比例的意义课堂教学文字实录
??±èàyμ?òaò??·ê?ò??ú?????ì?§??￡?ê??§?°?y?￠·′±èàyòaò?oíó?±èày?aê??aó|ó?ìaμ??ù′??￡?üê??ú?§éú??±èμ?òaò??￠D??êoí±è?μμ?òaò?ò??°?ó±è?μμ?·?·¨óDá???3?·?è?ê?μ??ù′?é???ò?2??§?°μ??￡????ê?D?±à?a′ó?ò??àíμ?±èàyμ?òaò???ì??ì?§??×?êμ??5?a￡??￡í?′ó?ò?üóD?ùê???!
±èàyμ?òaò???ì??ì?§??×?êμ??1
?ì?§?úèY￡oè??ì°?áù?ê????2á??±èàyμ?òaò??·
?ì?§??±ê￡o
1?￠ê1?§éúàí?a±èàyμ?òaò?￡??üó|ó?±èàyμ?òa?D??á???±è?ü·?3é±èày?￡?à???§éú??D??￠?é?aê?èú?á1áí¨μ??üá|?￡
2?￠?ú?-àúè?ê?±èày?￠?§?°±èàyμ?μ?1y3ì?D￡??à???§éúμ?·????￠í?àí?￠??à¨?üá|oíó?óúì??÷μ???é??￡
3?￠í¨1y×??÷ì????￠D?×éo?×÷μèêμ?ù???ˉ￡?ì??é3é1|μ??ìà??￡í¨1yá??a1ú?ìμ?±èàyé?í?1ú?ì·¨oíóD1?·¨?é?aê?￡?è??§éú?aμà×e??μ?°??¤1ú?ìê?????1???μ?ò???￡??ò??òa??DDo??a??ò????￡
?ì?§??μ?￡o±èàyμ?òaò??￡
?ì?§??μ?￡o?ò3??àμèμ?±è×é3é±èày?￡ ?ì??￡o?à??ì????t?￠?ì?§1òí??￡ ?ì?§??ê±￡o1??ê± ?ì?§1y3ì￡o
ò??￠?é?a?ìμ?
1?￠ê2?′ê?±è?
á???êy?à3yó??D×??aá???êyμ?±è
2?￠?ˉ?ò±è (1)?￠ò?á???3μ4D?ê±DDê?300?§?×￡?D′3??·3ìó?ê±??μ?±è￡?2￠?ˉ?ò?￡
300￡o4=75￡o1 (2)?￠à??÷ì???30?§??￡?í???ì???35?§??￡?D′3?à??÷ó?í???ì???μ?±è?￡
30￡o35=6￡o7
3?￠?ó?????÷±èμ?±è?μ?￡
12￡o16 ￡o 4.5￡o2.7 10￡o6
?t?￠ì??÷D??a
1. ′′éè?é?3￡?òy·￠????￡o
???t2￥·?￡oìì°2??μ?éy?ìò?ê?;?§D￡D??úò?μ?éy?ì???ˉ;°????áé??D1ú???ùó??á?e??μ?éy?ìò?ê??￡
òy3??êìa￡oí??§??￡?′ó?-???D?????′μ?á?ê2?′??????aμà?aD?1ú
3418
?ìμ?3¤oí?íê??àéù?e?
ì??D×àé?μ?1ú?ì3¤oí?í·?±eê?15à??×?￠10à??×;?ìêò??é?60à??×?￠40à??×;?§D￡éy?ìò?ê?2.4?×?￠1.6?×;ìì°2??éy?ìò?ê?5?×?￠10/3?×;
(éè??òaí?￡o?ìê|à?ó??à??ì?ê???2￥·????t￡??¤·￠á??§éúèè°?1ú?ìμ?μ??é?D￡?óDD§μ?òyè?á??§?°×ê?′D??￠￡?òa?ó?§éúè???1?2ì￡?òy·￠?§éú?§?°μ?óDòa×￠òa￡??a??ò?2??1?aì??????ˉìá1?á??ù′??￡)
?a????1ú?ìμ?3¤oí?í?÷2??àí?￡?μ?D?×′ê?ò??ùμ??￡???t3?ê?￡o???D?aè???12oí1ú1ú?ì·¨?·(1949?ê9??28è??D1úè????t??D-éì?áòéμúò??ìè?ì??áòé?÷?ˉí?1?2?)
μúò?ì?￡o
?ì???aoìé?￡?3¤·?D?￡???3¤ó????aèyó??t??±è￡??ì??×óé?·?×o??é?????D??????￡ò?D???′ó￡???ía?ó?2?±???a?ì??ê?·???èy￡??ó×ó;??D???D?￡???ía?ó?2?±???a?ì??ê?·???ò?￡??·1°óú′óD???óò?￡?ì??ì×?a°×é??￡
×D??1?2ì￡?ó?D?????￡?ò2?éò???ò???￡?·￠??á?ê2?′? 3¤oí?íμ?±èê?2.4￡o1.6; ±è?μê?1.5?￡
(éè??òaí?￡o?§éú?ú3?·?1?2ìμ??ù′?é?ò???1ú?ìμ?3¤oí?í????μ?1??μóDá?ò??¨μ??D?a￡??ú?§éúòa?±óú±í′?μ?ê±oò￡?è??§éú?°ò??-′ú???±
￡?í¨1y?°2??ü±?D??±?aò?òa?óμ?ìá3?￡??¤·￠?§éú??DD?üé?è?μ?????ó?ì???￡???×??oμ??D?a?-?éí¨1yêμ?ù2ù×÷ì???3?à′2￠?óò?ìáéy?￡)
2.àí?a±èàyμ?òaò?
