Grades 9–11
Language Development for Success
BOOK 2 Quadrilaterals, Circles, Polygons & Area, Three Dimensional Figures
Sealaska Heritage Institute The contents of this program were developed by Sealaska Heritage Institute through the support of a Special Projects 'HPRQVWUDWLRQ*UDQWIURPWKH86'HSDUWPHQWRI(GXFDWLRQ2I¿FHRI,QGLDQ(GXFDWLRQ &)'$$ +RZHYHUWKHFRQWHQWV do not necessarily represent the policy of the Department of Education and you should not assume endorsement. 2009 Integrating Culturally Responsive, Place-Based Content with Language Skills Development for Curriculum Enrichment
DEVELOPED BY Stephanie Hoage Steve Morley Jim MacDiarmid
Unit Assessments Bev Williams
LAYOUT & FORMATTING Matt Knutson
PRINTERS Capital Copy, Juneau, Alaska
PROJECT ASSISTANT Tiffany LaRue
2009 Table of Contents
BOOK 2
Introduction ......
The Developmental Language Process ...... 7
Math and the Developmental Language Process ..... 9
8QLW²4XDGULODWHUDOV ...... 11
8QLW²&LUFOHV ......
8QLW²3RO\JRQV $UHD ......
8QLW ²7KUHH'LPHQVLRQDO)LJXUHV ...... INTRODUCTION
2YHUWKH\HDUVPXFKKDVEHHQZULWWHQDERXWWKHVXFFHVVHVDQGIDLOXUHVRIVWXGHQWVLQ VFKRROV7KHUHLVQRHQGWRWKHVROXWLRQVRIIHUHGSDUWLFXODUO\IRUWKRVHVWXGHQWVZKRDUH struggling with academics. There have been efforts to bring local cultures into the class- URRPWKXVSURYLGLQJWKHVWXGHQWVZLWKIDPLOLDUSRLQWVRIGHSDUWXUHIRUOHDUQLQJ+RZHYHU most often such instruction has been limited to segregated activities such as arts and crafts or Native dancing rather than integrating Native culture into the overall learning SURFHVV7ZRFRUHFXOWXUDOYDOXHV Haa Aaní, WKHUHIHUHQFHIRUDQGXVDJH RIWKHODQG and Haa Shagóon, WKHW\LQJRIWKHSUHVHQWZLWKWKHSDVWDQGIXWXUH are known by both VWXGHQWVDQGSDUHQWVDQGFDQEHLQFOXGHGLQDFXUULFXOXPWKDWVLPXOWDQHRXVO\SURYLGHV DEDVLVIRUVHOILGHQWLW\DQGFXOWXUDOSULGHZLWKLQWKHHGXFDWLRQDOVHWWLQJ7KLVZLOOSURYLGH a valuable foundation for improved academic achievement.
:KLOHWKHLQFOXVLRQRI1DWLYHFRQFHSWVYDOXHVDQGWUDGLWLRQVLQWRDFXUULFXOXPSURYLGHVD YDOXDEOHIRXQGDWLRQIRUVHOILGHQWLW\DQGFXOWXUDOSULGHLWPD\QRWRQLWVRZQIXOO\DGGUHVV improved academic achievement.
7KLVSURJUDPLVGHVLJQHGWRPHHWWKHDFDGHPLFUHDOLWLHVIDFHGE\KLJKVFKRROVWXGHQWV HYHU\GD\XVLQJDGHYHORSPHQWDOSURFHVVWKDWLQWHJUDWHVculture with skills development. The values of Haa Aaní and Haa Shagóon are reinforced through the various activities in the program.
'XULQJPDWKOHVVRQVVWXGHQWVDUHH[SRVHGWRPDWKLQIRUPDWLRQDQGWRNH\YRFDEXODU\ WKDWUHSUHVHQWWKDWLQIRUPDWLRQ:KLOHWKHVWXGHQWVPD\DFTXLUHWKURXJKYDULRXVSURFHVV- HVWKHPDWKHPDWLFDOLQIRUPDWLRQWKHYRFDEXODU\LVRIWHQOHIWDWDQH[SRVXUHOHYHODQGLV QRWLQWHUQDOL]HGE\WKHP2YHUWLPHWKLVOHDGVWRlanguage-delay that impacts negatively on a student’s on-going academic achievement.
Due to language delayPDQ\1DWLYH$ODVNDQKLJKVFKRROVWXGHQWVVWUXJJOHZLWKWH[WVWKDW are beyond their comprehension levels and writing assignments that call for language WKH\GRQRWKDYH7RWKLVHQGLQWKLVUHVRXUFHSURJUDPHDFKNH\YRFDEXODU\ZRUGLQPDWK is viewed as a concept7KHZRUGVDUHLQWURGXFHGFRQFUHWHO\XVLQJSODFHEDVHGLQIRUPD- WLRQDQGFRQWH[WV8VLQJWKLVDSSURDFKWKHVWXGHQWVKDYHWKHRSSRUWXQLW\WRDFTXLUHQHZ information in manageable chunks; the sum total of which represent the body of informa- tion to be learned in the math program. In many high school math classes it is assumed WKDWWKHDFDGHPLFYRFDEXODU\LVEHLQJLQWHUQDOL]HGGXULQJWKHOHDUQLQJSURFHVVZKLFKLV most often an erroneous assumption.
— 5 — :KHQWKHNH\YRFDEXODU\FRQFHSWVKDYHEHHQLQWURGXFHGWKHVWXGHQWVDUHWKHQWDNHQ WKURXJK D VHTXHQFH RI OLVWHQLQJ VSHDNLQJ UHDGLQJ DQG ZULWLQJ DFWLYLWLHV GHVLJQHG WR instill the vocabulary into their long term memories - see the Developmental Language ProcessZKLFKIROORZV
It should be understood that these materials are not a curriculum UDWKHU WKH\ DUH resource materials designed to encourage academic achievement through intensive language development in the content areas.These resource materials are culturally responsive in that they utilize teaching and learning styles effective with Native students. $VWKHVWXGHQWVSURJUHVVWKURXJKWKHVWHSVRIWKH3URFHVVWKH\PRYHIURPDFRQFUHWH LQWURGXFWLRQRIWKHNH\YRFDEXODU\WRDV\PEROLFUHSUHVHQWDWLRQRIWKHYRFDEXODU\DQG ¿QDOO\WRWKHLUDEVWUDFWIRUPVUHDGLQJDQGZULWLQJ7KLVSURYLGHVDIRUPDWIRUWKHVWXGHQWV to develop language and skills that ultimately lead to improved academic performance.
The Integration of Place-Based, Culturally Responsive Math Content and Language Development
Introduction of Key Math Vocabulary
Math, Vocabulary Development Listening, speaking, reading & writing
Math Application Reinforcement Activities
— 6 — The Developmental Language Process
7KH'HYHORSPHQWDO/DQJXDJH3URFHVV '/3 LVGHVLJQHGWRLQVWLOOODQJXDJHLQWRORQJ term memory. The origin of the Process is rooted in the struggles faced by language- GHOD\HGVWXGHQWVSDUWLFXODUO\ZKHQWKH\¿UVWHQWHUVFKRRO
7KH3URFHVVWDNHVWKHVWXGHQWVFKLOGUHQWKURXJKGHYHORSPHQWDOVWHSVWKDWUHÀHFWWKH QDWXUDODFTXLVLWLRQRIODQJXDJHLQWKHKRPHDQGFRPPXQLW\,QLWLDOO\RQFHNH\ODQJXDJH LWHPVKDYHEHHQLQWURGXFHGFRQFUHWHO\WRWKHVWXGHQWVWKHYRFDEXODU\DUHXVHGLQWKH ¿UVWRIWKHODQJXDJHVNLOOV%DVLF/LVWHQLQJ7KLVVWDJHLQWKHSURFHVVUHSUHVHQWVinput DQGLVDFULWLFDOYHQXHIRUODQJXDJHDFTXLVLWLRQDQGUHWHQWLRQ$EDE\KHDUVPDQ\GLI- IHUHQWWKLQJVLQWKHKRPHJUDGXDOO\WKHEDE\EHJLQVWRlistenWRZKDWKHVKHKHDUV$V a result of the inputSURYLGHGWKURXJK%DVLF/LVWHQLQJWKHEDE\WULHVWRUHSHDWVRPHRI WKHODQJXDJHKHDUG±WKLVLVUHSUHVHQWHGE\WKHVHFRQGSKDVHRIWKH3URFHVV%DVLF Speaking - the oral output stage of language acquisition.
$VPRUHODQJXDJHJRHVLQWRDFKLOG¶VORQJWHUPPHPRU\KHVKHEHJLQVWRXQGHUVWDQG simple commands and phrases. This is a higher level of listening represented by the VWDJH/LVWHQLQJ&RPSUHKHQVLRQ:LWKWKHLQFUHDVHLQYRFDEXODU\DQGVHQWHQFHGHYHO- RSPHQWWKHFKLOGEHJLQVWRH[SORUHWKHXVHRIODQJXDJHWKURXJKWKHQH[WVWDJHLQ WKH3URFHVV&UHDWLYH6SHDNLQJ$OORIWKHVHVWHSVLQWKH3URFHVVUHÀHFWWKHQDWXUDO sequence of language development.
The listening and speaking skill areas represent trueODQJXDJHVNLOOV PRVWFXOWXUHV LQFOXGLQJ$ODVND1DWLYHFXOWXUHVQHYHUZHQWEH\RQGWKHPWRGHYHORSZULWWHQIRUPV2UDO traditions are inherent in the listening and speaking skills.
+RZHYHU(QJOLVKGRHVKDYHDEVWUDFWIRUPVRIODQJXDJHLQUHDGLQJDQGZULWLQJ0DQ\ Native children entering kindergarten come from homes where language is used differ- ently than in classic Western homes. This is not a value judgment of child rearing prac- WLFHVEXWDGH¿QLWHFURVVFXOWXUDOUHDOLW\7KHUHIRUHLWLVFULWLFDOWKDWWKH1DWLYHFKLOGEH introduced to the concepts of reading and writing before ever dealing with them as skills areas. It is vital for the children to understand that reading and writing are talk in print.
The Developmental Language Process integrates the real language skills of listening DQGVSHDNLQJZLWKWKHUHODWHGVNLOOVRIUHDGLQJDQGZULWLQJ$WWKLVVWDJHLQWKH3URFHVV WKHVWXGHQWVDUHLQWURGXFHGWRWKHSULQWHGZRUGVIRUWKH¿UVWWLPH7KHVHDEVWUDFWUHSUH- VHQWDWLRQVDUHQRZIDPLOLDUWKURXJKWKHOLVWHQLQJDQGVSHDNLQJDFWLYLWLHVDQGWKHUHOD- WLRQVKLSLVIRUPHGEHWZHHQWKHZRUGVDQGODQJXDJHEHJLQQLQJZLWK%DVLF5HDGLQJ
$VPRUHODQJXDJHJRHVLQWRWKHFKLOGUHQ¶VORQJWHUPPHPRULHVWKH\EHJLQWRFRPSUH- KHQGPRUHRIZKDWWKH\UHDGLQ5HDGLQJ&RPSUHKHQVLRQ
— 7 — 0DQ\$ODVNDQVFKRRODWWLFVDUH¿OOHGZLWKUHDGLQJSURJUDPVWKDWGLGQ¶WZRUN±LQUHDOLW\ any of the programs would have worked had they been implemented through a lan- JXDJHGHYHORSPHQWSURFHVV)RUPDQ\1DWLYHFKLOGUHQWKHSULQWHGZRUGFUHDWHVDQJVW SDUWLFXODUO\LIWKH\DUHVWUXJJOLQJZLWKWKHUHDGLQJSURFHVV2IWHQFKLOGUHQDUHDVNHGWR read language they have never heard.
1H[WLQWKH3URFHVVLV%DVLF:ULWLQJZKHUHWKHVWXGHQWVDUHDVNHGWRZULWHWKHNH\ ZRUGV)LQDOO\WKHPRVWGLI¿FXOWRIDOOWKHODQJXDJHVNLOOV&UHDWLYH:ULWLQJKDVWKHVWX- GHQWVZULWLQJVHQWHQFHVRIWKHLURZQXVLQJWKHNH\ZRUGVDQGODQJXDJHIURPWKHLUORQJ term memories. This high level skill area calls upon the students to not only retrieve ODQJXDJHEXWWRSXWWKHZRUGVLQWKHLUFRUUHFWRUGHUZLWKLQWKHVHQWHQFHVWRVSHOOWKH words correctly and to sequence their thoughts in the narrative.
The Developmental Language Process is represented in this chart:
$WWKHHQGRIWKH3URFHVVWKHVWXGHQWVSDUWLFLSDWHLQHQULFKPHQWDFWLYLWLHVEDVHGRQ recognized and reasearch-based best practices%\WKLVWLPHWKHLQIRUPDWLRQDQGYRFDE- XODU\ZLOOEHIDPLOLDUDGGLQJWRWKHVWXGHQWV¶IHHOLQJVRIFRQ¿GHQFHDQGVXFFHVV
7KH8QLW¶V$VVHVVPHQWLVDOVRDGPLQLVWHUHGGXULQJWKH([WHQVLRQ$FWLYLWLHVVHFWLRQRI the Process. This test provides the teacher with a clear indication of the students’ prog- UHVVEDVHGRQWKHREMHFWLYHVIRUEDVLFOLVWHQLQJEDVLFUHDGLQJUHDGLQJFRPSUHKHQVLRQ basic writing and creative writing.
Since the DLP is a processDQGQRWDSURJUDPLWFDQEHLPSOHPHQWHGZLWKDQ\PDWHUL- DOVDQGDWDQ\JUDGHRUUHDGLQHVVOHYHO$VWXGHQW¶VDELOLW\WRFRPSUHKHQGZHOOLQlisten- ing and readingDQGWREHFUHDWLYHO\H[SUHVVLYHLQspeaking and writingLVGHSHQGHQW upon how much language he/she has in long-term memory.
— 8 — Math & The Developmental Language Process
The Developmental Language Process can be applied effectively in the development of math concepts and their vocabulary. Not all math vocabulary lend themselves well to listening com- SUHKHQVLRQFUHDWLYHVSHDNLQJDQGFUHDWLYHZULWLQJDFWLYLWLHVDQGWKHUHIRUHWKH3URFHVVFDQEH adapted to create a fast track in math. This schema represents the use of the Process in math:
$FWLYLWLHVIRUOLVWHQLQJFRPSUHKHQVLRQFUHDWLYHVSHDNLQJDQGFUHDWLYHZULWLQJFDQEHXVHG depending upon the vocabulary being developed.
7KLVUHVRXUFHERRNLVGHVLJQHGWREHXVHGDSSUR[LPDWHO\RQFHSHUPRQWKIRUDVL[W\WRQLQHW\ PLQXWHOHVVRQ'XULQJWKLVWLPHWKHGHYHORSPHQWRImath vocabulary is the principle endeav- RUQRWWKHWHDFKLQJRIWKHPDWKFRQFHSWV+RZHYHUWKHPDWKFRQFHSWVIRUPWKHEDVHVIRUODQ- guage development.
Increased vocabulary development in math will ultimately lead to improved academic achieve- PHQWLQFUHDVHGVHOIHVWHHPDQGWRDKLJKHUVXFFHVVUDWHRQDFDGHPLFDVVHVVPHQWV
— 9 — — 10 — UNIT 6 Quadrilaterals
Sealaska Heritage Institute
Grade Level Expectations for Unit 6
Unit 6—Quadrilaterals
Alaska State Mathematics Standard A $VWXGHQWVKRXOGXQGHUVWDQGPDWKHPDWLFDOIDFWVFRQFHSWVSULQFLSOHVDQGWKHRULHV
$VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG $ FRQVWUXFWGUDZPHDVXUHWUDQVIRUPFRPSDUHYLVXDOL]HFODVVLI\DQGDQDO\]H WKHUHODWLRQVKLSVDPRQJJHRPHWULF¿JXUHV DQG
Alaska State Mathematics Standard C $VWXGHQWVKRXOGXQGHUVWDQGDQGEHDEOHWRIRUPDQGXVHDSSURSULDWHPHWKRGVWR GH¿QHDQGH[SODLQPDWKHPDWLFDOUHODWLRQVKLSV
$VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG & H[SUHVVDQGUHSUHVHQWPDWKHPDWLFDOLGHDVXVLQJRUDODQGZULWWHQSUHVHQWDWLRQV SK\VLFDOPDWHULDOVSLFWXUHVJUDSKVFKDUWVDQGDOJHEUDLFH[SUHVVLRQV & UHODWHPDWKHPDWLFDOWHUPVWRHYHU\GD\ODQJXDJH
GLEs The student demonstrates an understanding of geometric relationships by >@*LGHQWLI\LQJDQDO\]LQJFRPSDULQJRUXVLQJSURSHUWLHVRISODQH¿JXUHV VXPRILQWHULRURUH[WHULRUDQJOHVRIDSRO\JRQ
The student communicates his or her mathematical thinking by: > @36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQG RUV\PEROLFDOO\WUDQVODWLQJDPRQJWKHVHDOWHUQDWLYHUHSUHVHQWDWLRQV RUXVLQJ DSSURSULDWHYRFDEXODU\V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQG strategies and solutions >@36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRU V\PEROLFDOO\FRPPXQLFDWLQJPDWKLGHDVLQZULWLQJ RUXVLQJDSSURSULDWHYRFDEXODU\ V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQGVROXWLRQV
Vocabulary & Definitions
Introduction of Math Vocabulary
Regular polygon $UHJXODUSRO\JRQLVRQHLQZKLFKDOOVLGHVDUHFRQJUXHQWDQGDOODQJOHV DUHFRQJUXHQW(TXLODWHUDOWULDQJOHVDQGVTXDUHVDUHH[DPSOHVRIUHJX- ODUSRO\JRQV$UHJXODUSRO\JRQWKDW\RXPLJKWVHHIUHTXHQWO\LVDVWRS VLJQ±LWLVDUHJXODURFWDJRQZLWKHLJKWHTXDOVLGHV
Irregular polygon $Q\FORVHGSODQH¿JXUHZLWKVWUDLJKWVLGHVLVDQLUUHJXODUSRO\JRQXQ- less all of the sides and angles are congruent.
)ORRUSODQVRIEXLOGLQJVDUHIUHTXHQWO\LQWKHVKDSHRILUUHJXODUSRO\- gons:
Quadrilateral $TXDGULODWHUDOLVDQ\IRXUVLGHGSRO\JRQ
This plan view of a tribal house shows many different quadrilaterals.
— 17 — Introduction of Math Vocabulary
Parallelogram $SDUDOOHORJUDPLVDIRXUVLGHGSRO\JRQZLWKERWKSDLUVRIRSSRVLWHVLGHVSDUDOOHO to each other.
7KHIURQWRIWKLVROGEXLOGLQJZLWKFRUQHUVWKDWDUHQRORQJHUVTXDUHLVVKDSHG like a parallelogram.
