Μαθηματικά Β Δημοτικού - Βιβλίο μαθητή τχ1 - eBooks4Greeks.gr

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Μαθηματικά Β Δημοτικού - Βιβλίο μαθητή τχ1 - eBooks4Greeks.gr

eBooks4Greeks.gr


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Eapple·Ó·ÏËappleÙÈÎfi ÎÂÊ¿Ï·ÈÔÙ˘ ÂÓfiÙËÙ·˜.‡ÓÙÔÌÔ˜ ¤ÏÂÁ¯Ô˜ ÙˆÓ ÁÓÒÛÂˆÓ Î·È‰ÂÍÈÔÙ‹ÙˆÓ appleÔ˘ ‰È‰¿¯ÙËÎ·Ó ÛÙËÓÂÓfiÙËÙ·.KÂÊ¿Ï·È· Î·È ÂÓfiÙËÙ· fiappleÔ˘·Ó·Ê¤ÚÂÙ·È ÙÔ Âapple·Ó·ÏËappleÙÈÎfi.OÌ·‰ÔÛ˘ÓÂÚÁ·ÙÈΤ˜‰Ú·ÛÙËÚÈfiÙËÙ˜ (Û˘˙‹ÙËÛË ÛÙËÓÙ¿ÍË / ηٷÛ΢‹ appleÚÔ‚Ï‹Ì·ÙÔ˜).K·Ù·ÁÚ¿ÊÂÈ appleÚÔÛˆappleÈΤ˜·applefi„ÂȘ / ·˘ÙÔ·ÍÈÔÏÔÁ›ٷÈ.º¿ÎÂÏÔ˜ ÂÚÁ·ÛÈÒÓ.


Oι κεντρικοί ήρωες του βιβλίου εµφανίζονται για να βοηθήσουν στη σταθερή σεναριακή δοµή των δραστηριοτήτων ανακάλυψης.H EϤÓË O NÈÎfiÏ·˜ H ÕÓÓ· O XÚ‹ÛÙÔ˜ O apple›ı·˜H NÂÛ¯¿Ó O ¤ÙÚÔ˜ H M·Ú›Ó· O apple‡ÚÔ˜ H KÏfiÓÙÈ·À¡O∆π∫O π¡∞∫∞ ∞À∆O∞•πO§O°∏∏ ∫∞π ∂∆∂ƒO∞•πO§O°∏∏∆π Oª∞¢π∫∂ ∂ƒ°∞π∂ÙÔ˘ Ì·ıËÙ‹/ÙÚÈ·˜ ……………………………………....................................…………∏ÌÂÚÔÌËÓ›· ………………………………………….K˘ÎÏÒÓˆ fi,ÙÈ ÈÛ¯‡ÂÈ ÁÈ· ̤ӷ∫ [ηıfiÏÔ˘] § [Ï›ÁÔ] [appleÔχ]K˘ÎÏÒÓˆ fi,ÙÈ ÈÛ¯‡ÂÈ ÁÈ· Ù· ¿ÏÏ·apple·È‰È¿ Ù˘ ÔÌ¿‰·˜ ÌÔ˘∫ [ηıfiÏÔ˘] § [Ï›ÁÔ] [appleÔχ]..................................................................OÚÁ·ÓÒıËη ÛÙËÓ ÔÌ¿‰· ÁÚ‹ÁÔÚ· K § Î·È ¯ˆÚ›˜ ıfiÚ˘‚Ô.˘ÓÂÚÁ¿ÛÙËη ¯ˆÚ›˜ ʈӤ˜ Î·È Ù۷ΈÌÔ‡˜. K § OÚÁ·ÓÒıËΠÛÙËÓ ÔÌ¿‰· ÁÚ‹ÁÔÚ· K § K § K § Î·È ¯ˆÚ›˜ ıfiÚ˘‚Ô.˘ÓÂÚÁ¿ÛÙËΠ¯ˆÚ›˜ ʈӤ˜ Î·È Ù۷ΈÌÔ‡˜. K § K § K § OÈ ¿ÏÏÔÈ Î·Ù¿Ï·‚·Ó fiÛ· ÙÔ˘˜ ÂÍ‹ÁËÛ·. K § OÈ ¿ÏÏÔÈ Î·Ù¿Ï·‚·Ó fiÛ· ÙÔ˘˜ ÂÍ‹ÁËÛÂ. K § K § K § ŒÎ·Ó· ‰ÈÔÚıÒÛÂȘ Î·È Û˘ÌappleÏ‹ÚˆÛ· K § ÙȘ ȉ¤Â˜ ÙˆÓ ¿ÏψÓ.ŒÎ·Ó· ÎÚÈÙÈ΋ ÛÙȘ ȉ¤Â˜ ÙˆÓ ¿ÏÏˆÓ ¯ˆÚ›˜ K § Ó· ÙÔ˘˜ appleÏËÁÒÛˆ.µÚ‹Î· appleÔÏϤ˜ ‰È·ÊÔÚÂÙÈΤ˜ χÛÂȘ. K § ŒÎ·Ó ‰ÈÔÚıÒÛÂȘ Î·È Û˘ÌappleÏ‹ÚˆÛ K § K § K § ÙȘ ȉ¤Â˜ ÙˆÓ ¿ÏψÓ.ŒÎ·Ó ÎÚÈÙÈ΋ ÛÙȘ ȉ¤Â˜ ÙˆÓ ¿ÏÏˆÓ ¯ˆÚ›˜ K § K § K § Ó· ÙÔ˘˜ appleÏËÁÒÛÂÈ.µÚ‹Î appleÔÏϤ˜ ‰È·ÊÔÚÂÙÈΤ˜ χÛÂȘ. K § K § K § ∑‹ÙËÛ· ‚Ô‹ıÂÈ· ·applefi Ù· ¿ÏÏ· ̤ÏË K § Ù˘ ÔÌ¿‰·˜ ÌÔ˘.µÔ‹ıËÛ· Ù· ¿ÏÏ· ̤ÏË Ù˘ ÔÌ¿‰·˜ ÌÔ˘. K § ∑‹ÙËÛ ‚Ô‹ıÂÈ· ·applefi Ù· ¿ÏÏ· ̤ÏË K § K § K § Ù˘ ÔÌ¿‰·˜ ÙÔ˘.µÔ‹ıËÛ ٷ ¿ÏÏ· ̤ÏË Ù˘ ÔÌ¿‰·˜ ÙÔ˘. K § K § K §