(1)êμ?ù???ˉ￡o?????ù?Y??2?μ?·￠???-ò???ó??a????1ú?ì3¤oí?í??2?í?μ?1ú?ìíaD?￡?2￠±￡?¤2?±?D??￡
?ìê|?2êó
(2) ??±¨?1ê?￡o
?-à′?μò??μ???-μ?1ú?ìD?×′μ?3¤oí?í?÷ê??àéù? ???ü±￡?¤2?±?D??′?
??±¨?1ê? ?¤éè￡o
éú1￡o3¤ê?3à??×￡??íê?2à??×; àíóé ￡o
òò?a?′μ?í??D????1ú?ìμ?μ?3¤oí?í?ˉ?òoó??ê?3￡o2￡??ò?-μ?1ú
?ì3¤oí?íμ?±èê?ò2ê?3￡o2?ùò???óD×?D??￡
è?????í??§?D?? éú
2?￠éú
3?￠
àíóé￡o?°???￠oó??í?ê±à?′ó?ò??D??àí?μ?±?êy ??????′e
í??§???μμ?óDàíóD?Y￡???±￡?¤2?±?D?￡??ò???úì?±e???aμà￡?′ó?ò??2???·￠??á?ê2?′?
?aò?·￠???yê?1ú?ì·¨?D1??¨μ?￡o1ú?ìμ?3¤oí?íμ?±èê?3￡o2 (3)àí?aòaò?￡o
1?2ì?aD?±è??óDê2?′·￠??? ?aD?±è?ˉ?òoó??ê?3:2; á???±è?àμè 3￠ê?êéD′ 3￡o2=6￡o4 6￡o4=9￡o6 15￡o10=60￡o40 ?¤éè￡o
á???±è?àμè?í?D±èày; ±è?μ?àμèμ?±è?D×?±èày;
?-??òa°???μ?·￠??D′?úoú°?é??
?1óD??D?±èò2?éò?D′3é?a?ùμ?D?ê??
(éè??òaí?￡o?§éú?ú?D?a?￠2ù×÷?￠±íê?μ?1y3ì?D￡???1ú?ìμ?3¤oí?í?ù×é3éá?è??é??±è￡?2￠′ó?D?òμ?12D??a?a±è?μ?àμè?￡?ìê|í¨1yóDD§?êìaμ???·￠￡?′ùê1?§éú?a′??ú?a?ù1??μμ?±è?°?òμ?á??ü???§μ?±í??D?ê??′μèo?á??ó￡?′ó??ê1±èàyòaò?μ?3ê????μ??t3é)
?ò??°????a?ùμ?ê?×ó?D×?±èày?￡ °?êé￡o±èàyμ?òaò?
???ú??è??aê2?′?D±èày?
í??§????±èàyμ?òaò?ò??-óDá?×??oμ?àí?a￡?à?êy?§?ò??2?ò?D?2?á?￡?è?1?ó????ù?òá·D?oí×?è·D??í?üo?á?
°?êé￡o±íê?á???±è?àμèμ?ê?×ó?D×?±èày?￡
1?￠?ì?§ày1?￡ (1)?￠1?2ì?????é?3í??￡ ￠ù?￠?μò??μ?÷·ùí?μ??é?°?￡
￠ú?￠í??DóDê2?′?àí???′|? (2)?￠?aD?1ú?ìμ?3¤oí?í?÷ê??àéù? (3)?￠(???ìêòà?μ?1ú?ì)?a??1ú?ìμ?3¤oí?íμ?±è?μê??àéù? ?§éú??′e?ìê|°?êé￡o
60￡o40=
(4)?￠2ù3?é?μ?1ú?ìμ?3¤oí?íμ?±è?μê??àéù?ó??a??1ú?ìóDê2?′1??μ?
?§éú??′e3¤?￠?í±è?μ?￡
2.4￡o1.6=
á???1ú?ìμ?3¤oí?íμ?±è?μ?àμè?￡
°?êé:2.4:1.6=60:40 ò2?éò?D′3é2.4/1.6=60/40
(5)?￠?ò±èày?￡ ê|￡o?ú?a????1ú?ìμ?3?′??D￡????1?ü?ò3???D?±è?éò?×é3é±èày? 1y3ìòa?ó￡o
?§éú2???áííaá???1ú?ì3¤?￠?íμ?±è?μ?￡ ?ó3?1ú?ì3¤?￠?íμ?±è?μ￡?2￠×é3é±èày?￡ ??±¨?￡
1033= 15￡o10= 32210105￡o=15￡o10 5￡o=2.4:1.6 33152.41560= =
101.610402.43232è?￡o5￡o
èy?￠1?1ìá·?°
íê3é????33ò3?°×?ò?×??±?￡ μú1ìa?￡
?aμàìaê??D??á???±èê?·??ü×é3é±èày￡??ìê|?éò?1?à??§éúó??ó±è?μμ?·?·¨??DD?D???￡
μú2ìa?￡
?§éú?àá￠D′±èày￡??′?-D′μ??à?￡ í??§?????￥?à??á÷￡??μò??μ??ê????′D′μ?￡?ò?12?éò?D′?àéù??2?í?μ?±èày?￡
(?ù?Yèy??D??Dμ?????êy?Y×é3é±èày￡?òto?×??à??èy??D???ó|±?3é±èàyμ?D??ê?￡)
3?￠??ì?D??á?￡ (1)?￠ê2?′?D×?±èày? (2)?￠ò???±èàyê??éò???D′3é????2?í?μ?±èàyê??
