{"id":413702,"date":"2024-11-28T12:24:50","date_gmt":"2024-11-28T05:24:50","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=413702"},"modified":"2024-11-30T12:33:04","modified_gmt":"2024-11-30T05:33:04","slug":"tai-phan-mem-geogebra","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/tai-phan-mem-geogebra\/","title":{"rendered":"GeoGebra – Ph\u1ea7n m\u1ec1m v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1, c\u00f4ng th\u1ee9c To\u00e1n h\u1ecdc"},"content":{"rendered":"

T\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra – m\u1ed9t c\u00f4ng c\u1ee5 m\u1ea1nh m\u1ebd d\u00e0nh cho h\u1ecdc sinh, gi\u00e1o vi\u00ean v\u00e0 nh\u1eefng ng\u01b0\u1eddi \u0111am m\u00ea to\u00e1n h\u1ecdc. V\u1edbi kh\u1ea3 n\u0103ng v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 v\u00e0 tr\u1ef1c quan h\u00f3a c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc, ph\u1ea7n m\u1ec1m n\u00e0y mang \u0111\u1ebfn s\u1ef1 ti\u1ec7n l\u1ee3i v\u00e0 hi\u1ec7u qu\u1ea3 trong vi\u1ec7c h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y. Kh\u00f4ng ch\u1ec9 gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 th\u1ebf gi\u1edbi to\u00e1n h\u1ecdc m\u1ed9t c\u00e1ch sinh \u0111\u1ed9ng, GeoGebra c\u00f2n h\u1ed7 tr\u1ee3 m\u1ecdi c\u1ea5p \u0111\u1ed9, t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. H\u00e3y tham kh\u1ea3o h\u01b0\u1edbng d\u1eabn sau \u0111\u00e2y \u0111\u1ec3 t\u1ea3i ph\u1ea7n m\u1ec1m n\u00e0y v\u1ec1 m\u00e1y.<\/p>\n

Gi\u1edbi thi\u1ec7u s\u01a1 l\u01b0\u1ee3c v\u1ec1 ph\u1ea7n m\u1ec1m GeoGebra<\/h2>\n

GeoGebra l\u00e0 m\u1ed9t ph\u1ea7n m\u1ec1m to\u00e1n h\u1ecdc \u0111a n\u0103ng, \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 h\u1ed7 tr\u1ee3 h\u1ecdc sinh, gi\u00e1o vi\u00ean v\u00e0 nh\u1eefng ng\u01b0\u1eddi y\u00eau th\u00edch to\u00e1n h\u1ecdc trong vi\u1ec7c h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y. \u1ee8ng d\u1ee5ng n\u00e0y cho ph\u00e9p v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1, bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc v\u00e0 t\u00ednh to\u00e1n c\u00e1c c\u00f4ng th\u1ee9c m\u1ed9t c\u00e1ch tr\u1ef1c quan, d\u1ec5 d\u00e0ng. V\u1edbi giao di\u1ec7n th\u00e2n thi\u1ec7n, t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>\u00a0gi\u00fap ng\u01b0\u1eddi d\u00f9ng kh\u00e1m ph\u00e1 to\u00e1n h\u1ecdc qua nh\u1eefng h\u00ecnh \u1ea3nh s\u1ed1ng \u0111\u1ed9ng v\u00e0 r\u00f5 r\u00e0ng.<\/p>\n

\"tai-phan-mem-geogebra\"<\/p>\n

M\u1ed9t trong nh\u1eefng \u0111i\u1ec3m n\u1ed5i b\u1eadt c\u1ee7a GeoGebra l\u00e0 kh\u1ea3 n\u0103ng t\u00edch h\u1ee3p nhi\u1ec1u c\u00f4ng c\u1ee5 trong c\u00f9ng m\u1ed9t n\u1ec1n t\u1ea3ng. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 v\u1ebd \u0111\u1ed3 th\u1ecb, t\u1ea1o h\u00ecnh h\u1ecdc kh\u00f4ng gian ho\u1eb7c gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ngay tr\u00ean \u1ee9ng d\u1ee5ng. \u0110i\u1ec1u n\u00e0y kh\u00f4ng ch\u1ec9 ti\u1ebft ki\u1ec7m th\u1eddi gian m\u00e0 c\u00f2n t\u0103ng t\u00ednh hi\u1ec7u qu\u1ea3 trong vi\u1ec7c ti\u1ebfp c\u1eadn c\u00e1c kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc ph\u1ee9c t\u1ea1p.<\/p>\n

Ngo\u00e0i ra, GeoGebra c\u00f2n h\u1ed7 tr\u1ee3 nhi\u1ec1u t\u00ednh n\u0103ng h\u1eefu \u00edch nh\u01b0 t\u1ea1o t\u00e0i li\u1ec7u gi\u1ea3ng d\u1ea1y, chia s\u1ebb tr\u1ef1c tuy\u1ebfn v\u00e0 l\u01b0u tr\u1eef d\u1eef li\u1ec7u tr\u00ean \u0111\u00e1m m\u00e2y. \u0110i\u1ec1u n\u00e0y gi\u00fap gi\u00e1o vi\u00ean d\u1ec5 d\u00e0ng tr\u00ecnh b\u00e0y b\u00e0i gi\u1ea3ng, trong khi h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ef1 h\u1ecdc m\u1ecdi l\u00fac, m\u1ecdi n\u01a1i. \u0110\u1eb7c bi\u1ec7t, GeoGebra c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng tr\u00ean nhi\u1ec1u thi\u1ebft b\u1ecb nh\u01b0 m\u00e1y t\u00ednh, \u0111i\u1ec7n tho\u1ea1i v\u00e0 m\u00e1y t\u00ednh b\u1ea3ng, mang l\u1ea1i s\u1ef1 linh ho\u1ea1t cho ng\u01b0\u1eddi d\u00f9ng.<\/p>\n

