to verify geometric relatiohip, icludig cogruece of egmet ad parallelim or perpedicularity of pair of lie G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.6B prove two triagle are cogruet by applyig the Side-Agle-Side, Agle-Side-Agle, Side-Side-Sid e, Agle-Agle-Side, ad Hypoteue-Leg cogruece coditio G.6D verify theorem about the relatiohip i triagle, icludig proof of the Pythagorea Theorem, the um of iterior agle, bae agle of iocele triagle, midegmet, ad media, ad apply thee relatiohip to olve problem Prove two triagle are cogruet by applyig the ditace formula (G.2B) Verify/Prove the claificatio of variou polygo uig the ditace, lope, ad midpoit formula (G.2B)* Make cojecture baed o patter to etablih triagle cogruece utilizig a variety of tool, icludig real object, maipulative, patty paper, compa ad techology a appropriate (G.5A) Prove two triagle are cogruet by applyig the Side-Agle-Side cogruece coditio (G.6B) Prove two triagle are cogruet by applyig the Agle-Side-Agle cogruece coditio (G.6B) Prove two triagle are cogruet by applyig the Side-Side-Side cogruece coditio (G.6B) Prove two triagle are cogruet by applyig the Agle-Agle-Side cogruece coditio (G.6B) Prove two triagle are cogruet by applyig the Hypoteue-Leg cogruece coditio (G.6B) Verify/Prove bae agle of iocele triagle theorem ad olve problem (G.6D) Solve problem utilizig the Pythagorea Theorem ad bae agle of iocele triagle theorem (G.6D) Aalyze cogruece coditio to coect ad commuicate mathematical idea (G.6B) 5-6 Textbook Sectio : 3.3, 5.1, 5.2, 5.3, 5.4, 6.2, 6.3 Secod Gradig Period curriculum cotiued o ext page.

8 Readie Stadard() Tri a g l e P r o p e rt i e a d A tt ri b u t e G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.6A verify theorem about agle formed by the iterectio of lie ad lie egmet, icludig vertical agle, ad agle formed by parallel lie cut by a traveral ad prove equiditace betwee the edpoit of a egmet ad poit o it perpedicular biector ad apply thee relatiohip to olve problem G.6B prove two triagle are cogruet by applyig the Side-Agle-Side, Agle-Side-Agle, Side-Side-Side, Agle-Agle-Side, ad Hypoteue-Leg cogruece coditio G.5D verify the Triagle Iequality theorem uig cotructio ad apply the theorem to olve problem Make cojecture baed o patter of agle biector ad perpedicular biector i triagle utilizig a variety of tool (G.5A) Verfiy/Prove the Agle Biector Theorem (G.6A) Apply the Agle Biector Theorem to olve problem (G.6A) Verfiy/Prove the Perpedicular Biector Theorem (G.6A) Apply the Agle Biector Theorem to olve problem (G.6A) Make cojecture baed o patter of altitude ad media (G.6A) Verify/Prove the Cetroid Theorem ad utilize to olve problem (G.6D)* Make cojecture baed o patter of midegmet of triagle utilizig a variety of tool (G.5A)* Verify/Prove midegmet of triagle theorem ad utilize to olve problem (G.6D)* Verify the Triagle Iequality Theorem uig cotructio ad couter-example (G.5D) Solve mathematical ad real-world problem uig the Triagle Iequality Theorem (G.5D) Recogize ide agle relatiohip i triagle ad order ide ad agle accordig to ize (G.6D) Aalyze cogruece coditio to coect ad commuicate mathematical idea (G.6B) 9-10 Day G.6D verify theorem about the relatiohip i triagle, icludig proof of the Pythagorea Theorem, the um of iterior agle, bae agle of iocele triagle, midegmet, ad media, ad apply thee relatiohip to olve problem ( ACT) Textbook Sectio : 7.3, 8.1, 8.2, 8.3, 8.4 Secod Gradig Period curriculum cotiued o ext page.