Rectangle $UHFWDQJOHLVDIRXUVLGHGSRO\JRQZLWKIRXUULJKWDQJOHV
5HFWDQJOHVDUHDYHU\FRPPRQW\SHRITXDGULODWHUDO,WHPVVKDSHGOLNHUHFWDQ- JOHVLQFOXGHÀRRUVFHLOLQJVZDOOVZLQGRZVGRRUVVKHHWVRISDSHUDQGÀDJV
— 18 — Introduction of Math Vocabulary
Square $VTXDUHLVDIRXUVLGHGSRO\JRQZLWKIRXUULJKWDQJOHVDQGDOOIRXUVLGHVFRQJUX- ent.
)RUIXQFKDOOHQJHVWXGHQWVWR¿QGDOOVTXDUHVRQWKHFKHFNHU FKHVV ERDUG 7KHUHDUH[ [[[[ [[DQG[ VTXDUHV
Rhombus $UKRPEXVLVDSDUDOOHORJUDPZLWKIRXUFRQJUXHQWVLGHV
:KHQD¿VKLQJQHWLVVWUHWFKHGWKHPHVKWDNHVWKHVKDSHRIDUKRPEXV
— 19 — Introduction of Math Vocabulary
Diagonal $GLDJRQDOLVDOLQHVHJPHQWWKDWFRQQHFWVWZRQRQDGMDFHQWFRUQHUV YHUWLFHV RI a polygon.
,QWKLVGHVLJQUHFWDQJOHVDUHGLYLGHGLQWRWULDQJOHVE\GLDJRQDOV
Trapezoid $WUDSH]RLGLVDTXDGULODWHUDOZLWKRQHSDLURISDUDOOHOVLGHV
:KLFKZLQGRZ V RQWKLVERDWLVLQWKHVKDSHRIDWUDSH]RLG"
Here they are:
— 20 — Introduction of Math Vocabulary
Base of a trapezoid Either of the parallel sides of a trapezoid is referred to as a base of the trapezoid.
Leg of a trapezoid $OHJRIDWUDSH]RLGLVDVLGHWKDWLVQRWSDUDOOHOWRDQRWKHUVLGH
Isosceles trapezoid $QLVRVFHOHVWUDSH]RLGLVRQHLQZKLFKWKHOHJVDUHHTXDOLQOHQJWK The designer of this car used several isosceles trapezoids.
— 21 — Introduction of Math Vocabulary
Kite $NLWHLVDTXDGULODWHUDOZLWKWZRSDLUVRIDGMDFHQWVLGHVWKDWDUHFRQJUXHQWWR HDFKRWKHU+RZGR\RXWKLQNDNLWHJRWLWVQDPH"
Similar polygons 6LPLODUSRO\JRQVDUHLGHQWLFDOLQVKDSHEXWDUHQRWQHFHVVDULO\WKHVDPHVL]H
2QWKLVTXLOWWKHSDWWHUQLVPDGHZLWKVLPLODUWULDQJOHV
— 22 — Introduction of Math Vocabulary
Corresponding sides &RUUHVSRQGLQJVLGHVDUHWZRVLGHVRIGLIIHUHQWREMHFWVWKDWDUHVLWXDWHGLQWKH same way.
Proportional 3URSRUWLRQDOPHDQVWKDWWKHUDWLRLVWKHVDPH,QVLPLODUSRO\JRQVWKHVLGHVDUH SURSRUWLRQDOWRHDFKRWKHUDQGWKDWIDFWLVRIWHQXVHGWR¿QGPLVVLQJOHQJWKVDQG solve problems:
— 23 — — 24 — Language and Skills Development Using the Math Vocabulary Terms
Language & Skills Development
Illustration Sequence %HIRUHWKHDFWLYLW\EHJLQVJLYHWKHVWXGHQWVWKHPLQLLOOXVWUDWLRQVIURPWKLVXQLW 6D\DVHTXHQFHRIYRFDEXODU\ZRUGV IRXURU¿YHZRUGV $IWHU\RXKDYHVDLGWKH VHTXHQFHRIZRUGVWKHVWXGHQWVVKRXOG¿QGWKHQHFHVVDU\LOOXVWUDWLRQVWRUHSUH- LISTENING VHQWWKHVHTXHQFH\RXVDLG(DFKVWXGHQWVKRXOGOD\WKHIRXURU¿YHLOOXVWUDWLRQV Use the activity pages RQKLVKHUGHVNLQWKHVDPHRUGHUDV\RXVDLGWKHYRFDEXODU\ZRUGV5HSHDWWKLV from the Student process with other sequences of vocabulary words. Support Materials.
Illustration Jigsaw &XWHDFKRIWKHYRFDEXODU\LOOXVWUDWLRQVLQWRIRXUSLHFHV0L[WKHFXWRXWSLHFHV SPEAKING WRJHWKHUDQGGLVWULEXWHWKHPWRWKHVWXGHQWV DVWXGHQWPD\KDYHPRUHWKDQRQH LOOXVWUDWLRQVHFWLRQ :KHQ\RXVD\³*R´WKHVWXGHQWVVKRXOGDWWHPSWWRPDWFK the jigsaw sections they have to reproduce the original vocabulary illustrations. :KHQ WKH VWXGHQWV SXW WKH QHFHVVDU\ SLHFHV RI DQ LOOXVWUDWLRQ WRJHWKHU WKH\ VKRXOGLGHQWLI\WKHLOOXVWUDWLRQE\LWVYRFDEXODU\ZRUG&RQWLQXHXQWLODOOYRFDEX- lary illustrations have been put together and named in this way.
Half Time %HIRUHWKHDFWLYLW\EHJLQVFXWHDFKRIWKHVLJKWZRUGVLQKDOI.HHSRQHKDOIRI each sight word and give the remaining halves to the students. Hold up one of READING your halves and the student who has the other half of that word must show his half Use the activity pages from the Student DQVD\WKHVLJKWZRUG5HSHDWLQWKLVZD\XQWLODOOVWXGHQWVKDYHUHVSRQGHG$Q Support Materials. alternative to this approach is to give all of the word halves to the students. Say one of the sight words and the two students who have the halves that make up the sight word must show their halves. Depending upon the number of students in \RXUFODVV\RXPD\ZLVKWRSUHSDUHH[WUDVLJKWZRUGFDUGVIRUWKLVDFWLYLW\
What’s Your Letter? Provide each student with writing paper and a pen. Say a sight word. Each VWXGHQW VKRXOG WKHQ ZULWH 21( OHWWHU IURP WKDW ZRUG DQ\ OHWWHU 5HYLHZ WKH students’ responses to determine if all letters from the sight word were used. If WRITING DOOOHWWHUVIURPWKHVLJKWZRUGZHUHQRWXVHGFDOOXSRQWKHVWXGHQWVWRLGHQWLI\ Use the activity pages WKHOHWWHUVWKDWDUH³PLVVLQJ´5HSHDWZLWKRWKHUVLJKWZRUGV from the Student Support Materials.
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Student Support Materials
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— 61 — — 62 — True-False Sentences (Listening and/or Reading Comprehension)
1. In regular polygonsDOORIWKHDQJOHVDUHFRQJUXHQW 2. $OORIWKHVLGHVRIDQirregular polygon could be congruent. $Q\¿JXUHZLWKIRXUVLGHVLVDquadrilateral. Opposite sides of a parallelogram are congruent. The adjacent sides of a rectangle are congruent. ,IDOOIRXUVLGHVRIDTXDGULODWHUDODUHWKHVDPHOHQJWKLWLVDsquare. 7. $NLWHLVRQHW\SHRIrhombus. $diagonal connects two corners of a polygon. 9. $UHFWDQJOHLVDOVRDtrapezoid. 10.The base of a trapezoid is one of the two parallel sides. 11.$leg of a trapezoid is not parallel to any other side. 12. The bases of an isosceles trapezoid are congruent. $kite has two pairs of congruent sides. $UHFWDQJOHDQGDNLWHDUHsimilar polygons. Corresponding sidesRIWZR¿JXUHVDUHLQWKHVDPHSRVLWLRQRQHDFK ¿JXUH When a pair of line segments has the same ratio as another pair of seg- PHQWVWKH\DUHproportional.
$QVZHUV 77)7)))7 )77)7)77
1. $UHFWDQJOHLVDregular polygon. 2. $VTXDUHLVDQirregular polygon. $UKRPEXVDVTXDUHDQGDNLWHDUHH[DPSOHVRIquadrilaterals. 5LJKWDQJOHVDUHQHYHUIRXQGLQparallelograms. $Q\IRXUVLGHGSRO\JRQZLWKIRXUULJKWDQJOHVLVDrectangle. $square is a regular polygon. 7. $rhombus has four congruent sides. $diagonal is always longer than any side of a polygon. 9. Two sides of a trapezoid are parallel to each other. 10. Only the longest side of a trapezoid is called the base. 11.Every trapezoid has four legs. 12.The legs of an isosceles trapezoid are congruent. $WUDSH]RLGPLJKWDOVREHDkite. 14.Similar polygonsKDYHWKHVDPHVKDSHEXWQRWDOZD\VWKHVDPHVL]H ,IWZRVLGHVDUHDGMDFHQWWRHDFKRWKHUWKH\DUHcorresponding sides. 16.Proportional sides can be found on any two trapezoids.
$QVZHUV ))7)777) 7))7)7))
— 63 — Match the Halves $UKRPEXVLVOLNHDVTXDUH $WKH\DUHSURSRUWLRQDO
2. The diagonal of a quadrilateral %UHJXODUSRO\JRQZLWKIRXUVLGHV
$Q\IRXUVLGHGSRO\JRQ &SDUDOOHORJUDPV
:KHQVHJPHQWVKDYHWKHVDPHUDWLR D. it is an irregular polygon.
7ZRSDLUVRIFRQJUXHQWDGMDFHQWVLGHV E. are similar polygons.
6TXDUHVDQGUHFWDQJOHVDUHW\SHVRI )ZLWKRXWVTXDUHFRUQHUV
$UHJXODUSRO\JRQ G. is not parallel to any other side
7KHOHJRIDWUDSH]RLG H. corresponding sides.
$VTXDUHLVD I. is called a quadrilateral.
,ILWVWZROHJVDUHWKHVDPHOHQJWK -([DFWO\WZRSDUDOOHOVLGHV
$ELJVTXDUHDQGDVPDOOVTXDUH .FDQKDYHDQ\QXPEHURIVLGHV
12. Sides of objects that are situated the L. a rhombus. same way are $UHFWDQJOHFDQQRWDOVREH M. Divides it into two triangles.
,IDOORIWKHVLGHVDQGDOORIWKHDQJOHVDUH N. it is an isosceles trapezoid. QRWFRQJUXHQW (LWKHURQHRILWVSDUDOOHOVLGHV O. are found on a kite.
$WUDSH]RLGKDV P. Is the base of a trapezoid.
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— 64 — 'H¿QLWLRQV
Regular polygon: a polygon in which all sides are congruent and all angles are congruent. Irregular polygon:DQ\FORVHGSODQH¿JXUHZLWKVWUDLJKWVLGHVLVDQLUUHJXODU SRO\JRQXQOHVVDOORIWKHVLGHVDQGDQJOHVDUHFRQJUXHQW Quadrilateral: any four-sided polygon. Parallelogram: a four-sided polygon with both pairs of opposite sides parallel to each other. Rectangle: a four-sided polygon with four right angles. Square: a four-sided polygon with four right angles and all four sides congruent. Rhombus: a parallelogram with four congruent sides. Diagonal:DOLQHVHJPHQWWKDWFRQQHFWVWZRQRQDGMDFHQWFRUQHUV YHUWLFHV RID polygon. Trapezoid: a quadrilateral with one pair of parallel sides. Base of a trapezoid: Either of the parallel sides of a trapezoid is referred to as a base of the trapezoid. Leg of a trapezoid: a side that is not parallel to another side. Isosceles trapezoid: a trapezoid in which the legs are equal in length. Kite: a quadrilateral with two pairs of adjacent sides that are congruent to each other. Similar polygons:SRO\JRQVWKDWDUHLGHQWLFDOLQVKDSHEXWDUHQRWQHFHVVDULO\ the same size. Corresponding sides: two sides of different objects that are situated in the same way. Proportional: having the same ratio.
— 65 — Which Belongs 1. $QRUGLQDU\GRRUWRDURRPLV DQLUUHJXODUSRO\JRQDUHJXODUSRO\JRQDWUDSH]RLG 2. 7RPDNHDQHZWDEOHWKDWZDVELJJHUWKDQWKHROGRQH6DPGRXEOHGWKHOHQJWKRIHDFK VLGHRIWKHWDEOH7KHVLGHVRIWKHWZRWDEOHVZHUH GLDJRQDOLVRVFHOHVSURSRUWLRQDO 6TXDUHVUHFWDQJOHVDQGUKRPELDUHDOOW\SHVRI SDUDOOHORJUDPVWUDSH]RLGVUHJXODU SRO\JRQV 2QHZDOORIDKRXVHZDVVKDSHGOLNHD UHFWDQJOHWUDSH]RLGNLWH EHFDXVHWKHÀRRUDQG WKHFHLOLQJZHUHSDUDOOHOEXWWKHVLGHVRIWKHZDOOZHUHDWRGGDQJOHV %HWKKDGDER[RIWRRWKSLFNVWKDWZHUHDOOWKHVDPHOHQJWKDQGVKHFRXOGFRQQHFWWKHP DWWKHLUWLSVWRPDNH UHFWDQJOHVWUDSH]RLGVUHJXODUSRO\JRQV $PRYLHVFUHHQLVDOPRVWDOZD\VD UHFWDQJOHUKRPEXVNLWH 7. $ EDVHOHJGLDJRQDO RIDWUDSH]RLGLVRQHRILWVVLGHVWKDWLVQRWSDUDOOHOWRDQRWKHU side. 7RPDNH DVTXDUHDNLWHDQLVRVFHOHVWUDSH]RLG $OH[FXWDQHTXLODWHUDOWULDQJOHDORQJ a line parallel to its base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¶WJHWWKHFRUQHUVTXLWHVTXDUHVRHDFKQDSNLQZDVVKDSHGOLNHD WUDSH]RLGUHFW- DQJOHUKRPEXV 7HGG\JRWNLFNHGRXWRIWKHVRIWEDOOJDPHEHFDXVHKHUDQIURP¿UVWEDVHWRWKLUGEDVH DORQJD GLDJRQDOVLGHOHJ RIWKHGLDPRQG 7KUHHFODVVURRPVDORQJRQHZDOORIWKHKLJKVFKRROKDGZLQGRZVRQ FRUUHVSRQGLQJ VLGHVSDUDOOHORJUDPVGLDJRQDOV $6FUDEEOHERDUGLV WUDSH]RLGDOUHFWDQJXODUVTXDUH
1. Irregular polygon 7. Leg of a trapezoid 5KRPEXV 2. Proportional Isosceles Diagonal Parallelograms 9. 4XDGULODWHUDO &RUUHVSRQGLQJVLGHV Trapezoid 10..LWH Square 5HJXODUSRO\JRQ 11.%DVHRIDWUDSH]RLG 5HFWDQJOH 12.Similar polygons
— 66 — Multiple Choice
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,IWZRVLGHVRIDTXDGULODWHUDODUHWKHVDPHOHQJWKEXWDUHQRWRSSRVLWHHDFK RWKHUWKHQLWLVD $SDUDOOHORJUDP %NLWH &ERWKRIWKHDERYH
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,IERWKSDLUVRIRSSRVLWHVLGHVRIDIRXUVLGHG¿JXUHDUHSDUDOOHOLWPLJKWEHD $UKRPEXV %DSDUDOOHORJUDP &HLWKHURIWKHDERYH
:KLFKRIWKHIROORZLQJDUHDOZD\VVLPLODUSRO\JRQV" $WZRVTXDUHV %WZRUHFWDQJOHV &WZRUKRPEL
:KLFKRIWKHIROORZLQJLVQRWDSDUDOOHORJUDP" $DUHFWDQJOH %DWUDSH]RLG &DUKRPEXV
:KLFKRIWKHIROORZLQJLVDOZD\VDQLUUHJXODUSRO\JRQ" $DUHFWDQJOH %DSDUDOOHORJUDP &DWUDSH]RLG
— 67 — 6TXDUHVUHFWDQJOHVWUDSH]RLGVSDUDOOHORJUDPVNLWHVDQGUKRPELDUHDOO $TXDGULODWHUDOV %VLPLODU3RO\JRQV &LUUHJXODUSRO\JRQV
,QHYHU\FDVHDUHFWDQJOHLVDOVRD $SDUDOOHORJUDP %VTXDUH &UHJXODUSRO\JRQ
$VHJPHQWWKDWFRQQHFWVWZRRSSRVLWHFRUQHUVRIDTXDGULODWHUDOLVLWV $OHJ %DOWLWXGH &GLDJRQDO
$OOUHFWDQJOHVDUHQRWUHJXODUSRO\JRQVEHFDXVH $WKH\GRQ¶WKDYHIRXUFRQJUXHQWDQJOHV %WKH\GRQ¶WKDYHIRXUFRQJUXHQWVLGHV &WKHDUHQRWDOZD\VSDUDOOHORJUDPV
+RZPDQ\VLGHVRIDQLVRVFHOHVWUDSH]RLGDUHFRQJUXHQW" $WZR %WKUHH &IRXU
:KLFKRIWKHIROORZLQJDUHH[DPSOHVRISDUDOOHORJUDPV" $LVRVFHOHVWUDSH]RLGVVTXDUHVDQGNLWHV %VTXDUHVUHFWDQJOHVDQGUKRPEL &WUDSH]RLGVUHFWDQJOHVDQGTXDGULODWHUDOV
:KLFKSDUWVRIDWUDSH]RLGPLJKWEHFRQJUXHQW" $OHJV %EDVHV &DGMDFHQWVLGHV
6LGHVRISRO\JRQVWKDWKDYHVLPLODUSRVLWLRQVRUVLWXDWLRQVDUH $SURSRUWLRQDOVLGHV %FRPSOHPHQWDU\VLGHV &FRUUHVSRQGLQJVLGHV
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— 68 — Complete the Sentence
1. $BBBBBBBBBLVDTXDGULODWHUDOEXWQRWDSDUDOOHORJUDPRUDWUDSH]RLG 2. Two opposite corners of a quadrilateral are connected by a BBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBBBBKDYHWKHVDPHVKDSHEXWQRWDOZD\VWKH same size. $UHJXODUSRO\JRQZLWKIRXUVLGHVLVDBBBBBBBBBBBBBBBB 7KHBBBBBBBBRIDWUDSH]RLGLVSDUDOOHOWREXWQRWFRQJUXHQWWRLWVRSSRVLWH side. ,IDOORIWKHVLGHVRIDSRO\JRQDUHFRQJUXHQWDQGDOORILWVDQJOHVDUHDOVR FRQJUXHQWLWLVD Q BBBBBBBBBBBBBBBB 7. $Q\TXDGULODWHUDOWKDWLVQRWDVTXDUHLVD Q BBBBBBBBBBBBBBBBBBBBBBBB ,IDSRO\JRQKDVPRUHWKDQWKUHHVLGHVEXWOHVVWKDQ¿YHVLGHVLWLVD BBBBBBBBBBBBBBBBBBBBBBB 9. :KHQERWKSDLUVRIRSSRVLWHVLGHVRIDTXDGULODWHUDODUHSDUDOOHOLWLVD BBBBBBBBBBBBBBBBBB 10.$UXJZLWKIRXUVWUDLJKWVLGHVLVVKDSHGOLNHDBBBBBBBBBBBBBBBLIDOORI its corners are right angles. 11.$BBBBBBBBBRIDWUDSH]RLGLVQRWSDUDOOHOWRDQ\RWKHUVLGH 12.7KHGLIIHUHQFHEHWZHHQDVTXDUHDQGDBBBBBBBBBBBBBBBBBLVWKDWD square has 90o angles at each corner. 7KHVLGHVRIWZRUHFWDQJOHVHDFKKDGDUDWLRRI VRWKH\ZHUH BBBBBBBBBBBBBBBBBB 7KHOHJVRIDQBBBBBBBBBBBBBBBBBBBBBBWUDSH]RLGDUHFRQJUXHQWWR each other. 7ZRKRXVHVZHUHQH[WGRRUWRHDFKRWKHUDQGWKHLU BBBBBBBBBBBBBBBBBBBBBBZHUHIDFLQJWKHVWUHHW 2QO\RQHSDLURIVLGHVRIDBBBBBBBBBBBBBBBBDUHSDUDOOHOWRHDFKRWKHU
$QVZHUV
1. .LWH 9. Parallelogram 2. Diagonal 10.5HFWDQJOH6TXDUH Similar polygons 11.Leg Square 12.5KRPEXV %DVH Proportional 5HJXODUSRO\JRQ Isosceles 7. Irregular polygon &RUUHVSRQGLQJVLGHV 4XDGULODWHUDO Trapezoid
— 69 — Creative Writing
Have the students write sentences of their own, based on the picture below. When finished, have each student read his/her sentences to the others.