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8AӷηχappleÙˆ ÙË Û˘ÌÌÂÙÚ›· Á‡Úˆ ÌÔ˘ÙÔ ÂÚÁ·ÛÙ‹ÚÈ ˙ˆÁÚ·ÊÈ΋˜Œ¯ˆ ‰ÂÈ Û˘ÌÌÂÙÚÈο Û¯¤‰È·ÛÙÔ Ûapple›ÙÈ Ù˘ ÁÈ·ÁÈ¿˜ ÌÔ˘!¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„ËEÁÒ ¤¯ˆ ‰ÂÈ Û ÛÙÔÏ›‰È·!Ò˜ ÂϤÁ¯ˆ ·Ó ¤Ó· Û¯‹Ì· Â›Ó·È Û˘ÌÌÂÙÚÈÎfi;∆· apple·È‰È¿ ‰Ô˘ÏÂ‡Ô˘Ó Û ÔÌ¿‰Â˜. ∫¿ı apple·È‰› ·ÎÔ˘Ìapple¿ÂÈ ÙËÓ apple·Ï¿ÌË ÙÔ˘ appleÚÒ-Ù· Û ¯ÚÒÌ·. MÂÙ¿ ÙËÓ ·ÎÔ˘Ìapple¿ÂÈ Û ¯·ÚÙ› appleÔ˘ Â›Ó·È ÙÛ·ÎÈṲ̂ÓÔ ÛÙË Ì¤ÛË.‰ÈappleÏÒÓˆ·ÓÔ›Áˆ‚Ϥappleˆñ O ¡ÈÎfiÏ·˜ ˙ˆÁÚ¿ÊÈÛ ÌÈÛfi Ûapple›ÙÈ ÛÙÔ ÙÛ·ÎÈṲ̂ÓÔ ¯·ÚÙ›:ÙÔ ‰›appleψÛ ÙÔ ¿ÓÔÈÍ ›‰Â:ñ fiÛÔÈ ‹ÏÈÔÈ Î·È applefiÛ· Û‡ÓÓÂÊ· ı· ˘apple¿Ú¯Ô˘Ó ÛÙÔ ¯·ÚÙ› ÙÔ˘ ÃÚ‹ÛÙÔ˘; ∑ˆÁÚ·Ê›˙ˆ.‰ÈappleÏÒÓˆ˙ˆÁÚ·Ê›˙ˆ·ÓÔ›ÁˆÃÚËÛÈÌÔappleÔÈÔ‡ÌÂÙÈ Â›‰Â ÙÔ Î·ıÚÂÊÙ¿ÎÈÁÈ· Ó· ÂϤÁÍÔ˘ÌÂÙË Û˘ÌÌÂÙÚ›·.K·Ù·Û΢‹ «ÂȉÒÏÔ˘» - ∫·ÙÔappleÙÚÈ΋ Û˘ÌÌÂÙÚ›·- E‡ÚÂÛË ¿ÍÔÓ· Û˘ÌÌÂÙÚ›·˜.26E›ÎÔÛÈ ¤ÍÈ


∂ÚÁ·Û›Â˜EÓfiÙËÙ· 11. ªÂ ÙÔ ¯¿Ú·Î¿ ÌÔ˘ ʤÚÓˆ fiappleÔ˘ ÌappleÔÚÒ ÙÔÓ ¿ÍÔÓ· Û˘ÌÌÂÙÚ›·˜ fiappleˆ˜ ÛÙÔ apple·-Ú¿‰ÂÈÁÌ·.2. Ãڈ̷ٛ˙ˆ ÙÔ Û˘ÌÌÂÙÚÈÎfi ÙˆÓ Û¯Â‰›ˆÓ (Ì ÙÔ ›‰ÈÔ ·ÎÚÈ‚Ò˜ ¯ÚÒÌ·).˘Ìapple¤Ú·ÛÌ·ñ ŸÙ·Ó ‰ÈappleÏÒÛÔ˘Ì ÛÙË Ì¤ÛË ¤Ó· Û¯‹Ì· Î·È Ù· ‰˘Ô ÌÈÛ¿ ÙÔ˘ Â›Ó·È ·ÎÚÈ‚Ò˜›‰È·, ÙfiÙ ·˘Ùfi ÙÔ Û¯‹Ì· Â›Ó·È Û˘ÌÌÂÙÚÈÎfi.·Ú·‰Â›ÁÌ·Ù·:ñ ∏ ÁÚ·ÌÌ‹ appleÔ˘ ¯ˆÚ›˙ÂÈ ¤Ó· Û˘ÌÌÂÙÚÈÎfi Û¯‹Ì· Û ‰˘Ô ›‰È· ÌÈÛ¿ ϤÁÂÙ·È¿ÍÔÓ·˜ Û˘ÌÌÂÙÚ›·˜.·Ú·‰Â›ÁÌ·Ù·:E›ÎÔÛÈ ÂÊÙ¿27


Eapple·Ó·ÏËappleÙÈÎfiKÂÊ¿Ï·È· 1- 8AYTOA•IO§O°HH°Ú¿Êˆ ¤Ó· ‰˘Ô appleÚ¿ÁÌ·Ù· appleÔ˘ ÛÙ· ÎÂÊ¿Ï·È· 1 ¤ˆ˜ 8:ñ ªÔ˘ ¿ÚÂÛ·Ó ...............................................................................................................................................................................................................................................ñ ªÂ ‰˘ÛÎfiÏ„·Ó .........................................................................................................................................................................................................................................ñ ŒÌ·ı· ηϿ ...............................................................................................................................................................................................................................................˘ÌappleÏËÚÒÓˆ ÙȘ ÂÚÁ·Û›Â˜.˘˙ËÙ¿Ì ÛÙËÓ Ù¿ÍË appleÔȘ Ì·˜ ‰˘ÛÎfiÏ„·Ó Î·È ÁÈ·Ù›.1. ºÙÈ¿¯Óˆ ·ÚÈıÌÔ‡˜ Ì „ËÊ›· ‹ ÛÙÔÓ ¿‚·Î· Î·È ÌÂÙ¿ ÙÔ˘˜ Áڿʈ Ì ϤÍÂȘ.ñM ϤÍÂȘ ..................................................O ‰ÈappleÏ·Ófi˜ ÌÔ˘ appleÚÔÙ›ÓÂÈ ÙÔÓ ·ÚÈıÌfi appleÔ˘ Â›Ó·È 1 ÌÔÓ¿‰· ÌÂÁ·Ï‡ÙÂÚÔ˜ ...........ñM ϤÍÂȘ ..................................................O ‰ÈappleÏ·Ófi˜ ÌÔ˘ appleÚÔÙ›ÓÂÈ ÙÔÓ ·ÚÈıÌfi appleÔ˘ Â›Ó·È 1 ‰Âο‰· ÌÈÎÚfiÙÂÚÔ˜ ..............2. BÚ›ÛΈ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.ññÙËÓ ·ÚÈıÌËÙÈ΋ ·Ï˘Û›‰·: 13, 15, 17, 19, ..., ..., ..., ..., 29, 31ÙËÓ ·ÚÈıÌÔÁÚ·ÌÌ‹:EÌapple¤‰ˆÛË - Âapple¤ÎÙ·ÛË ÙˆÓ ÁÓÒÛÂˆÓ Î·È ‰ÂÍÈÔًوÓappleÔ˘ ‰È‰¿¯ÙËÎ·Ó ÛÙËÓ ÂÓfiÙËÙ·.28E›ÎÔÛÈ Ô¯ÙÒ