???￠×÷òμ
íê3é????á·?°áùμú1??3ìa?￡ ???t3?ê?￡o
???D?aè???12oí1ú1ú?ì?·
(1990?ê6??28è?μú???ìè?1úè???′ú±í′ó?á3￡???ˉ?±?áμúê???′??áòéí¨1y) μúò?ì?
?aá????¤1ú?ìμ?×e??￡?????1???μ?1ú?ò1???￡?·￠??°?1ú?÷ò???é?￡??ù?Y?ü·¨￡????¨±?·¨?￡ μú?tì?
?D?aè???12oí1ú1ú?ìê???D?oì?ì?￡
?D?aè???12oí1ú1ú?ì°′???D1úè????t??D-éì?áòéμúò??ìè?ì??áòé?÷?ˉí?1?2?μ?1ú?ì??·¨?μ?÷??×÷?￡ ??
??oó·′??￡o
??D???3ì±ê×??·??3?￡oò????ìóy?×??μ?êy?§?ì?§???ˉ2?μ?òa??êóè??§éú??μ??aê??üá|￡??1òa1?×￠êy?§?aê?μ?ó|ó????μ?￡±??ú???òá|?óè??§éú?úàí?a±èàyòaò?μ??ù′?é?￡?ì??é?aê?μ?D?3é1y3ì?￡
1.°????§éúò?óDμ??aê??-?é￡??ò×??§éúμ??eμ??￡
??D???3ì±ê×??·??3?￡??§éúμ??§?°???ˉ±?D??¨á￠?ú?§éúμ?ò?óD?aê??-?é?ù′???é?￡?±??ú???òò??′?°±èμ??aê?μ?è?￡??e?￥òyè?D??a￡??aê?ò??§éú×?éíò?óDμ??aê?oí?-?é?a?ù′?μ??÷?ˉ?¨11μ?1y3ì￡??ò±?D?ê1?§éú?úò?óDμ??aê?oí?-?é?D?§?°D??a?￡±èàyμ?òaò??úéú???DóD×?1?·oμ?ó|ó?￡???óú?§éúμ??aê?′￠±?òa??á?μ??¤2a￡??ò?ò×??§?°?eμ??￡
2.o?àíéè???êìa?é?3￡??¤·￠?§éú?y???????￡
??ó??à??ì??ò?§éú?1ê?óD1??ò1ú1ú?ì3????ú2?í?3?o?μ?×êá?????￡?2???·á??á??ì??êéμ?×ê?′￡??1óDD§μ??¤·￠á??§éúμ?°?1úèè?é?￡?ú?§éú????μ??éD÷???D???-???¨???ú?ì??êéμ??÷ìaí?é?￡?òyμ??§éú1?2ìêy?Y?￠·￠??1??é￡??ì??ìá3???óDì???D?μ?òa?ó￡o?-ò???3?′?2?í?￡?μ?2?×?D?μ?1ú?ì?￡òa??×?μ?2?×?D?￡??§éú±?è?òa1?2ìí??D????1ú?ìμ?3¤
oí?í￡?ò2ò??¨?á·￠??3¤oí?íμ?±è?μê?ò??¨μ?￡??a?í???ì??êé?Dμ?D??￠3ê??￡?±??aá??§éúμ?óDD§?????ùμ?￡?2￠í¨1y?°ò??-′ú???±??×??oμ??D?a?-?éí¨1yêμ?ù2ù×÷?óò??é?¤oíìáéy;í?ê±￡??à??1ú?ìμ?3¤oí?í?éò?×é3é?à??±èàyê?￡?ó??a±èàyòaò?μ?òy3?ìá1?á???·á??μ?×ê?′?￡
3.?à??á??§éúé?óú?????￠??á÷μ?á?o??§?°·?ê?
?ú??á÷?D??×2?￠?ú??á÷?D?￥21?￠?ú??á÷?Dìáéy?￡?ìê|×é?ˉè?°àD?μ???á÷??±¨￡?′ùê1?§éú?ú2???μ??ù???￠±íê??D?ü?óé?è?μ??????￡±èoí±èàyê??§éúèYò×?ì?yμ?μ?á???????￡??ìê|×é?ˉ?§éúì???￡?′ó???ü?ó×?è·μ?àí?aá?±èàyμ?òaò?￡?í??1á?????￡??à??á??§éúá?o?μ?????·?ê??￡
±èàyμ?òaò???ì??ì?§??×?êμ??2
?ì?§?úèY: ?ì??êéμú32?a33ò3?°?àó|μ?×?ò?×??￡
?ì?§??±ê:
1. ?aê?ó????ü￡oê1?§éúàí?a±èàyμ?òaò?￡??üó|ó?±èàyμ?òaò??D??á???±è?ü·?113é±èày?￡
2.1y3ìó?·?·¨￡oí¨1y?ˉê??￠?ˉ???￠1?2ì?￠?????￠ì???μè·?ê?￡?ê1?§éú×??÷??è??aê?￡?è???2?ó??ì?§???ˉ?￡
3.?é?D?￠ì??èó????μ1?￡o?à???§éú?úêμ?êéú???D·￠??êy?§μ?′??ú￡?2￠?úêμ?êéú???D?ü?Dêüμ?êy?§μ?è¤??￡?ìá???§éú?§?°êy?§μ??y??D??￡ ??μ?oí??μ?:
1?￠è?ê?±èày?￠àí?a±èàyμ?òaò??￡
2?￠ó|ó?±èàyμ?òaò??D??á???±è?ü·?113é±èày?￡ ?ì?§×?±?; ?à??ì????t ?ì?§1y3ì:
ò??￠μ?è?