— 70 — Place-Based Practice Activity
+DYHVWXGHQWVPDNHGHVLJQVIRUVNLKDWVTXLOWVERUGHUVUXJVEODQNHWVRU other objects using different types of quadrilaterals.
&KDOOHQJHJURXSVRIVWXGHQWVWRFRPHXSZLWKDGHVLJQWKDWKDVH[DPSOHVRI DOOVL[WHHQWHUPVIURPWKLVXQLW([FKDQJHGHVLJQVZLWKDQRWKHUJURXSDQGVHHLI \RXFDQ¿QGDOORIWKHLUH[DPSOHV
8VLQJERRNVLQWHUQHWVRXUFHVDWULSWRDPXVHXPRUDYLVLWIURPDORFDODUW H[SHUWVWXG\WUDGLWLRQDOGHVLJQV RQEDVNHWVEODQNHWVER[HVWULEDOKRXVHVHWF WR¿QGH[DPSOHVTXDGULODWHUDOV
— 71 — — 72 — Unit Assessment
— 73 — — 74 — Geometry: Unit 6 Quadrilaterals
Name: ______Date: ______
1) Look at the illustration below and circle the letter of the word or words that match the illustration.
Matt....insert parallelogram illustration
a) irregular polygon
b) regular polygon
c) quadrilateral
d) parallelogram
2) Look at the illustration below and circle the word or words that match the illustration.
Matt....insert regular polygon illustration
a) irregular polygon
b) regular polygon
c) quadrilaterals
d) parallelogram
— 75 — 3) Look at the illustration below and circle the word or words that match the illustration.
Matt....insert regular polygon illustration
a) irregular polygon
b) regular polygon
c) quadrilaterals
d) parallelogram
4) Any four-sided polygon is a ______.
a) irregular polygon
b) regular polygon
c) quadrilateral
d) parallelogram
Match the key vocabulary on the left with the correct definition on the right. Place the letter of the definition in front of the word it matches.
5) _____ rectangle a. a parallelogram with four congruent sides. 6) _____ square b. a four-sided polygon with four right angles and all four sides 7) _____ trapezoid congruent
8) _____ rhombus c. the ratio is the same
d. A quadrilateral with one pair of 9) _____ proportional parallel sides
e. a four-sided polygon with four right angles
— 76 — Fill in the Blanks: Complete each statement below with the word that fits best. Choose the word from the Word Bank.
Word Bank corresponding diagonal isosceles rhombus similar similar
10) A/an trapezoid is one in which the legs are equal in length.
11) polygons are identical in shape, but are are not necessarily the same size.
12) polygons are identical in shape, but are not necessarily the same size.
13) sides are two sides of different objects that are situated in the same way.
14) A/an is a line segment that connects two nonadjacent corners (vertices) of a polygon.
Illustrations: illustrations will be used in the following items to identify key concepts.
15) In the illustration below, place an X on the part of the drawing that represents a base of the trapezoid.
Matt...insert illustration for base of the trapezoid
— 77 —
16) In the illustration below, put an X on the part of the drawing that represent the leg of a trapezoid.
Matt...insert the illustration for the leg of a trapezoid
— 78 — Geometry: Unit 6 Quadrilaterals Name: ______Date: ______
1) Look at the illustration below and circle the letter of the word or words that match the illustration.
Matt....insert parallelogram illustration
a) irregular polygon
b) regular polygon
c) quadrilateral
d) parallelogram
2) Look at the illustration below and circle the word or words that match the illustration.
Matt....insert regular polygon illustration
a) irregular polygon
b) regular polygon
c) quadrilaterals
d) parallelogram
— 79 — 3) Look at the illustration below and circle the word or words that match the illustration.
Matt....insert regular polygon illustration
a) irregular polygon
b) regular polygon
c) quadrilaterals
d) parallelogram
4) Any four-sided polygon is a ______.
a) irregular polygon
b) regular polygon
c) quadrilateral
d) parallelogram
Match the key vocabulary on the left with the correct definition on the right. Place the letter of the definition in front of the word it matches.
5) e rectangle a. a parallelogram with four congruent sides. 6) b square b. a four-sided polygon with four right angles and all four sides 7) d trapezoid congruent
8) a rhombus c. the ratio is the same
d. A quadrilateral with one pair of 9) c proportional parallel sides
e. a four-sided polygon with four right angles
— 80 — Match the key vocabulary on the left with the correct definition on the right. Place the letter of the definition in front of the word it matches.
5) e rectangle a. a parallelogram with four congruent sides. 6) b square b. a four-sided polygon with four right angles and all four sides 7) d trapezoid congruent
8) a rhombus c. the ratio is the same
d. A quadrilateral with one pair of 9) c proportional parallel sides
e. a four-sided polygon with four right angles
Fill in the Blanks: Complete each statement below with the word that fits best. Choose the word from the Word Bank.
Word Bank corresponding diagonal isosceles rhombus similar similar
10) A/an isosceles trapezoid is one in which the legs are equal in length.
11) similar polygons are identical in shape, but are are not necessarily the same size.
12) similar polygons are identical in shape, but are not necessarily the same size.
13) corresponding sides are two sides of different objects that are situated in the same way.
— 81 — 14) A/an diagonal is a line segment that connects two nonadjacent corners (vertices) of a polygon.
Illustrations: illustrations will be used in the following items to identify key concepts.
15) In the illustration below, place an X on the part of the drawing that represents a base of the trapezoid.
Matt...insert illustration for base of the trapezoid
Matt...insert illustration for base of the trapezoid. Place an X on theX base.'
16) In the illustration below, put an X on the part of the drawing that represent the leg of a trapezoid.
Matt...insert the illustration for the leg of a trapezoidX Matt...insert the illustration for the leg of a trapezoid with an X on the let.
— 82 — UNIT 7 Circles
Sealaska Heritage Institute
Grade Level Expectations for Unit 7
Unit 7—Circles
Alaska State Mathematics Standard A $VWXGHQWVKRXOGXQGHUVWDQGPDWKHPDWLFDOIDFWVFRQFHSWVSULQFLSOHVDQGWKHRULHV
$VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG $ FRQVWUXFWGUDZPHDVXUHWUDQVIRUPFRPSDUHYLVXDOL]HFODVVLI\DQGDQDO\]H WKHUHODWLRQVKLSVDPRQJJHRPHWULF¿JXUHV DQG
Alaska State Mathematics Standard C $VWXGHQWVKRXOGXQGHUVWDQGDQGEHDEOHWRIRUPDQGXVHDSSURSULDWHPHWKRGVWR GH¿QHDQGH[SODLQPDWKHPDWLFDOUHODWLRQVKLSV
$VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG & H[SUHVVDQGUHSUHVHQWPDWKHPDWLFDOLGHDVXVLQJRUDODQGZULWWHQSUHVHQWD- WLRQVSK\VLFDOPDWHULDOVSLFWXUHVJUDSKVFKDUWVDQGDOJHEUDLFH[SUHVVLRQV & UHODWHPDWKHPDWLFDOWHUPVWRHYHU\GD\ODQJXDJH
GLEs The student demonstrates an understanding of geometric relationships by > @*LGHQWLI\LQJDQDO\]LQJFRPSDULQJRUXVLQJSURSHUWLHVRIFLUFOHV GHJUHHVLQ DFLUFOH
The student demonstrates an understanding of geometric relationships by >@*LGHQWLI\LQJDQDO\]LQJFRPSDULQJRUXVLQJSURSHUWLHVRISODQH¿JXUHV FHQWUDODQJOHVFKRUGVLQVFULEHGDQJOHVRUDUFVRIDFLUFOH
The student communicates his or her mathematical thinking by > @36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRUV\P- EROLFDOO\WUDQVODWLQJDPRQJWKHVHDOWHUQDWLYHUHSUHVHQWDWLRQV RUXVLQJDSSURSULDWH YRFDEXODU\V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQG solutions >@36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRU V\PEROLFDOO\FRPPXQLFDWLQJPDWKLGHDVLQZULWLQJ RUXVLQJDSSURSULDWHYRFDEXODU\ V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQGVROXWLRQV
Vocabulary & Definitions
Introduction of Math Vocabulary
Circle $FLUFOHLVDFORVHGFXUYHZKRVHSRLQWVDUHDOORQWKHVDPHSODQH DQGDWWKHVDPHGLVWDQFHIURPD¿[HGSRLQW WKHFHQWHU :KDWZRXOG KDSSHQLIDZKHHOZHUHQRWDFLUFOH"
Circumference 7KHFLUFXPIHUHQFHLVWKHSHULPHWHURURXWHUERXQGDU\RIDFLUFOH and also the distance around the outside of a circle.
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Radius $UDGLXVLVDOLQHVHJPHQWWKDWFRQQHFWVWKHFHQWHURIDFLUFOHZLWKD SRLQWRQLWVFLUFXPIHUHQFHRUWKHOHQJWKRIWKDWOLQHVHJPHQW
'RZQKLOOVNLHUVPHDVXUHWKH³VLGHFXWUDGLXV´RIVNLVWRGHWHUPLQH how well the skis will turn.
— 89 — Introduction of Math Vocabulary
Diameter $GLDPHWHULVDOLQHVHJPHQWEHWZHHQWZRSRLQWVRQDFLUFOHZKLFK passes through the center. The word diameter also refers to the length of this line segment.
The saw that these men are using must be longer than the diameter of the tree.
Arc $QDUFRIDFLUFOHLVDQ\XQEURNHQSDUWRILWVFLUFXPIHUHQFH
7KHZRUG³DUF´FRPHVIURPD/DWLQZRUG³DUFXV´ZKLFKPHDQVDERZDUFKRU curve.
— 90 — Introduction of Math Vocabulary
Semicircle $VHPLFLUFOHLVKDOIDFLUFOHRUDQDUFZLWKo.
:KHQ\RXORRNDWDKDOIPRRQ\RXDUHVHHLQJDVHPLFLUFOH
Central angle $FHQWUDODQJOHLVDQDQJOHZKRVHYHUWH[LVDWWKHFHQWHURIDFLUFOH
The hands of a clock form central angles.
Sector $VHFWRURIDFLUFOHLVDSDUWRIDFLUFOHWKDWLVERXQGHGE\WZR UDGLLDQGWKHDUFEHWZHHQWKHP $SLHFHRISLHLVDVHFWRU — 91 — Introduction of Math Vocabulary Chord $FKRUGLVDOLQHVHJPHQWLQWKHLQWHULRURIDFLUFOHWKDWKDVERWK endpoints on a circle. Segments of the strings of a guitar form chords of the circular sound hole. Tangent 7DQJHQWPHDQVWRXFKLQJDWDVLQJOHSRLQW WKHSRLQWRIWDQJHQF\ without crossing over. The word tangent is used with lines and curves that touch each other. ,QWKLVSLFWXUHWKHUXOHULVSRVLWLRQHGVRWKDWLWLVWDQJHQWWRWKHJHDUZKHHORIWKH ELF\FOHLQRUGHUWRPHDVXUHWKHWHQVLRQRIWKHFKDLQ — 92 — Introduction of Math Vocabulary Circumscribed If something is circumscribed it is surrounded by the smallest circle RURWKHU¿JXUH SRVVLEOH 7RPDNHWKLVRUQDPHQWDVWDUZDVFLUFXPVFULEHGE\DFLUFOH Inscribed :KHQVRPHWKLQJLVLQVFULEHGLWLVRQWKHLQVLGHRIDQRWKHU¿JXUH touching it in as many points as possible. These circles are inscribed LQRWKHU¿JXUHV 7KLVLVDV\PEROIRUZDVKLQJLQVWUXFWLRQVWKDWPHDQV³'R1RW7XPEOH'U\´,W uses a circle inscribed in a square. Pi 3LV\PEROL]HGDVis a letter of the Greek alphabet. In mathemat- LFVLWVWDQGVIRUWKHUDWLRRIWKHFLUFXPIHUHQFHRIDFLUFOHWRLWVGLDPH- WHU:KHQWKHFLUFXPIHUHQFHLVGLYLGHGE\WKHGLDPHWHURIDQ\FLUFOH the value of LVRU «« &G — 93 — Introduction of Math Vocabulary Secant $VHFDQWLVDOLQHWKDWLQWHUVHFWVDFLUFOH RUDQRWKHUFXUYH DW two points. Concentric &RQFHQWULFPHDQVKDYLQJDFRPPRQFHQWHU 5DLQGURSVFUHDWHGWKHVHFRQFHQWULFFLUFOHVRQZDWHU Annulus $QDQQXOXVLVDUHJLRQEHWZHHQWZRFRQFHQWULFFLUFOHVWKDWDUHGLIIHUHQW sizes. &RPPRQH[DPSOHVRIDQQXOLDUHHDV\WR¿QGDQGLQFOXGHWLUHVZDVKHUVDQG compact discs. — 94 — Language and Skills Development Using the Math Vocabulary Terms Language & Skills Development Pencil of Fortune %HIRUHWKHDFWLYLW\EHJLQVSUHSDUHDVWHQFLOZKLFKFRQWDLQVVPDOOYHUVLRQVRIWKH vocabulary illustrations. Provide each student with a copy of the stencil. Each student should cut out his/her illustrations. The students should then lay their LOOXVWUDWLRQVRQWKHLUGHVNV DURXQGWKHHGJHVRIWKHLUGHVNV :KHQWKHVWXGHQWV KDYHDUUDQJHGWKHLULOOXVWUDWLRQVLQWKLVZD\HDFKVWXGHQWVKRXOGWKHQSODFHD LISTENING pen or pencil in the center of his/her desk. Say a vocabulary word. The stu- Use the activity pages dents should then spin their pencils/pens on their desks. When the pencils/pens from the Student VWRSVSLQQLQJDQ\VWXGHQWRUVWXGHQWVZKRVHSHQFLOVSHQVDUHSRLQWLQJWRWKH Support Materials. YRFDEXODU\LOOXVWUDWLRQIRUWKHZRUG\RXVDLGZLQ V WKHURXQG:KHQDVWXGHQW ZLQVLQWKLVZD\KHVKHPD\UHPRYHWKDWLOOXVWUDWLRQIURPKLVKHUGHVN7KHZLQ- ner or winners of this activity are those students who have no illustrations left on their desks. Feel the Number Mount the vocabulary illustrations on the chalkboard and number each one. +DYHDVWXGHQWVWDQGIDFLQJWKHLOOXVWUDWLRQV6WDQGEHKLQGWKHVWXGHQWDQGXVH \RXULQGH[¿QJHUWR³ZULWH´RQHRIWKHLOOXVWUDWLRQQXPEHUVRQKLVKHUEDFN:KHQ SPEAKING WKHVWXGHQWIHHOVWKHQXPEHUKHVKHVKRXOGRUDOO\LGHQWLI\WKHLOOXVWUDWLRQZLWK WKDWQXPEHU7KLVDFWLYLW\PD\DOVREHGRQHLQWHDPIRUP,QWKLVFDVH³ZULWH´ one of the numbers on the back of the last player in each team. When you say ³*R´WKHODVWSOD\HULQHDFKWHDPVKRXOGZULWHWKHQXPEHURQWKHEDFNRIWKH VWXGHQWLQIURQWRIKLPKHUDQGVRRQ:KHQWKH¿UVWSOD\HULQHDFKWHDPIHHOV WKHQXPEHUKHPXVWQDPHWKHLOOXVWUDWLRQZLWKWKDWQXPEHU7KH¿UVWWHDPWRGR WKLVZLQVWKHURXQG7KH¿UVWSOD\HULQHDFKWHDPVKRXOGPRYHWRWKHEDFNRIWKH team after each round of the activity. Reflection Mount the sight word cards on the chalkboard. Group the students into two teams. +DYHWKH¿UVWSOD\HUIURPHDFKWHDPVWDQGLQIURQWRIWKHFKDONERDUGIDFLQJWKH READING VLJKWZRUGFDUGV*LYHHDFKRIWKHWZRSOD\HUVDVPDOOXQEUHDNDEOHPLUURU6WDQG Use the activity pages from the Student VRPHGLVWDQFHEHKLQGWKHWZRSOD\HUVDQGKROGXSDYRFDEXODU\LOOXVWUDWLRQ IRU Support Materials. RQHRIWKHVLJKWZRUGVRQWKHFKDONERDUG 7KHWZRSOD\HUVPXVWWKHQORRNRYHU their shoulders with the mirrors to see the illustration you are holding. When a VWXGHQWVHHVWKHLOOXVWUDWLRQ\RXDUHKROGLQJKHVKHPXVWSRLQWWRLWVVLJKWZRUG RQWKHFKDONERDUG7KH¿UVWSOD\HUWRGRWKLVFRUUHFWO\ZLQVWKHURXQG5HSHDWZLWK other pairs of players until all students have participated. Numbered Illustrations Mount the vocabulary illustrations on the chalkboard and number each illustra- WLRQ3URYLGHHDFKVWXGHQWZLWKZULWLQJSDSHUDQGDSHQ&DOOWKHQXPEHURIDQ WRITING illustration. Each student should write the vocabulary word for the illustration Use the activity pages UHSUHVHQWHGE\WKDWQXPEHU5HSHDWXQWLODOOYRFDEXODU\ZRUGVIRUWKHLOOXVWUD from the Student WLRQVKDYHEHHQZULWWHQ5HYLHZWKHVWXGHQWV¶UHVSRQVHV Support Materials. — 97 — Student Support Materials — 101 — — 103 — — 105 — — 107 — — 109 — — 111 — — 113 — — 115 — — 117 — — 119 — — 121 — — 123 — — 125 — — 127 — — 129 — — 131 — — 132 — True-False Sentences (Listening and/or Reading Comprehension) 1. $OORIWKHSRLQWVRIDcircle are coplanar. 