ENOTHTA13.µÚ›ÛΈ ÙÔ ÌÈÛfi Î·È ÙÔ ÔÏfiÎÏËÚÔ.ŸÏ· Ù· ÌappleÈÛÎfiÙ· Â›Ó·È 32. ‹Ú· Ù· ÌÈÛ¿ ÂÁÒ Î·È Ù· ÌÈÛ¿ Ô ·‰ÂÚÊfi˜ ÌÔ˘.ñ fiÛ· ÌappleÈÛÎfiÙ· apple‹ÚÂ Ô Î·ı¤Ó·˜ Ì·˜; ∂ÎÙÈÌÒ: ÂÚ›appleÔ˘ ..............¢Â›¯Óˆ ÛÙÔÓ ¿‚·Î·:ÂÁÒÔ ·‰ÂÚÊfi˜ ÌÔ˘ñ Œ‰ˆÛ· ÛÙË Ê›ÏË ÌÔ˘ ÙÔ ÌÈÛfi ¯·ÚÙ˙ÈÏ›ÎÈ ÌÔ˘. ∆ÒÚ· ¤¯ˆ 8 ú. fiÛ· ¯Ú‹Ì·Ù· ›¯·ÛÙËÓ ·Ú¯‹ Î·È applefiÛ· ¤¯ÂÈ ÙÒÚ· Ë Ê›ÏË ÌÔ˘;∑ˆÁÚ·Ê›˙ˆ:ÙÒÚ·, ÂÁÒ ¤¯ˆ ..........úÙÒÚ·, Ë Ê›ÏË ÌÔ˘ ¤¯ÂÈ ..........úÕÚ·, ÛÙËÓ ·Ú¯‹ ›¯· ............ ú.4. ÷ڿ˙ˆ ‰ÚfiÌÔ˘˜ Ì ÙÔ ¯¿Ú·Î·.∞µ = 5 ÂÎ.µ° = 6 ÂÎ.∏ ÁÚ·ÌÌ‹ ∞µ° ¤¯ÂÈ Û˘ÓÔÏÈÎfi Ì‹ÎÔ˜ ...... ÂÎ.5. µÚ›ÛΈ ÙÔ Ï¿ıÔ˜. •·Ó·Áڿʈ ÛˆÛÙ¿ ÙËÓ ·ÚÈıÌËÙÈ΋ ·Ï˘Û›‰·.ñ 7, 17, 27, 47, 57, 77, 97ñ 79, 77, 75, 72, 70, 69, 667,79,E›ÎÔÛÈ ÂÓÓ¤·29


9T· ‰›‰˘Ì·BÚ›ÛΈ ÙÔ ÌÈÛfi Î·È ÙÔ ‰ÈappleÏ¿ÛÈÔÛÙÔ˘˜ ·ÚÈıÌÔ‡˜ 0-100¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„Ë∏ ∂ϤÓË ·applefiÎÙËÛ ‰˘Ô Í·‰ÂÚÊ¿ÎÈ· ‰›‰˘Ì·, ÙË ∑ˆ‹ Î·È ÙÔÓ ∞ϤͷӉÚÔ!ªÔÈ¿˙Ô˘Ó appleÔχ, ·ÏÏ¿Â›Ó·È ‰È·ÊÔÚÂÙÈο! ÙÈ ‰È·Ê¤ÚÔ˘Ó ÌÂٷ͇ ÙÔ˘˜ Ù· „ËÊ›· ÙÔ˘ ·ÚÈıÌÔ‡ 11;T· apple·È‰È¿ apple·›˙Ô˘Ó Ì ÙȘ οÚÙ˜ ÙˆÓ „ËÊ›ˆÓ. fiÛÔ˘˜ ‰È„‹ÊÈÔ˘˜ ·ÚÈıÌÔ‡˜ ÌappleÔÚÔ‡ÌÂÓ· ÊÙÈ¿ÍÔ˘Ì appleÔ˘ Ó· ¤¯Ô˘Ó Ù· ›‰È· „ËÊ›·;ñ ∏ ÔÌ¿‰· Ù˘ ÕÓÓ·˜‚ڋΠ3 ·ÚÈıÌÔ‡˜.ñ ∏ ÔÌ¿‰· ÙÔ˘ ¡ÈÎfiÏ·‚ڋΠ4 ·ÚÈıÌÔ‡˜.¯1. ˘ÌappleÏËÚÒÓÔ˘Ì ÙÔ˘˜ ·ÚÈıÌÔ‡˜ appleÔ˘ Ï›appleÔ˘Ó.°È· Ó· ÙÔ˘˜ ÊÙÈ¿ÍÔ˘ÌÂ,apple·›ÚÓÔ˘Ì ‰˘Ô ÊÔÚ¤˜ÙÔ ›‰ÈÔ „ËʛԅÙÔÓ ·ÚÈıÌfi 55 ‰ÂÓ ¤¯ÂÈ ›‰È· ·Í›·ÙÔ appleÚÒÙÔ „ËÊ›Ô 5 Ì ÙÔ ¿ÏÏÔ 5!ŸÙ·Ó ‰È·‚¿˙Ô˘Ì ÙÔÓ ·ÚÈıÌfi 55,ϤÌ ‰È·ÊÔÚÂÙÈÎfi fiÓÔÌ· Áȷοı appleÂÓÙ¿ÚÈ.˘˙ËÙ¿Ì ÛÙËÓ Ù¿ÍË: TÈ Ì·˜ ‰˘ÛÎfiÏÂ„Â Î·È ÁÈ·Ù›;2. ∂ÍËÁÒ Û ¤Ó· Û˘ÌÌ·ıËÙ‹ ÌÔ˘ appleÒ˜ ͯˆÚ›˙Ô˘Ì ٷ ‰‡Ô ›‰È· „ËÊ›· ÙÔ˘ ·ÚÈıÌÔ‡ 33:→ ŸÙ·Ó ‰È·‚¿˙Ô˘ÌÂ: ·Îԇ̠ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ..................... Î·È .......................→ ŸÙ·Ó ÁÚ¿ÊÔ˘ÌÂ: ÁÚ¿ÊÔ˘Ì ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ................... + ......................→ ŸÙ·Ó ˙ˆÁÚ·Ê›˙Ô˘ÌÂ: ÔÌ·‰ÔappleÔÈԇ̠............ ‰Âο‰Â˜ Î·È ............... ÌÔÓ¿‰Â˜.∞Í›· ı¤Û˘ „ËÊ›Ô˘ - ‡ÚÂÛË ÌÈÛÔ‡ Î·È ‰ÈappleÏ¿ÛÈÔ˘ÛÙÔ˘˜ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 100. ¡ÔÂÚÔ› ˘appleÔÏÔÁÈÛÌÔ›.30 TÚÈ¿ÓÙ·