1?￠??í??§????ò?ò???é??§?ú?ò???§1yμ?±èμ??aê?￡?￡??-?ü?μ?μê2?′?D±è?ê2?′?D±è?μ?ê2?′?D±èμ??ù±?D??ê?
2?￠?ò???aμàá?±èμ??°??3yò?oó???ùμ?μ?éì?D×?±è?μ?￡???ù?ó±è?μ????????1??μ??e?
?ó3?????????±èμ?±è?μ?￡
16￡o20 3.2￡o0.8 2￡o0.5
??í??§??1?2ìò???￡???á???±èμ?±è?μ?àμè?
3.2:0.8μ?±è?μoí2￡o0.5μ?±è?μ?àμè?￡
òò?a?aá???±èμ?±è?μ?àμè￡??ùò??aá???±èò2ê??àμèμ?￡??ò??°??ü??ó?μèo?á??eà′(°?êé;3.2￡o0.8=2￡o0.5)???a?ù±íê?á???±è?àμèμ?ê?×ó?D×?ê2?′????a?íê??ò???a?ú??òa?§?°μ??úèY?￡(°?êé??ìa:±èàyμ?òaò?)
?t?￠ì???D??a
1?￠3?ê??ì2?μú32ò3μ??é?°í?
??í??§??è???1?2ì?a??·ùí?￡??????aμàá???D?D??￠?
μúò?·ùí?μ??úèYê?ìì°2??éy1ú?ìò?ê?;μú?t·ùí?μ??úèYê?D￡?°éy?ìò?ê?;μúèy·ùí?μ??úèYê??ìêò3??°;μú??·ùí?μ??úèYê?????ò?ê??￡
??í??§???òò??ò??·ùí??DóDê2?′12í?μ????÷?
(??óD1ú?ì)?￡
1ú?ìê??ò??1ú?òμ??ó?÷￡??ò??2?òa??òaí??a?ò???a?ú1ú?ì￡??ò??±?D?×e???ü￡?èè°??ü?￡
2?￠???μ3?????1ú?ìμ?3¤oí?í?÷ê??àéù?
3?ê????t????1ú?ì3¤ó??íμ???ì?êy?Y￡?D′3??ü??3¤ó??íμ?±è?￡
3?￠??í??§??·?±eD′3??§D￡à?á???1ú?ì￡?3¤oí?íμ?±è?μê??àéù ?ù?Y?§éúμ???′e￡?°?êé
33 2ù3?é?μ?1ú?ì￡o2.4￡o1.6= ?ìêòà?μ?1ú?ì￡o60￡o40=
22 ????·￠??á?ê2?′??aá???±èóDê2?′1??μ?
3 ?aá???±èμ?±è?μ??ê??￡?ü???àμè?￡ 2 òò?a?aá???±è?àμè￡??ùò??ò???éò?°??ü??ó?μèo?á??eà′?￡
°?êé￡o(2.4￡o16=60￡o40)???a?ù(??×??a??ê?×óoí?′?°ìaμ?ê?×ó3.2￡o0.8=2￡o0.5)±íê?á???±è?àμèμ?ê?×ó?D×?±èày?￡
òa?óè?°àí??§???áò??a?￡
4?￠éèòé￡?é???μ???·ùí??D￡????1?ü?ò3???D?±è?éò?×é3é±èày?￡
5?￠±èàyê?óé????±è×é3éμ?￡??a????±è±?D???±?ê2?′ì??t??D??á???±è?ü2??ü×é3é±èày￡?
1??üê??′ê2?′?è?1?2??üò????′3?á???±èê?2?ê??àμèμ?￡????′°ì?
èy?￠?ìê|D??á￡o
í¨1yé???μ??§?°￡??ò???aμàá?±èàyê?óéá????àμèμ?±è×é3éμ?￡??ú?D??á???±è?ü2??ü×é3é±èàyê±￡?1??üê??′×??aá???±èê?2?ê??àμè?￡è?1?2??üò????′3?á???±èê?2?ê??àμè￡??éò??è·?±e°?á???±è?ò?ˉ?òê??ó3?±è?μoó?ù?′?￡
àyè?￡o?D????????×é?Dμ?á???±è?ü2??ü×é3é±èày?￡
6￡o10oí9￡o15
11￡o2oí￡o4 3631
16￡o10=
￡o2=
536311
9￡o15=
￡o4=
56243311 =(±è?μ?àμè)
?ù
55624 6￡o10oí9￡o15(?ü×é3é±èày)
D′3é￡o6￡o10=9￡o15 ±è???°±è?±oí?°±èày?±μ?á????????￡
11￡o2oí￡o4(2??ü×é3é±èày) 36
òyμ??§éú′óòaò?é?.??êyé????ü????DD±è??￡?×?oó1é?é￡o±èê?óéá???êy×é3é￡?ê?ò???ê?×ó￡?±íê?á???êy?à3y;±èàyê?óé????êy×é3é￡?ê?ò???μèê?￡?±íê?á???±è?àμèμ?ê?×ó?￡
???￠??ì?á·?°
1?￠?ì2?μú33ò3×?ò?×?μú1ìa.
2?￠?ì2?μú33ò3×?ò?×?μú2ìa.
???￠1?1ìá·?°￡o
(???t3?ê?)
áù?￠×ü?á
í¨1y?a?ú??μ??§?°￡?????óDê2?′ê????
