Samenvatting wiskunde 2: wiskunde = wijs periode 1
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Course
Wiskunde 2
Institution
Karel De Grote-Hogeschool (KdG)
Book
Wiskunde = Wijs !
Dit is een samenvatting van alles wat je moet leren voor het examen van de eerste periode. Ik weet dat het weinig pagina's lijken in verhouding met het dikke boek, maar alles staat er in. (+ppt) Bekijk zelf goed wat jij moet kennen in het leerstof overzicht. Er staan lesideeën in en nog veel meer....
9. EXTRA: GEBRUIK V VERHOUDINGSTABELLEN...................................7
DEEL 2: GEÏNTEGREERDE OEFENINGEN................................................7
10. PROBLEEMOPLOSSEND DENKEN & METACOGNITIE.........................7
Metacognitie.......................................................................................................................................................................7
Probleemoplossend denken...............................................................................................................................................7
Fase 1 analyseren..........................................................................................................................................................8
Fase 2 model opbouwen/kiezen...................................................................................................................................8
Fase 3 wiskundige technieken toepassen.....................................................................................................................8
Fase 4: interpreteren & controleren.............................................................................................................................8
Klassieke fouten v lln.....................................................................................................................................................9
Organisatie les...............................................................................................................................................................9
1 vraagstuk/probleem aanbieden............................................................................................................................9
2 leergesprek............................................................................................................................................................9
3 zelfstandig oplossen..............................................................................................................................................9
4 wat zijn de gevonden strategieën.........................................................................................................................9
5 proces evaluatie...................................................................................................................................................10
Aandachtspunten........................................................................................................................................................10
!! Bordschema !!..........................................................................................................................................................10
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,11. ONGELIJKE VERDELINGEN & MENGSELS.......................................10
Ongelijke verdelingen.......................................................................................................................................................10
Meer dan/ minder dan................................................................................................................................................10
Keer meer dan/ keer minder dan................................................................................................................................10
Aandachtspunten........................................................................................................................................................10
Mengsels...........................................................................................................................................................................11
Type 1 zoek de totale hoeveelheid.............................................................................................................................11
Type 2 zoek de verhoudingen.....................................................................................................................................12
Type 3 zoek de delen...................................................................................................................................................12
DEEL 3 MEETKUNDE.........................................................................13
13. VORMLEER................................................................................. 14
Vlakke figuren...................................................................................................................................................................14
Veelhoeken VS niet-veelhoeken.................................................................................................................................14
eerste graad.................................................................................................................................................................15
2e graad........................................................................................................................................................................15
3e graad........................................................................................................................................................................15
veelhoeken..................................................................................................................................................................16
Driehoeken DH.......................................................................................................................................................16
Vierhoeken.............................................................................................................................................................17
Bijkomende eigenschappen...................................................................................................................................21
Eigenschappen v diagonalen..................................................................................................................................21
Meer-hoeken..........................................................................................................................................................21
Niet-veelhoeken..........................................................................................................................................................21
Cirkel.......................................................................................................................................................................21
Ruimte figuren..................................................................................................................................................................22
Veelvlakken & niet-veelvlakken..................................................................................................................................22
Veelvlakken indelen volgens aantal zijden..................................................................................................................23
Kubus......................................................................................................................................................................23
Balk.........................................................................................................................................................................24
Niet-veelvlakken..........................................................................................................................................................24
Ontwikkeling v ruimte fig............................................................................................................................................25
Kubus......................................................................................................................................................................25
Balk.........................................................................................................................................................................25