EÓfiÙËÙ· 23. fiÛÔÈ Ù¤ÙÔÈÔÈ ·ÚÈıÌÔ› ˘apple¿Ú¯Ô˘Ó ̤¯ÚÈ ÙÔ 100; ·Ú·ÙËÚÒ ÙÔ apple·Ú¿‰ÂÈÁÌ· Î·È Û˘-ÌappleÏËÚÒÓˆ: ∆Ô˘˜ Áڿʈ Ì ÙË ÛÂÈÚ¿ ·applefi ÙÔ ÌÈÎÚfiÙÂÚÔ ÛÙÔ ÌÂÁ·Ï‡ÙÂÚÔ.∂ÚÁ·Û›Â˜1. ¢È·‚¿Û·Ì 33 ÛÂÏ›‰Â˜ ·applefi ÙÔ ‚È‚Ï›Ô Ì·˜ Î·È ÊÙ¿Û·Ì ·ÎÚÈ‚Ò˜ ÛÙË Ì¤ÛË. ∆Ô ‚ȂϛԤ¯ÂÈ ‰ËÏ·‰‹ Û˘ÓÔÏÈο ‰ÈappleÏ¿ÛȘ ÛÂÏ›‰Â˜. fiÛ˜ Â›Ó·È ÔÈ ÛÂÏ›‰Â˜ ÙÔ˘ ‚È‚Ï›Ô˘;ñ ∂ÎÙÈÌÒ: ÂÚ›appleÔ˘ ................ ÛÂÏ›‰Â˜.ñ ÀappleÔÏÔÁ›˙ˆ 3 3 + 3 3 = (.... + ....) + (3 + 3) = ....Ì ·ÎÚ›‚ÂÈ·:30 ... ... ...2. °È· Ó· ÊÙÈ¿ÍÔ˘Ì 1 ηӿٷ appleÔÚÙÔηϿ‰·, ÛÙ‡„·Ì 18 appleÔÚÙÔοÏÈ·. fiÛ· appleÔÚÙÔοÏÈ·ı· ÛÙ‡„Ô˘Ì ÁÈ· Ó· ÊÙÈ¿ÍÔ˘Ì 2 ηӿÙ˜ appleÔÚÙÔηϿ‰·;ñ ∂ÎÙÈÌÒ: ÂÚ›appleÔ˘ ................ appleÔÚÙÔοÏÈ·.ñ ÀappleÔÏÔÁ›˙ˆ 1 8 + 1 8 =(.... + ....) + (.... + ....) = .... + .... = ....Ì ·ÎÚ›‚ÂÈ·:... ... ... ...3. O ·ÚÈÔ˜ £ˆÌ¿˜ Ô Ù·¯˘‰ÚfiÌÔ˜ ¤¯ÂÈ 36 ÁÚ¿ÌÌ·Ù· Ó· ÌÔÈÚ¿ÛÂÈ. ªÔ›Ú·Û ٷ ÌÈÛ¿.fiÛ· ¯ÚÂÈ¿˙ÂÙ·È Ó· ÌÔÈÚ¿ÛÂÈ ·ÎfiÌË;ñ ∂ÎÙÈÌÒ: ÂÚ›appleÔ˘ ................ ÁÚ¿ÌÌ·Ù·.ñ ÀappleÔÏÔÁ›˙ˆ 10 363 Œ¯ÂÈ ·ÎfiÌË Ó· ÌÔÈÚ¿ÛÂÈÌ ·ÎÚ›‚ÂÈ·: 5.... ÁÚ¿ÌÌ·Ù·.30 6..............˘Ìapple¤Ú·ÛÌ·ñ Àapple¿Ú¯Ô˘Ó ·ÚÈıÌÔ› appleÔ˘ ¤¯Ô˘Ó ›‰È· „ËÊ›·, ηı¤Ó· fï˜ ¤¯ÂÈ ¿ÏÏË ·Í›· ÂappleÂȉ‹‚Ú›ÛÎÂÙ·È Û ‰È·ÊÔÚÂÙÈ΋ ı¤ÛË.ñ O ¿‚·Î·˜ Ì·˜ ‚ÔËı¿ÂÈ Ó· ‰›ÓÔ˘Ì Û οı „ËÊ›Ô ÂÓfi˜ ·ÚÈıÌÔ‡ ÙËÓ ·Í›· ÙÔ˘.¢ ªñ appleÂÓ‹ÓÙ· apple¤ÓÙ 50 + 5 = (10 + 10 + 10 + 10 + 10) + 555·Ú·‰Â›ÁÌ·Ù·:¢ ªñ ›ÎÔÛÈ ‰‡Ô 2 2 20 + 2 = (10 + 10) + 2TÚÈ¿ÓÙ· ¤Ó·31


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EÓfiÙËÙ· 23. ·Ú·ÙËÚÒ ÙȘ ÛÙÚ·ÙËÁÈΤ˜ ÙˆÓ apple·È‰ÈÒÓ Î·È ÙȘ Û˘ÌappleÏËÚÒÓˆ.ñ3 + ............ = 50¿Ú· 7+ ... = ...∂›Ó·È appleÈÔ Â‡ÎÔÏÔ Ó· οÓÂȘappleÚfiÛıÂÛË, ÂappleÂȉ‹ 3+ 7 =10Î·È 10+ ... = 50.+1 +1 +1+1+1 +1+1EÁÒ appleÈÔ Â‡ÎÔÏ· οӈ·Ê·›ÚÂÛË:50 – 3-1-1-150 - 1 - 1 - 1= ...ñ19 + ............ = 50∂ÚÁ·Û›·ÃÚËÛÈÌÔappleÔÈÒ ÎÈ ÂÁÒÙÔ apple¿ÙËÌ· ÛÙË ‰Âο‰·.19+ 1 = 2020+ ... = 50ÕÚ·, ÌÔ˘ Ï›appleÔ˘Ó 1+... = ...ÃÚËÛÈÌÔappleÔÈÒ ÎÈ ÂÁÒ ÙÔ apple¿ÙËÌ· ÛÙˉÂο‰· ÛÙËÓ ·Ê·›ÚÂÛË: 50 – 19.YappleÔÏÔÁ›˙ˆ ÙÔ ·appleÔÙ¤ÏÂÛÌ· Û ‰‡Ô‚‹Ì·Ù·:→ 50 – 10 ‚Ú›ÛΈ .....→ ...... – 9 ‚Ú›ÛΈ..... ÕÚ·, ......˘Ó¯›˙ˆ ÙË ÁÚ·ÌÌ‹ ∞µ°¢∂ ̤¯ÚÈ ÙÔ Z.∆Ô Û˘ÓÔÏÈÎfi Ì‹ÎÔ˜ Ù˘ Â›Ó·È .... + .... + .... + .... + .... = .... ÂÎ.Zñ fiÛÔ ı· ‹Ù·Ó Û˘ÓÔÏÈο ÙÔ Ì‹ÎÔ˜ Ù˘ ÁÚ·ÌÌ‹˜ ·Ó Û˘Ó¤¯È˙· Ì ÙÔÓ ›‰ÈÔ ÙÚfiappleÔ Ì¤¯ÚÈ ÙÔÛËÌÂ›Ô ; ....... ÂÎ.ñ ∞Ó ÙÔ Î¿ı ‚‹Ì· ‹Ù·Ó 6 ÂÎ. ·ÓÙ› ÁÈ· 3 ÂÎ., applefiÛÔ ı· ‹Ù·Ó Û˘ÓÔÏÈο ÙÔ Ì‹ÎÔ˜ Ù˘ÁÚ·ÌÌ‹˜ ·applefi ÙÔ A ¤ˆ˜ ÙÔ ; ................ ÂÎ.˘˙ËÙ¿Ì ÙȘ χÛÂȘ appleÔ˘ ‚ڋηÌ ÛÙËÓ Ù¿ÍË.˘Ìapple¤Ú·ÛÌ·ºÙ¿ÓÔ˘Ì Û ¤Ó·Ó ·ÚÈıÌfi, apple·Ú¿‰ÂÈÁÌ·, ÛÙÔÓ 51:- ›Ù appleÚÔÛı¤ÙÔÓÙ·˜ ·ÚÈıÌÔ‡˜ Û ¤Ó· ÌÈÎÚfiÙÂÚfi ÙÔ˘, apple.¯.: 45+5+1- ›Ù ·Ê·ÈÚÒÓÙ·˜ ·ÚÈıÌÔ‡˜ ·applefi ¤Ó· ÌÂÁ·Ï‡ÙÂÚfi ÙÔ˘, apple.¯.: 61– 10TÚÈ¿ÓÙ· ÙÚ›·33