M\u1ed9t s\u1ed1 \u0111\u1eb7c \u0111i\u1ec3m th\u00f4ng d\u1ee5ng c\u1ee7a ph\u1ea7n m\u1ec1m GeoGebra<\/h2>\n

Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u chi ti\u1ebft h\u01a1n v\u1ec1 c\u00e1ch t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>, ch\u00fang ta s\u1ebd c\u00f9ng kh\u00e1m ph\u00e1 c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m th\u00f4ng d\u1ee5ng c\u1ee7a \u1ee9ng d\u1ee5ng n\u00e0y nh\u00e9. V\u1ec1 c\u01a1 b\u1ea3n, GeoGebra s\u1edf h\u1eefu nhi\u1ec1u \u0111\u1eb7c \u0111i\u1ec3m n\u1ed5i b\u1eadt, mang \u0111\u1ebfn tr\u1ea3i nghi\u1ec7m h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y to\u00e1n h\u1ecdc hi\u1ec7u qu\u1ea3.<\/p>\n

\u0110\u1ea7u ti\u00ean, ph\u1ea7n m\u1ec1m n\u00e0y t\u1ea1o ra m\u1ed9t m\u00f4i tr\u01b0\u1eddng t\u00edch h\u1ee3p \u0111a d\u1ea1ng. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh \u0111\u1ea1i s\u1ed1, v\u1ebd \u0111\u1ed3 th\u1ecb h\u00ecnh h\u1ecdc, v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c ph\u00e9p to\u00e1n s\u1ed1 h\u1ecdc tr\u00ean c\u00f9ng m\u1ed9t giao di\u1ec7n, gi\u00fap ti\u1ebft ki\u1ec7m th\u1eddi gian v\u00e0 d\u1ec5 d\u00e0ng theo d\u00f5i qu\u00e1 tr\u00ecnh l\u00e0m vi\u1ec7c.<\/p>\n

\"tai-phan-mem-geogebra-1\"<\/p>\n

M\u1ed9t \u0111\u1eb7c \u0111i\u1ec3m \u1ea5n t\u01b0\u1ee3ng kh\u00e1c l\u00e0 t\u00ednh linh ho\u1ea1t trong thao t\u00e1c. GeoGebra cho ph\u00e9p t\u1ea1o ra c\u00e1c \u0111\u1ed3 th\u1ecb \u0111\u1ed9ng v\u00e0 t\u01b0\u01a1ng t\u00e1c tr\u1ef1c ti\u1ebfp v\u1edbi ch\u00fang. Vi\u1ec7c \u0111i\u1ec1u ch\u1ec9nh th\u00f4ng s\u1ed1 v\u00e0 quan s\u00e1t s\u1ef1 thay \u0111\u1ed5i tr\u00ean \u0111\u1ed3 th\u1ecb gi\u00fap ng\u01b0\u1eddi d\u00f9ng hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 b\u1ea3n ch\u1ea5t c\u1ee7a c\u00e1c kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc. \u0110\u00e2y l\u00e0 c\u00f4ng c\u1ee5 l\u00fd t\u01b0\u1edfng cho nh\u1eefng ai mu\u1ed1n kh\u00e1m ph\u00e1 c\u00e1c kh\u00eda c\u1ea1nh ph\u1ee9c t\u1ea1p c\u1ee7a \u0111\u1ea1i s\u1ed1 v\u00e0 h\u00ecnh h\u1ecdc.<\/p>\n

Kh\u00f4ng ch\u1ec9 d\u1eebng l\u1ea1i \u1edf vi\u1ec7c v\u1ebd \u0111\u1ed3 th\u1ecb, GeoGebra c\u00f2n h\u1ed7 tr\u1ee3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 nh\u1eadp s\u1ed1 li\u1ec7u, t\u1ea1o bi\u1ec3u \u0111\u1ed3 v\u00e0 th\u1ef1c hi\u1ec7n ph\u00e2n t\u00edch m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng. T\u00ednh n\u0103ng n\u00e0y \u0111\u1eb7c bi\u1ec7t h\u1eefu \u00edch trong vi\u1ec7c nghi\u00ean c\u1ee9u v\u00e0 gi\u1ea3ng d\u1ea1y c\u00e1c b\u00e0i h\u1ecdc v\u1ec1 th\u1ed1ng k\u00ea ho\u1eb7c \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. H\u01a1n n\u1eefa, GeoGebra \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 h\u1ed7 tr\u1ee3 t\u1ed1i \u01b0u cho vi\u1ec7c gi\u1ea3ng d\u1ea1y. Gi\u00e1o vi\u00ean c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u1ea7n m\u1ec1m n\u00e0y \u0111\u1ec3 minh h\u1ecda b\u00e0i gi\u1ea3ng, trong khi h\u1ecdc sinh c\u00f3 th\u1ec3 t\u1ef1 th\u1ef1c h\u00e0nh c\u00e1c b\u00e0i to\u00e1n ngay tr\u00ean \u1ee9ng d\u1ee5ng.<\/p>\n