2. The circumference of a circle is the same as its perimeter. $radius and a chord of a circle are the same thing. The diameter of a circle is also a chord. Each circle can have only one arc. One quarter of a circle is a semicircle. 7. $central angleKDVLWVYHUWH[DWWKHFHQWHURIDFLUFOH $Q\SLHVKDSHGSLHFHRIDFLUFOHLVDsector. 9. $chord has endpoints that are on a circle. 10.$OLQHWKDWLV tangent to a circle touches it at only one point. 11.$WULDQJOHLQVLGHDFLUFOHLVcircumscribedE\WKHFLUFOHLIHDFKYHUWH[LV on the circle. 12.$QLUUHJXODUSRO\JRQFDQQRWEHinscribed in a circle. $ODUJHFLUFOHKDVDKLJKHUYDOXHRI pi than a small circle. $secant does not have endpoints on a circle. 15.Concentric circles intersect each other. $Qannulus is formed by concentric circles. $QVZHUV 77)7))7) 777 ))7)7 1. $circle can have a radius that is longer than its diameter. 2. The center of a circle is also on its circumference. The radius of a circle has one endpoint at the center. &RQFHQWULFFLUFOHVDOZD\VKDYHWKHVDPHGLDPHWHUV $Qarc is part of the circumference of a circle. $semicircle is also an arc. 7. 7KHUHDUHH[DFWO\WZHOYHcentral angles in each circle. $sector of a circle has two sides formed by radii. 9. Part of a chord might be outside of the circle. 10.Each circle has a limited number of tangents. 11.$Q\¿JXUHLQVLGHDFLUFOHLVVDLGWREHcircumscribed. 12.The sides of a triangle would be tangents of a circle inscribed in the triangle. The value of pi is the same for every circle. $FXUYHGOLQHPLJKWEHDsecant. 15.Concentric circles have the same center. $FKRUGDQGDUDGLXVDUHVLGHVRIDQannulus. $QVZHUV ))7)77)7 )))7 7)7) — 133 — Match the Halves 1. The radius of a circle $GRHVQRWLQWHUVHFWDFLUFOH 2. Two radii and an included arc %LVVKDSHGOLNHDFLUFOH make 3L]]DV¶VL]HV &DVHFWRURIDFLUFOH $WDQJHQW D. is shaped like an arc. )ROGDFLUFOHLQKDOI E. the circle is on the outside. $VHFDQW )KDVDYHUWH[DWWKHFHQWHU 7. The top of a tuna can G. is an annulus ,IVRPHWKLQJLVFLUFXPVFULEHGE\D H. has two endpoints on the circle circle 9. If something is inscribed in a circle I. you would need to know the circumference. $UDLQERZ J. the value of pi is obtained. 11. When the circumference is .\RXFDQVHHFRQFHQWULFFLUFOHV divided by the diameter 12. The central angle of a circle L. refer to the diameter. 7KHVLGHZDOORIDWLUH M. for a semicircle. 7RFKRRVHFKDLQVIRUWLUHV N. it is inside the circle. :KHQ\RXORRNDWWKHOHQVRID O. has one endpoint at the center. camera $FKRUGRIDFLUFOH P. does intersect a circle 2&/$03%1 ('-)*,.+ — 134 — 'H¿QLWLRQV Circle: a closed curve whose points are all on the same plane and at the same GLVWDQFHIURPD¿[HGSRLQW WKHFHQWHU Circumference WKHSHULPHWHURURXWHUERXQGDU\RIDFLUFOHDQGDOVRWKHGLV- tance around the outside of a circle. Radius: a line segment that connects the center of a circle with a point on its FLUFXPIHUHQFHRUWKHOHQJWKRIWKDWOLQHVHJPHQW Diameter: a line segment between two points on a circle which passes through the center. The word diameter also refers to the length of this line segment. Arc: any unbroken part of a circle’s circumference. Semicircle KDOIDFLUFOHRUDQDUFZLWKR Central angle:DQDQJOHZKRVHYHUWH[LVDWWKHFHQWHURIDFLUFOH Sector: a part of a circle that is bounded by two radii and the arc between them. Chord: a line segment in the interior of a circle that has both endpoints on a circle. Tangent WRXFKLQJDWDVLQJOHSRLQW WKHSRLQWRIWDQJHQF\ ZLWKRXWFURVVLQJRYHU Circumscribed VXUURXQGHGE\WKHVPDOOHVWFLUFOH RURWKHU¿JXUH SRVVLEOH Inscribed RQWKHLQVLGHRIDQRWKHU¿JXUHWRXFKLQJLWLQDVPDQ\SRLQWVDVSRV- sible. Pi: the ratio of the circumference of a circle to its diameter. Secant DOLQHWKDWLQWHUVHFWVDFLUFOH RUDQRWKHUFXUYH DWWZRSRLQWV Concentric: having a common center. Annulus: a region between two concentric circles that are different sizes. — 135 — Which Belongs $OLQHWKDWWRXFKHVDFLUFOHEXWGRHVQRWLQWHUVHFWLWLVD WDQJHQWVHFDQWFKRUG $Q\SDUWRIWKHFLUFXPIHUHQFHRIDFLUFOHLV DVHFWRUDVHPLFLUFOHDQDUF LILWLVDQ unbroken part. $FLUFOHWKDWLVLQVLGHDVTXDUHLV FLUFXPVFULEHGLQVFULEHGFRQFHQWULF LILWWRXFKHVHDFK side of the square. (DFKSRLQWRQWKHSHULPHWHURID VTXDUHFLUFOHWULDQJOH LVHTXLGLVWDQWIURPLWVFHQWHU $ FKRUGUDGLXVVHFDQW LQWHUVHFWVDFLUFOHDWWZRSRLQWV 7R¿QGWKH GLDPHWHUUDGLXVFLUFXPIHUHQFH RIDFLUFOH\RXFRXOGPHDVXUHDFURVVLWIURP RQHVLGHWRWKHRWKHUDVORQJDV\RXPHDVXUHGWKURXJKWKHFHQWHU $QDQJOHZLWKLWVYHUWH[LQVLGHDFLUFOHLVD VHFWRUFKRUGFHQWUDODQJOH RQO\LIWKHYHUWH[ is at the center. $FHQWUDODQJOHLQWHUVHFWVDFLUFOHWRIRUP DQDUFDVHFWRUDVHPLFLUFOH $ FLUFXPIHUHQFHUDGLXVFKRUG RIDFLUFOHLVDOZD\VORQJHUWKDQLWVGLDPHWHU $GRQXWVKDSHLV DVHFWRUDQDUFDQDQQXOXV 7KHFLUFXPIHUHQFHRIDFLUFOHKDVRQO\RQHSRLQWLQFRPPRQZLWKD UDGLXVGLDPHWHU FKRUG 2QHW\SHRIDUFLVD VHFWRUVHPLFLUFOHVHFDQW $QXPHULFDOYDOXHWKDWLVWKHVDPHIRUHYHU\FLUFOHLV FLUFXPIHUHQFHGLDPHWHUSL $GLDPHWHULVDOVRD FKRUGVHFDQWWDQJHQW :KHQ9DOHULHIRXQGDKXODKRRSWKDW¿WRYHUDER[VRWKDWHDFKFRUQHURIWKHER[ WRXFKHGLWVKHKDG LQVFULEHGFLUFXPVFULEHGFLUFOHG WKHER[ 2QDZKHHOWKHULPDQGWKHWLUHDUH FRQFHQWULFLQVFULEHGWDQJHQW FLUFOHV 1. Tangent 7. &HQWUDODQJOH Pi 2. $UF Sector &KRUG Inscribed 9. &LUFXPIHUHQFH &LUFXPVFULEHG &LUFOH 10.$QQXOXV &RQFHQWULF Secant 11.5DGLXV Diameter 12. Semicircle — 136 — Multiple Choice 7REHJLQDIRONGDQFHGDQFHUVIRUPHGWZRFLUFOHVRQHLQVLGHWKHRWKHU7KLVLVDQH[DPSOHRI $WDQJHQWFLUFOHV %FRQFHQWULFFLUFOHV &LQVFULEHGFLUFOHV $QQZDVPDNLQJDURXQG³VWXIIVDFN´IRUKHUFDPSLQJWULS6KHFXWRXWDFLUFOHIRUWKHERWWRP RIWKHEDJ,QRUGHUWRPHDVXUHWKHPDWHULDOVKHQHHGHGWRFXWIRUWKHPDLQSDUWRIWKHEDJ ZKDWZRXOGVKHQHHGWRNQRZDERXWKHUFLUFOH" $,WVFLUFXPIHUHQFH %,WVFHQWUDODQJOH &,WVGLDPHWHU %HQMDPLQKDGDFDQRIVPRNHGVDOPRQWKDWKHZDQWHGWRJLYHKLVPRPDVDSUHVHQW+H PDGHDER[WKDWH[DFWO\¿WDURXQGWKHFDQ/RRNLQJGRZQRQWKHFDQLQWKHER[KHVDZ $$VTXDUHFLUFXPVFULEHGE\DFLUFOH %$FLUFOHLQVFULEHGLQDVTXDUH &$QDQQXOXV 7KHFDU¶VWLUHVZHUHEXULHGLQVQRZULJKWXSWRWKHLUD[OHVVRHDFKRQHORRNHGOLNHD $6HFWRURIDFLUFOH %&KRUG &6HPLFLUFOH 7RPDNHDQ³DQJHOIRRG´FDNH+HUPDQXVHGDURXQGSDQZLWKDKROHLQWKHPLGGOH7KHFDNH ZDVVKDSHGOLNHD Q $6HFWRU %$UF &$QQXOXV 7RUDLVHPRQH\WKHFOXEZDVVHOOLQJSL]]DE\WKHVOLFH7KH\ZHUHFDUHIXOWRFXWHDFKSL]]D VRWKDWDOOVL[VOLFHVZHUHH[DFWO\WKHVDPHVL]H(DFKVOLFHZDVD $6HFWRU %6HPLFLUFOH &6HFDQW $IRUHVWHUZDQWHGWRFRXQWWKHQXPEHURIVSUXFHWUHHVWKDWZHUHORFDWHGZLWKLQ¿IW\IHHWRID ODUJHUHGFHGDUVRKHPHDVXUHGDFLUFOHZLWKD¿IW\IRRW $$UF %5DGLXV &'LDPHWHU 7KRPDVZDONHGRQHWKLUGRIWKHZD\RQWKHVLGHZDONDURXQGWKHWUDI¿FFLUFOH+HZDONHG DORQJD Q $$UF %&KRUG &&LUFOH — 137 — $FORVHGFXUYHZKRVHSRLQWVDUHDOORQWKHVDPHSODQHDQGDWWKHVDPHGLVWDQFHIURPD¿[HG SRLQW WKHFHQWHU LVFDOOHGD $6HFDQW %$UF &&LUFOH 7ZRVSRNHVRQDZKHHOEHJLQDWWKHFHQWHURIWKHZKHHODQGH[WHQGWRLWVHGJHIRUPLQJD $&HQWUDODQJOH %&KRUG &6HFDQW 6RPHFKLOGUHQVWDQGLQJLQDFLUFOHWDNHWXUQVWRVVLQJDEDOORIVWULQJWRDQRWKHUSHUVRQOHWWLQJWKH string unwind as it is tossed. They end up with segments of string stretched across the circle in all directions. Each segment of string is a $7DQJHQW %6HFDQW &&KRUG $ZKHHOLVUROOLQJDORQJDOLQHRQWKHÀRRUDQGRQO\RQHSRLQWRQWKHZKHHODWDWLPHWRXFKHVWKH line. The line would be a $&KRUG %7DQJHQW &'LDPHWHU :KHQ\RXSXWDFLUFXODUKDWRQ\RXUKHDG\RXPLJKWVD\WKDW\RXUKHDGLV $,QVFULEHGLQWKHKDW %&LUFXPVFULEHGE\WKHKDW &$GMDFHQWWRWKHKDW )RUHYHU\FLUFOH3LLVWKHUDWLRRI $7KHFLUFXPIHUHQFHWRWKHGLDPHWHU %7KHFLUFXPIHUHQFHWRWKHUDGLXV &$Q\FHQWUDODQJOHWRLWVFKRUG $EXWWRQKROHPXVWEHDWOHDVWDVORQJDVZKLFKPHDVXUHPHQWRIWKHEXWWRQ $&LUFXPIHUHQFH %5DGLXV &'LDPHWHU -HIIPDGHDPRXVHWUDSE\OD\LQJDORQJVWLFNDFURVVWKHWRSRIDURXQGEXFNHWIXOORIZDWHU7KH stick formed a $5DGLXV %7DQJHQW &6HFDQW $QVZHUV %$%&&$%$ &$&%%$&& — 138 — Complete the Sentence 1. 7R¿QGWKHGLDPHWHURIDURXQGWUHHWUXQN+HOHQPHDVXUHGDURXQGWKHWUHHDQG GLYLGHGE\BBBBBBBBBBBBBBBBBBBB 2. $BBBBBBBBBBBBBBBBBBBLVDOLQHWKDWLQWHUVHFWVDFLUFOHLQWZRSODFHV 7KHGLVWDQFHDURXQGWKHRXWVLGHRIDGLQQHUSODWHLVLWVBBBBBBBBBBBBBBBBBBBB If the dinner plate was sitting on a square placemat so that its edges were even with WKHVLGHVRIWKHSODFHPDWLWZRXOGEHOLNHDFLUFOHBBBBBBBBBBBBBBBBBBLQ RUE\ D square. $SLHFKDUWLVGLYLGHGLQWRBBBBBBBBBBBBBBBBBBB 7KHORQJHVWGLVWDQFHDFURVVDURXQGIU\LQJSDQZRXOGEHWKHBBBBBBBBBBBBBBBBBB of the pan. 7. 7KHFXUYHDWWKHWRSRIDZLQGRZLVVKDSHGOLNHRQHWKLUGRIDFLUFOHVRLWZRXOGEH D Q BBBBBBBBBBBBBBBBBBBBBBBBBBBBBRIWKHFLUFOH ,IDVOLFHRIDURXQGFDNHZDVFXWSHUIHFWO\LWVWZRVLGHVZRXOGIRUPD Q BBBBBBBBBBBBBBBBBBBRIWKHFDNH 9. ,WLVLPSRUWDQWWKDWDZKHHOEHVKDSHGOLNHDSHUIHFWBBBBBBBBBBBBBBBBBB 10.7KHOLGRIDEXFNHWKDGDURXQGKROHFXWRXWRILWVPLGGOHVRLWZDVVKDSHGOLNH D Q BBBBBBBBBBBBBBBBB 11.6XHDQG6DPZHUHULGLQJRQD)HUULVZKHHOLQGLIIHUHQW³FDUV´7KHVKRUWHVWGLVWDQFH EHWZHHQWKHPZRXOGEHDBBBBBBBBBBBBBBBBBRIWKHFLUFOHIRUPHGE\WKHZKHHO 12.$VWUDLJKWNQLIHWKDWLVQH[WWRDSODWHDQGEDUHO\WRXFKLQJLWZRXOGEH BBBBBBBBBBBBBBBBWRWKHSODWH $VTXDUHODEHOMXVWEDUHO\¿WWKHWRSRIWKHMDURIMDP DOORILWVFRUQHUVWRXFKHG WKH ULPRIWKHOLG7KHODEHOZDVBBBBBBBBBBBBBBBBBBBBBBBBBE\WKHULP $BBBBBBBBBBBBBBBBBBBBBBBBBBBBRIDFLUFOHIRUPVHDFKVLGHRIHDFKFHQWUDO angle. :KHQ$ODQDWHKDOIRIDSL]]DKHZDVHDWLQJDBBBBBBBBBBBBBBBBBBBBBBBBBB 7ZRWKLQJVZLWKWKHVDPHFHQWHUDUHBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB $QVZHUV 1. Pi 9. &LUFOH 2. Secant 10.$QQXOXV &LUFXPIHUHQFH 11.&KRUG Inscribed 12.Tangent Sectors &LUFXPVFULEHG Diameter 5DGLXV 7. $UF Semicircle &HQWUDODQJOH &RQFHQWULF — 139 — Creative Writing Have the students write sentences of their own, based on the picture below. When finished, have each student read his/her sentences to the others. — 140 — Place-Based Practice Activity $VNVWXGHQWVWRXVHVRPHWKLQJZLWKDFLUFXODUVKDSHWKDWLVSDUWRIWKHLUGDLO\ lives to illustrate the terms in the unit. 7KH\FDQPHDVXUHLW¿QGLQJLWVUDGLXVGLDPHWHUDQGFLUFXPIHUHQFH7KH\FDQ XVHRWKHUFRPPRQPDWHULDOVWRGHSLFWVHFDQWVFKRUGVWDQJHQWVDUFVFHQ- WUDODQJOHVDQGVHFWRUVRIWKHLUREMHFWFRYHUXSKDOIRILWWRPDNHDVHPLFLUFOH LQVFULEHLWDQGFLUFXPVFULEHLW7KH\FDQPDNHDQRWKHUFLUFOHWKDWLVFRQFHQWULF DQGWKHQ¿QGDQDQQXOXV Make a digital camera available in the classroom for students who do not have RQHDWKRPH7KH\FDQWDNHGLJLWDOSLFWXUHVRIWKHLULOOXVWUDWLRQVDQGVKDUHWKHLU ZRUNZLWKDSRVWHUERRNOHWRUSRZHUSRLQWSUHVHQWDWLRQ — 141 — — 142 — Unit Assessment — 143143 — — 144 — Geometry: Unit 7-Circles Name: ______Date: ______ Fill in the Blank: Read each sentence carefully and choose a word from the Word Bank that that best fits the sentence. Word Bank annulus chord circle concentric PI tangent 1) An is a region between two concentric circles that are different sizes 2) means touching at a single point without crossing over and is used with lines and curves that touch each other. 3) A is a closed curve whose points are all on the same plane and at the same distance from a fixed point (the center). 4) In mathematics, 03C0, stands for the ratio of the circumference of a circle to its diameter. Scrambled Words: unscramble the words below and write the correct word in the space provided. Use the definition to help. 5) usidar: a line segment that connects the center of a circle with a point on its circumference, or, the length of that line segment 6) teremaid: a line segment between two points on a circle which passes through the center 7) reohc: a line segment in the interior of a circle that has both endpoints on a circle 8) ntaces: a line that intersects a circle (or another curve) at two points — 145 — 9) ecnerefmucric: the perimeter or outer boundary of a circle, and also the distance around the outside of a circle Matching: Match the key vocabulary word on the left with the illustration that matches it on the right. Place the letter from the illustration in front of the correct word. 10) _____ arc a. illustration of central angle 11) _____ semicircle 12) _____ diameter b. illustration of arc 13) _____ central angle c. illustration of diameter d. illustration of semicircle Multiple Choice: Look at the illustration for each item, and choose the word that matches the illustration. 