11 °ÓˆÚ›˙ˆ ηχÙÂÚ· Ù· ΤÚÌ·Ù· ÙÔ˘ ¢ÚÒ ( €)ÙÔ Î˘ÏÈΛÔÔÈÔ Î¤ÚÌ· ¤¯ÂÈ ÙË ÌÂÁ·Ï‡ÙÂÚË ·Í›·;¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„Ë1 Ï. 2 Ï. 5 Ï. 10 Ï. 20 Ï. 50 Ï. 1 ú 2 úÙÔ˘ ú ÙÔ˘ ú ÙÔ˘ ú ÙÔ˘ ú ÙÔ˘ ú ÌÈÛfi ¢ÚÒO ¡ÈÎfiÏ·˜ ı¤ÏÂÈ Ó· ·ÁÔÚ¿ÛÂȤӷ ¯˘Ìfi Î·È ¤Ó· ÎÔ˘ÏÔ‡ÚÈ.50 Ï. 80 Ï.Œ‰ˆÛÂÎ·È apple‹Ú ڤÛÙ·O ¡ÈÎfiÏ·˜ apple·Ú·Ù‹ÚËÛ fiÙÈ ÔÈ apple›Ûˆ fi„ÂÈ˜ÙˆÓ ÓÔÌÈÛÌ¿ÙˆÓ appleÔ˘ apple‹Ú ڤÛÙ· ‰ÂÓ Â›Ó·È ›‰È˜!∫È ¿ÏÏ· apple·È‰È¿ ¤¯Ô˘Ó ‰ÂÈ ‰È·ÊÔÚÂÙÈο ΤÚÌ·Ù· Ù˘ ›‰È·˜ ·Í›·˜.∆· apple·È‰È¿ apple·Ú·ÙËÚÔ‡Ó fiÙÈ Ù· ΤÚÌ·Ù· ÙÔ˘ ¢ÚÒ ¤¯Ô˘Ó ÙË Ì›· fi„Ë .......................Î·È ÙËÓ ¿ÏÏË ..............................ñ ÔÈÔ apple·È‰› ¤¯ÂÈ Î¤ÚÌ·Ù· ÌÂÁ·Ï‡ÙÂÚ˘ ·Í›·˜ (˘appleÔÁÚ·ÌÌ›˙ˆ):H ÕÓÓ·;O ÃÚ‹ÛÙÔ˜;ñ ·Ú·ÙËÚÒ appleÚÔÛ¯ÙÈο Î·È Û˘ÌappleÏËÚÒÓˆ.→+ = → + =→+..................... = → +..................... =→+........................ =→+ ............................=°ÓˆÚÈÌ›· Ì ٷ ΤÚÌ·Ù· ÙÔ˘ ¢ÚÒ. ∫ÔÈÓ‹ Î·È ‰È·ÊÔÚÂÙÈ΋ fi„ËÎÂÚÌ¿ÙˆÓ, ·Ó·ÁÓÒÚÈÛË Ù˘ ·Í›·˜ ÙÔ˘˜ Î·È ÙˆÓ Û¯¤ÛÂˆÓ ÌÂٷ͇ÙÔ˘˜. ÚÒÙË ÁÓˆÚÈÌ›· Ì ٷ Ú¤ÛÙ·.34 TÚÈ¿ÓÙ· Ù¤ÛÛÂÚ·


∂ÚÁ·Û›Â˜¡ÔÌÈÛÌ·ÙÈÎfi MÔ˘Û›Ôhttp://www.nm.culture.grEÓfiÙËÙ· 21. ·Ú·ÙËÚԇ̠ٷ ΤÚÌ·Ù· ÙÔ˘ ¢ÚÒ. ÔÈ· Â›Ó·È Ù· ΤÚÌ·Ù· appleÔ˘ ¤¯Ô˘Ó ÙË ÌÂ-Á·Ï‡ÙÂÚË ·Í›·; µ¿˙ˆ ✔: Ù· ‰›¯ÚˆÌ· Ù· ÌÔÓfi¯ÚˆÌ·∞applefi Ù· ÌÔÓfi¯ÚˆÌ·, appleÔÈÔ Î¤ÚÌ· ¤¯ÂÈ ÙË ÌÂÁ·Ï‡ÙÂÚË ·Í›·; ................................................2. µ¿˙ˆ (ÛˆÛÙfi) ‹ § (Ï¿ıÔ˜) ÛÙȘ ÂÎÙÈÌ‹ÛÂȘ Ù˘ NÂÛ¯¿Ó:ñññŒ¯ˆ appleÂÚÈÛÛfiÙÂÚ··applefi 1ú 50 Ï.Œ¯ˆ appleÂÚ›appleÔ˘ 1úŒ¯ˆ appleÂÚ›appleÔ˘ 2úñññŒ¯ˆ appleÂÚÈÛÛfiÙÂÚ··applefi 2úŒ¯ˆ appleÂÚ›appleÔ˘ 1úŒ¯ˆ appleÂÚ›appleÔ˘ 1ú 50 Ï.3. µ¿˙ˆ § ÛÙË Û˘Ó·ÏÏ·Á‹ appleÔ˘ Â›Ó·È Ï·Óı·Ṳ̂ÓË:80 ÏÂappleÙ¿Œ‰ˆÛ· 1ú Î·È ‰ÂÓ apple‹Ú· Ú¤ÛÙ·.Œ‰ˆÛ· 1ú Î·È apple‹Ú· Ú¤ÛÙ· 20 Ï.1ú Î·È 40 ÏÂappleÙ¿ Œ‰ˆÛ· 2ú Î·È apple‹Ú· Ú¤ÛÙ· 40 Ï.Œ‰ˆÛ· 1ú Î·È 50 Ï. ∫·È apple‹Ú· Ú¤ÛÙ· 10 Ï.˘Ìapple¤Ú·ÛÌ·ŸÙ·Ó ͤڈ ÙËÓ ·Í›· ÙˆÓ ÎÂÚÌ¿ÙˆÓ ÙÔ˘ ¢ÚÒ, ÌappleÔÚÒ Ó· Ù· ·ÓÙ·ÏϿ͈ Ì ¿ÏϷΤÚÌ·Ù· ÙÔ˘ ¢ÚÒ appleÔ˘ Û˘ÓÔÏÈο ¤¯Ô˘Ó ÙËÓ ›‰È· ·Í›·.·Ú¿‰ÂÈÁÌ·: = + 50 Ï.1ú 50 Ï.100 Ï.TÚÈ¿ÓÙ· apple¤ÓÙÂ35


