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Samenvatting Wiskunde 2
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Samenvatting powerpoints wiskunde 2 - Noemie Slaets - 1e jaar BOLO (semester 2) - - Geslaagd met 17/20
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By: chelseyvanheste • 4 months ago
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ambercloetens
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WISKUNDE 2Amber Cloetens
BOLO 1A
,DEEL 1: DIDACTISCHE RICHTLIJNEN ............................................................................................................. - 8 -
WAAR HAALT DE LERAAR INHOUDEN........................................................................................................................ - 8 -
DIDACTISCHE KRACHTLIJNEN .................................................................................................................................. - 8 -
1/ Betekenisvolle situaties ......................................................................................................................... - 8 -
2/ CSA-model ............................................................................................................................................. - 9 -
3/ Handelingsniveaus van Galperin ......................................................................................................... - 10 -
4/ Inzichtelijke aanpak ............................................................................................................................. - 10 -
5/ Belang van correct wiskundig verwoorden.......................................................................................... - 10 -
6/ Automatiseren – Memoriseren............................................................................................................ - 10 -
7/ Inductief werken .................................................................................................................................. - 10 -
8/ Gebruik van verhoudingstabellen ........................................................................................................ - 11 -
DEEL 2: GETALLENKENNIS ......................................................................................................................... - 12 -
1/ FUNCTIES VAN GETALLEN ..................................................................................................................... - 12 -
BASISKENNIS..................................................................................................................................................... - 12 -
LEERLIJN .......................................................................................................................................................... - 12 -
INHOUD/DIDACTIEK ........................................................................................................................................... - 12 -
1/ Getal als hoeveelheid .......................................................................................................................... - 12 -
2/ Getal als rangorde ............................................................................................................................... - 13 -
3/ Getal als code ...................................................................................................................................... - 13 -
4/ Getal als verhouding............................................................................................................................ - 14 -
5/ Getal als maatgetal ............................................................................................................................. - 14 -
Aandachtspunten ..................................................................................................................................... - 14 -
Inoefenen ................................................................................................................................................. - 15 -
2/ TALSTELSELS ......................................................................................................................................... - 16 -
BASISKENNIS ............................................................................................................................................ - 16 -
DOELEN .................................................................................................................................................... - 16 -
LEERLIJN .......................................................................................................................................................... - 16 -
INHOUD/DIDACTIEK ................................................................................................................................. - 16 -
1/ ADDITIEVE SYSTEMEN ..................................................................................................................................... - 17 -
1/ Egyptisch talstelsel .............................................................................................................................. - 17 -
2/ Romeins talstelsel ................................................................................................................................ - 17 -
Aandachtspunten ................................................................................................................................................. - 17 -
Regels.................................................................................................................................................................... - 18 -
Voorbeelden en inoefenen ................................................................................................................................... - 18 -
2/ POSITIESYSTEMEN ......................................................................................................................................... - 19 -
1/ Twintigdelig stelsel van de Maya’s ...................................................................................................... - 19 -
2/ Tiendelig of decimaal stelsel................................................................................................................ - 20 -
Regels.................................................................................................................................................................... - 21 -
Notatie .................................................................................................................................................................. - 21 -
Kardinatie ............................................................................................................................................................. - 21 -
Translatie .............................................................................................................................................................. - 22 -
Tellen .................................................................................................................................................................... - 22 -
Ordinatie ............................................................................................................................................................... - 22 -
Inoefenen.............................................................................................................................................................. - 23 -
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,3/ GETALVERZAMELINGEN ........................................................................................................................ - 24 -
BASISKENNIS ............................................................................................................................................ - 24 -
DOELEN .................................................................................................................................................... - 24 -
LEERLIJN .......................................................................................................................................................... - 24 -
INHOUD/DIDACTIEK ................................................................................................................................. - 24 -
OVERZICHT ....................................................................................................................................................... - 24 -
1/ NATUURLIJKE GETALLEN .................................................................................................................................. - 25 -
Inoefenen ................................................................................................................................................. - 25 -
Aandachtspunten ..................................................................................................................................... - 25 -
2/ GEHELE GETALLEN ......................................................................................................................................... - 25 -
Negatieve getallen leren en schrijven ...................................................................................................... - 25 -
Gehele getallen interpreteren .................................................................................................................. - 26 -
Gehele getallen ordenen .......................................................................................................................... - 26 -
Verschil bepalen tussen 2 gehele getallen ............................................................................................... - 26 -
Inoefenen ................................................................................................................................................. - 26 -
3/ RATIONALE GETALLEN..................................................................................................................................... - 26 -
4/ BREUKEN .............................................................................................................................................. - 27 -
BASISKENNIS ............................................................................................................................................ - 27 -
DOELEN .................................................................................................................................................... - 27 -
LEERLIJN .......................................................................................................................................................... - 27 -
INHOUD/DIDACTIEK ................................................................................................................................. - 27 -
BREUKBEGRIP ................................................................................................................................................... - 27 -
Een geheel verdelen in gelijke delen ........................................................................................................ - 27 -
1/ Concrete fase ................................................................................................................................................... - 27 -