H\u01b0\u1edbng d\u1eabn t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra mi\u1ec5n ph\u00ed tr\u00ean m\u00e1y t\u00ednh<\/h2>\n

\u0110\u1ec3 t\u1ea3i v\u00e0 c\u00e0i \u0111\u1eb7t GeoGebra mi\u1ec5n ph\u00ed tr\u00ean m\u00e1y t\u00ednh, b\u1ea1n ch\u1ec9 c\u1ea7n th\u1ef1c hi\u1ec7n m\u1ed9t v\u00e0i b\u01b0\u1edbc \u0111\u01a1n gi\u1ea3n. \u0110\u1ea7u ti\u00ean, h\u00e3y truy c\u1eadp trang web ch\u00ednh th\u1ee9c c\u1ee7a GeoGebra th\u00f4ng qua tr\u00ecnh duy\u1ec7t. Tr\u00ean giao di\u1ec7n trang ch\u1ee7, t\u00ecm m\u1ee5c “Download” v\u00e0 ch\u1ecdn phi\u00ean b\u1ea3n GeoGebra Classic 6 ph\u00f9 h\u1ee3p v\u1edbi h\u1ec7 \u0111i\u1ec1u h\u00e0nh m\u00e1y t\u00ednh c\u1ee7a b\u1ea1n.<\/p>\n

\"tai-phan-mem-geogebra-2\"<\/p>\n

Sau khi t\u1ea3i t\u1ec7p c\u00e0i \u0111\u1eb7t v\u1ec1, b\u1ea1n m\u1edf th\u01b0 m\u1ee5c ch\u1ee9a t\u1ec7p v\u00e0 nh\u1ea5p \u0111\u00fap v\u00e0o t\u1ec7p v\u1eeba t\u1ea3i \u0111\u1ec3 b\u1eaft \u0111\u1ea7u qu\u00e1 tr\u00ecnh c\u00e0i \u0111\u1eb7t. M\u1ed9t h\u1ed9p tho\u1ea1i s\u1ebd xu\u1ea5t hi\u1ec7n, y\u00eau c\u1ea7u b\u1ea1n x\u00e1c nh\u1eadn quy\u1ec1n c\u00e0i \u0111\u1eb7t sau khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>.<\/p>\n

\"tai-phan-mem-geogebra-3\"<\/p>\n

T\u1ea1i \u0111\u00e2y, b\u1ea1n ch\u1ecdn “Run” \u0111\u1ec3 ti\u1ebfp t\u1ee5c. Qu\u00e1 tr\u00ecnh c\u00e0i \u0111\u1eb7t s\u1ebd di\u1ec5n ra trong v\u00e0i ph\u00fat, t\u00f9y thu\u1ed9c v\u00e0o c\u1ea5u h\u00ecnh m\u00e1y t\u00ednh.<\/p>\n

\"tai-phan-mem-geogebra-4\"<\/p>\n

Khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra <\/b><\/strong>v\u00e0\u00a0c\u00e0i \u0111\u1eb7t ho\u00e0n t\u1ea5t, b\u1ea1n s\u1ebd th\u1ea5y bi\u1ec3u t\u01b0\u1ee3ng GeoGebra xu\u1ea5t hi\u1ec7n tr\u00ean m\u00e0n h\u00ecnh. Nh\u1ea5p v\u00e0o bi\u1ec3u t\u01b0\u1ee3ng n\u00e0y \u0111\u1ec3 m\u1edf \u1ee9ng d\u1ee5ng v\u00e0 b\u1eaft \u0111\u1ea7u kh\u00e1m ph\u00e1 c\u00e1c c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc m\u00e0 ph\u1ea7n m\u1ec1m mang l\u1ea1i. N\u1ebfu c\u1ea7n thi\u1ebft, b\u1ea1n c\u00f3 th\u1ec3 t\u00f9y ch\u1ec9nh ng\u00f4n ng\u1eef ho\u1eb7c giao di\u1ec7n \u0111\u1ec3 ph\u00f9 h\u1ee3p v\u1edbi nhu c\u1ea7u s\u1eed d\u1ee5ng.<\/p>\n

\"tai-phan-mem-geogebra-5\"<\/p>\n

\u0110\u1eb7c bi\u1ec7t, qu\u00e1 tr\u00ecnh t\u1ea3i v\u00e0 c\u00e0i \u0111\u1eb7t n\u00e0y ho\u00e0n to\u00e0n mi\u1ec5n ph\u00ed. GeoGebra lu\u00f4n l\u00e0 m\u1ed9t l\u1ef1a ch\u1ecdn tuy\u1ec7t v\u1eddi cho nh\u1eefng ai mu\u1ed1n c\u1ea3i thi\u1ec7n hi\u1ec7u qu\u1ea3 h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y to\u00e1n h\u1ecdc.<\/p>\n

C\u00e1ch s\u1eed d\u1ee5ng ph\u1ea7n m\u1ec1m GeoGebra \u0111\u1ec3 v\u1ebd \u0111\u1ed3 th\u1ecb<\/h2>\n