12ÙËÓ ·ÁÔÚ¿Ò˜ ˘appleÔÏÔÁ›˙Ô˘Ì ٷ Ú¤ÛÙ· ÛÙȘ ·ÁÔÚ¤˜ appleÔ˘ οÓÔ˘ÌÂ;∏ ÕÓÓ· Î·È ÔÈ Ê›ÏÔÈ Ù˘ apple‹Á·Ó ÛÙ· Ì·Á·˙È¿.YappleÔÏÔÁ›˙ˆ Ù· Ú¤ÛÙ·¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„ËŒ‰ˆÛ·‹ ....... ú9úñÎ·È apple‹Ú· Ú¤ÛÙ· 50 Ï.Œ‰ˆÛ·‹ ...... ú1ú 80 Ï.ñÎ·È apple‹Ú· Ú¤ÛÙ·4ú 50 Ï.ñŒ‰ˆÛ·Î·È apple‹Ú· Ú¤ÛÙ·‹ ....... Ï.50 Ï.ñŒ‰ˆÛ·Î·È ‰ÂÓ apple‹Ú· Ú¤ÛÙ·.‹ ........ úÎ·È ........ Ï.ñ ÔÈÔ apple·È‰› apple‹Ú ٷ appleÂÚÈÛÛfiÙÂÚ· Ú¤ÛÙ·; ..............................................................ñ∞Ó Â›¯·Ì 10 ¢ÚÒ, ÙÈ ı· ÌappleÔÚÔ‡Û·Ì ӷ ·ÁÔÚ¿ÛÔ˘ÌÂ;µ¿˙ˆ ✔ ÛÙÔ ÛˆÛÙfi.ñ 1 ‚È‚Ï›Ô Î·È 1 apple·Î¤ÙÔ ·˘ÙÔÎfiÏÏËÙ·ñ 2 ÎÔ‡apple˜ñ 10 ÙÚ›ÁˆÓ·ñ 10 apple·Î¤Ù· ·˘ÙÔÎfiÏÏËÙ·ñ 2 ‚È‚Ï›·ñ 20 ÙÚ›ÁˆÓ·˘˙ËÙ¿Ì ÛÙËÓ Ù¿ÍË Ì·˜ ÙȘ χÛÂȘ appleÔ˘ ‚ڋηÌÂ.ñ ∞Ó ·ÁÔÚ¿ÛÔ˘Ì ÙÚ›· ÙÚ›ÁˆÓ·,ñ appleÒ˜ appleÚ¤appleÂÈ Ó· appleÏËÚÒÛÔ˘Ì ÁÈ· Ó· ÌËÓ apple¿ÚÔ˘Ì ڤÛÙ·;ñ appleÒ˜ appleÚ¤appleÂÈ Ó· appleÏËÚÒÛÔ˘Ì ÁÈ· Ó· apple¿ÚÔ˘Ì ڤÛÙ· ;∏ ¤ÓÓÔÈ· «Ù· Ú¤ÛÙ·»: ∂‡ÚÂÛË.36 TÚÈ¿ÓÙ· ¤ÍÈ


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EÓfiÙËÙ· 3ñ ·Ú·ÙËÚÒ appleÚÔÛ¯ÙÈο Î·È Û˘Ó¯›˙ˆ Ó· ¯ÚˆÌ·Ù›˙ˆ Ù· ÌÔÙ›‚·.A. B.°.¢.E.∫˘ÎÏÒÓˆ ÙÔ ÛˆÛÙfi:O ¡ÈÎfiÏ·˜ ¤¯ÂÈ ÛÙËÓ ÌappleÏÔ‡˙· ÙÔ˘ ÙÔ ÌÔÙ›‚Ô ∞, µ, °, ¢ ‹ ∂;˘Ìapple¤Ú·ÛÌ·°ÂˆÌÂÙÚÈÎfi ÌÔÙ›‚Ô Ï¤Ì ÌÈ· ÛÂÈÚ¿ ·applefi ÁˆÌÂÙÚÈο Û¯‹Ì·Ù· appleÔ˘ Âapple·Ó·Ï·Ì‚¿-ÓÔÓÙ·È Ì ÙÔÓ ›‰ÈÔ ·ÎÚÈ‚Ò˜ ÙÚfiappleÔ. ∞Ó ‚Úԇ̠ٷ ÁˆÌÂÙÚÈο Û¯‹Ì·Ù· appleÔ˘ Âapple·Ó·-Ï·Ì‚¿ÓÔÓÙ·È (ÛÙÔÈ¯Â›Ô ÙÔ˘ ÌÔÙ›‚Ô˘), ÌappleÔÚԇ̠ӷ ÙÔ Û˘Ó¯›ÛÔ˘Ì Ì ÙÔÓ ›‰ÈÔÙÚfiappleÔ. ·Ú¿‰ÂÈÁÌ·:‹·Ú¿ÓÙ· ÂÊÙ¿47


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EÓfiÙËÙ· 3∂ÚÁ·Û›Â˜1.O apple‡ÚÔ˜ ¤¯ÂÈ 13 οÚÙ˜. O ÃÚ‹ÛÙÔ˜ ¤¯ÂÈ 18Î·È Ë ª·Ú›Ó· ¤¯ÂÈ 23. ÔÈÔ apple·È‰› ¤¯ÂÈ:- TȘ appleÂÚÈÛÛfiÙÂÚ˜ οÚÙ˜; ......................................- TȘ ÏÈÁfiÙÂÚ˜ οÚÙ˜; .................................................- fiÛ˜ οÚÙ˜ ¤¯Ô˘Ó fiÏ· Ù· apple·È‰È¿; ...................................................ñ fiÛ˜ οÚÙ˜ appleÚ¤appleÂÈ Ó· ¤¯Ô˘Ó ·ÎfiÌ· Ô apple‡ÚÔ˜ Î·È applefiÛ˜ Ô ÃÚ‹ÛÙÔ˜ ÁÈ· Ó·¤¯Ô˘Ó ÙfiÛ˜ οÚÙ˜ fiÛ˜ Î·È Ë ª·Ú›Ó·;O apple‡ÚÔ˜ ............ οÚÙ˜. O XÚ‹ÛÙÔ˜ ............ οÚÙ˜.ñ fiÛ˜ οÚÙ˜ appleÚ¤appleÂÈ Ó· ‰ÒÛÂÈ Ë ª·Ú›Ó· ÛÙÔ ÃÚ‹ÛÙÔ Î·È ÛÙÔ apple‡ÚÔ, ÒÛÙ ӷ¤¯Ô˘Ó fiÏ· Ù· apple·È‰È¿ ›ÛÔ ·ÚÈıÌfi ·applefi οÚÙ˜;ÙÔ XÚ‹ÛÙÔ ........................... ÙÔ apple‡ÚÔ ........................ª·Ú›Ó· XÚ‹ÛÙÔ˜ apple‡ÚÔ˜2. O ¡ÈÎfiÏ·˜ ¤¯ÂÈ 20 ·˘ÙÔÎÈÓËÙ¿ÎÈ· ÌappleÏÂ, ÎfiÎÎÈÓ· Î·È ÌÔ‚.∆· ÌappleÏÂ Â›Ó·È fiÛ· Î·È Ù· ÎfiÎÎÈÓ·. ∆· ÌÔ‚ Â›Ó·È Ù· ÏÈÁfiÙÂ-Ú·. fiÛ· ·˘ÙÔÎÈÓËÙ¿ÎÈ· ÌappleÔÚ› Ó· ›ӷÈ:ÌappleÏ .......................ÎfiÎÎÈÓ· ...................ÀappleÔÏÔÁ›˙ˆ Ì ·ÚÈıÌÔ‡˜:˘˙ËÙ¿Ì ÛÙËÓ Ù¿ÍË ÙȘ χÛÂȘ appleÔ˘ ÛÎÂÊًηÌÂ.˘Ìapple¤Ú·ÛÌ·∆ËÓ ¤ÎÊÚ·ÛË «ÙfiÛ· fiÛ·» ÙË ¯ÚËÛÈÌÔappleÔÈԇ̠ÁÈ· appleÔÛfiÙËÙ˜ appleÔ˘Â›Ó·È ›Û˜ ÌÂٷ͇ ÙÔ˘˜.·Ú¿‰ÂÈÁÌ·: T· ÌappleÏÂÙÔ˘Â›Ó·È ÙfiÛ· fiÛ· Î·È Ù· ÎfiÎÎÈÓ·ÂÓ‹ÓÙ· ÂÊÙ¿57