14) Look at the following illustration. Select the key vocabulary word that defines the illustration. Matt...insert illustration for circumscribed. a) inscribed b) concentric c) circumscribed 15) Look at the following illustration. Select the key vocabulary word that defines the illustration. Matt...insert the illustration for concentric a) inscribed b) concentric c) circumscribed — 146 — 16) Look at the following illustration. Select the key vocabulary word that define the illustration. Matt...insert illustration for concentric a) inscribed b) concentric c) circumscribed True/False: Read each statement below to decide if it is true or false. Circle the correct answer. 17) An arc of a circle is any unbroken part of its circumference. a) True b) False 18) A semicircle is half a circle, or an arc with 360o. a) True b) False 19) A central angle is an angle whose vertex is at the center of a circle. a) True b) False 20) The value of 03C0 is 22/7 or 3.14159 = C/d a) True b) False — 147 — — 148 — Geometry: Unit 7-Circles Name: ______Date: ______ Fill in the Blank: Read each sentence carefully and choose a word from the Word Bank that that best fits the sentence. Word Bank annulus chord circle concentric PI tangent 1) An annulus is a region between two concentric circles that are different sizes 2) tangent means touching at a single point without crossing over and is used with lines and curves that touch each other. 3) A circle is a closed curve whose points are all on the same plane and at the same distance from a fixed point (the center). 4) In mathematics, PI 03C0, stands for the ratio of the circumference of a circle to its diameter. Scrambled Words: unscramble the words below and write the correct word in the space provided. Use the definition to help. 5) usidar: a line segment that connects the center of a circle with a point on its circumference, or, the length of that line segment radium 6) teremaid: a line segment between two points on a circle which passes through the center diameter 7) reohc: a line segment in the interior of a circle that has both endpoints on a circle chord 8) ntaces: a line that intersects a circle (or another curve) at two points secant 9) ecnerefmucric: the perimeter or outer boundary of a circle, and also the distance around the outside of a circle circumference — 149 — Matching: Match the key vocabulary word on the left with the illustration that matches it on the right. Place the letter from the illustration in front of the correct word. 10) b arc a. illustration of central angle 11) d semicircle 12) c diameter b. illustration of arc 13) a central angle c. illustration of diameter d. illustration of semicircle Multiple Choice: Look at the illustration for each item, and choose the word that matches the illustration. 14) Look at the following illustration. Select the key vocabulary word that defines the illustration. Matt...insert illustration for circumscribed. a) inscribed b) concentric c) circumscribed 15) Look at the following illustration. Select the key vocabulary word that defines the illustration. Matt...insert the illustration for concentric a) inscribed b) concentric c) circumscribed — 150 — 16) Look at the following illustration. Select the key vocabulary word that define the illustration. Matt...insert illustration for concentric a) inscribed b) concentric c) circumscribed True/False: Read each statement below to decide if it is true or false. Circle the correct answer. 17) An arc of a circle is any unbroken part of its circumference. a) True b) False 18) A semicircle is half a circle, or an arc with 360o. a) True b) False 19) A central angle is an angle whose vertex is at the center of a circle. a) True b) False 20) The value of 03C0 is 22/7 or 3.1415922026202603C0 = C/d. a) True b) False — 151 — — 152 — UNIT 8 Polygons & Area Sealaska Heritage Institute Grade Level Expectations for Unit 8 Unit 8—Polygons and Area Alaska State Mathematics Standard A $VWXGHQWVKRXOGXQGHUVWDQGPDWKHPDWLFDOIDFWVFRQFHSWVSULQFLSOHVDQGWKHRULHV $VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG $ FRQVWUXFWGUDZPHDVXUHWUDQVIRUPFRPSDUHYLVXDOL]HFODVVLI\DQGDQDO\]H WKHUHODWLRQVKLSVDPRQJJHRPHWULF¿JXUHV DQG Alaska State Mathematics Standard C $VWXGHQWVKRXOGXQGHUVWDQGDQGEHDEOHWRIRUPDQGXVHDSSURSULDWHPHWKRGVWR GH¿QHDQGH[SODLQPDWKHPDWLFDOUHODWLRQVKLSV $VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG & H[SUHVVDQGUHSUHVHQWPDWKHPDWLFDOLGHDVXVLQJRUDODQGZULWWHQSUHVHQWD- WLRQVSK\VLFDOPDWHULDOVSLFWXUHVJUDSKVFKDUWVDQGDOJHEUDLFH[SUHVVLRQV & UHODWHPDWKHPDWLFDOWHUPVWRHYHU\GD\ODQJXDJH GLEs The student demonstrates an understanding of geometric relationships by >@*LGHQWLI\LQJDQDO\]LQJFRPSDULQJRUXVLQJSURSHUWLHVRISODQH¿JXUHV VXPRILQWHULRURUH[WHULRUDQJOHVRIDSRO\JRQ The student demonstrates a conceptual understanding of geometric drawings or constructions by >@*GUDZLQJPHDVXULQJRUFRQVWUXFWLQJJHRPHWULFPRGHOVRISODQH¿JXUHV FRQWDLQLQJSDUDOOHODQGRUSHUSHQGLFXODUOLQHVDQJOHVSHUSHQGLFXODUELVHFWRUV FRQJUXHQWDQJOHVUHJXODUSRO\JRQV / The student communicates his or her mathematical thinking by > @36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRUV\P- EROLFDOO\WUDQVODWLQJDPRQJWKHVHDOWHUQDWLYHUHSUHVHQWDWLRQV RUXVLQJDSSURSULDWH YRFDEXODU\V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQG solutions >@36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRU V\PEROLFDOO\FRPPXQLFDWLQJPDWKLGHDVLQZULWLQJ RUXVLQJDSSURSULDWHYRFDEXODU\ V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQGVROXWLRQV Vocabulary & Definitions Introduction of Math Vocabulary Note: For fun, a You Tube video (“TMBG: Here Come the 123s Nonagon”, http://ie.youtube.com/watch?v=x5ohtlewREI, gives a singing introduction to polygons (nonagons, hexagons, etc.) Review from previous units: $SRO\JRQLVDFORVHGSODQH¿JXUHZLWKVWUDLJKWVLGHV Regular polygon $UHJXODUSRO\JRQLVRQHLQZKLFKDOOVLGHVDUHFRQJUXHQWDQGDOODQJOHV DUHFRQJUXHQW(TXLODWHUDOWULDQJOHVDQGVTXDUHVDUHH[DPSOHVRIUHJXODU polygons. ,IDOORIWKHVLGHVRIDSRO\JRQDUHQRWFRQJUXHQWRUDOORILWVDQJOHVDUHQRW FRQJUXHQWLWLVDQLUUHJXODUSRO\JRQ+HUHDUHUHJXODUSRO\JRQVZLWK DQG VLGHV $VRFFHUEDOOLVPDGHRIUHJXODUSRO\JRQVZLWKIRXUVL[DQGWHQVLGHV Base 7KHEDVHLVWKHERWWRPVLGHRID¿JXUHRUWKHVLGHWRZKLFKDQDOWLWXGHLV GUDZQ,IWKHWRSLVSDUDOOHOWRWKHERWWRP DVLQDWUDSH]RLGRUSULVP ERWK the top and bottom are called bases. 7KLV³SRO\JRQPDQ´LVVLWWLQJRQWKHEDVHRIDWULDQJOH+DYHVWXGHQWVSRLQWRXW bases for other polygons in the picture. — 159 — Introduction of Math Vocabulary Altitude The altitude or height is the shortest distance between WKHEDVHRIDJHRPHWULF ¿JXUHDQGLWVWRSZKHWKHU WKDWWRSLVDYHUWH[RUDQRWKHUEDVH $VNVWXGHQWVWRLGHQWLI\WKHVKDSHRIWKHIURQWRIWKLV ZDOOWHQW DSHQWDJRQ 7KHQ DVNWKHPZKDWWKH\ ZRXOGPHDVXUHWR¿QGWKHDOWLWXGHDVVXPLQJWKHEDVH LVWKHVLGHDORQJWKHJURXQG 7KH\ZRXOGPHDVXUH WKH]LSSHU Apothem $QDSRWKHPLVWKHOLQHVHJPHQWIURPWKHFHQWHURIDUHJXODU SRO\JRQWRWKHPLGSRLQWRIDVLGHRUWKHOHQJWKRIWKLVVHJ- ment. 1RWH $SRWKHPLVSURQRXQFHGZLWKWKHHPSKDVLVRQWKH¿UVW V\OODEOHZLWKWKH³D´SURQRXQFHGDVLQDSSOH $SXKWKXP This quilt design is made with apothems. The larger squares are divided along their apothems to make the blocks of four small squares. Area $UHDLVWKHH[WHQWRIDWZRGLPHQVLRQDOVXUIDFHRUUHJLRQZLWKLQ JLYHQERXQGDULHV ,WLVPHDVXUHGLQVTXDUHXQLWVVXFKDVVTXDUH PLOHVVTXDUHPHWHUVRUVTXDUH LQFKHV 7KLVPDSRI6RXWKHDVW$ODVNDKDVERXQGDULHVGUDZQWRGLYLGHLWXSLQWRDUHDV that correspond to boroughs and census areas. — 160 — Introduction of Math Vocabulary Concave $FRQFDYHSRO\JRQLVRQHIRUZKLFKDGLDJRQDOFDQEH drawn that contains points that are outside the polygon. 7KLQNRIDFRQFDYHSRO\JRQDV³FDYHGLQ´ Convex $FRQYH[SRO\JRQLVRQHIRUZKLFKQRVLGHFDQEHH[WHQGHGWRLQWHUVHFWDQ\ RWKHUVLGHRUYHUWH[ LWFDQEHFXWE\DVWUDLJKWOLQHLQDWPRVWWZRSRLQWV Perimeter )RUDSRO\JRQWKHSHULPHWHULVWKHVXPRIWKHOHQJWKVRIDOORILWVVLGHV $VNVWXGHQWVZK\WKH\PLJKWZDQWWRPHDVXUHWKHSHULPHWHURIDSRO\- JRQ 7KH\ PLJKWZDQWWRRUGHUPDWHULDOVIRUDIHQFHRUDERUGHU WKHUHDUH PDQ\PRUHSRVVLEOHDQVZHUV $IHQFHVXUURXQGVWKHSHULPHWHURIWKLVROGJDUGHQDW3RUFXSLQH&UHHN near Haines about 100 years ago. — 161 — Introduction of Math Vocabulary Pentagon $SHQWDJRQLVDSRO\JRQZLWK¿YHVLGHV 7KLVÀRZHUFDOOHGDZLOGPRUQLQJJORU\KDVDSHQWDJRQVKDSH Hexagon $KH[DJRQLVDSRO\JRQZLWKVL[VLGHV $KH[DJRQDOVKDSHLVIUHTXHQWO\IRXQGLQQDWXUH([DPSOHVLQFOXGHVQRZÀDNHV ODYDFROXPQVDQGKRQH\FRPEV Heptagon $KHSWDJRQLVDSRO\JRQZLWKVHYHQVLGHV 6RPHFRLQVVXFKDVWKLV%ULWLVKSHQFHDUHVKDSHGOLNHKHSWDJRQV Octagon $QRFWDJRQLVDSRO\JRQZLWKHLJKWVLGHV This trampoline is in the shape of an octagon. — 162 — Introduction of Math Vocabulary Nonagon $QRQDJRQLVDSRO\JRQZLWKQLQHVLGHV 2QHH[DPSOHRIDQRQDJRQLVIRXQGRQWKHERWWRPRIWKLVJODVV Decagon $GHFDJRQLVDSRO\JRQZLWKWHQVLGHV 7KHVWDUVRQWKH$ODVND)ODJDUHGHFDJRQV$VNVWXGHQWVLIWKHVH DUHUHJXODURULUUHJXODUGHFDJRQV ,UUHJXODU $UHWKH\FRQFDYHRU FRQYH[" &RQYH[ Dodecagon $GRGHFDJRQLVDSRO\JRQZLWKWZHOYHVLGHV $VNVWXGHQWVZK\DGRGHFDJRQPLJKWEHDJRRGVKDSHIRUDFORFNIDFH 2QD FORFNWLPHPHDVXUHPHQWVDUHGLYLGHGLQWRWZHOYHHTXDOSDUWV N-gon $QQJRQLVDSRO\JRQZLWKQVLGHV — 163 — Introduction of Math Vocabulary Exterior angle (of a polygon) $QH[WHULRUDQJOHRIDSRO\JRQLVDQDQJOHEHWZHHQRQHVLGHRID SRO\JRQDQGWKHH[WHQVLRQRIDQDGMDFHQWVLGH +HUHLVDQH[DPSOHRIDQH[WHULRUDQJOHRIDWULDQJOHIRUPHGE\VSRNHVRQD bicycle wheel. — 164 — Language and Skills Development Using the Math Vocabulary Terms Language & Skills Development Nod and Clap Mount the vocabulary illustrations on the chalkboard. Point to one of the illustra- tions and say its name. The students should nod their heads to indicate that you VDLGWKHFRUUHFWYRFDEXODU\ZRUGIRUWKHLOOXVWUDWLRQ+RZHYHUZKHQ\RXSRLQW WRDQLOOXVWUDWLRQDQGVD\DQLQFRUUHFWQDPHIRULWWKHVWXGHQWVVKRXOGFODSWKHLU LISTENING KDQGV21&(5HSHDWWKLVSURFHVVXQWLODOORIWKHYRFDEXODU\LOOXVWUDWLRQVKDYH Use the activity pages been used a number of times in this way. from the Student Support Materials. One to Six 3URYLGHHDFKVWXGHQWZLWKWZREODQNÀDVKFDUGV(DFKVWXGHQWVKRXOGWKHQZULWH DQXPEHURQHDFKRIKLVÀDVKFDUGVEHWZHHQRQHDQGVL[RQHQXPEHUSHUFDUG :KHQWKHVWXGHQWV¶QXPEHUFDUGVDUHUHDG\WRVVWZRGLFHDQGFDOOWKHQXPEHUV VKRZLQJ$Q\VWXGHQWRUVWXGHQWVZKRKDYHWKRVHWZRQXPEHUVPXVWWKHQLGHQ SPEAKING WLI\ D YRFDEXODU\ LOOXVWUDWLRQ \RX VKRZ 7KH VWXGHQWV PD\ H[FKDQJH QXPEHU cards periodically during this activity. What’s the Word? %HIRUHWKHDFWLYLW\EHJLQVSUHSDUHFOR]XUHVHQWHQFHVRQVHQWHQFHVWULSV OHDYLQJ RXWWKHVLJKWZRUGV :ULWHWKHVLJKWZRUGVRQLQGLYLGXDOVLJKWZRUGFDUGV0RXQW WKHVHQWHQFHVWULSVRQWKHFKDONERDUG/D\WKHVLJKWZRUGVRQWKHÀRRULQIURQWRI WKHFKDONERDUG*URXSWKHVWXGHQWVLQWRWZRWHDPV:KHQ\RXVD\³*R´WKH¿UVW player from each team must rush to the sight words. Each player must select a READING VLJKWZRUGDQGWKHQSODFHLWLQLWVFRUUHFWVHQWHQFHRQWKHFKDONERDUG5HSHDWWKLV Use the activity pages SURFHVVXQWLODOOVWXGHQWVKDYHKDGDQRSSRUWXQLW\WRUHVSRQG EHFHUWDLQWRKDYH from the Student DVXI¿FLHQWQXPEHURIFOR]XUHVHQWHQFHVIRUWKLVDFWLYLW\ $QDOWHUQDWLYHDSSURDFK Support Materials. for this activity is to provide each student with a sight word card. Hold up one of your sentence strips and the student or students who have the sight word that EHVWFRPSOHWHVWKHVHQWHQFH\RXDUHKROGLQJVKRXOGVKRZWKHLUFDUGV+DYHWKH VWXGHQWVH[FKDQJHVLJKWZRUGFDUGVSHULRGLFDOO\GXULQJWKHDFWLYLW\ What’s the Title %HIRUHWKHDFWLYLW\EHJLQVSUHSDUHDSDUDJUDSKUHODWHGWRmotion. Do not title the paragraph. Provide each student with a copy of the paragraph and a pencil/pen. WRITING 7KHVWXGHQWVVKRXOGUHDGWKHSDUDJUDSKVLOHQWO\7KHQHDFKVWXGHQWVKRXOGFUH- Use the activity pages ate a title for it. They should write their titles at the top of the paragraph. When from the Student WKHVWXGHQWVDUH¿QLVKHGKDYHHDFKVWXGHQWUHDGKLVKHUWLWOHRUDOO\ Support Materials. — 167 — Student Support Materials — 171 — — 173 — — 175 — — 177 — — 179 — — 181 — — 183 — — 185 — — 187 — — 189 — — 191 — — 193 — — 195 — — 197 — — 199 — — 201 — — 203 — — 204 — True-False Sentences (Listening and/or Reading Comprehension) 1. $regular polygon has all sides congruent and all angles congruent. 2. Each polygon has only one base. $SRO\JRQPD\KDYHPRUHWKDQRQHEDVHEXWRQO\RQHaltitude. There are as many apothems as there are sides on a polygon. ,WLVLPSRVVLEOHWR¿QGWKHarea of a concave polygon. $Q/VKDSHGÀRRUSODQLVDQH[DPSOHRIDconcave polygon 7. $OOUHJXODUSRO\JRQVDUHconvex. The perimeter of a polygon is longer than any of its sides. 9. $ pentagon can never have two parallel sides. 10.$hexagon shape is found in honeycombs. 11.$heptagon has eight sides. 12.$Qoctagon is one of the shapes that are found on a soccer ball. $nonagon has two more sides than a heptagon. DecagonsDUHQHYHUFRQYH[ $dodecagon has more sides than a decagon. One type of an n-gon might have 27 sides. 17.&RQFDYHSRO\JRQVFDQQRWKDYHexterior angles. $QVZHUV 7))7)777 )7))7)77 1. ,IDOOWKHVLGHVRIDSRO\JRQDUHFRQJUXHQWLWLVDOZD\VDregular polygon. 