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10 Readie Stadard() G.3B determie the image or pre-image of a give two-dimeioal figure uder a compoitio of rigid traformatio, a compoitio of o-rigid traformatio, ad a compoitio of both, icludig dilatio where the ceter ca be ay poit i the plae Determie whether a figure ha bee tralated, rotated, reflected or dilated to create a ew figure (G.3A) Tralate a give figure i a coordiate plae (G.3A) Reflect a give figure over the x -axi, y -axi or a give lie i a coordiate plae (G.3A) Rotate a figure a give degree i a coordiate plae (G.3A) Decribe traformatio of figure i a plae uig coordiate otatio (G.3A) Tr a f o r m a ti o G.3A decribe ad perform traformatio of figure i a plae uig coordiate otatio G.3C idetify the equece of traformatio that will carry a give pre-image oto a image o ad off the coordiate plae G.3D idetify ad ditiguih betwee reflectioal ad rotatioal ymmetry i a plae figure G.6C apply the defiitio of cogruece, i term of rigid traformatio, to idetify cogruet figure ad their correpodig ide ad agle Determie what type of traformatio wa applied to a figure from coordiate otatio (G.3A) Idetify cogruet figure reultig from rigid traformatio, icludig tralatio, reflectio, ad rotatio (G.6C) Idetify correpodig ide ad agle of cogruet figure i term of rigid traformatio (G.6C) Determie the image or pre-image of a give figure uder a compoitio of rigid traformatio, icludig tralatio, reflectio, rotatio (G.3B) Dilate a give figure by a cale factor both greater tha ad le tha 1 (G.3A) Determie the cale factor of a give dilatio (G.3A) Determie the image or pre-image of a dilatio where the ceter i ay poit o the plae (G.3B) Ditiguih betwee rigid ad o-rigid traformatio (G.3B) 7-9 Day Determie the image or pre-image of a give figure uder a compoitio of o-rigid traformatio, icludig dilatio (G.3B) Determie the image or pre-image of a figure uder a compoitio of both rigid ad o-rigid traformatio (G.3B) Idetify the equece of traformatio that will carry a give pre-image oto a image o the coordiate plae (G.3C) Determie the equece of traformatio that reult i a image that i created by a erie of dilatio where the ceter of dilatio i ot coitet (horizotal ad vertical tretche) (G.3C)* Idetify reflectioal ad rotatioal ymmetry i a plae figure (G.3D)

11 Textbook Sectio : 2.1, 2.2, 2.3, 11.1 Learig Aemet Midterm Exam 5-7 Day

12 Readie Stadard() Third Gradig Period (47 ) G.7B apply the Agle-Agle criterio to verify imilar triagle ad apply the proportioality of the correpodig ide to olve problem (ACT, SAT) Idetify imilar figure give a dilatio of a triagle (G.7A) Idetify proportioal ide give a dilatio of a triagle (G.7A) Idetify cogruet correpodig agle give a dilatio of a triagle (G.7A) Solve mathematical ad real-world problem utilizig the defiitio of imilarity i term of a dilatio (G.7A) Tri a gl e Si mi la rit y G.7A apply the defiitio of imilarity i term of a dilatio to idetify imilar figure ad their proportioal ide ad the cogruet correpodig agle G.8A prove theorem about imilar triagle, icludig the Triagle Proportioality Theorem, ad apply thee theorem to olve problem Prove the Agle-Agle, Side Agle-Side, ad Side Side-Side Similarity Theorem (G.8A) Solve mathematical ad real-world problem utilizig the Agle-Agle, Side Agle-Side, ad Side Side-Side Similarity Theorem (G.8A) Solve mathematical ad real-world problem ivolvig more tha two imilar triagle uig the Agle-Agle, Side-Agle-Side, ad Side-Side-Side Similarity Theorem (G.8A)* Verify imilar triagle by applyig the Agle-Agle Theorem (G.7B) Prove the Triagle Proportioality Theorem (G.8A) Solve mathematical ad real-world problem uig the Triagle Proportioality Theorem (G.8A) 7-8 Solve problem give imilar triagle by applyig the proportioality of correpodig ide (G.7B) Prove the Triagle Agle Biector Theorem (G.8A) Solve mathematical ad real-world problem uig the Triagle Agle Biector Theorem (G.8A) Textbook Sectio : 12.4,13.3 Third Gradig Period curriculum cotiued o the ext page