±èàyμ?òaò???ì??ì?§??×?êμ??3
?ì?§??±ê￡o
1?￠àí?a±èàyμ?òaò??￡
2?￠????×é3é±èàyμ?±?òaì??toí·?·¨?￡
3?￠?á??ó?±èàyμ?òaò?×é3é±èày￡??ì?é×é3éμ?±èàyê?·??yè·￡??üó?á???D?ê?D′±èày?￡
4?￠?ú±èàyòaò?μ??§?°ì????D￡??à???§éúμ?1?2ì?￠±è???￠·????￠í?àí?￠??à¨?üá|oíó?óúì??÷μ???é??￡
5?￠??DD°?1ú?÷ò??ìóy?￡ ?ì?§??μ?￡oàí?a±èàyμ?òaò?;
?ì?§??μ?￡o????×é3é±èàyμ?ì??t￡??ü?yè·×é3é±èày; ?ì?§1??ü￡o?á??ó?±èàyμ?òaò??ì?éá???±èê?·??ü×é3é±èày?￡ ?ì??×?±?￡o?à??ì????t ?ì?§1y3ì￡o
(ò?)?′?°×?±?
1?￠ì??°μ?è?
ê|￡oí??§??￡?é??§?ú?ò???§?°á?±è￡??a?ú???ò???ìD??§?°oí±èóD1?μ??aê??a?a±èày?￡?ú?§?°???°￡??ò???èà′?′?°óD1?±èμ?ò?D??aê??￡
??éè??òaí?￡o?a?ùéè??￡??a????é?￡??òμ￥?÷á?￡?è??§éú?÷°×?a?ú??òa?§?°μ??úèYê?ê2?′￡?oí??D??aê?óD1??￡??
2?￠?§éú??ò?:ê2?′ê?±è?μ????′?óò???±èμ?±è?μ?
3?￠??????????×é?Dá???±èμ?±è?μ?￡
6:10oí9:15 6:4oí￡o 0.6:0.2oí￡o 20:5oí1:4 ê|￡o1?2ìò?é???×é±è?DóD??óD±è?μ?àμèμ?±è?è?1?óD???ò3?à′?￡
?ìê|?μ?÷￡oòò?a?aá???±èμ?±è?μ?àμè￡??ùò??aá???±èò2ê??àμèμ?￡??ò???éò?ó?μèo?á??eà′?￡
(°?êé￡o6:10=9:15 6:4=￡o)
??éè??òaí?￡oòyμ??§éú·￠??￡?á???±è?μ?àμèμ?±è?éò?ó?μèo?á??ó?￡í¨1y?a?ùéè??￡?è??§éú3?2??D?aμ?±èàyó?±èóD1?￡?é?í??aê???μ??ú?úáa?μ￡??1?éò??ò3??aê?μ?á??óμ?￡??μμí?§éú?§?°???è￡??aàí?a±èàyμ?òaò?×?o??ìμ?￡?í?ê±??DDá?·￠é￠????μ??μá·?￡??
(?t)ì???±èàyμ?òaò? 3?ê?ày12?í?
ê|￡oí??§??￡??′?a???±í?￡?????·￠??á??e??ú2?í?μ?3?o?1ú?ìμ?′óD?ò??ù?e?(2?ò??ù)
?ìê|??3?￡oê?μ?￡??aê??ò???D?aè???12oí1úμ?1ú?ì￡?ê?×?1úμ??ó?÷oí±ê???￡?ò??????è???òa×e??oí°??¤?ü￡??aD?1ú?ìμ?′óD?2?ò?￡?ê?2?ê?1ú?ì??×??à′ó?í×??à′ó?????êμ?ú??×÷1ú?ìμ?3?′?μ±?Dò2′??ú×?óDè¤μ?±è￡?????ì??????Dμ?°????e?
ê|￡o??í??§??D′3?????1ú?ì3¤oí?íμ?±è￡?2￠????3?±è?μ?￡
121312133414
- 1
(????1ú?ì?íoí3¤μ?±è;??á???1ú?ìμ?3¤??±è;??á???1ú?ìμ??í??±èμè?￡)
?aD?±è?ü×é3é±èày?e??§éúD′±è￡?2￠D′3?±èày?￡
??éè??òaí?￡o?ì?§±èàyμ?òaò?ê?±???μ?ò?????òaμ??úèY￡??aà?2éó?á?′óì?êaμ?ò?°?μ?í?àí·?ê?μ???·￠ê??ì?§￡?è??§éúí¨1y1?2ì?￠±è???￠òyμ??§éú·￠???ü??????μ?12D?￡?′ó??3é?ó??à¨3?±èàyμ?òaò?￡??à???§éúμ??????üá|￡?ò2é?í?á?°?1ú?÷ò??ìóy?￡??
èy?￠±èàyμ?òaò???ó?
1?￠????￡o±èàyóé????±è×é3é? è?òaá???±è???ü×é3é±èày?e??aê2?′?
á???±è?ü·?×é3é±èàyμ?1??üê?ê2?′?
2?￠?D??á·?°￡o
(1)?￠??????×é?Dá???±è?ü×é3é±èày?e??aê2?′? 1??5oí3??12 10??20oí30??60 (2)?￠ ?D??????????ê?×óê?2?ê?±èày￡??aê2?′?
10??11???????????( ) 8??10=0.8?????????( ) 7??14 <28??14???????( )
3?￠D′3?á???±è?μê?3μ?±è￡?2￠×é3é±èày?￡
4?￠±èàyê?óé±è×é3éμ?￡?D?×éí??§?μò??μ±èoí±èàyóDê2?′??±e? D??á￡o′óD?ê?é???·?￡?±èóéá???êy×é3é￡?ê?ò???ê?×ó;±èàyóé????êy×é3é￡?ê?ò???μèê??￡
±èàyμ?òaò???ì??ì?§??×?êμ??4
1?￠±èàyμ?òaò? μúò???ê±
(ò?)?ì2?·???
