How Can Vector Math Be Fun and Engaging for Students?

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To make vector math engaging for students, incorporate interactive activities such as group problem-solving or real-world applications like physics demonstrations involving work and torque. Utilize visual aids and hands-on tools, like vector addition with arrows, to illustrate concepts like cross and dot products. Encourage students to participate by creating small projects or challenges related to vector properties, such as calculating the volume of a parallelogram. Incorporating technology, such as simulations or online games focused on vectors, can also enhance engagement. Overall, the key is to create a dynamic learning environment that fosters participation and curiosity.
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I need to do a basic review of the general vector concepts like cross and dot product, projections, there applications like work and torque, and volume of a parallelogram and all the basic properties of vectors. Basically I need to present the topic to the class and make my presentation entertaing and I have to engage the class or get the students involved in some way. I barely have any ideas, all i want to do is go up and talk but i need some kind of activity for the students... any suggestions??
 
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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