13 Sp ec ial Ri g ht Tr ia gl e /P yt ha g or ea T he or e m Rig ht Tr ia gl e - Tr ig o o m et ry Readie Stadard() G.9B apply the relatiohip i pecial right triagle ad ad the Pythagorea theorem, icludig Pythagorea triple, to olve Problem (ACT, SAT) G.8B idetify ad apply the relatiohip that exit whe a altitude i draw to the hypoteue of a right triagle, icludig the geometric mea, to olve problem Textbook Sectio : 13.1, 13.2, 13.4 Readie Stadard() G.9A determie the legth of ide ad meaure of agle i a right triagle by applyig the trigoometric ratio ie, coie, ad taget to olve problem (ACT, SAT) Textbook Sectio : 13.1, 13.2, 13.4 Solve problem uig Pythagorea triple (G.9B) Determie if a give right triagle i a pecial right triagle ( or ) (G.9B) Solve problem applyig the pecial right triagle relatiohip ad/or Pythagorea Theorem (G.9B) Solve problem with multiple triagle by applyig the pecial right triagle relatiohip ad/or Pythagorea Theorem (G.9B)* Solve mathematical ad real-world problem give a altitude draw to the hypoteue of a right triagle ad applyig imilar triagle relatiohip (G.8B) Solve mathematical ad real-world problem give a altitude draw to the hypoteue of a right triagle applyig geometric mea (G.8B) Fid miig ide legth of right triagle i mathematical ad real-world problem uig trigoometric ratio (ie, coie, taget) (G.9A) Third Gradig Period curriculum cotiued o the ext page Fid miig agle meaure of right triagle i mathematical ad real-world problem uig trigoometric ratio (ie, coie, taget) icludig applicatio ituatio ivolvig agle of elevatio ad depreio (G.9A) Solve problem ivolvig the Law of Sie ad Coie (G.9A)*

14 Readie Stadard() Qu ad ril at er al G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.6D verify theorem about the relatiohip i triagle, icludig proof of the Pythagorea Theorem, the um of iterior agle, bae agle of iocele triagle, midegmet, ad media, ad apply thee relatiohip to olve problem G.6E prove a quadrilateral i a parallelogram, rectagle, quare, or rhombu uig oppoite ide, oppoite agle, or diagoal ad apply thee relatiohip to olve problem Make cojecture baed o patter of iterior ad exterior agle of a polygo (G.5A) Verify/Prove um of iterior ad exterior agle theorem ad olve problem (G.6D) Make cojecture baed o patter of diagoal of quadrilateral (G.5A) Prove a quadrilateral i a parallelogram uig oppoite ide, oppoite agle, ad diagoal (G.6E) Prove a quadrilateral i a rectagle uig oppoite ide, oppoite agle, ad diagoal (G.6E) Prove a quadrilateral i a quare (G.6E) Prove a quadrilateral i a rhombu (G.6E) Solve real-world problem uig quadrilateral relatiohip (G.6E) Solve mathematical ad real-world problem utilizig propertie of kite ad trapezoid (G.5A)* Make cojecture baed o patter of midegmet trapezoid (G.5A)* Verify/Prove the Trapezoid Midegmet Theorem (G.6D)* 9-10 Textbook Sectio : 9.1, 9.2, 9.3, 9.4, *9.5 Third Gradig Period curriculum cotiued o the ext page