22ÙÔ ¯ˆÚ¿ÊÈAӷχˆ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 100.EÈÛ·ÁˆÁ‹ ÛÙËÓ appleÚÔapple·›‰ÂÈ·ªÂ appleÔÈÔ˘˜ ›‰ÈÔ˘˜ ·ÚÈıÌÔ‡˜ ÌappleÔÚԇ̠ӷ ÊÙÈ¿ÍÔ˘Ì ÙÔ 12;¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„Ë∏ ∂ϤÓË Ì ÙÔ Ê›ÏÔ Ù˘ ÙÔ ÃÚ‹ÛÙÔ ‚ÔËıÔ‡Ó ÙÔ˘˜ apple·appleappleÔ‡‰Â˜ ÙÔ˘˜ ÛÙÔÓ Î‹appleÔ:Ê˘ÙÂ‡Ô˘Ó Ï·¯·ÓÈο Û ÛÂÈÚ¤˜.∆· 24 Ï¿¯·Ó· Û applefiÛ˜ ›‰È˜ÛÂÈÚ¤˜ ı· Ù· Ê˘Ù¤„Ô˘ÌÂ;Àapple¿Ú¯Ô˘Ó appleÔÏÏÔ› ÙÚfiappleÔÈ.3 + 3 + 3 + 3 + 3 + 3 + 3 + 3‹ 8 ÊÔÚ¤˜ ÙÔ 3 (8 x 3).2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2‹ 12 ÊÔÚ¤˜ ÙÔ 2 (12 x 2).12 + 12 ‹ 2 x 12. 6 + 6 + 6 + 6 ‹ 4 x 6.Yapple¿Ú¯ÂÈ ¿ÏÏÔ˜ ÙÚfiappleÔ˜; ∑ˆÁÚ·Ê›˙ˆ.∞ıÚÔÈÛÙÈ΋ ·Ó¿Ï˘ÛË ‰È„‹ÊÈˆÓ Û ›‰ÈÔ˘˜ ‹ ‰È·ÊÔÚÂÙÈÎÔ‡˜fiÚÔ˘˜. ∂ÈÛ·ÁˆÁ‹ ÛÙËÓ appleÚÔapple·›‰ÂÈ·.58 ÂÓ‹ÓÙ· Ô¯ÙÒ


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26BÚ›ÛΈ ÙËÓ appleÚÔapple·›‰ÂÈ· ÙÔ˘ 8O ÊÔ‡ÚÓÔ˜ ÙÔ˘ Î˘Ú Ù·Ì¿ÙËÒ˜ ÌappleÔÚԇ̠ӷ ‚Úԇ̠ÙËÓ appleÚÔapple·›‰ÂÈ· ÙÔ˘ 8;¢Ú·ÛÙËÚÈfiÙËÙ· – ∞Ó·Î¿Ï˘„ËO ÊÔ‡ÚÓÔ˜ ÙÔ˘ Î˘Ú Ù·Ì¿ÙË Â›Ó·È ‰È¿ÛËÌÔ˜. ∂›Ó·È apple·Ú·‰ÔÛÈ·Îfi˜ ÊÔ‡ÚÓÔ˜ Ì ͇-Ï·. ÙÔ „ˆÌ› ‰Â ‚¿˙Ô˘Ó Û˘ÓÙËÚËÙÈο. ŸÏÔ˜ Ô ÎfiÛÌÔ˜ ·ÁÔÚ¿˙ÂÈ „ˆÌ›. T· „ˆÌÈ¿ ÙÂ-ÏÂÈÒÓÔ˘Ó Û˘¯Ó¿ appleÚÈÓ ·applefi ÙÔ ÌÂÛË̤ÚÈ.∫·ÏË̤ڷ, ΢ڛ· ∂ÈÚ‹ÓË!£· apple¿Úˆ 3 ÊÚ·ÓÙ˙fiϘÁÈ·Ù› ‹Úı·Ó Ù· ÂÁÁÔÓ¿ÎÈ·ÌÔ˘ ·applefi ÙË ¢Ú¿Ì·!ñ ∞Ó ¤Ó· „ˆÌ› ÎÔÛÙ›˙ÂÈ , applefiÛ· appleÚ¤appleÂÈ Ó· appleÏËÚÒÛÂÈ Ë ÁÈ·ÁÈ¿ ÒÛÙÂÓ· ·ÁÔÚ¿ÛÂÈ 3 „ˆÌÈ¿;∂ϤÁ¯ˆ Ì ٷ ‰¿¯Ù˘Ï¿ ÌÔ˘.4........ñ O Î˘Ú Ù·Ì¿Ù˘ Á¤ÌÈÛ ˆ˜ ÙÒÚ· 9 ÊÔÚ¤˜ ÙÔ Î·Ï¿ıÈ Ì ٷ „ˆÌÈ¿. ∞Ó ÙÔ Î·Ï¿ıȯˆÚ¿ÂÈ 8 „ˆÌÈ¿, applefiÛ˜ Û˘ÓÔÏÈο ÊÚ·ÓÙ˙fiϘ ¤ÊÙÈ·Í ̤¯ÚÈ ÙÒÚ·;∂ϤÁ¯ˆ Ì ٷ ‰¿¯Ù˘Ï¿ ÌÔ˘.816 ................ .... ........∏ appleÚÔapple·›‰ÂÈ· ÙÔ˘ 8 ·ÍÈÔappleÔÈÒÓÙ·˜ ÙËÓ appleÚÔapple·›‰ÂÈ· ÙÔ˘ 4.H ·ÓÙÈÌÂÙ¿ıÂÛË ÛÙÔÓ appleÔÏÏ·appleÏ·ÛÈ·ÛÌfi.70 E‚‰ÔÌ‹ÓÙ·


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ENOTHTAñ ˘ÌappleÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ appleÔ˘ Ï›appleÔ˘Ó Î¿ı ÊÔÚ¿, ¤ÙÛÈ ÒÛÙ ÙÔ ·appleÔÙ¤ÏÂÛÌ·Ó· Ì·˜ ‰›ÓÂÈ ÙÔÓ ·ÚÈıÌfi-ÛÙfi¯Ô:4ñ ¢Â›¯Óˆ ÛÙÔappleϤÁÌ· Ù·ÁÈÓfiÌÂÓ·:ñ 3 x 6 =ñ 6 x 3 =ŒÊÙÈ·Í· ‰‡Ô ........................................................................ñ ∆È Û¯‹Ì· ı· Û¯ËÌ·ÙÈÛÙ› Ì ÙÔ ÁÈÓfiÌÂÓÔ 3 x 3;∑ˆÁÚ·Ê›˙ˆ Î·È ÂÍËÁÒ:ŒÊÙÈ·Í· ¤Ó· ....................................................................2. §‡Óˆ appleÚÔ‚Ï‹Ì·Ù·.ñ ªÂ 2 ú Î·È 50 Ï. ·ÁÔÚ¿˙Ô˘ÌÂÚ˘˙fiÁ·Ï· ·ÁÔÚ¿˙Ô˘ÌÂ;→ ∂ÎÙÈÌÒ:ñ 5 Ú˘˙fiÁ·Ï·ñ ÏÈÁfiÙÂÚ· ·applefi 5 Ú˘˙fiÁ·Ï·ñ appleÂÚÈÛÛfiÙÂÚ· ·applefi 5 Ú˘˙fiÁ·Ï·Ú˘˙fiÁ·Ï·. ªÂ 10 ú applefiÛ·→ ∂ϤÁ¯ˆ ÙËÓ ¿appleÔ„‹ ÌÔ˘Ì ˙ˆÁÚ·ÊÈ΋:ºÙÈ¿¯Óˆ Ì ÙËÓ ÔÌ¿‰· ÌÔ˘ ¤Ó· appleÚfi‚ÏËÌ· appleÔÏÏ·appleÏ·ÛÈ·ÛÌÔ‡ appleÔ˘ ÙÔ·appleÔÙ¤ÏÂÛÌ¿ ÙÔ˘ Â›Ó·È ÌÂÁ·Ï‡ÙÂÚÔ ·applefi ÙÔ 40 Î·È ÌÈÎÚfiÙÂÚÔ ·applefi ÙÔ 72.E‚‰ÔÌ‹ÓÙ· ÂÊÙ¿77


