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Học sinh sẽ nắm được khái niệm cơ bản của tọa độ và véc tơ, bao gồm cách xác định tọa độ của một điểm và cách biểu diễn một véc tơ trong hệ tọa độ.

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Học sinh sẽ biết cách ứng dụng kiến thức về tọa độ và véc tơ vào giải quyết các bài toán thực tế, chẳng hạn như bài toán chuyển động và lực.

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Làm thế nào để chúng ta xác định tọa độ của một điểm trong hệ tọa độ? Véc tơ là gì và làm sao để biểu diễn một véc tơ?

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Giáo viên trình bày về cách xác định tọa độ của một điểm và cách biểu diễn véc tơ trong hệ tọa độ. Giáo viên có thể sử dụng Padlet để chia sẻ các ví dụ minh họa.

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Học sinh thực hiện các bài tập nhỏ về việc xác định tọa độ của điểm và biểu diễn véc tơ dưới sự hướng dẫn của giáo viên. Học sinh có thể thảo luận nhóm và gửi kết quả lên Padlet.

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Find the length of a line segment and the coordinates of its midpoint. Draw the line segment in the coordinate system :

Find the coordinates of a vector given by two points and calculate the size of a vector. Draw a vector in the coordinate system :

Find the coordinates of vectors -v, 2v, -2.5v and draw the vectors in the coordinate system, if :

Find out whether the given vectors are linearly dependent (collinear). If so, find the coefficient of collinearity k :

Consider three vectors u = (-1;5), v = (2.7;3.8), w = (4.2;-6). Find the coordinates of vectors :

Find the scalar product of vectors :

Find the size of the angle between vectors :

Find out whether the given vectors are perpendicular to each other :

Consider two vectors u = (3;-2), v = (-1; b). Determine the parameter b so that :

Find the vector u that is perpendicular to the vector v = (3;4) and the size of which is 15.

Prove that the triangle ABC, A[16;1;-2], B[-9;1;-2], C[0;1;10], is right-angled. Find its perimeter, area and the size of its internal angles.

Consider three points A[0;1;2], B[1;2;0], C[2;0;1].

a) Prove that the points A, B, C form a triangle.
b) Find the size of the internal angle α.
c) Find the length of the median of side a and the coordinates of the centroid T.
d) Find the perimeter of the triangle ABC.
e) Find the area of the triangle ABC.

You might be also interested in:

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Mathematics exercises. Find the coordinates of a vector, size of a vector, angle between two vectors and the scalar product of vectors on Math-Exercises.com.

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Học sinh tự làm các bài tập về tọa độ và véc tơ từ các tài liệu tự học hoặc trang web học trực tuyến. Kết quả được nộp lại cho giáo viên để đánh giá.

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Học sinh sẽ được chia thành các nhóm nhỏ và giao nhiệm vụ giải quyết một vấn đề liên quan đến tọa độ và véc tơ. Mỗi nhóm sẽ trình bày kết quả trên Padlet.

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Disney Editable design templates featuring beloved classics

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Group activity Vectors & Illustrations for Free Download | Freepik

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Find & Download the most popular Group Activity Vectors on Freepik ✓ Free for commercial use ✓ High Quality Images ✓ Made for Creative Projects. #freepik #vector

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Giáo viên sẽ quan sát và kiểm tra sự tham gia của học sinh trong các hoạt động thực hành có hướng dẫn và hoạt động nhóm.

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Học sinh sẽ làm một bài kiểm tra ngắn để đánh giá mức độ hiểu biết về tọa độ điểm và tọa độ véc tơ.

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7.2 Vectors in the coordinate plane | Quizizz

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7.2 Vectors in the coordinate plane quiz for 11th grade students. Find other quizzes for and more on Quizizz for free!

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Học sinh sẽ thảo luận về những gì mình đã học được trong bài học và những ứng dụng thực tế của kiến thức này.

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Mỗi học sinh sẽ viết một phiếu thoát để tóm tắt những điểm chính của bài học và tự đánh giá mức độ hiểu biết của mình.

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Học sinh sẽ hoàn thành các bài tập về tọa độ được giao về nhà giúp củng cố kiến thức đã học.

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Học sinh sẽ hoàn thành các bài tập về véc tơ nhằm rèn luyện kỹ năng giải bài toán liên quan đến véc tơ.

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Học sinh có thể truy cập các trang web học trực tuyến để tiếp tục ôn tập và nâng cao kiến thức về tọa độ và véc tơ.

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Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School:

"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

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maths numeracy starter mathematics math topics teacher

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Vectors Lesson Starters and Online Activities

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Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!!Keep it up and thank you!"