S\u1eed d\u1ee5ng GeoGebra \u0111\u1ec3 v\u1ebd \u0111\u1ed3 th\u1ecb l\u00e0 m\u1ed9t tr\u1ea3i nghi\u1ec7m \u0111\u01a1n gi\u1ea3n v\u00e0 th\u00fa v\u1ecb, \u0111\u1eb7c bi\u1ec7t sau khi b\u1ea1n \u0111\u00e3 t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra <\/b><\/strong>v\u1ec1 m\u00e1y t\u00ednh. \u0110\u1ea7u ti\u00ean, m\u1edf \u1ee9ng d\u1ee5ng GeoGebra v\u00e0 tr\u00ean m\u00e0n h\u00ecnh ch\u00ednh, b\u1ea1n s\u1ebd th\u1ea5y \u00f4 nh\u1eadp ph\u01b0\u01a1ng tr\u00ecnh. T\u1ea1i \u0111\u00e2y, h\u00e3y nh\u1eadp ph\u01b0\u01a1ng tr\u00ecnh m\u00e0 b\u1ea1n mu\u1ed1n v\u1ebd, ch\u1eb3ng h\u1ea1n y=x2+3x+2. Ngay sau \u0111\u00f3, \u0111\u1ed3 th\u1ecb s\u1ebd t\u1ef1 \u0111\u1ed9ng hi\u1ec3n th\u1ecb tr\u00ean m\u00e0n h\u00ecnh, gi\u00fap b\u1ea1n quan s\u00e1t tr\u1ef1c quan k\u1ebft qu\u1ea3.<\/p>\n

\"tai-phan-mem-geogebra-6\"<\/p>\n

N\u1ebfu b\u1ea1n mu\u1ed1n s\u1eed d\u1ee5ng th\u00eam c\u00e1c c\u00f4ng c\u1ee5 h\u1ed7 tr\u1ee3, h\u00e3y v\u00e0o m\u1ee5c “Graphing” v\u00e0 ch\u1ecdn bi\u1ec3u t\u01b0\u1ee3ng h\u00ecnh m\u0169i t\u00ean. T\u1ea1i \u0111\u00e2y, nhi\u1ec1u t\u00f9y ch\u1ecdn nh\u01b0 \u0111i\u1ec3m, \u0111o\u1ea1n th\u1eb3ng, hay vect\u01a1 s\u1ebd hi\u1ec7n ra, h\u1ed7 tr\u1ee3 vi\u1ec7c ph\u00e2n t\u00edch v\u00e0 gi\u1ea3i th\u00edch \u0111\u1ed3 th\u1ecb m\u1ed9t c\u00e1ch r\u00f5 r\u00e0ng h\u01a1n.<\/p>\n

\"tai-phan-mem-geogebra-7\"<\/p>\n

\u0110\u1ed1i v\u1edbi c\u00e1c b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p h\u01a1n khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra <\/b><\/strong>v\u00e0 s\u1eed d\u1ee5ng, t\u00ednh n\u0103ng 3D Calculator trong GeoGebra cho ph\u00e9p b\u1ea1n v\u1ebd \u0111\u1ed3 th\u1ecb kh\u00f4ng gian ba chi\u1ec1u. Ch\u1ec9 c\u1ea7n nh\u1eadp ph\u01b0\u01a1ng tr\u00ecnh li\u00ean quan \u0111\u1ebfn tr\u1ee5c x, y, v\u00e0 z, \u1ee9ng d\u1ee5ng s\u1ebd hi\u1ec3n th\u1ecb h\u00ecnh h\u1ecdc 3D tr\u1ef1c quan.<\/p>\n

\"tai-phan-mem-geogebra-8\"<\/p>\n

Ngo\u00e0i ra, n\u1ebfu b\u1ea1n mu\u1ed1n l\u01b0u b\u00e0i to\u00e1n ho\u1eb7c \u0111\u1ed3 th\u1ecb v\u1eeba v\u1ebd, h\u00e3y v\u00e0o bi\u1ec3u t\u01b0\u1ee3ng d\u1ea5u ba g\u1ea1ch ngang \u1edf g\u00f3c tr\u00ean m\u00e0n h\u00ecnh, ch\u1ecdn “Save” v\u00e0 \u0111\u1eb7t t\u00ean t\u1ec7p. T\u00ednh n\u0103ng n\u00e0y r\u1ea5t ti\u1ec7n l\u1ee3i \u0111\u1ec3 l\u01b0u tr\u1eef v\u00e0 chia s\u1ebb d\u1eef li\u1ec7u khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra <\/b><\/strong>v\u00e0 s\u1eed d\u1ee5ng.<\/p>\n

\"tai-phan-mem-geogebra-9\"<\/p>\n

Cu\u1ed1i c\u00f9ng, b\u1ea1n c\u00f3 th\u1ec3 t\u00f9y ch\u1ec9nh giao di\u1ec7n ph\u1ea7n m\u1ec1m, bao g\u1ed3m ng\u00f4n ng\u1eef, k\u00edch th\u01b0\u1edbc ch\u1eef, v\u00e0 c\u00e1c t\u00f9y ch\u1ecdn kh\u00e1c trong m\u1ee5c “Settings”. \u0110\u1eebng qu\u00ean l\u01b0u l\u1ea1i thay \u0111\u1ed5i b\u1eb1ng c\u00e1ch nh\u1ea5n “Save Settings”.<\/p>\n

C\u00e1c t\u00ednh n\u0103ng \u0111\u1eb7c tr\u01b0ng khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra v\u00e0 s\u1eed d\u1ee5ng<\/h2>\n