14. MEETKUNDIGE RELATIES.............................................................26
Evenwijdige & loodrechte stand......................................................................................................................................26
Snijdende & evenwijdige rechten in het vlak..............................................................................................................26
loodrechte stand..............................................................................................................................................................26
DEEL 4 METEN EN METEND REKENEN................................................26
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,15. DE MEETLEERLIJN (PPT)..............................................................26
Fase 1 kwalitatief meten..................................................................................................................................................26
Voorwerpen kwalitatief vergelijken............................................................................................................................26
Rangschikken obv een kwalitatieve vergelijking.........................................................................................................27
samenstellen en optellen v gelijksoortige grootheden...............................................................................................27
Fase 2a kwantitatieve fase...............................................................................................................................................27
Fase 2b kwantitatieve fase...............................................................................................................................................27
16. FORMULES................................................................................. 27
Omtrek..............................................................................................................................................................................27
F1 Kwalitatief vergelijken............................................................................................................................................27
F2a Natuurlijke maateenheden...................................................................................................................................28
F2b standaardmaateenheden.....................................................................................................................................28
omtrek v niet-veelhoeken......................................................................................................................................28
Oppervlakte (opp)............................................................................................................................................................29
F1 vergelijken...............................................................................................................................................................29
Op elkaar leggen (eerste graad).............................................................................................................................29
Knippen & plakken (2e graad).................................................................................................................................29
Meestal omstructureren (3e graad)........................................................................................................................29
F2a natuurlijke maateenheden...................................................................................................................................29
F2b standaardmaateenheden.....................................................................................................................................29
Rechthoek....................................................................................................................................................................30
Paralellogram...............................................................................................................................................................30
Driehoek......................................................................................................................................................................31
Driehoek als helft v parallellogram........................................................................................................................31
Driehoek als helft v rechthoek...............................................................................................................................31
Ruit...............................................................................................................................................................................32
Omstructureren tot parallellogram........................................................................................................................32
Ruit aanvullen tot rechthoek..................................................................................................................................32
Opp v niet-veelhoeken................................................................................................................................................32
Grillige figuren........................................................................................................................................................32
Opp v cirkel.............................................................................................................................................................33
Opp v ruimte fig...........................................................................................................................................................33
Balk.........................................................................................................................................................................33
Kubus......................................................................................................................................................................34
cilinder....................................................................................................................................................................34
Volume.............................................................................................................................................................................34
Balk..............................................................................................................................................................................35
Kubus...........................................................................................................................................................................35
, Automatiseren & memoriseren
Inductief werken
Gebruik v verhoudingstabellen
2. Betekenisvolle situaties
Lln komen constant in contact met situaties die ze kunnen wiskundig kunnen
doorgronden
Lkr moet zorgen dat lln verband leren zien tss wiskunde & realiteit
Gebruik wiskundig denkproces
1. Stel essentiële elementen & relaties vo uit situatie
2. Stel wiskundig model op waar die elementen & relaties inzitten op passende wijze
3. Pas binnen model wiskundige technieken toe om tot resultaten te komen
4. Controleer & interpreteer de resultaten op ≠ manieren
Lkr zet steeds betekenisvolle situatie centraal zodat lln link tss situatie & wiskunde beter
kunnen inzien
Gebruikt betekenisvolle situaties
- Om inzicht te krijgen in begrip
- Bij inoefenen v leerstof
- Bij afsluiten v les om leerstof toe te passen op realistische situaties
Aandachtspunten
- Centraal stellen v relatie tss situatie & realiteit
- Ontdekken v praktisch & maatschappelijk nu
- Betrekken v betekenisvolle situaties verhoogt motivatie
3. CSA-model
Wiskunde = zeer abstract
In lessen moeten we lln tot die abstractie brengen
Vo ied een proces
Gebruik hulpmiddelen -> CSA-model
Concreet – schematisch – abstract
Concreet
Lln leren motorisch handelen met materiaal dat ze kunnen manipuleren
Didactisch, alledaags, keuze materiaal
Bv pizza
materiaal
Schematisch
Lln leren do gebruik v schematische voorstellingen
Opbouw
1. Afbeelding v werkelijkheid bv 10 noten tekenen op bord
2. Afbeelding die in de plaats komt v werkelijkheid bv 10 kruisjes ipv noten tekenen
3. Afbeelding v gestructureerde materiaal
4. Tabellen
5. Getallenlijnen
6. Figuren bv vierhoek is ook schema
4
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