Vận dụng cặp phạm trù "cái chung - cái riêng" trong dạy học toán ở tiểu học

UAN DUNG CAP PHAM TRU "CAI CHUNG - CAI RIENG

TRONG DAY HOC TOAN 6 TIEU HOC

O ThS. PHAM THI THANH TU*

Tfong chuong trinh todn ndi ehung, mdn Todn

d tieu hpe ndi rieng thudng ddn ddt hpe sinh

(HS) di tir nhtfng trudng hpp rieng rdi khdi

qudt len, duo ve bdi todn (BT) tdng qudt hon. Khi

gidi bdi tdp, HS Iqi vdn dyng nhifng khdi niem

ehung, quy tde tdng qudt vdo tCrng trudng hop

rieng cy the. Ve mat phuong phdp ludn, giira edi

ehung vd edi rieng ed mdi quan he ehdt ehe vdi

nhau: - Mdt cdi rieng ed the Id trudng hop ddc

biet cuo nhieu edi ehung khde nhau; - Mdt edi

ehung dem dqc biet hdo tung bd phdn se eho

nhieu edi rieng khde nhau.

Dudi ddy Id mdt so vi dy minh hpo eho viee vdn

dyng edp phqm tri) «edi ehung - edi rieng" trong

dqy hpe todn d tieu hpe.

1. Dqc biet hda h/ng thdnh phdn cua mdt

BT (edi ehung) se cho nhieu BT mdi (edi rieng)

khde nhau. Thdng thudng, trude mdt BT, HS gdp

khd khdn trong viec tim Idi gidi. Viee dqc biet hdo

cde yeu to cuo BT se tqo ro dupe BT mdi md HS d l

ddng tim dupe Idi gidi hon; Gidi quyet BT mdi se

Id mdt su gpi y, djnh hudng eho viee tim tdi, phdt

hien cdeh gidi BT ban ddu.

Vf dy 1 (edi ehung): Cho tu gide ABCD. Tren

cqnh AD ldy hai diem E, F sao eho: AE = EF =

FD. Tren cqnh BC ldy hoi diem H, G sao cho: BH

= HG = GC. Nd'i EH, FG. Hdy chirng td dien tieh

tu gide EFGH bdng - dien tieh tu gide ABCD

(hinh Ij.

Dinh hudng Idi gidi:

Mdtkhdc,doS^gg + S^ =

3^ADB"'" - S - 3^BDC

- S

3^ABCD nen

^EDGB- T^ABCD(2) . 3 ABCD>

TCr I ), (2)suyraS,p3, = -S^,^ .

<^>

Khai thdc BT: Ddc biet hdo dp ddi cqnh eCra tu

gide ABCD trong vi dy tren, chdng hqn eho cqnh AD

= 0 hoqe cqnh AB = 0 to ed ede BT rieng khde nhau:

BT rieng 1: Cho tom gide ABC, gpi P, Q Id

hai diem thude canh BC sao eho: BP = PQ = QC.

Hdy ehung td dien tieh tom gide APQ bdng -dien

tieh torn gide ABC (hinh 2j.

Dinh hudng Idi gidi: Van dyng tinh ehdt neu

hoi tom gide ed cirng ehieu coo thi dien tieh ti le

thudn vdi dp ddi ddy

hoy tl so dien tieh bdng

ti so dp ddi cuo hai ddy.

BT rieng 2: Cho tom

gide ADC. Gpi M, N Id

hai diem thude cqnh AD

sao cho A M = M N =

ND vd P, Q Id hai diem thude cqnh AC sao eho:

AP = PQ = QC. Hdy ehung td dien tich tu gide

MNQP bdng - dien tieh tam gide ADC (hinh 3j.

Dinh huong Idi gidi:

•^i.i,Kir-. — ^Kif~^r./ ^Av*D— ^kjicr^' L.'O ^nr^/- ~ T *^ •^MNQ NQD' AMP MPQ- •^[X3C 3 "ADC nen

P Q

Hinh 3

SADQ= ySADC'^uy ro

S - i s

^MNQP 3 ^ADC"

Nhdn xet: BT rieng

2 Id mdt trudng

hop ddc biet eua BT

ehung dd eho khi tu gide ABCD cd cqnh AB = 0

hoy triet tieu cqnh AB.

2. Mdt BT (dugc coi Id cdi rieng) cd the Id

trudng hqp dqc biet cua nhieu BT (cdi ehung)

TCf mdt BT (trudng hpp rieng), to md rdng vd'n

de thdnh cde BT mdi (mdt trudng hpp ehung, tdng

qudt). Hay ndi edeh khde, BT ban ddu Id trudng

hpp ddc biet eua ede BT mdi md rdng. Thye te

*TrUoingDaihpcVinli

Tap ehi Giao due 56 25 6 (ki a • a/aon)