??±èàyμ?òaò??·ê?è??ì°?áù?ê????2áμú??μ￥?aP40-P43μ??úèY￡?ê?óúêμ?ùó?×?o?áìóò￡???±èày?·μ??ì?§ê??ú?§éúò??-?§?°á?ê±??μ￥???°±è?±￡?2￠ò??-?úêμ?êéú???D?yà?á??°?ê?￠???￠è??±?DD??-?éμ??ù′?é???DD?ì?§μ??￡±èàyê?±è±è?ü?ó?′?óμ?êyμ?è?ê??￡òò′?￡??ì2???ó?á?ó??§éúéú???ü?Dáa?μμ???2???DD?ì?§?￡è??§éú?Dêüêy?§?aê?ó?êμ?êéú??μ?áa?μ￡??¤·￠?§éú?§?°μ??y??D?￡?í?ê±?à??á??§éúμ?°?1ú?÷ò???é??￡
(?t)?§?é·???
?§éú??è??úêμ?êéú???DóDá?ò?D??DD?μ?è?ê?oí?-?é￡?μ?ê?è±·|???úμ?è?ê?oíêy?§????μ?1y3ì?￡??è?èy?ê??μ??§éú?êá??1oüD?￡?μ?ê?°àé?′ó2?·??§éú?§?°ì??è?1ê?????è???μ?￡?3é?¨?ú?ê??ò2ê?2?′íμ??￡òò′?￡?òa1?×￠?§éúμ?éú???-?é￡?è??§éú?ú??ì??é?3?D?Dêü±èày￡?óéà?ê|òyμ?￡??§éú?÷?ˉ?§?°μ?·?ê?à′?§?°±èày?￡
?ì?§?úèY￡oP40??43±èàyμ?òaò? ?ì?§??μ?￡o
1?￠ê1?§éúàí?a±èàyμ?òaò?￡??ü?yè·?D??á???±èê?·??ü×é3é±èày?￡
2?￠í¨1yòyμ?ì????￠??à¨1é?é?￠ì????￠o?×÷?§?°￡??à???§éú3é?ó??à¨?üá|?￡
3?￠ê1?§éú3?2??D?aê?????ê??à?￥áa?μ?￠±??ˉ·￠?1μ??￡ ?ì?§??μ?￡o±èàyμ?òaò?
?ì?§??μ?￡oó|ó?±èàyμ?òaò??D??á???êy?ü·?3é±èày￡?2￠?yè·μ?×é3é±èày?￡ ?ì?§1y3ì￡o
ò??￠??1??é?a￡??′?°?ìμ?
1?￠??í??§????ò?ò???é??§?ú?ò???§1yμ?±èμ??aê?￡??-?ü?μ?μê2?′?D×?±è?2￠?ùày?μ?÷ê2?′ê?±èμ??°???￠oó??oí±è?μ?￡
?ìê|°??§éú?ùμ?ày×ó°?êé3?à′￡?2￠×￠?÷±èμ??÷2?·?μ???3??￡
2?￠?ò???aμàá?±èμ??°oó???à3y?ùμ?μ?éì?D×?±è?μ￡??????á?ó±è?μ?e? ?ìê|°?êé3???????×é±è￡?è??§éú?ó3??ü??μ?±è?μ?￡
12:16
【比例的意义课堂教学文字实录】4.5:2.7
10:6 ?§éú?ó3??÷±èμ?±è?μoó￡??ùìá?ê￡o??á???±èμ?±è?μ?àμè? (4.5:2.7μ?±è?μoí10:6μ?±è?μ?àμè?￡)
?ìê|?μ?÷￡oòò?a?aá???±èμ?±è?μ?àμè￡??ùò??aá???±èò2ê??àμèμ?￡??ò??°??ü??ó?μèo?á??eà′?￡(°?êé￡o4.5:2.7=10:6)???a?ù±íê?á???±è?àμèμ?ê?×ó?D×?ê2?′????a?íê??a?ú???ò??òa?§?°μ??úèY?￡(°?êé??ìa￡o±èàyμ?òaò?)