15 Readie Stadard() Are a of P ol yg o G.11B determie the area of compoite two-dimeioal figure compried of a combiatio of triagle, parallelogram, trapezoid, kite, regular polygo, or ector of circle to olve problem uig appropriate uit of meaure G.11A apply the formula for the area of regular polygo to olve problem uig appropriate uit of meaure Determie the area of mathematical ad real-world problem utilizig additio ad ubtractio of area, ivolvig compoite two-dimeioal figure compried of a combiatio of triagle, parallelogram, trapezoid, kite, circle or regular polygo uig appropriate uit of meaure (G.11B) Solve mathematical ad real-world problem uig the formula for the area of regular polygo give the apothem, uig appropriate uit of meaure (G.11A) Solve mathematical ad real-world problem uig trigoometry ad the formula for the area of regular polygo, uig appropriate uit of meaure (G.11A) 6-7 Textbook Sectio : 18.1, 18.3, 18.4 Readie Stadard() Sur fa ce Ar ea G.10B determie ad decribe how chage i the liear dimeio of a hape affect it perimeter, area, urface area, or volume, icludig proportioal ad o-proportioal dimeioal chage G.11C apply the formula for the total ad lateral urface area of three-dimeioal figure, icludig prim, pyramid, coe, cylider, phere, ad compoite figure, to olve problem uig appropriate uit of meaure Idetify 3-Dimeioal hape baed o their characteritic (G.11C) Idetify the hape of two-dimeioal cro-ectio of prim, pyramid, cylider, coe, ad phere created by a plae cuttig through the figure (G.10A) Idetify three-dimeioal object geerated by rotatio of two-dimeioal hape (G.10A) Model 3-dimeioal cro ectio ad object geerated by rotatio i order to idetify the correct object (G.10A) Explai how the formula for total ad lateral urface area relate to the area of compoite figure (G.11C) 6-7 G.10A idetify the hape of two-dimeioal cro-ectio of prim, pyramid, cylider, coe, ad phere ad idetify three-dimeioal object geerated by rotatio of two-dimeioal hape Solve mathematical ad real-world problem uig the formula for the total ad lateral urface area of three-dimeioal figure, icludig prim, pyramid, coe, cylider, phere, ad compoite figure, uig appropriate uit of meaure (G.11C) Textbook Sectio : 17.1, 17.2, 17.3, 17.4

16 Fourth Gradig Period (46 ) *Sprig Learig Aemet April 8-26 Readie Stadard() Vol u m e G.11D apply the formula for the volume of three-dimeioal figure, icludig prim, pyramid, coe, cylider, phere, ad compoite figure, to olve problem uig appropriate uit of meaure (ACT, SAT) Explai how the formula for volume relate to the area of compoite figure (G.11D) Solve mathematical ad real-world problem uig the formula for the volume of three-dimeioal figure, icludig prim, pyramid, coe, cylider, phere, ad compoite figure, uig appropriate uit of meaure (G.11D) 5-6 Textbook Sectio : 16.1, 16.2, 16.3, 16.4 Readie Stadard() Di m e i o C ha ge G.10B determie ad decribe how chage i the liear dimeio of a hape affect it perimeter, area, urface area, or volume, icludig proportioal ad o-proportioal dimeioal chage Decribe ad compare the effect o perimeter whe oe or more dimeio are chaged (both proportioal ad o-proportioal) (G.10B) Decribe ad compare the effect o area whe oe or more dimeio are chaged (both proportioal ad o-proportioal) (G.10B) Decribe ad compare the effect o urface area whe oe or more dimeio are chaged (both proportioal ad o-proportioal) (G.10B) Decribe ad compare the effect o volume whe oe or more dimeio are chaged (both proportioal ad o-proportioal) (G.10B) Decribe ad compare the effect o area, perimeter, urface area, ad volume whe a erie (multiple et) of dimeio chage occur (G.10B)* 4-5 Textbook Sectio : 16.1, 16.2, 16.3, 16.4 Fourth Gradig Period curriculum cotiued o the ext page