V\u1ec1 c\u01a1 b\u1ea3n, GeoGebra s\u1ebd \u0111i k\u00e8m v\u1edbi m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng \u0111\u1eb7c tr\u01b0ng so v\u1edbi c\u00e1c ph\u1ea7n m\u1ec1m v\u1ebd \u0111\u1ed3 th\u1ecb kh\u00e1c. C\u1ee5 th\u1ec3 nh\u01b0:<\/p>\n

Graphing Calculator<\/h3>\n

Graphing Calculator l\u00e0 m\u1ed9t t\u00ednh n\u0103ng n\u1ed5i b\u1eadt trong GeoGebra, mang \u0111\u1ebfn kh\u1ea3 n\u0103ng v\u1ebd v\u00e0 t\u00ednh to\u00e1n \u0111\u1ed3 th\u1ecb tr\u1ef1c quan v\u00e0 hi\u1ec7u qu\u1ea3. Sau khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ti\u1ec7n \u00edch n\u00e0y \u0111\u1ec3 nh\u1eadp c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc v\u00e0 xem k\u1ebft qu\u1ea3 \u0111\u1ed3 th\u1ecb ngay l\u1eadp t\u1ee9c. T\u00ednh n\u0103ng n\u00e0y h\u1ed7 tr\u1ee3 nhi\u1ec1u lo\u1ea1i \u0111\u1ed3 th\u1ecb kh\u00e1c nhau nh\u01b0 h\u00e0m s\u1ed1, \u0111\u01b0\u1eddng th\u1eb3ng, parabol, elip v\u00e0 hyperbol, \u0111\u00e1p \u1ee9ng nhu c\u1ea7u h\u1ecdc t\u1eadp v\u00e0 nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc.<\/p>\n

M\u1ed9t \u0111i\u1ec3m \u0111\u00e1ng ch\u00fa \u00fd c\u1ee7a Graphing Calculator l\u00e0 kh\u1ea3 n\u0103ng ph\u00e2n t\u00edch c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 t\u00ecm c\u00e1c \u0111i\u1ec3m quan tr\u1ecdng nh\u01b0 \u0111i\u1ec3m c\u1eaft, c\u1ef1c tr\u1ecb, \u0111i\u1ec3m u\u1ed1n ho\u1eb7c gi\u00e1 tr\u1ecb bi\u00ean c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n

\"tai-phan-mem-geogebra-10\"<\/p>\n

Ngo\u00e0i ra, ph\u1ea7n m\u1ec1m c\u00f2n t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c v\u00e0 c\u00e1c gi\u00e1 tr\u1ecb kh\u00e1c li\u00ean quan \u0111\u1ebfn bi\u1ec3u \u0111\u1ed3, gi\u00fap vi\u1ec7c ph\u00e2n t\u00edch h\u00e0m s\u1ed1 tr\u1edf n\u00ean d\u1ec5 d\u00e0ng v\u00e0 chi ti\u1ebft. Khi b\u1ea1n thay \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c bi\u1ec3u th\u1ee9c, \u0111\u1ed3 th\u1ecb s\u1ebd t\u1ef1 \u0111\u1ed9ng c\u1eadp nh\u1eadt, mang l\u1ea1i s\u1ef1 linh ho\u1ea1t v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n

T\u00ednh n\u0103ng t\u01b0\u01a1ng t\u00e1c c\u0169ng l\u00e0 m\u1ed9t \u01b0u \u0111i\u1ec3m c\u1ee7a Graphing Calculator. B\u1ea1n c\u00f3 th\u1ec3 ph\u00f3ng to, thu nh\u1ecf, di chuy\u1ec3n ho\u1eb7c \u0111i\u1ec1u ch\u1ec9nh c\u00e1c tham s\u1ed1 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 quan s\u00e1t s\u1ef1 thay \u0111\u1ed5i c\u1ee7a \u0111\u1ed3 th\u1ecb. \u0110\u1eb7c bi\u1ec7t, GeoGebra c\u00f2n cho ph\u00e9p l\u01b0u l\u1ea1i c\u00e1c \u0111\u1ed3 th\u1ecb \u0111\u00e3 v\u1ebd, qua \u0111\u00f3 gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng truy c\u1eadp v\u00e0 t\u00e1i s\u1eed d\u1ee5ng khi c\u1ea7n thi\u1ebft.<\/p>\n

GeoGebra 3D Graphing Calculator<\/h3>\n

GeoGebra 3D Graphing Calculator l\u00e0 m\u1ed9t t\u00ednh n\u0103ng \u0111\u1eb7c bi\u1ec7t gi\u00fap ng\u01b0\u1eddi d\u00f9ng v\u1ebd v\u00e0 t\u01b0\u01a1ng t\u00e1c v\u1edbi c\u00e1c \u0111\u1ed3 th\u1ecb trong kh\u00f4ng gian ba chi\u1ec1u. Sau khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>, b\u1ea1n c\u00f3 th\u1ec3 nh\u1eadp c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u1ea1o c\u00e1c m\u00f4 h\u00ecnh 3D nh\u01b0 m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng cong, hay c\u00e1c b\u1ec1 m\u1eb7t ph\u1ee9c t\u1ea1p. T\u00ednh n\u0103ng n\u00e0y mang \u0111\u1ebfn g\u00f3c nh\u00ecn tr\u1ef1c quan h\u01a1n v\u1ec1 c\u00e1c kh\u00e1i ni\u1ec7m h\u00ecnh h\u1ecdc v\u00e0 \u0111\u1ea1i s\u1ed1 trong kh\u00f4ng gian.<\/p>\n