2/ Schematische fase ............................................................................................................................................ - 28 -
Teller, noemer, breukstreep ..................................................................................................................... - 28 -
VERSCHIJNINGSVORMEN ..................................................................................................................................... - 29 -
1/ De breuk als resultaat van een verdeelsituatie ................................................................................... - 29 -
1.1/ De breuk als deel van 1 geheel...................................................................................................................... - 29 -
1.2/ De breuk als deel van een hoeveelheid......................................................................................................... - 29 -
2/ Breuk als operator ............................................................................................................................... - 30 -
3/ Breuk als getal ..................................................................................................................................... - 30 -
4/ Breuk als verhouding ........................................................................................................................... - 30 -
5/ Breuk als kans ...................................................................................................................................... - 31 -
SOORTEN BREUKEN ............................................................................................................................................ - 32 -
1/ Stambreuken ....................................................................................................................................... - 32 -
2/ Gelijknamige breuken .......................................................................................................................... - 32 -
3/ Gelijkwaardige breuken....................................................................................................................... - 32 -
4/ Echte en onechte breuken ................................................................................................................... - 33 -
BREUKEN VEREENVOUDIGEN ................................................................................................................................ - 33 -
BREUKEN GELIJKNAMIG MAKEN ............................................................................................................................ - 33 -
BREUKEN VERGELIJKEN ....................................................................................................................................... - 34 -
Fase 1: stambreuken vergelijken.............................................................................................................. - 34 -
Fase 2: gelijknamige breuken vergelijken ................................................................................................ - 35 -
Fase 3: gerelateerde breuken vergelijken ................................................................................................ - 35 -
Fase 4: ongelijknamige breuken vergelijken ............................................................................................ - 35 -
Inoefenen ................................................................................................................................................. - 35 -
RELATIE BREUKEN, KOMMAGETALLEN, PROCENTEN ................................................................................................... - 36 -
Hulpkaarten ............................................................................................................................................. - 36 -
Inoefenen ................................................................................................................................................. - 36 -
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, 5/ KOMMAGETALLEN ............................................................................................................................... - 37 -
BASISKENNIS ............................................................................................................................................ - 37 -
DOELEN .................................................................................................................................................... - 37 -
LEERLIJN .......................................................................................................................................................... - 37 -
INHOUD/DIDACTIEK ................................................................................................................................. - 37 -
BEGRIPPEN ....................................................................................................................................................... - 37 -
AANKNOPINGSPUNTEN LEERLIJN ........................................................................................................................... - 38 -
AANBRENG ....................................................................................................................................................... - 38 -
Geldrekenen ............................................................................................................................................. - 38 -
Uitbreiding positiestelsel.......................................................................................................................... - 38 -
CSA................................................................................................................................................................ - 39 -
INOEFENEN....................................................................................................................................................... - 39 -
6/ PROCENTEN.......................................................................................................................................... - 40 -
BASISKENNIS ............................................................................................................................................ - 40 -
DOELEN .................................................................................................................................................... - 40 -
LEERLIJN .......................................................................................................................................................... - 40 -
INHOUD/DIDACTIEK ................................................................................................................................. - 40 -
BEGINSITUATIE .................................................................................................................................................. - 40 -
AANBRENG VAN HET BEGRIP ................................................................................................................................ - 40 -
VISUEEL VOORSTELLEN ........................................................................................................................................ - 41 -
1/ Concreet .............................................................................................................................................. - 41 -
2/ Schematisch ......................................................................................................................................... - 41 -
3/ Abstract ............................................................................................................................................... - 41 -
RELATIEVE BETEKENIS ......................................................................................................................................... - 41 -
TOEPASSINGEN ................................................................................................................................................. - 42 -
1/ Procent als operator ............................................................................................................................ - 42 -
4 mogelijke oplossingsmethodes .......................................................................................................................... - 42 -
2de soort oefeningen: Hoeveel procent bedraagt het deel van het geheel? ........................................................ - 43 -
3de soort oefeningen: Hoeveel bedraagt het geheel?........................................................................................... - 43 -
2/ Procent in vergelijkingssituaties .......................................................................................................... - 44 -
3/ Groeipercentages ................................................................................................................................ - 45 -
1ste soort oefeningen: een hoeveelheid vermeerderen met een % (toename) à EINDWAARDE ONBEKEND .... - 45 -
2ste soort oefeningen: een hoeveelheid vermeerderen met een % (toename) à BEGINWAARDE ONBEKEND .. - 46 -
3de soort oefeningen: een hoeveelheid vermeerderen met een % (toename) à TOENAME ONBEKEND ......... - 46 -
4de soort oefeningen: Een hoeveelheid verminderen met een % (afname) à EINDWAARDE ONBEKEND.......... - 47 -
5de soort oefeningen: Een hoeveelheid verminderen met een % (afname) à BEGINWAARDE ONBEKEND ....... - 47 -
6de soort oefeningen: Een hoeveelheid verminderen met een % (afname) à AFNAME ONBEKEND .................. - 47 -
7/ VEELVOUDEN EN DELERS ...................................................................................................................... - 48 -
BASISKENNIS ............................................................................................................................................ - 48 -
DOELEN .................................................................................................................................................... - 48 -
LEERLIJN .......................................................................................................................................................... - 48 -
INHOUD/DIDACTIEK ................................................................................................................................. - 48 -
BASISBEGRIPPEN EN KENMERKEN .......................................................................................................................... - 48 -
Veelvouden .............................................................................................................................................. - 48 -
Kleinste gemeenschappelijk veelvoud ...................................................................................................... - 48 -
Delers ....................................................................................................................................................... - 50 -
Even of oneven ......................................................................................................................................... - 51 -
Grootste gemeenschappelijke deler ......................................................................................................... - 51 -
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