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INDEX°ÓˆÛÙÈΤ˜ appleÂÚÈÔ¯¤˜∫ÂÊ¿Ï·È· fiappleÔ˘ ·Ó·appleÙ‡ÛÛÂÙ·È Ô ‚·ÛÈÎfi˜ ÛÙfi¯Ô˜Úfi‚ÏËÌ·:∆· ‚‹Ì·Ù· appleÚÔ˜ ÙË Ï‡ÛË 5, 20, 53∂ÎÙ›ÌËÛË 21, 45, 49, 53∂apple·Ï‹ı¢ÛË 12, 37, 44, 45, 46, 49, 53ÙÚ·ÙËÁÈΤ˜ Âapple›Ï˘Û˘ appleÚÔ‚Ï‹Ì·ÙÔ˜(˙ˆÁÚ·ÊÈ΋, apple›Ó·Î·˜, ‰ÂÓÙÚԉȿÁÚ·ÌÌ·, ÂappleÔappleÙÈÎfi ˘ÏÈÎfi) 3, 22, 30, 37, 45, 46, 49, 50, 53ŒÏÂÁ¯Ô˜, ‰ÈfiÚıˆÛË, Û˘ÌappleÏ‹ÚˆÛË, ηٷÛ΢‹ appleÚÔ‚Ï‹Ì·ÙÔ˜ 20, 21, 23, 49, 53∞ÚÈıÌÔ› – ∞ÚÈıÌÔ› Î·È appleÚ¿ÍÂȘ∞ıÚÔÈÛÙÈ΋ ·Ó¿Ï˘ÛË 10, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30,34, 35, 36, 41, 43, 44, 45, 46, 49, 50, 54∞Í›· ı¤Û˘ „ËÊ›Ô˘2, 6, 9, 7, 34, 35, 36, 41, 43, 54∞Ó¿ÁÓˆÛË, ÁÚ·Ê‹ 2, 6, 7, 41, 54¢Âη‰ÈÎfi Û‡ÛÙËÌ· ·Ú›ıÌËÛ˘ 2, 6, 7, 34, 35, 36, 41, 43, 54¢È¿Ù·ÍË 2, 6, 41, 54∫·Ù·Û΢‹ Û ¿‚·Î· 2, 6, 7, 34, 35, 36, 41, 43, 54·ÚÂÌ‚ÔÏ‹, Û‡ÁÎÚÈÛË 6ºˆÓÔÏÔÁÈ΋ ·Ó¿Ï˘ÛË 2, 6, 7, 34, 35, 36, 41, 43, 54ªÈÛfi / ‰ÈappleÏ¿ÛÈÔ 7, 9∆¯ÓÈΤ˜ οıÂÙ˘ appleÚfiÛıÂÛ˘ Ì ÎÚ·ÙÔ‡ÌÂÓÔ 34T¯ÓÈ΋ οıÂÙ˘ ·Ê·›ÚÂÛ˘ Ì ‰·ÓÂÈÎfi 35, 36ªÂÙÚ‹ÛÂȘªÔÓ¿‰Â˜ ̤ÙÚËÛ˘ ‚¿ÚÔ˘˜: ÁÚ·ÌÌ¿ÚÈÔ, ÎÈÏfi 38, 39, 46ªÔÓ¿‰Â˜ ̤ÙÚËÛ˘ ÂappleÈÊ¿ÓÂÈ·˜ 31ªÔÓ¿‰Â˜ ̤ÙÚËÛ˘ Ì‹ÎÔ˘˜: 4, 15EηÙÔÛÙfiÌÂÙÚÔ, ̤ÙÚÔ 42ªÔÓ¿‰Â˜ ̤ÙÚËÛ˘ ¯ÚfiÓÔ˘:ŒÙÔ˜, Ì‹Ó˜, ‚‰ÔÌ¿‰Â˜, Ë̤ڷ, 32, 33flÚ· (·ÎÚÈ‚Ò˜ Î·È ÌÈÛ‹) 47, 48¡ÔÌ›ÛÌ·Ù· ÙÔ˘ ¢ÚÒ:K¤ÚÌ·Ù· 11X·ÚÙÔÓÔÌ›ÛÌ·Ù· 40ªÔÙ›‚Ô∞ÚÈıÌËÙÈÎfi ÌÔÙ›‚Ô 19, 22°ÂˆÌÂÙÚÈÎfi ÌÔÙ›‚Ô 16°ÂˆÌÂÙÚ›·˘ÌÌÂÙÚ›· 8°ÂˆÌÂÙÚÈο ÛÙÂÚ¿ 13°ÂˆÌÂÙÚÈο Û¯‹Ì·Ù· 3, 7, 13, 14, 15


ªÂ ·applefiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘appleÒÓÔÓÙ·È ·applefi ÙÔÓOÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ µÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ-¿Ó ÛÙ· ¢ËÌfiÛÈ· ¯ÔÏ›·. ∆· ‚È‚Ï›· ÌappleÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È appleÚÔ˜appleÒÏËÛË fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ appleÚÔ˜ ·applefi‰ÂÈÍË Ù˘ ÁÓËÛÈfiÙËÙ¿˜ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘appleÔ appleÔ˘ ‰È·Ù›ıÂÙ·È appleÚÔ˜ appleÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È-‚ÏÈfiÛËÌÔ ıˆÚÂ›Ù·È ÎÏ„›Ù˘appleÔ Î·È Ô apple·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈ-Ó· Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7, ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã).BIB§IOHMO∞apple·ÁÔÚ‡ÂÙ·È Ë ·Ó·apple·Ú·ÁˆÁ‹ ÔappleÔÈÔ˘‰‹appleÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, appleÔ˘Î·Ï‡appleÙÂÙ·È ·applefi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔappleÔÈ·‰‹appleÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ÙË ÁÚ·appleÙ‹ ¿‰ÂÈ· ÙÔ˘ ·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.


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KÂÊ¿Ï·ÈÔ 60 1 23 4 56 7 8 9


KÂÊ¿Ï·È· 4, 8, 14, 42, 51


KÂÊ¿Ï·ÈÔ 3Κεφάλαιο 25


KÂÊ¿Ï·ÈÔ 13


KÂÊ¿Ï·ÈÔ 7


KÂÊ¿Ï·ÈÔ 13


KÂÊ¿Ï·È· 17, 32, 33


KÂÊ¿Ï·È· 17, 32, 33


KÂÊ¿Ï·ÈÔ 47

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