Ph\u1ea7n m\u1ec1m cung c\u1ea5p nhi\u1ec1u c\u00f4ng c\u1ee5 h\u1ed7 tr\u1ee3 m\u1ea1nh m\u1ebd cho vi\u1ec7c ph\u00e2n t\u00edch \u0111\u1ed3 th\u1ecb 3D. B\u1ea1n c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m c\u1eaft, \u0111i\u1ec3m u\u1ed1n, c\u1ef1c tr\u1ecb ho\u1eb7c t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng cong. Nh\u1eefng t\u00ednh to\u00e1n n\u00e0y gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c thu\u1ed9c t\u00ednh kh\u00f4ng gian c\u1ee7a c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc, ph\u1ee5c v\u1ee5 t\u1ed1t cho vi\u1ec7c h\u1ecdc t\u1eadp v\u00e0 nghi\u00ean c\u1ee9u.<\/p>\n

\"tai-phan-mem-geogebra-11\"<\/p>\n

\u0110\u1eb7c bi\u1ec7t, t\u00ednh n\u0103ng t\u01b0\u01a1ng t\u00e1c c\u1ee7a GeoGebra 3D Graphing Calculator cho ph\u00e9p b\u1ea1n xoay, ph\u00f3ng to, thu nh\u1ecf ho\u1eb7c di chuy\u1ec3n c\u00e1c m\u00f4 h\u00ecnh. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng quan s\u00e1t c\u00e1c chi ti\u1ebft c\u1ee7a \u0111\u1ed3 th\u1ecb t\u1eeb nhi\u1ec1u g\u00f3c \u0111\u1ed9 kh\u00e1c nhau, t\u1ea1o ra tr\u1ea3i nghi\u1ec7m h\u1ecdc to\u00e1n sinh \u0111\u1ed9ng v\u00e0 th\u00fa v\u1ecb.<\/p>\n

Ngo\u00e0i ra, c\u00e1c \u0111\u1ed3 th\u1ecb 3D sau khi ho\u00e0n th\u00e0nh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef \u0111\u1ec3 t\u00e1i s\u1eed d\u1ee5ng ho\u1eb7c chia s\u1ebb trong c\u00e1c b\u00e0i gi\u1ea3ng v\u00e0 t\u00e0i li\u1ec7u h\u1ecdc t\u1eadp. \u0110\u00e2y l\u00e0 c\u00f4ng c\u1ee5 h\u1eefu \u00edch cho gi\u00e1o vi\u00ean, h\u1ecdc sinh v\u00e0 nh\u1eefng ai \u0111am m\u00ea kh\u00e1m ph\u00e1 to\u00e1n h\u1ecdc kh\u00f4ng gian.<\/p>\n

T\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra \u0111\u1ec3 s\u1eed d\u1ee5ng t\u00ednh n\u0103ng GeoGebra Geometry<\/h3>\n

GeoGebra Geometry l\u00e0 m\u1ed9t t\u00ednh n\u0103ng m\u1ea1nh m\u1ebd d\u00e0nh cho vi\u1ec7c v\u1ebd v\u00e0 ph\u00e2n t\u00edch c\u00e1c h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. Trong GeoGebra, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5 n\u00e0y \u0111\u1ec3 t\u1ea1o ra c\u00e1c h\u00ecnh nh\u01b0 \u0111o\u1ea1n th\u1eb3ng, tam gi\u00e1c, h\u00ecnh ch\u1eef nh\u1eadt, \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 nhi\u1ec1u h\u00ecnh kh\u00e1c. Vi\u1ec7c v\u1ebd h\u00ecnh tr\u1edf n\u00ean \u0111\u01a1n gi\u1ea3n nh\u1edd giao di\u1ec7n tr\u1ef1c quan, gi\u00fap ng\u01b0\u1eddi d\u00f9ng thao t\u00e1c nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n

M\u1ed9t \u0111i\u1ec3m n\u1ed5i b\u1eadt c\u1ee7a GeoGebra Geometry l\u00e0 kh\u1ea3 n\u0103ng t\u01b0\u01a1ng t\u00e1c \u0111\u1ed9ng. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 di chuy\u1ec3n c\u00e1c \u0111i\u1ec3m, c\u1ea1nh ho\u1eb7c g\u00f3c \u0111\u1ec3 quan s\u00e1t s\u1ef1 thay \u0111\u1ed5i trong h\u00ecnh h\u1ecdc. V\u00ed d\u1ee5, khi k\u00e9o m\u1ed9t \u0111\u1ec9nh tam gi\u00e1c, c\u00e1c c\u1ea1nh li\u00ean quan s\u1ebd t\u1ef1 \u0111\u1ed9ng \u0111i\u1ec1u ch\u1ec9nh \u0111\u1ec3 ph\u1ea3n \u00e1nh m\u1ed1i quan h\u1ec7 h\u00ecnh h\u1ecdc m\u1edbi.<\/p>\n