2. The base of a polygon is always a straight line segment. $SRO\JRQ¶ValtitudeLVPHDVXUHGIURPDEDVHWRLWVWRSPRVWYHUWH[RUVLGH $QapothemLVPHDVXUHGIURPWKHFHQWHURIDSRO\JRQWRDYHUWH[ 5. Area is a two-dimensional measurement. If a polygon is irregular it is also concave. 7. ,IDOOWKHVLGHVRIDSRO\JRQDUHHTXDOLWLV convex. ,IDSRO\JRQKDVWZRSDUDOOHOVLGHVWKHVDPHOHQJWKRQO\RQHRIWKHPLV included in the perimeter. 9. $pentagonFDQEHFRQYH[RUFRQFDYH 10.$VL[SRLQWHGVWDULVVKDSHGOLNHDhexagon. 11.5HJXODUheptagons DUHDFKDOOHQJHWR¿QGLQWKHDYHUDJHOLYLQJURRP 12.$VWRSVLJQLVVKDSHGOLNHDQoctagon. Most classrooms are shaped like nonagons. In the word decagonWKHQXPEHULVLQGLFDWHGE\WKHSUH¿[³GHF´MXVWOLNH the word decimal. $dodecagon has twice as many sides as a decagon. $Qn-gon always has an odd number of sides. 17.One side of a polygon forms one side of its exterior angle. $QVZHUV )77)7))) 7)77)7))7 — 205 — Match the Halves $FORVHGSODQH¿JXUHPDGHZLWKWHQ $LVPHDVXUHGWRDYHUWH[RUDSDUDOOHO line segments is a side. $UHJXODUSRO\JRQPXVWKDYHDOO %EDVHV sides congruent and 7KHDOWLWXGHRIDSRO\JRQ &QLQHWRRWKSLFNV $VL[SRLQWHGVWDULV D. pentagon. $PRGHORIDQRQDJRQFRXOGEH E. has seven sides. constructed using 7RFUHDWHDQH[WHULRUDQJOH )RQHVLGHRIDSRO\JRQLVH[WHQGHG $GRGHFDJRQKDVWZLFHDVPDQ\ *FRQYH[ sides as $KH[DJRQPLJKWEHFUHDWHGE\ H. decagon. 9. If two sides of a polygon are paral- I. an octagon OHOERWKDUHFDOOHG $SRO\JRQLVFDOOHGKHSWDJRQDOLILW J. perimeter. 11. To make a fence for an octagonal .WZRGLPHQVLRQV GRJ\DUGDPHDVXUHPHQWLVQHHG- ed for the $³7VKDSHG´EXLOGLQJKDVHLJKW L. also all angles congruent. VLGHVVRLWVÀDWURRILVVKDSHGOLNH (DFKVLGHRIDUHJXODUSRO\JRQ M. an n-gon. has $UHDLVDPHDVXUHPHQWZLWK N. cutting two corners off a square to make two new sides. +DOIRIDUHJXODURFWDJRQZRXOG O. an apothem. be a $SRO\JRQZLWKDQXQNQRZQ P. concave number of sides is $OOUHJXODUSRO\JRQVDUH 4DKH[DJRQ +/$3&)41 %(-,2.'0* — 206 — 'H¿QLWLRQV Regular polygon: one in which all sides are congruent and all angles are con- gruent. Base: WKHERWWRPVLGHRID¿JXUHRUWKHVLGHWRZKLFKDQDOWLWXGHLVGUDZQ,IWKH WRSLVSDUDOOHOWRWKHERWWRP DVLQDWUDSH]RLGRUSULVP ERWKWKHWRSDQGERWWRP are called bases. Altitude: WKHVKRUWHVWGLVWDQFHEHWZHHQWKHEDVHRIDJHRPHWULF¿JXUHDQGLWV WRSZKHWKHUWKDWWRSLVDYHUWH[RUDQRWKHUEDVH Apothem: the line segment from the center of a regular polygon to the midpoint RIDVLGHRUWKHOHQJWKRIWKLVVHJPHQW Area: WKHH[WHQWRIDWZRGLPHQVLRQDOVXUIDFHRUUHJLRQZLWKLQJLYHQOLQHV,WLV measured in square units. Concave: such that a straight line might be drawn that intersects it in four or more points. Convex: such that QRVLGHFDQEHH[WHQGHGWRLQWHUVHFWDQ\RWKHUVLGHRUYHUWH[ Perimeter: the sum of the lengths of the sides. Pentagon DSRO\JRQZLWK¿YHVLGHV Hexagon DSRO\JRQZLWKVL[VLGHV Heptagon: a polygon with seven sides. Octagon: a polygon with eight sides. Nonagon: a polygon with nine sides. Decagon: a polygon with ten sides. Dodecagon: a polygon with twelve sides. n-gon: a polygon with n sides. Exterior angle RIDSRO\JRQ DQDQJOHEHWZHHQRQHVLGHRIDSRO\JRQDQGWKH H[WHQVLRQRIDQDGMDFHQWVLGH — 207 — Which Belongs 1. ,IDSRO\JRQKDVRQHGR]HQVLGHVLWLVD WZHOYRJRQGRGHFDJRQKHSWDJRQ 2. 7KH SHULPHWHUDUHDDSRWKHP RIDSRO\JRQLVWKHVXPRIDOOLWVVLGHV ,IRQHPRUHVLGHZDVDGGHGWRDKH[DJRQWKHUHVXOWZRXOGEHD SHQWDJRQQRQDJRQ KHSWDJRQ 7KH DOWLWXGHEDVHDSRWKHP LVWKHVDPHDVWKHKHLJKWRIDSRO\JRQ $SRO\JRQZLWKQLQHDOWLWXGHVZRXOGEH DRFWDJRQDQRQDJRQDQLQRJRQ ,IQROLQHFDQLQWHUVHFWDSRO\JRQPRUHWKDQWZLFHLWLV FRQFDYHUHJXODUFRQYH[ 7. )RUDJLYHQEDVHRIDSRO\JRQWKH DSRWKHPKHLJKWSHULPHWHU ZRXOGEHVKRUWHUWKDQ the altitude. ,IDVHJPHQWFRQQHFWLQJWZRYHUWLFHVRIDSRO\JRQLVRXWVLGHWKHSRO\JRQLWLV FRQFDYH UHJXODUFRQYH[ 9. 7KH VLGHDSRWKHPEDVH RIDSRO\JRQLVWKHVLGHIURPZKLFKWKHDOWLWXGHLVPHDVXUHG 10.,IWKHQXPEHURIVLGHVRIDSRO\JRQLVWKHVDPHDVWKHQXPEHURI\HDUVLQDGHFDGHLW LVD WHQDJRQGHFDJRQGRGHFDJRQ 11.$IDPRXVEXLOGLQJLQ:DVKLQJWRQ'&LVVKDSHGOLNHDQGQDPHGIRUD QRQDJRQSHQWD- JRQQJRQ 12.,I\RXGRQ¶WNQRZWKHQXPEHURIVLGHVRIDSRO\JRQ\RXZRXOGFDOOLWDQ LUUHJXODUSRO\- JRQQJRQRFWDJRQ ,IWKHVLGHVRIDSRO\JRQDUHGLIIHUHQWOHQJWKVLWFDQQRWEHD UHJXODUFRQYH[FRQFDYH polygon. $OWLWXGHDUHDSHULPHWHU LVDWZRGLPHQVLRQDOPHDVXUHPHQW $Q RFWDJRQKH[DJRQSHQWDJRQ KDVWKHVDPHQXPEHURIVLGHVDVDQRFWRSXVKDV legs. $SRO\JRQZLWKVL[DQJOHVLVD VH[DJRQKH[DJRQKHSWDJRQ 17.$Q H[WHULRUDQJOHDSRWKHPDOWLWXGH RIDSRO\JRQLVRQWKHRXWVLGHRILW 1. dodecagon 7. apothem regular 2. perimeter concave area heptagon 9. base octagon altitude 10.decagon KH[DJRQ nonagon 11.pentagon 17.H[WHULRUDQJOH FRQYH[ 12.n-gon — 208 — Multiple Choice 6XSSRVH\RXFDQZDONLQDVWUDLJKWOLQHIURPRQHFRUQHURIDEXLOGLQJWRDQRWKHURQWKH RXWVLGHRIWKHEXLOGLQJ+RZFDQ\RXGHVFULEHWKHEXLOGLQJ¶VVKDSH" D FRQFDYH E FRQYH[ F UHJXODU ,IDQRFWDJRQKDGRQHPRUHVLGHZKDWZRXOGLWEH" D KHSWDJRQ E GHFDJRQ F QRQDJRQ :KLFKGHVFULEHVWKHVKDSHRIDVWRSVLJQ" D DSHQWDJRQ E DFRQFDYHSRO\JRQ F UHJXODUSRO\JRQ :KDWLVWKHGLVWDQFHIURPDEDVHRIDSRO\JRQWRDQRSSRVLWHYHUWH[RUEDVH" D WKHKHLJKW E WKHDOWLWXGH F ERWKRIWKHDERYH $QRFWRJHQDULDQLVDSHUVRQLQWKHLUµV:KLFKSRO\JRQKDVWKHVDPHQXPEHURIVLGHVDV WKHGHFDGHVRIDQRFWRJHQDULDQ¶VOLIH" D DQRFWDJRQ E DGHFDJRQ F DQRQDJRQ ,IRQHVLGHRIDSRO\JRQLVH[WHQGHGZKLFKRIWKHIROORZLQJLVIRUPHG" D DQH[WHULRUDQJOH E DSHULPHWHU F DQDSRWKHP :KDWNLQGRISRO\JRQPLJKWKDYHRQHKXQGUHGVLGHV" D DFRQFDYHSRO\JRQ E DQQJRQ F ERWKRIWKHDERYH 7KHGHFLPDOV\VWHPLVEDVHGRQWKHQXPEHUWHQ:KLFKSRO\JRQLVDOVREDVHGRQWKH QXPEHUWHQ" D DGRGHFDJRQ E DSHQWDJRQ F DGHFDJRQ :KLFKRIWKHIROORZLQJGRHVQRWHYHULQWHUVHFWDYHUWH[RIDSRO\JRQ" D DQDOWLWXGH E DQDSRWKHP F DQH[WHULRUDQJOH — 209 — 7R¿QGWKHDPRXQWRIFDUSHWQHHGHGIRUDURRPZKLFKRIWKHIROORZLQJÀRRUPHDVXUHPHQWVZRXOG EHQHHGHG" D WKHSHULPHWHU E WKHDUHD F WKHDSRWKHP :KLFKRIWKHIROORZLQJLVWUXHRIDQ\UHJXODUSRO\JRQ" D ,WLVFRQFDYH E 2QHEDVHLVORQJHUWKDQDQRWKHU F ,WLVFRQYH[ :KDWLVDOZD\VWUXHRIDSRO\JRQZLWK¿YHVLGHV" D ,WLVDUHJXODUSRO\JRQ E ,WLVDFRQFDYHSRO\JRQ F ,WLVDSHQWDJRQ :KLFKPDWFKHVWKHQXPEHURIVLGHVRIDSRO\JRQ" D WKHQXPEHURISRVVLEOHEDVHV E WKHQXPEHURISRVVLEOHSHULPHWHUV F WKHQXPEHURISRVVLEOHH[WHULRUDQJOHV :KLFKRIWKHIROORZLQJKDVVHYHQDSRWKHPV" D DKHSWDJRQ E DKH[DJRQ F DKHIWDJRQ +RZPDQ\VLGHVGRHVDGRGHFDJRQKDYH" D WZHQW\ E WZR F WZHOYH +RZZRXOG\RX¿QGWKHSHULPHWHURIDQRQDJRQ" D PXOWLSO\WKHEDVHWLPHVWKHDOWLWXGH E DGGWKHPHDVXUHPHQWVRIDOORILWVVLGHV F DGGWKHPHDVXUHPHQWVRIDOO DSRWKHPV +RZPDQ\VLGHVGRHVDKH[DJRQKDYH" D VHYHQ E VL[W\ F QRQHRIWKHDERYH $QVZHUV $&&%$$%& %%&$$$&%& — 210 — Complete the Sentence 1. $ Q BBBBBBBBBBBBBBBBBBBBKDVDOOVLGHVFRQJUXHQWDQGDOODQJOHVFRQJUXHQW 2. $Q\SRO\JRQZLWKWHQVLGHVLVD Q BBBBBBBBBBBBBBBBBBBBB $QDQJOHIRUPHGE\WKHVLGHRIDSRO\JRQDQGWKHH[WHQVLRQRIDQRWKHUVLGHLVD Q BBBBBBBBBBBBBBBBBBBBBBBBBRIWKHSRO\JRQ $ Q BBBBBBBBBBBBBBBBBBBBBLVDSRO\JRQZLWKQLQHVLGHV $¿YHVLGHGSRO\JRQLVFDOOHGD Q BBBBBBBBBBBBBBBBBBBBBBBBB $ Q BBBBBBBBBBBBBBBBBBBBBBBBBBKDVDQHQGSRLQWDWWKHFHQWHURIDSRO\JRQ 7. $ Q BBBBBBBBBBBBBBBBBBBBBBBBFDQKDYHDQ\QXPEHURIVLGHV $Q\SRO\JRQZLWKVHYHQVLGHVLVFDOOHGD Q BBBBBBBBBBBBBBBBBBBBBBBBB 9. 7RPHDVXUHWKHH[WHQWRIDUHJLRQRIDSODQH\RXZRXOG¿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regular polygon 10.concave 2. decagon 11.perimeter H[WHULRUDQJOH 12.KH[DJRQ nonagon altitude pentagon dodecagon apothem base 7. n-gon FRQYH[ heptagon 17.octagon 9. area — 211 — Creative Writing ,Q DQLQYHQWRUE\WKHQDPHRI&KULVWRSKHU0RQFNWRQFUHDWHGDSX]]OHFDOOHG(WHUQLW\LQYROYHG tiling a dodecagon with 209 irregularly shaped polygons called polydrafters. The game included D SUL]HIRU any person who could solve the puzzle. In just PRQWKVWZR\RXQJ &DPEULGJHPDWKHPDWL- cians produced a result. This is an image of the inventory of polydraft- ers that came with the game. Students can use the words from the unit to talk about the irregular SRO\JRQVVKRZQUHIHU- ring to them by number. — 212 — Place-Based Practice Activity +DYHVWXGHQWVGUDZÀRRUSODQVIRUDWHHQFHQWHUDUHPRWHFDELQDFODVVURRPDKRXVHRU another type of structure that they might use alone or with their friends. (DFKÀRRUSODQVKRXOGLQFOXGHDWOHDVWRQHUHJXODUSRO\JRQZLWKPRUHWKDQIRXUVLGHV 6WXGHQWVFDQQDPHWKHSRO\JRQVRQWKHLUÀRRUSODQVDQG¿QGWKHLUDUHDVDQGSHULPHWHUV)RU UHJXODUSRO\JRQVWKH\FDQODEHODQDSRWKHP $VNVWXGHQWVWRVKDUHWKHÀRRUSODQVZLWKWKHFODVV :KDWDUHWKHDGYDQWDJHVRIHDFKVKDSHXVHGRQWKHÀRRUSODQV":KDWDUHWKHGLVDGYDQ- WDJHV" 2QDVWUHHWPDSRI\RXUWRZQ¿QGSRO\JRQVZLWKPRUHWKDQIRXUVLGHV8VHWKHPDSVFDOHWR ¿QGWKHDUHDVDQGSHULPHWHUVRIWKHSRO\JRQV — 213 — — 214 — Unit Assessment — 215215 — — 216 — Geometry: Unit 8-polygons and area Name: ______Date: ______ Word Bank altitude apothem area base concave polygon 1) An is the line segment from the center of a regular polygon to the midpoint of a side, or the length of this segment. 2) The is the extent of a two-dimensional surface or region within given boundaries. 3) The bottom side of a figure is the . 4) The or height is the shortest distance between the base of a geometric figure and its top, whether that top is a vertex or another base. Label Illustrations: Write the correct label below each of the illustrations below. 5) Matt...insert illustration of a pentagon ______ 6) Matt...insert an illustration of a heptagon. ______ — 217 — 7) Matt...insert illustration of a hexagon ______ 8) insert illustration of an octagon. ______ 9) Matt...insert illustration of a regular polygon ______ Matching: Match the key vocabulary on the left with the correct definition on the right. Place the letter of the definition in front of the word it matches. 10) _____ nonagon a. a polygon with ten sides b. a polygon with 12 sides 11) _____ decagon c. a polygon with nine sides 12) _____ dodecagon d. polygon with all sides congruent 13) _____ hexagon and all angles congruent e. a polygon with 6 sides 14) _____ pentagon f. a polygon with 5 sides 15) _____ regular polygon — 218 — Multiple Choice: Choose the word that matches the illustration. Circle the letter in front of the correct word. 16) Choose the word that fits the following illustration. Matt...insert illustration for a concave polygon a) concave polygon b) convex polygon c) exterior angle of a polygon 17) Choose the word that fits the following illustration. Matt..insert illustration of a exterior angle of a polygon a) concave polygon b) convex polygon c) exterior angle of a polygon 18) Choose the word that fits the following illustration. Matt..insert illustration of a convex polygon a) concave polygon b) convex polygon c) exterior angle of a polygon — 219 — — 220 — Geometry: Unit 8-polygons and area Name: ______Date: ______ Word Bank altitude apothem area base concave polygon 1) An apothem is the line segment from the center of a regular polygon to the midpoint of a side, or the length of this segment. 2) The area is the extent of a two-dimensional surface or region within given boundaries. 3) The bottom side of a figure is the base . 4) The altitude or height is the shortest distance between the base of a geometric figure and its top, whether that top is a vertex or another base. Label Illustrations: Write the correct label below each of the illustrations below. 5) Matt...insert illustration of a pentagon pentagon 6) Matt...insert an illustration of a heptagon. heptagon — 221 — 7) Matt...insert illustration of a hexagon hexagon 8) Insert illustration of an octagon. octagon 9) Matt...insert illustration of a regular polygon regular polygon Matching: Match the key vocabulary on the left with the correct definition on the right. Place the letter of the definition in front of the word it matches. 