17 Cir cl e Readie Stadard() G.5A ivetigate patter to make cojecture about geometric relatiohip, icludig agle formed by parallel lie cut by a traveral, criteria required for triagle cogruece, pecial egmet of triagle, diagoal of quadrilateral, iterior ad exterior agle of polygo, ad pecial egmet ad agle of circle chooig from a variety of tool (ACT, SAT) G.11B determie the area of compoite two-dimeioal figure compried of a combiatio of triagle, parallelogram, trapezoid, kite, regular polygo, or ector of circle to olve problem uig appropriate uit of meaure G.4D compare geometric relatiohip betwee Euclidea ad pherical geometrie, icludig parallel lie ad the um of the agle i a triagle G.12A apply theorem about circle, icludig relatiohip amog agle, radii, chord, taget, ad ecat, to olve o-cotextual problem (ACT, SAT) G.12B apply the proportioal relatiohip betwee the meaure of a arc legth of a circle ad the circumferece of the circle to olve problem G.12C apply the proportioal relatiohip betwee the meaure of the area of a ector of a circle ad the area of the circle to olve problem Idetify circle vocabulary icludig type of arc, lie, egmet ad their otatio (G.12A) Make cojecture baed o patter of cetral ad icribed agle of circle (G.5A) Make cojecture baed o patter of quadrilateral icribed i a circle (G.5A) Solve problem uig cetral agle ad icribed agle (G.12A) Make cojecture baed o patter of taget to a circle ad circumcribed agle of circle (G.5A) Solve problem by applyig chord-chord, ecat-ecat, ad ecat-taget product theorem (G.12A Solve problem by applyig the proportioal relatiohip betwee the meaure of the area of a ector of a circle ad the area of the circle (G.12C) Determie the area of egmet of circle (compoite two-dimeioal figure compried of a combiatio of triagle ad ector of circle) to olve problem, icludig applicatio problem, uig appropriate uit of meaure (G.11B) Solve multi-tep problem ivolvig compoite area of circle ad arc legth i real world ettig (G.11B)* Solve problem by applyig the proportioal relatiohip betwee the meaure of a arc legth of a circle ad the circumferece of the circle (G.12B) Fid the agle meaure i radia give degree ad i degree give radia (G.12D) Fid the equatio of a circle with ceter at the origi ad radiu r (G.12E) Fid the equatio of a circle with ceter at ( h,k ) ad radiu r (G.12E) G.12D decribe radia meaure of a agle a the ratio of the legth of a arc itercepted by a cetral agle ad the radiu of the circle (ACT, SAT) G.12E how that the equatio of a circle with ceter at the origi ad radiu r i x 2 + y 2 = r 2 ad determie the equatio for the graph of a circle with radiu r ad ceter (h, k), (x - h) 2 + (y - k) 2 =r 2 (SAT) Write the equatio of a circle give a poit o the circle ad the ceter (G.12E) Graph the circle give the equatio of a circle (G.12E Decribe the characteritic of hape i Euclidea ad Spherical Geometry (G.4D) Compare ad cotrat parallel lie i Euclidea ad Spherical Geometry (G.4D) Compare ad cotrat the Triagle Sum Theorem i Euclidea ad Spherical Geometry (G.4D) Textbook Sectio : 14.1, 14.2, 14.3, 14.4, 14.5, 15.2, 15.3, 15.4

18 Fourth gradig period curriculum cotiued o the ext page.

19 Readie Stadard() Pro ba bil ity G.13C idetify whether two evet are idepedet ad compute the probability of the two evet occurrig together with or without replacemet (ACT, SAT) G.13A develop trategie to ue permutatio ad combiatio to olve cotextual problem G.13B determie probabilitie baed o area to olve cotextual problem Determie probabilitie i everyday life problem baed o area (G.13B) Determie whether two evet are idepedet (G.13C) Compute the probability of two idepedet evet occurrig together with ad without replacemet (G.13C) Compute the probability of two depedet evet occurrig together (G.13C)* Create repreetatio to record ad orgaize data (G.13C) Develop trategie (fudametal coutig priciple ad factorial) to develop patter to explai permutatio ad combiatio to olve cotextual problem (G.13A) G.13D apply coditioal probability i cotextual problem (ACT, SAT) Evaluate the reaoablee of a olutio uig a problem olvig model (G.13A) G.13E apply idepedece i cotextual problem (ACT, SAT) Solve real-world problem ivolvig coditioal probability (G.13D) Solve real-world problem ivolvig idepedece probability (G.13E) Textbook Sectio : 18.2, 19.1, 19.2, , 20.1, 20.2 Semeter Review ad Exam 5-7