\"tai-phan-mem-geogebra-12\"<\/p>\n

T\u00ednh n\u0103ng \u0111o l\u01b0\u1eddng trong GeoGebra Geometry c\u0169ng r\u1ea5t h\u1eefu \u00edch. Ph\u1ea7n m\u1ec1m h\u1ed7 tr\u1ee3 \u0111o \u0111\u1ed9 d\u00e0i, di\u1ec7n t\u00edch, chu vi, v\u00e0 c\u1ea3 g\u00f3c gi\u1eefa c\u00e1c \u0111o\u1ea1n th\u1eb3ng. C\u00e1c ph\u00e9p \u0111o n\u00e0y \u0111\u01b0\u1ee3c hi\u1ec3n th\u1ecb ngay tr\u00ean h\u00ecnh, gi\u00fap vi\u1ec7c t\u00ednh to\u00e1n tr\u1edf n\u00ean tr\u1ef1c quan v\u00e0 d\u1ec5 hi\u1ec3u.<\/p>\n

Ngo\u00e0i ra, GeoGebra Geometry c\u00f2n gi\u00fap gi\u00e1o vi\u00ean t\u1ea1o c\u00e1c b\u00e0i gi\u1ea3ng sinh \u0111\u1ed9ng, d\u1ec5 ti\u1ebfp c\u1eadn. C\u00e1c h\u00ecnh h\u1ecdc \u0111\u01b0\u1ee3c minh h\u1ecda r\u00f5 r\u00e0ng, h\u1ed7 tr\u1ee3 vi\u1ec7c gi\u1ea3ng d\u1ea1y v\u00e0 h\u1ecdc t\u1eadp m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3. H\u1ecdc sinh c\u00f3 th\u1ec3 th\u1ef1c h\u00e0nh tr\u1ef1c ti\u1ebfp tr\u00ean ph\u1ea7n m\u1ec1m \u0111\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c.<\/p>\n

Resources<\/h3>\n

T\u00ednh n\u0103ng Resources<\/b><\/strong>\u00a0trong GeoGebra cung c\u1ea5p m\u1ed9t kho t\u01b0 li\u1ec7u phong ph\u00fa, h\u1ed7 tr\u1ee3 h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y to\u00e1n h\u1ecdc hi\u1ec7u qu\u1ea3. Sau khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>, ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 truy c\u1eadp h\u00e0ng ng\u00e0n b\u00e0i gi\u1ea3ng, t\u00e0i li\u1ec7u h\u01b0\u1edbng d\u1eabn v\u00e0 s\u00e1ch tham kh\u1ea3o li\u00ean quan \u0111\u1ebfn to\u00e1n h\u1ecdc c\u0169ng nh\u01b0 c\u00e1c l\u0129nh v\u1ef1c li\u00ean quan. C\u00e1c t\u00e0i nguy\u00ean n\u00e0y \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf tr\u1ef1c quan, gi\u00fap vi\u1ec7c ti\u1ebfp c\u1eadn ki\u1ebfn th\u1ee9c tr\u1edf n\u00ean d\u1ec5 d\u00e0ng h\u01a1n.<\/p>\n

M\u1ed9t \u0111i\u1ec3m \u0111\u00e1ng ch\u00fa \u00fd l\u00e0 GeoGebra c\u00f2n cung c\u1ea5p c\u00e1c \u0111\u1ed3 th\u1ecb v\u00e0 b\u00e0i gi\u1ea3ng t\u01b0\u01a1ng t\u00e1c. Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y c\u00e1c \u0111\u1ed3 h\u1ecda, b\u00e0i gi\u1ea3ng minh h\u1ecda s\u1eb5n \u0111\u1ec3 s\u1eed d\u1ee5ng trong gi\u1ea3ng d\u1ea1y ho\u1eb7c l\u00e0m b\u00e0i t\u1eadp th\u1ef1c h\u00e0nh. T\u00ednh n\u0103ng n\u00e0y mang l\u1ea1i s\u1ef1 thu\u1eadn ti\u1ec7n l\u1edbn, \u0111\u1eb7c bi\u1ec7t v\u1edbi gi\u00e1o vi\u00ean v\u00e0 h\u1ecdc sinh.<\/p>\n

\"tai-phan-mem-geogebra-13\"<\/p>\n

Ph\u1ea7n m\u1ec1m h\u1ed7 tr\u1ee3 t\u00ecm ki\u1ebfm t\u00e0i nguy\u00ean theo t\u1eeb kh\u00f3a, ch\u1ee7 \u0111\u1ec1 ho\u1eb7c m\u1ee9c \u0111\u1ed9 kh\u00f3. C\u00e1c t\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i r\u00f5 r\u00e0ng theo t\u1eebng m\u1ea3ng ki\u1ebfn th\u1ee9c, \u0111\u1ed9 tu\u1ed5i ho\u1eb7c lo\u1ea1i n\u1ed9i dung, gi\u00fap b\u1ea1n nhanh ch\u00f3ng l\u1ef1a ch\u1ecdn t\u00e0i li\u1ec7u ph\u00f9 h\u1ee3p v\u1edbi nhu c\u1ea7u s\u1eed d\u1ee5ng. Ngo\u00e0i ra, ng\u01b0\u1eddi d\u00f9ng c\u00f2n c\u00f3 th\u1ec3 \u0111\u00f3ng g\u00f3p t\u00e0i nguy\u00ean c\u1ee7a m\u00ecnh v\u00e0o kho t\u00e0i li\u1ec7u chung, qua \u0111\u00f3 t\u1ea1o n\u00ean m\u1ed9t c\u1ed9ng \u0111\u1ed3ng chia s\u1ebb tri th\u1ee9c r\u1ed9ng l\u1edbn.<\/p>\n