?t?￠òyμ?ì???￡??§?°D??a
1?￠?ì?§±èàyμ?òaò??￡ (1)3?ê?P40ày1?￡
????1ú?ìμ?3¤oí?íμ?±è·?±eê??àéù?????·?±e??3?ò???1ú?ì3¤oí?íμ?±è?￡
2.4:1.6
60:40
????1ú?ì3¤oí?íμ?±è?μóDê2?′1??μ?(???àμè) 2.4￡o1.6=3/260￡o40=3/2 ?ó?a?ù±íê?á???±è?àμèμ?ê?×ó?D×?±èày?￡
±èàyò2?éò?D′3é￡o2.4/1.6 = 60/40 (2)è?í??§????ò???3?ê?μ?1ú?ì?1óD??D??éò?×é3é±èày òyμ??§éú?μ3??íó?3¤ò2?éò?×é3é±èày?￡
àyè?40￡o60=1.6￡o2.4(°?êé)
?aD?1ú?ì3¤μ?±èó??íμ?±èò2?éò?×é3é±èày àyè?￡o5:2.4=10/3￡o1.6(°?êé)
???a?ù±íê?á???±è?àμèμ?ê?×ó?D×?±èày?￡
??×?±èàyê?4.5:2.7=10:6ìá?ê￡o?°?-?ü?μ?μê2?′?D×?±èày??±òyμ??§éú1?2ìê?±íê?á???±è?àμè?￡è?oó°?êé￡o±íê?á???±è?àμèμ?ê?×ó?D×?±èày?￡2￠è??§éú???áò?±é?￡
?°′ó±èàyμ?òaò??ò???éò??aμà￡?±èàyê?óé????±è×é3éμ???aá???±è±?D???±?ê2?′ì??t?òò′??D??á???±è?ü2??ü×é3é±èày￡?1??üê??′ê2?′?è?1?2??üò????′3?á???±èê?2?ê??àμèμ?￡????′°ì??±
?ù?Y?§éúμ???′e￡??ìê|D??á￡oí¨1yé???μ??§?°￡??ò???aμàá?±èàyê?óéá????àμèμ?±è×é3éμ??￡?ú?D??á???±è?ü2??ü×é3é±èàyê±￡?1??üê??′?aá???±èê?2?ê??àμè?￡è?1?2??üò????′3?á???±èê?2?ê??àμè￡??éò??è·?±e°?á???±è?ˉ?òò?oó?ù?′?￡àyè??D??10:12oí35:
42?aá???±è?ü2??ü×é3é±èày￡??èòa??3? 10: 12=￡?35: 42=￡??ùò? 10:12=35:42?￡(ò?é??ùày±??μ±?°?êé?￡)
(3)±è???°±è?±oí?°±èày?±á????????￡ ?ìê|￡oé??§?ú?ò???§?°á??°±è?±￡????úó??aμàá??°±èày?±μ?òaò?￡????′?°±è?±oí?°±èày?±óDê2?′??±e???
òyμ??§éú′óòaò?é??￠??êyé???DD??±è￡?×?oó?ìê|1é?é￡o±èê?±íê?á???êy?à3y￡?óDá???;±èàyê?ò???μèê?￡?±íê?á???±è?àμè￡?óD?????￡
èy?￠?aê?ó|ó??￡
(ò?)×?ò?×?￠ùè??§éú?è×??￡
6:10oí9:15
20:5oí1:4
1/2:1/3oí6:4
0.6:0.2oí3/4:1/4 ?§éú?D??oó￡??????μ3??D??μ??ù?Y?￡ ￠ú×?P40?°×?ò?×??±μú?tìa?￡
è??§éú?′êé￡?2?3-ìa￡??±?ó°??ü×é3é±èàyμ?á???±èD′?úá·?°±?é?￡??ìê|±??2êó±??ú??￡???×?μ?2???μ?￡?è??????μ?μê????ù×?μ?￡??′?′×??o×?μ???2????￡
(?t)?a???êìa
?ù?Y±í???D?à??ó|μ?á?μ?±è?D???ü·?×é3é±èày￡?òa?ó?§éú°??ü×é3éμ?±èàyD′3?à′ ê?·?êyD?ê?μ?±èàyê?òa?ó?§éúó?·?êyμ?D?ê?±íê??￡
±èàyμ?òaò???ì??ì?§??×?êμ??5
?ì?§??±ê￡o
1.?aê?ó????ü￡oè?ê?±èày￡??aμà±èàyμ?μ??ú??oíía??￡?àí?aoí????±èàyμ??ù±?D??ê￡??á?D??á???±è?ü·?×é3é±èày?￡
2.1y3ìó?·?·¨￡oí¨1y×??÷ì????￠o?×÷??á÷?￠1?2ì?￠±è??￡??à???§éú·????￠±è???￠3é?óoí??à¨μ??üá|￡??-àúè?ê?±èàyoí±èàyμ??ù±?D??êμ?1y3ì?￡
3.?é?Dì??èó????μ1?￡oì??á1ú?ì?Dòto?μ?êy?§1??é￡?·á??1?óú1ú?ìμ??aê?￡??à???§éú°?1ú?ì?￠°?×?1úμ??é?D?￡
?ì?§??μ?￡o
àí?a±èàyμ?òaò?￡?ì???±èàyμ??ù±?D??ê?￡
?ì?§??μ?￡o
ì???±èàyμ??ù±?D??êoíó|ó?òaò?￡??á?D??á???±è?ü·?×é3é±èày?￡
?ì?§1y3ì￡o
ò??￠′′éè?é?3￡?éèòé?¤è¤
í??§??￡?1ú?ìê??D?aè???12oí1úμ??ó?÷?￡??μ±?üò?éy1ú?ìê±￡??ò??D??D3??úá???×?1úμ?èè°?oí×÷?aò????D1úè?μ?×?oà?￡èè°?1ú?ì?íê?èè°?×?1ú￡?1ú?ì???ò???a?′??òa￡???????2????ü?àμ?á??aò?D?1ú?ìμ??aê????????1ú?ìμ?′óD?óD??D?á??a?
?§éú??????′e(íú?ò?§éúéú???-?é)
í??§???aμàμ????à￡??μ?÷í??§????ê±è???1?2ì￡?ê???óDD?è??￡
?t?￠òyμ?ì???￡?×??÷?¨11
???ˉò?￡oì???±èàyμ?òaò?
1.??á??aμ???D?1?óú1ú?ì′óD?μ??aê??
?§éú??á÷￡????§éú3?·?μ???á÷?ú?á?￡
2.????×D??1?2ì￡??áo??ò??é??ú???§μ?±èμ??à1??aê?￡?1à??ò???????1???1ú?ì3¤oí?í?ò???íoí3¤????ê?·?′??úê2?′1??é?
(1)2?2a
?¤éè￡oéú1?￠3¤oí?íμ?±è?μ?àμè;éú2?￠?íoí3¤μ?±è?μ?àμè￡?