10) c nonagon a. a polygon with ten sides b. a polygon with 12 sides 11) a decagon c. a polygon with nine sides 12) b dodecagon d. polygon wilth all sides congruent 13) e hexagon and all angles congruent e. a polygon with 6 sides 14) f pentagon f. a polygon with 5 sides 15) d regular polygon — 222 — Multiple Choice: Choose the word that matches the illustration. Circle the letter in front of the correct word. 16) Choose the word that fits the following illustration. Matt...insert illustration for a concave polygon a) concave polygon b) convex polygon c) exterior angle of a polygon 17) Choose the word that fits the following illustration. Matt..insert illustration of a exterior angle of a polygon a) concave polygon b) convex polygon c) exterior angle of a polygon 18) Choose the word that fits the following illustration. Matt..insert illustration of a convex polygon a) concave polygon b) convex polygon c) exterior angle of a polygon — 223 — — 224 — UNIT 9 Three Dimensional Figures Sealaska Heritage Institute Grade Level Expectations for Unit 9 Unit 9—Three Dimensional Figures Alaska State Mathematics Standard A $VWXGHQWVKRXOGXQGHUVWDQGPDWKHPDWLFDOIDFWVFRQFHSWVSULQFLSOHVDQGWKHRULHV $VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG $ FRQVWUXFWGUDZPHDVXUHWUDQVIRUPFRPSDUHYLVXDOL]HFODVVLI\DQGDQDO\]H WKHUHODWLRQVKLSVDPRQJJHRPHWULF¿JXUHV DQG Alaska State Mathematics Standard C $VWXGHQWVKRXOGXQGHUVWDQGDQGEHDEOHWRIRUPDQGXVHDSSURSULDWHPHWKRGVWR GH¿QHDQGH[SODLQPDWKHPDWLFDOUHODWLRQVKLSV $VWXGHQWZKRPHHWVWKHFRQWHQWVWDQGDUGVKRXOG & H[SUHVVDQGUHSUHVHQWPDWKHPDWLFDOLGHDVXVLQJRUDODQGZULWWHQSUHVHQWDWLRQV SK\VLFDOPDWHULDOVSLFWXUHVJUDSKVFKDUWVDQGDOJHEUDLFH[SUHVVLRQV & UHODWHPDWKHPDWLFDOWHUPVWRHYHU\GD\ODQJXDJH GLEs The student communicates his or her mathematical thinking by > @36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQG RUV\PEROLFDOO\WUDQVODWLQJDPRQJWKHVHDOWHUQDWLYHUHSUHVHQWDWLRQV RUXVLQJ DSSURSULDWHYRFDEXODU\V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQG strategies and solutions >@36UHSUHVHQWLQJPDWKHPDWLFDOSUREOHPVQXPHULFDOO\JUDSKLFDOO\DQGRU V\PEROLFDOO\FRPPXQLFDWLQJPDWKLGHDVLQZULWLQJ RUXVLQJDSSURSULDWHYRFDEXODU\ V\PEROVRUWHFKQRORJ\WRH[SODLQMXVWLI\DQGGHIHQGVWUDWHJLHVDQGVROXWLRQV Vocabulary & Definitions Introduction of Math Vocabulary 5HYLHZIURPSUHYLRXVXQLWV FRQJUXHQWEDVHYHUWH[SRO\JRQDQGSUH¿[HVVXFK DVSHQWDKH[DKHSWDRFWDHWF Solid DVROLG VKRUWIRUJHRPHWULFVROLGRUVROLGJHRPHWULF¿JXUH LVDWKUHH GLPHQVLRQDOFORVHG¿JXUHWKDWKDVDERXQGDU\ %XLOGLQJVDQGSROHVOLNHWKHRQHVLQWKLVSLFWXUHRID&KLHI¶VKRXVHLQ :UDQJHOOUHSUHVHQWJHRPHWULFVROLGV Cone $FRQHLVDVROLGZLWKDVLQJOHEDVHWKDWLVDFLUFOHWDSHULQJWRD YHUWH[,WFRQVLVWVRIDFLUFOHLWVLQWHULRUDJLYHQSRLQWQRWRQWKH SODQHRIWKHFLUFOHDQGDOOWKHVHJPHQWVIURPWKHSRLQWWRWKHFLUFOH )DPLOLDUH[DPSOHVRIFRQHVDUHLFHFUHDPFRQHVDQGWUDI¿FFRQHV WUDI¿FFRQHV DUHRIWHQFXWRIIDWWKHWRSVRWKDWWKH\DUHQRWFRPSOHWHFRQHV 9ROFDQRHVDUH VKDSHGOLNHFRQHV3RLQWRXWWRVWXGHQWVWKDWDVYROFDQRHVHURGHWKH\EHJLQWR lose their conical shape. Sphere $VSKHUHLVDWKUHHGLPHQVLRQDOVROLGFRQVLVWLQJRIDOOSRLQWVHTXLGLVWDQWIURPD JLYHQSRLQW*OREHVVFRRSVRILFHFUHDPDQGEDOOEHDULQJVDUHH[DPSOHVRI VSKHUHVDQGZHRIWHQWKLQNRIWKHHDUWKDVDVSKHUHHYHQWKRXJKLWLVQRWSHU- fectly spherical. $EDVNHWEDOOLVRQHH[DPSOHRIDVSKHUH — 231 — Introduction of Math Vocabulary Hemisphere $KHPLVSKHUHLVKDOIRIDVSKHUH:H¶YHDOOKHDUGRIWKH1RUWKHUQKHPL- VSKHUH WKHKDOIRIWKHHDUWKQRUWKRIWKH(TXDWRU DQGWKH6RXWKHUQ KHPLVSKHUH6LQFHWKHHDUWKLVQRWDSHUIHFWVSKHUHLWVKHPLVSKHUHVDUH also not perfect hemispheres. The word hemisphere might be used for RWKHUWKLQJVWKDWDUHQRWUHDOO\VSKHUHVVXFKDVWKHULJKWDQGOHIWKHPLVSKHUHVRI WKHEUDLQ,QJHRPHWU\WKHWHUPKHPLVSKHUHPHDQVKDOIRIDSHUIHFWVSKHUH Polyhedron $VROLGZLWKQRFXUYHGVXUIDFHVRUHGJHV$OOIDFHVDUHSRO\JRQVDQGDOOHGJHV DUHOLQHVHJPHQWV:DOOWHQWVSDSHUVWDUVDQGFHUHDOER[HVDUHMXVWVRPHH[- amples of polyhedra. Pyramid $S\UDPLGLVDSRO\KHGURQZLWKDVLQJOHEDVHWKDWLVDSRO\JRQWDSHULQJWRDYHU- WH[7KH(J\SWLDQVEXLOWS\UDPLGVEXWWKHUHDUHH[DPSOHVRIS\UDPLGVFORVHU WRKRPHVXFKDVSRLQWHGURRIVRUUDGLRWRZHUV6RPHWLPHVWKHFDSVRQIHQFH posts are shaped like pyramids. Apex $QDSH[LVWKHYHUWH[RUWRSSRLQWRIDFRQHRUS\UDPLG,QWKHSKRWRD ELUGLVDWWKHDSH[RIDS\UDPLG — 232 — Introduction of Math Vocabulary Tetrahedron $WHWUDKHGURQLVDS\UDPLGZLWKDWULDQJXODUEDVH,WKDVIRXUWUL- angular surfaces. The tetrahedron shape is seen in nature in the VWUXFWXUHRIDYHU\FRPPRQPROHFXOHPHWKDQH &+ 7KHIRXU hydrogen atoms lie in each corner of a tetrahedron with the carbon atom in the centre. One of the leading journals in organic chemistry is called ³7HWUDKHGURQ´ Cylinder $F\OLQGHULVDVROLGWKDWKDVWZRFRQJUXHQWFLUFOHVLQSDUDOOHOSODQHVDVLWVEDVHV 7KHF\OLQGHULVFRPSRVHGRIWKHWZRFLUFOHVDOOWKHSRLQWVLQWKHLULQWHULRUVDQGDOO RIWKHVHJPHQWVSDUDOOHOWRWKHD[LVWKDWFRQQHFWWKHFLUFOHV&RPPRQH[DPSOHV RIF\OLQGHUVDUHVWUDZVEDWWHULHVRUWDQNV &DQVRIVDOPRQ DQGORWVRIRWKHUNLQGVRIIRRG DUHVKDSHGOLNHF\OLQ- ders. Prism $SULVPLVDVROLGZKRVHEDVHVDUHFRQJUXHQWSRO\JRQVLQSDUDOOHOSODQHV6HJ- PHQWVFRQQHFWWKHFRUUHVSRQGLQJYHUWLFHVRIWKHSRO\JRQVVR that all of the prism’s side surfaces are parallelograms. Triangular prisms have triangles as bases and rectangular prisms have rect- angles as bases. This Swiss chocolate bar is shaped like a triangu- lar prism. Axis 7KHD[LVRIDF\OLQGHULVWKHOLQHIRUPHGE\WKHFHQWHUVRIWKH bases of a cylinder. — 233 — Introduction of Math Vocabulary Parallelepiped $SDUDOOHOHSLSHGLVDSULVPZLWKVL[UHFWDQJXODUVXUIDFHV(DFKVXUIDFH is parallel to its opposite surface. The shape of a parallelepiped makes LWHDV\WRVWDFN0RVWER[HVDUHVKDSHGOLNHSDUDOOHOHSLSHGV&KHHVH EXWWHUDQGRWKHUSDFNDJHGIRRGLWHPVRIWHQFRPHLQWKHVKDSHRID parallelepiped. Regular $UHJXODUVROLGLVDVROLGZLWKUHJXODUSRO\JRQDOEDVH V (DFKVLGHRIWKH base is congruent to every other side and each angle is congruent to every RWKHUDQJOH7KLVFDQGOHKDVWZRUHJXODUKH[DJRQVDVEDVHV ,IWKHVROLGLVDSRO\KHGURQLWLVUHJXODURQO\LIDOOWKHVLGHVDUHFRQJUXHQWUHJXODU SRO\JRQV 6HHSODWRQLFVROLG Right 5LJKWVROLGV³VWUDLJKWXSDQGGRZQ´5LJKWF\OLQGHUVDQGSULVPVKDYHEDVHV aligned directly one above the other so that the sides are perpendicular to the EDVHV5LJKWS\UDPLGVDQGFRQHVLQZKLFKWKHDSH[LVDOLJQHGGLUHFWO\DERYHWKH center of the base. This stack of coins is shaped like a right cylinder. — 234 — Introduction of Math Vocabulary Oblique 2EOLTXHVROLGVDUH³VODQWHG´7KH\DUHF\OLQGHUVS\UDPLGVDQGFRQHV WKDWDUHQRWULJKWVROLGVVRWKDWWKHEDVHVDUHQRWDOLJQHGGLUHFWO\RQH DERYHWKHRWKHURUWKHDSH[LVQRWGLUHFWO\DERYHWKHFHQWHURIWKH base. This mountain has the shape of an oblique pyramid. Platonic solid $SODWRQLFVROLGLVDUHJXODUSRO\KHGURQ,WVVXUIDFHVDUHFRQJUXHQWUHJXODUSRO\- JRQVDQGDOORILWVDQJOHVDUHFRQJUXHQW7KHUHDUHRQO\¿YHSRVVLEOHVKDSHV RISODWRQLFVROLGV 7HWUDKHGURQ WULDQJXODUVXUIDFHV +H[DKHGURQ VTXDUH VXUIDFHV 2FWDKHGURQ WULDQJXODUVXUIDFHV 'RGHFDKHGURQ SHQWDJRQDO VXUIDFHV ,FRVDKHGURQ WULDQJXODUVXUIDFHV The platonic solids were discovered by the ancient Greeks and named after the ancient Greek philosopher Plato; Plato specu- ODWHGWKDWWKHVH¿YHVROLGVZHUHWKHVKDSHVRIWKHEDVLFFRPSR- QHQWVRIWKHXQLYHUVH&XEHVRFWDKHGUDDQGWHWUDKHGUDDSSHDU LQPROHFXOHVDQGFU\VWDOVDQGGRGHFDKHGUDDQGLFRVDKHGUDDSSHDULQVRPH viruses and tiny marine animals. Cube $FXEHLVWKHFRPPRQQDPHIRUDUHJXODUKH[DKHGURQ,WVVL[ VXUIDFHVDUHDOOVTXDUHVDQGDOORIWKHDQJOHVDUHULJKWDQJOHV $FRPPRQFXEHLVDVXJDUFXEH$VNVWXGHQWVWRFRPHXS ZLWKRWKHUFRPPRQH[DPSOHV GLFH5XELN¶VFXEHHWF — 235 — Introduction of Math Vocabulary Similar solids Similar solids are identical in shape but not necessarily the same size. 5HPLQGVWXGHQWVWKDWWKH\KDYHDOUHDG\OHDUQHGDERXWVLPLODUWULDQJOHV DQGRWKHUVLPLODUSRO\JRQV%DOOVFRPHLQDOONLQGVRIW\SHVDQGVL]HV DQGDUHH[DPSOHVRIVLPLODUVROLGV — 236 — Language and Skills Development Using the Math Vocabulary Terms Language & Skills Development Does It Fit? Mount the vocabulary illustrations on the chalkboard. Provide each student with writing paper and a pen. Point to an illustration and say a sentence. If the sen- WHQFH\RXVD\JRHVZLWKWKHLOOXVWUDWLRQWKHVWXGHQWVVKRXOGPDNHFKHFNPDUNV RQWKHLUSDSHUV+RZHYHULIWKHVHQWHQFH\RXVD\GRHVQRWJRZLWKWKHLOOXVWUD- LISTENING WLRQWKHVWXGHQWVVKRXOGPDNHDQ³;´RQWKHLUSDSHUV5HSHDWWKLVSURFHVVZLWK Use the activity pages RWKHU LOOXVWUDWLRQV DQG VHQWHQFHV 5DWKHU WKDQ KDYLQJ WKH VWXGHQWV ZULWH WKHLU from the Student Support Materials. UHVSRQVHV\RXPD\KDYHWKHP³FODS´IRUVHQWHQFHVZKLFKGRQRWJRZLWKLOOXV- WUDWLRQVDQG³QRG´IRUVHQWHQFHVZKLFKGRJRZLWKWKHLOOXVWUDWLRQV\RXSRLQWWR Calendar Bingo %HIRUHWKHDFWLYLW\EHJLQVSUHSDUHDSDJHWKDWFRQWDLQVDFDOHQGDUSDJH FRP- SOHWHZLWKGD\VDQGGDWHV 3URYLGHHDFKVWXGHQWZLWKDFRS\RIWKHFDOHQGDU SDJH$OVRSURYLGHHDFKVWXGHQWZLWKVPDOOPDUNHUV(DFKVWXGHQWVKRXOG place the markers on different dates on his/her calendar page. Mount the vocab- XODU\LOOXVWUDWLRQVRQWKHFKDONERDUG&DOODVWXGHQW¶VQDPHDQGVD\DGDWHLQWKH SPEAKING PRQWK,IDPDUNHULVQRWRQWKHGDWH\RXQDPHGKHVKHVKRXOGVD\DFRPSOHWH VHQWHQFHDERXWDYRFDEXODU\LOOXVWUDWLRQ\RXSRLQWWR+RZHYHULIDPDUNHULVRQ WKHGDWH\RXFDOOHGKHVKHPD\³SDVV´WRWKHQH[WSOD\HU5HSHDWWKLVSURFHVV until all students have participated. You may wish to provide each student with more than one marker for this activity. Mixed-up Sentences %HIRUHWKHDFWLYLW\EHJLQVSUHSDUHDQXPEHURI³PL[HGXSVHQWHQFHV´UHODWLQJWRWKH FRQFHSWEHLQJVWXGLHGDQGXVLQJWKHVLJKWZRUGV:ULWHWKHPL[HGXSVHQWHQFHVRQ WKHFKDONERDUG&DOOXSRQLQGLYLGXDOVWXGHQWVWRUHDGWKHVHQWHQFHVVD\LQJWKHZRUGV RIWKHVHQWHQFHVLQWKHLUFRUUHFWRUGHU$QDOWHUQDWLYHDSSURDFKWRWKHRQHDERYHLV WRKDYHWKHPL[HGXSVHQWHQFHVZULWWHQRQVHQWHQFHVWULSV*URXSWKHVWXGHQWVLQWR READING WZRWHDPV6KRZWKH¿UVWSOD\HULQHDFKWHDPRQHRIWKHPL[HGXSVHQWHQFHV7KH Use the activity pages ¿UVWSOD\HUWRFRUUHFWO\UHDGWKHVHQWHQFHZLWKWKHZRUGVLQWKHLUFRUUHFWRUGHUZLQV from the Student WKHURXQG5HSHDWXQWLODOOSOD\HUVKDYHSDUWLFLSDWHG5DWKHUWKDQKDYLQJWKHSOD\HUV Support Materials. PHUHO\UHDGWKHPL[HGXSVHQWHQFHV\RXPD\ZLVKWROD\WKHVHQWHQFHVWULSVRQWKH ÀRRUDWWKHIURQWRIWKHFODVVURRP3ODFHWZRSDLUVRIVFLVVRUVEHVLGHWKHVHQWHQFH VWULSV:KHQ\RXVD\³*R´WKH¿UVWSOD\HULQHDFKWHDPPXVWUXVKWRWKHVFLVVRUV VHOHFWRQHRIWKHVHQWHQFHVWULSVDQGFXWHDFKZRUGRXW7KHQWKHSOD\HUPXVWUHDU- UDQJH WKH ZRUGV WR FUHDWH WKH VHQWHQFH 5HSHDW XQWLO DOO SOD\HUV KDYH SOD\HG 2I FRXUVHWKLVDFWLYLW\FDQDOVREHGRQHDVDQactivity sheet with the students. The Other Half &XWHDFKRIWKHVLJKWZRUGVLQKDOI*LYHHDFKVWXGHQWDVKHHWRIZULWLQJSDSHUD WRITING pen and one of the word-halves. Each student should glue the word-half on his/ Use the activity pages her writing paper and then complete the spelling of the word. You may wish to from the Student have enough word-halves prepared so that each student completes more than Support Materials. RQHZRUG$IWHUZDUGVUHYLHZWKHVWXGHQWV¶UHVSRQVHV — 239 — Student Support Materials — 243 — — 245 — — 247 — — 249 — — 251 — — 253 — — 255 — — 257 — — 259 — — 261 — — 263 — — 265 — — 267 — — 269 — — 271 — — 273 — — 275 — — 277 — — 278 — True-False Sentences (Listening and/or Reading Comprehension) 1. $solid is a three dimensional shape enclosed by a boundary. 2. Soda cans are almost always shaped like cones. $sphere might have an oblong shape. The southern hemisphere is half of the earth. $FRQHLVRQHW\SHRIpolyhedron. The base of a pyramidKDVDWOHDVWWKUHHVLGHVEXWPD\KDYHPDQ\PRUH 7. $Qapex is the top point of a cone or a pyramid. $tetrahedron is a type of polyhedron with four surfaces. 9. Cylinders can have square bases. 10.The height of a prism is always greater than its width. 11.The axis of a cylinder connects the centers of the bases. 12.$parallelepiped might have eight surfaces. $regular solid has a base with all sides congruent and all angles congruent. In a rightSULVPWKHEDVHVDUHVLWXDWHGGLUHFWO\RQHDERYHWKHRWKHU ,IWKHEDVHRIDSULVPLVQRWDUHJXODUSRO\JRQLWLVDQoblique prism. 7KHUHDUHH[DFWO\¿YHNLQGVRIplatonic solids. 17.It is possible for a cube to be oblique. $FHUHDOER[DQGVKRHER[DUHsimilar solids. $QVZHUV 7))7)777 ))7)77)7)) 1. $FLUFOHLVRQHW\SHRIsolid. 2. $coneKDVDFLUFOHDVDEDVHWDSHULQJWRDSRLQW Most globes are shaped like spheres. $hemisphere is a sphere that is not quite round. $polyhedron does not have any curved edges. 6. Pyramids always have four sides. 7. The apex of a cone is always directly over the center of the base. Every tetrahedron is a platonic solid. 9. ,IDVROLGKDVWZRFRQJUXHQWFLUFOHVLQSDUDOOHOSODQHVDVEDVHVLWLVDcylin- der. 10.$prismLVDOLNHDF\OLQGHUH[FHSWWKDWLWVEDVHVDUHSRO\JRQV 11.$QHGJHPLJKWDOVREHDQaxis. 12.In a parallelepiped, each surface is parallel to the opposite surface. $regular pyramid might have a star-shaped base. ,IWKHEDVHRIDSULVPKDVULJKWDQJOHVLWLVDright prism. 15. Oblique VROLGVDUHVODQWHG WKHDSH[LVQRWRYHUWKHFHQWHURIWKHEDVHRUWKH two bases are offset. $platonic solid might have sides that are heptagons. 17.