M\u1ed9t s\u1ed1 ph\u1ea7n m\u1ec1m v\u1ebd \u0111\u1ed3 th\u1ecb kh\u00e1c tr\u00ean m\u00e1y t\u00ednh n\u1ed5i b\u1eadt hi\u1ec7n nay<\/h2>\n

Hi\u1ec7n nay, c\u00f3 nhi\u1ec1u ph\u1ea7n m\u1ec1m h\u1ed7 tr\u1ee3 v\u1ebd \u0111\u1ed3 th\u1ecb tr\u00ean m\u00e1y t\u00ednh v\u1edbi c\u00e1c t\u00ednh n\u0103ng n\u1ed5i b\u1eadt, \u0111\u00e1p \u1ee9ng nhu c\u1ea7u h\u1ecdc t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y hi\u1ec7u qu\u1ea3.<\/p>\n

Microsoft Mathematics<\/strong> l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 ti\u1ec7n l\u1ee3i kh\u00e1c, \u0111\u1eb7c bi\u1ec7t ph\u00f9 h\u1ee3p v\u1edbi h\u1ecdc sinh. Ph\u1ea7n m\u1ec1m n\u00e0y h\u1ed7 tr\u1ee3 v\u1ebd \u0111\u1ed3 th\u1ecb, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh c\u01a1 b\u1ea3n m\u1ed9t c\u00e1ch nhanh ch\u00f3ng. Gi\u1ed1ng nh\u01b0 khi t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>, ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 t\u1ea1o ra c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc tr\u1ef1c quan v\u00e0 d\u1ec5 d\u00e0ng thao t\u00e1c.<\/p>\n

Ngo\u00e0i GeoGebra, Desmos <\/b><\/strong>c\u0169ng l\u00e0 m\u1ed9t ph\u1ea7n m\u1ec1m ph\u1ed5 bi\u1ebfn, \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf v\u1edbi giao di\u1ec7n th\u00e2n thi\u1ec7n v\u00e0 d\u1ec5 s\u1eed d\u1ee5ng. Desmos t\u1eadp trung v\u00e0o vi\u1ec7c v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 v\u00e0 cung c\u1ea5p t\u00ednh n\u0103ng t\u01b0\u01a1ng t\u00e1c \u0111\u1ed9ng, cho ph\u00e9p ng\u01b0\u1eddi d\u00f9ng thay \u0111\u1ed5i tham s\u1ed1 v\u00e0 quan s\u00e1t k\u1ebft qu\u1ea3 ngay l\u1eadp t\u1ee9c.<\/p>\n

\"tai-phan-mem-geogebra-14\"<\/p>\n

Mathematica<\/strong> l\u00e0 m\u1ed9t ph\u1ea7n m\u1ec1m chuy\u00ean s\u00e2u d\u00e0nh cho nh\u1eefng ai c\u1ea7n x\u1eed l\u00fd c\u00e1c b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p. Ph\u1ea7n m\u1ec1m n\u00e0y h\u1ed7 tr\u1ee3 v\u1ebd \u0111\u1ed3 th\u1ecb 2D, 3D v\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u chi ti\u1ebft. Tuy nhi\u00ean, chi ph\u00ed s\u1eed d\u1ee5ng c\u00f3 th\u1ec3 kh\u00e1 cao \u0111\u1ed1i v\u1edbi m\u1ed9t s\u1ed1 ng\u01b0\u1eddi d\u00f9ng.<\/p>\n

Cu\u1ed1i c\u00f9ng, Microsoft Mathematics<\/b><\/strong>\u00a0l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 ti\u1ec7n l\u1ee3i kh\u00e1c, \u0111\u1eb7c bi\u1ec7t ph\u00f9 h\u1ee3p v\u1edbi h\u1ecdc sinh. Ph\u1ea7n m\u1ec1m n\u00e0y h\u1ed7 tr\u1ee3 v\u1ebd \u0111\u1ed3 th\u1ecb, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh c\u01a1 b\u1ea3n m\u1ed9t c\u00e1ch nhanh ch\u00f3ng.<\/p>\n

T\u1ea1m k\u1ebft<\/h2>\n

V\u1edbi s\u1ef1 k\u1ebft h\u1ee3p gi\u1eefa c\u00f4ng ngh\u1ec7 hi\u1ec7n \u0111\u1ea1i v\u00e0 t\u00ednh \u1ee9ng d\u1ee5ng cao, vi\u1ec7c t\u1ea3i ph\u1ea7n m\u1ec1m GeoGebra<\/b><\/strong>\u00a0\u0111ang ng\u00e0y c\u00e0ng \u0111\u01b0\u1ee3c y\u00eau th\u00edch v\u00e0 s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i. \u0110\u00e2y th\u1ef1c s\u1ef1 l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 c\u1ea7n thi\u1ebft trong h\u00e0nh tr\u00ecnh chinh ph\u1ee5c to\u00e1n h\u1ecdc. B\u00ean c\u1ea1nh \u0111\u00f3, b\u1ea1n c\u0169ng c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam m\u1ed9t s\u1ed1 b\u00e0i vi\u1ebft th\u1ee7 thu\u1eadt \u0111\u00e1ng ch\u00fa \u00fd kh\u00e1c t\u1ea1i trang tin nhanh c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<\/p>\n

Xem th\u00eam:<\/p>\n