(2)D?×é?é?¤
????D?×éè???á???1???1ú?ì￡??é?¤ò???????1ú?ì3¤oí?í????′??úμ?1??é?￡
(3)?1ê???á÷D?×é?é?¤?á1?￡??§éúμ?oú°??°°?êéμ?3??á???￡
?¤éè￡o????1ú?ìμ?3¤oí?íμ?±è??ê?3￡o2￡?????μ?±è?μ?àμè?￡
????1ú?ìμ??íoí3¤μ?±èê?2￡o3￡?????μ?±è?μ?àμè?￡
?ìê|D??á￡o240￡o160ó?144￡o96μ?±è?μ?àμè?ò???éò?°?±è?μ?àμèμ?ê?×óD′3é 240￡o160=144￡o96 ?ò 240/160=144/96
?ò??°?±íê?á???±è?àμèμ?ê?×ó?D×?±èày￡?×é3é±èàyμ?????êy?D×?±èàyμ???￡?á???μ?á????D×?±èàyμ?(ía??)￡??D??μ?á????D×?±èàyμ?(?ú??)?￡à¨o??Dμ??éò?è??§éú?μò??μ?￡
???????ü?μ3?ò???±èày?e??μò??μ??ê????′àí?a±èàyμ??
???′?D??á???±èê?2?ê?3é±èày?
ê?ò?ê?￡??D????????×é?Dμ?á???±è?éò?×é3é±èày?￡
2:3oí6:9 4:2oí28:40 5:2oí10:4 20:5oí1:4
???ˉ?t￡oì???±èàyμ??ù±?D??ê
1.à?ó??§éúáD?ùμ?±èàyoí?D??ìa?Dμ?±èày￡?′óμ¨2???ò???￡?????±èàyá????ú??oíá???ía???????á′??úê2?′1??μ?
2.D?×é?ú?é?¤2?2a?á1?
3.?1ê??é?¤2?2a?é???￡μ?3??á??￡?
?¤éè￡o
?°?ú±èàyà?￡?á???ía???à3?μ??y?íμèóúá????ú???à3?μ?μ?êy?±?￡
?°?ú±èàyà?￡?°?á???ía??3??eà′￡??ù°?á????ú??3??eà′￡??ü??μ?μ?êyê?ò??ùμ??±?￡
?ìê|1é?é×ü?á?￡
í??§???μμ???￡??ú±èàyà?￡?á???ía??μ??yμèóúá????ú??μ??y?￡?a?íê?±èàyμ??ù±?D??ê?￡
°?êé￡o±èàyμ??ù±?D??ê?￡
?-?üó?·?êyD?ê?±íê?ò?é?±èày????ù?óá????ú??oíá???ía??μ??y???(·?×óoí·?????2??à3?)
èy?￠???ˉ?μá·?￠ó|ó?í??1
í??§???§?°á?±èàyμ?òaò?ó?D??ê￡????′?üà?ó??ü???a??êμ?ê?êìa?e?
1.?D????????×é?Dμ?á???±è?éò?×é3é±èày?
(1) 6:9oí 9:12
(2)1/2:1/5oí5/8:1/4
(3)1.4:2 oí 7:10
(4) 0.5:0 .2oí10:4
2.?D???￡
(1)±íê?á???±è?àμèμ?ê?×ó?D×?±èày ( )
(2)0.6:1.6ó?3:4?ü×é3é±èày ( )
(3)è?1?4a=5b￡????′a:b=4:5( )
3.ì???
5:2=80:( )
2:7=( )￡o5
1.2:2.5=( )￡o4
?úò???±èàyà?￡?á???ía???￥?aμ1êy￡????Dò????ú??ê?6￡?áíò????ú??ê?( )?￡
?úò???±èàyà?￡?á????ú??μ??yê?12￡????Dò???ía??ê?2.4￡?áíò???ía??ê?( )?￡
4.D′3?±è?μê?5μ?á???±è￡?2￠×é3é±èày
5.?ù?Y3a=5b°??ü×é3éμ?±èàyD′3?à′?￡
???￠×??÷·′???￠é?è?ì??é
í¨1y?a?ú??μ??§?°??óDê2?′ê????
±èàyμ?òaò???ì??ì?§??×?êμ???à1?????￡o
?? ??±èàyμ?òaò??·?ì?§êμ??5?a
?? D??§áù?ê??êy?§?a±èày?ì°?·???′óè?o??ˉ
?? D??§áù?ê??êy?§???a±èày?·?ì°?·?±?èy?a
?? áù?ê??êy?§???y±èày?·ó?D??ì?§éè???ì°?
?? D??§áù?ê??êy?§ó?D??ì°??￡°?
?? áù?ê??êy?§?ú???′?°×êá???×ü
?? D??§áù?ê????·′±èày?·êy?§?????ì?§éè??°?ày
?? D??§áù?ê??êy?§??·′±èày?·ó??ê?ì°?èy?a
?? ??±èμ?ó|ó??·?ì?§éè??ó??ì?§·′??5?a
?? ×?D?3?èyêy?§?ú???′?°×êá?2021
推荐阅读
- 部编二下《彩色的梦》教学实录
- 幼儿急疹出疹后没精神怎么回事？幼儿急疹的原因
- 浅谈厦门物通博联AGV车辆监控系统的组成、功能及优势
- 彪悍的Graphcore第二代IPU！加速落地超大规模数据中心、金融、医疗健康等领域
- 光模块的命名
- 蓄电池的充电与检查
- 导线截面积与载流量的估算口诀
- 电力谐波系统分析对安全生产的干扰和危害及电
- 什么是分流电阻_分流电阻的计算方法
- 分流电阻的作用是什么_分流电阻的选择