$cubeLVDUHJXODUKH[DKHGURQ 18. Similar solids have the same shape but different sizes. $QVZHUV )77)7))) 77)7))7)77 — 279 — Match the Halves $SRO\KHGURQLVDVROLGZLWK $DWHWUDKHGURQ $WUDI¿FFRQHLVFXWRIIDWWKHWRSVRLWLV %DFLUFOH 7KHEDVH V RIDUHJXODUVROLG &VL[TXDGULODWHUDOVXUIDFHV $WKUHHGLPHQVLRQDO¿JXUHLVFDOOHG D. is directly over the center of the base. )RXUWULDQJXODUVXUIDFHVMRLQWRPDNH E. the same distance from the center. $SDUDOOHOHSLSHGKDV )VLPLODUVROLGV $FXEHLVD G. a polygonal base. $VROLGZLWKWZRSDUDOOHOFRQJUXHQW H. straight edges and surfaces. polygons as bases is 9. Every point on a sphere is I. congruent circles $VXJDUFXEHDQGD5XELN¶VFXEHDUH J. a solid. $F\OLQGHUKDVEDVHVWKDWDUH .DSULVP 12. If a sphere is divided in two by a plane L. one base aligned directly over the WKURXJKLWVFHQWHUHDFKSDUWLV other. $OORIWKHHGJHVDUHFRQJUXHQWRQD 0UHJXODUKH[DKHGURQ 7KHFHQWHUVRIDF\OLQGHU¶VEDVHV 1PLVVLQJLWVDSH[ 7KHDSH[RIDULJKWS\UDPLG O. platonic solid. $FRQHWDSHUVWRDSRLQWIURP 3DUHLQWHUVHFWHGE\LWVD[LV $QREOLTXHF\OLQGHUGRHVQRWKDYH 4DKHPLVSKHUH $S\UDPLGWDSHUVWRDQDSH[IURP 5DUHUHJXODUSRO\JRQV $QVZHUV +15-$&0. (),423'%/* — 280 — 'H¿QLWLRQV SolidDWKUHHGLPHQVLRQDO¿JXUHHQFORVHGE\DERXQGDU\ Cone - a solid with a circular base tapering to a point that is not on the same plane as the base. Sphere - a three dimensional solid consisting of all points equidistant from a given point. Hemisphere - half of a sphere. Polyhedron - a solid with surfaces that are all polygons and edges that are all line segments. PyramidDSRO\KHGURQZLWKDVLQJOHSRO\JRQDOEDVHWDSHULQJWRDYHUWH[ ApexWKHYHUWH[RUWRSSRLQWRIDFRQHRUS\UDPLG Tetrahedron - a pyramid with a triangular base. Cylinder - a solid whose two bases are congruent circles in parallel planes Prism - a cylinder whose bases are polygons. Axis RIDF\OLQGHU WKHOLQHWKDWSDVVHVWKURXJKWKHFHQWHUVRIWKHEDVHVRID cylinder. ParallelepipedDSULVPZLWKVL[UHFWDQJXODUVXUIDFHVHDFKSDUDOOHOWRLWV opposite surface. Regular VROLG DS\UDPLGRUSULVPZLWKDUHJXODUSRO\JRQDVDEDVHRUD polyhedron with congruent regular polygons on all sides. Right VROLG F\OLQGHUVDQGSULVPVWKDWKDYHEDVHVDOLJQHGGLUHFWO\RQHDERYH WKHRWKHURUS\UDPLGVDQGFRQHVLQZKLFKWKHDSH[LVDOLJQHGGLUHFWO\DERYHWKH center of the base. Oblique VROLG $F\OLQGHUS\UDPLGRUFRQHVWKDWLVQRWDULJKWVROLG Platonic solidDSODWRQLFVROLGLVRQHRI¿YHSRVVLEOHUHJXODUSRO\KHGUD CubeDUHJXODUKH[DKHGURQRUDVROLGZLWKVL[VTXDUHVXUIDFHV Similar solids - solids that are identical in shape but not necessarily the same size. — 281 — Which Belongs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he set of all the points in space that are one mile from a radio transmitter has the VKDSHRID SODWRQLFVROLGFLUFOHVSKHUH ,IWKHEDVHVRIDF\OLQGHUDUHDOLJQHGGLUHFWO\RQHDERYHWKHRWKHULWLVD UHJXODUULJKW REOLTXH F\OLQGHU $VROLGZLWKVL[VTXDUHVLGHVLVD FXEHWHWUDKHGURQTXDGULKHGURQ $SLQJSRQJEDOODQGDYROOH\EDOODUH F\OLQGHUVSODWRQLFVROLGVVLPLODUVROLGV $ S\UDPLGSULVPSRO\KHGURQ LVDVROLGWKDWKDVRQHSRO\JRQDVDEDVHWDSHULQJWRD point. $VROLGZLWKWZRFRQJUXHQWSDUDOOHOSRO\JRQVDVEDVHVLVD FRQHS\UDPLGSULVP ,IWKHVLGHVRIDSULVPDUHQRWSHUSHQGLFXODUWRLWVEDVHLWLV REOLTXHULJKWUHJXODU $GRGHFDKHGURQLVRQHNLQGRI SULVPSODWRQLFVROLGREOLTXHVROLG 1. tetrahedron 7. cone cube 2. D[LV parallelepiped similar solids hemisphere 9. polyhedron pyramid cylinder 10.DSH[ prism regular 11.sphere 17.oblique solids 12.right platonic solid — 282 — Multiple Choice 1. Which of the following is notVKDSHGOLNHDFRQH" D DQLFHFUHDPKROGHU E DIXQQHO F DZLWFK¶VKDW G DQRUDQJHMXLFHFDQ :KDWLVWKHQDPHIRUKDOIRIDJOREHRUDVSKHUH" D KHPLVSKHUH E VHPLVSKHUH F KRORVSKHUH G KDOIRVSKHUH :KLFKLVWUXHRIDWHWUDKHGURQ" D LWLVDUHJXODUSRO\KHGURQDQGDSODWRQLFVROLG E LWVIRXUVXUIDFHVDUHHTXLODWHUDOWULDQJOHV F DDQGEDUHERWKWUXH G QHLWKHUDQRUELVWUXH +RZPDQ\VLGHVDUHSRVVLEOHIRUWKHEDVHRIDS\UDPLG" D WKHEDVHRIDS\UDPLGDOZD\VKDVIRXUVLGHV E WKHEDVHRIDS\UDPLGDOZD\VKDVWKUHHVLGHV F WKHEDVHRIDS\UDPLGFDQKDYHDQ\QXPEHURIVLGHVJUHDWHUWKDQRUHTXDOWR G WKHEDVHRIDS\UDPLGDOZD\VKDVDQHYHQQXPEHURIVLGHV $FXEHLVDOVRD D KH[DKHGURQ E SDUDOOHOHSLSHG F SULVP G DOORIWKHDERYH :KLFKRIWKHIROORZLQJKDVDQDSH[" D DF\OLQGHURUDFRQH E DFRQHRUDS\UDPLG F DS\UDPLGRUDSULVP G DSDUDOOHOHSLSHGRUDS\UDPLG $SULVPPLJKWDOVREHD D SDUDOOHOHSLSHG E S\UDPLG F WHWUDKHGURQ G QRQHRIWKHDERYH :KLFKRIWKHIROORZLQJDUHVROLGV" D FXEHVSRO\KHGURQVUHFWDQJOHVDQGFRQHV E RFWDKHGURQVF\OLQGHUVS\UDPLGVDQGVSKHUHV F GRGHFDKHGURQVWULDQJOHVSDUDOOHOHSLSHGVDQGSULVPV G KH[DKHGURQVWHWUDKHGURQVFXEHVDQGSDUDOOHORJUDPV 9. If two objects are similar solids D WKH\KDYHH[DFWO\WKHVDPHVKDSH E WKH\KDYHH[DFWO\WKHVDPHVKDSHDQGVL]H F WKH\FDQQHYHUKDYHWKHVDPHVL]H G WKH\DUHWKHVDPHVL]HEXWQRWWKHVDPHVKDSH ,QRUGHUWR¿QGWKHD[LVRIDF\OLQGHULWLVQHFHVVDU\WR¿QG D WKHOHQJWKRIHDFKVLGH E WKHGLDPHWHURIWKHEDVH F WKHDQJOHRIHDFKFRUQHU G WKHFHQWHURIHDFKEDVH — 283 — $SDUDOOHOHSLSHGPLJKWDOVREHFODVVL¿HGDV D DFXEHDWHWUDKHGURQDQGDSULVP E DSULVPDSRO\KHGURQDQGDKH[DKHGURQ F DUHJXODUSULVPDF\OLQGHUDQGDS\UDPLG G DKHPLVSKHUHDKH[DKHGURQDQGDSULVP :KDWW\SHRIEDVHGRHVDUHJXODUSULVPRIS\UDPLGKDYH" D DUHJXODUSRO\KHGURQ E DUHJXODUSRO\JRQ F DSHUIHFWFLUFOH G DQ\SRO\JRQZLWKWKUHHVLGHVRUPRUH :KLFKRIWKHIROORZLQJKDYHEDVHVWKDWDUHFRQJUXHQWDQGLQSDUDOOHOSODQHV" D ULJKWFLUFXODUF\OLQGHUVSULVPVDQGFXEHV E ULJKWFLUFXODUFRQHVSDUDOOHOHSLSHGVDQGKHPLVSKHUHV F SULVPVFXEHVDQGSODWRQLFVROLGV G UHJXODUULJKWSULVPVS\UDPLGVDQGWXEHV ,IWKHDSH[RIDFRQHLVQRWDOLJQHGGLUHFWO\RYHUWKHFHQWHURIWKHEDVHWKHFRQHLV D UHJXODU E FLUFXODU F REOLTXH G ULJKW :KLFKRIWKHIROORZLQJLVDWUXHVWDWHPHQWDERXWDVSKHUH" D WKHHDUWKLVDSHUIHFWVSKHUH E DQ\WKUHHGLPHQVLRQDOFXUYHG¿JXUHLVDVSKHUH F DVSKHUHKDVWZREDVHV G HYHU\SRLQWRQDVSKHUHLVWKHVDPHGLVWDQFHIURPLWVFHQWHU ,IWKHWZREDVHVRIDSULVPDUHDOLJQHGGLUHFWO\RQHRYHUWKHRWKHULWLVD D UHJXODUSULVP E REOLTXHSULVP F ULJKWSULVP G WULDQJXODUSULVP 17. 5HJXODUSRO\KHGURQVDUHDOVRFDOOHG D SODWRQLFVROLGV E ULJKWF\OLQGHUV F UHJXODUSULVPV G VLPLODUVROLGV $SRO\KHGURQPLJKWKDYHWKHVKDSHRID D FRQH E S\UDPLG F VSKHUH G KHPLVSKHUH $QVZHUV '$&&'%$% $'%%$&'&$% — 284 — Complete the Sentence 1. $VL[VLGHGSULVPZLWKHDFKVLGHSDUDOOHOWRLWVRSSRVLWHLVDBBBBBBBBBBBBBB 2. ,IWZRREMHFWVDUHBBBBBBBBBBBBBBBBBBWKH\KDYHWKHVDPHVKDSHEXWQRWDOZD\V the same size. BBBBBBBBBBBBBBBBBSULVPVDQGS\UDPLGVKDYHUHJXODUSRO\JRQVDVEDVHV 7KHUHDUHRQO\¿YHW\SHVRIUHJXODUSRO\KHGUDDQGWKH\DUHFDOOHG BBBBBBBBBBBBBBBBB $BBBBBBBBBBBBBBBBBBBBLVDVROLGZLWKHYHU\SRLQWHTXLGLVWDQWIURPLWVFHQWHU ,IDVROLGKDVFXUYHGHGJHVLWFDQ¶WEHDBBBBBBBBBBBBBBBBBBBBBBBB 7. $ Q BBBBBBBBBBBBBBBBLVIRXQGRQDFRQHRUDS\UDPLG $VROLGZLWKIRXUVXUIDFHVLVFDOOHGDBBBBBBBBBBBBBBBBBBBBBBBBBB 9. ,IDVROLGKDVWZRFRQJUXHQWSDUDOOHOFLUFOHVDVEDVHVLWLVD BBBBBBBBBBBBBBBBBBBBB 10.$VSKHUHDS\UDPLGRUDQLFRVDKHGURQLVDW\SHRIBBBBBBBBBBBB 11.2QHEDVHRID Q BBBBBBBBBBBBBBBBBBBBSULVPLVQRWDOLJQHGGLUHFWO\RYHUWKH other one. 12.$VROLGZLWKFRQJUXHQWSDUDOOHOEDVHVRIDQ\SRO\JRQDOVKDSHLVD Q BBBBBBBBBBBBBBBBBBBB $ Q BBBBBBBBBBBBBBBBLVDOLQHWKDWSDVVHVWKURXJKWKHFHQWHUVRIERWKEDVHVRID cylinder. 7KHDSH[RID Q BBBBBBBBBBBBBBBBBBBBBS\UDPLGLVGLUHFWO\RYHUWKHFHQWHURILWV base. ,IDVROLGWDSHUVWRDSRLQWIURPDFLUFXODUEDVHLWLVFDOOHGD Q BBBBBBBBBBBBBBBBB ,IDVSKHUHLVGLYLGHGLQWRWZRHTXDOSDUWVHDFKSDUWLVD Q BBBBBBBBBBBBBBBBBBBB 17.$BBBBBBBBBBBBBBBBBBBBBBBLVDSRO\KHGURQWKDWKDVRQHEDVHWDSHULQJWRDSRLQW $QRWKHUQDPHIRUDUHJXODUKH[DKHGURQLVBBBBBBBBBBBBBBBBBBB $QVZHUV 1. Parallelepiped 10.Solid 2. Similar solids 11.Oblique regular 12.Prism Platonic solid D[LV sphere right Polyhedron &RQH 7. $SH[ hemisphere tetrahedron 17.Pyramid 9. &\OLQGHU &XEH — 285 — Creative Writing 'HVFULEHWKHJHRPHWULFVROLGVLQWKLV SLFWXUHRIWKH$OHXWUHORFDWLRQFDPSDW.LOOLVQRR — 286 — Place-Based Practice Activity 1. &RQVWUXFWVROLGVXVLQJFRQVWUXFWLRQSDSHUWRRWKSLFNVDQGJXPGURSVRURWKHU materials. Make ornaments or decorations shaped like platonic solids and/or RWKHUSRO\KHGURQVDQGGRQDWHWKHPWRDORFDOHYHQW3LRQHHU+RPHRUSUH- school. 2. 'LVFXVVWKHXWLOLW\RIGLIIHUHQWVKDSHVIRUEXLOGLQJVWDQNVSDFNDJLQJDQGRWK- HUXVHVWKDWDUHUHOHYDQWWR\RXUWRZQ:KLFKDUHHDVLHUWREXLOG":KLFKZRXOG ZDVWHVSDFHLQDVKLSSLQJFRQWDLQHU":KLFKZRXOGVKHGUDLQDQGVQRZ"$VN VPDOOJURXSVRIVWXGHQWVWRFKRRVHDQDSSURSULDWHVKDSHDQGGHVLJQDKRXVH VFKRROWHHQFHQWHUWDQNRURWKHUREMHFWEDVHGRQWKHGLVFXVVLRQ — 287 — — 288 — Unit Assessment — 289289 — — 290 — Geometry: Unit 9-Three Dimensional Figures Name: ______Date: ______ Illustrations: In items 1-4, draw the geometric figure listed for each item and give two examples from everyday life that are the shape of this figure. 1) Draw a cone. List two examples from everyday life that are shaped like a cone. Example 1______ Example 2______ 2) Draw a sphere. List two examples from everyday life that are shaped like a sphere. Example 1______ Example 2______ — 291 — 3) Draw a pyramid. List two examples from everyday like that are shaped like a pyramid. Example 1.______ Example 2.______ 4) Draw a polyhedra. List two examples from everyday like that are shaped like a polyhedra. Example 1.______ Example 2.______ Fill in the Blank. Complete each statement below with the word that fits best. Choose the words from the Word Bank. Word Bank apex cube oblique solids prism regular solid Right solids solid 5) A/an is the vertex or top point of a cone or pyramid. 6) A/an is a solid whose bases are congruent polygons in parallel planes. Segments connect the corresponding vertices of the polygons, so that all of the side surfaces are parallelograms. 7) A is a regular hexahedron with six surfaces that are all squares and all right angles. — 292 — 8) 15. are slanted; cylinders, pyramids, and cones that are not right solids, and the bases are not aligned directly one above the other, or the apex is not directly above the center of the base. 9) Are straight up and down with cylinders and prisms that have bases aligned directly one above the other so that the sides are perpendicular to the base, and the apex is aligned directly above the center of the base. 10) A/an has a regular polygonal base(s); each side of the base is congruent to every other side and each angle is congruent to every other angle. 11) A geometric figure is a three-dimensional closed figure that has a boundary. 12) True/False: Read the following statements carefully to decide if they are true or false. Circle the correct answer. 13) A platonic solid is a regular polyhedron; its surfaces are congruent regular polygons, and all of its angles are congruent a) True b) False 14) Platonic solids come in only 3 shapes- Tetrahedron (4 triangular surfaces), Hexahedron (6 square surfaces), Octahedron (8 triangular surfaces). a) True b) False 15) Similar solids are identical in shape but not necessarily the same size. a) True b) False 16) A parallelepiped is a prism with six rectangular surfaces. Each surface is parallel to its opposite surface. Its shape makes things easy to stack, so most boxes are shaped like parallelepipeds. a) True b) False — 293 — — 294 — Geometry: Unit 9-Three Dimensional Figures Name: ______Date: ______ Illustrations: In items 1-4, draw the geometric figure listed for each item and give two examples from everyday life that are the shape of this figure. 1) Draw a cone. List two examples from everyday life that are shaped like a cone. Example 1______ Example 2______Matt...insert illustration of a cone Real life examples of a cone include: a volcano, some ice cream cones (not the ice cream), traffic cones that are used during highway construction. 2) Draw a sphere. List two examples from everyday life that are shaped like a sphere. Example 1______ Example 2______ Matt...insert illustration of a sphere. Real life examples of a sphere include: scoops of ice cream, ball bearings on a car, the earth (almost) — 295 — 3) Draw a pyramid. List two examples from everyday like that are shaped like a pyramid. Example 1.______ Example 2.______ Matt...insert a pyramid Examples of pyramids include: the Egyptian pyramids, some radio towers, some pointed roofs 4) Draw a polyhedra. List two examples from everyday like that are shaped like a polyhedra. Example 1.______ Example 2.______Matt...insert a polyhedra Examples of polyhedras include: wall tents, cereal boxes and paper stars because they do not have curved surfaces or edges. Fill in the Blank. Complete each statement below with the word that fits best. Choose the words from the Word Bank. Word Bank apex cube oblique solids prism regular solid Right solids solid 5) A/an apex is the vertex or top point of a cone or pyramid. 6) A/an prism is a solid whose bases are congruent polygons in parallel planes. Segments connect the corresponding vertices of the polygons, so that all of the side surfaces are parallelograms. — 296 — 7) A cube is a regular hexahedron with six surfaces that are all squares and all right angles. 8) oblique solids are slanted; cylinders, pyramids, and cones that are not right solids, and the bases are not aligned directly one above the other, or the apex is not directly above the center of the base. 9) Right solids are straight up and down with cylinders and prisms that have bases aligned directly one above the other so that the sides are perpendicular to the base, and the apex is aligned directly above the center of the base. 10) A/an regular solid has a regular polygonal base(s); each side of the base is congruent to every other side and each angle is congruent to every other angle. 11) A geometric solid figure is a three-dimensional closed figure that has a boundary. 12) True/False: Read the following statements carefully to decide if they are true or false. Circle the correct answer. 13) A platonic solid is a regular polyhedron; its surfaces are congruent regular polygons, and all of its angles are congruent a) True b) False 14) Platonic solids come in only 3 shapes- Tetrahedron (4 triangular surfaces), Hexahedron (6 square surfaces), Octahedron (8 triangular surfaces). a) True b) False 15) Similar solids are identical in shape but not necessarily the same size. a) True b) False 16) A parallelepiped is a prism with six rectangular surfaces. Each surface is parallel to its opposite surface. Its shape makes things easy to stack, so most boxes are shaped like parallelepipeds. a) True b) False — 297 — — 298 —