Vectors in Real Life

  I usually teach vectors about once every other year and usually when I have to teach a semester or two of physics because its easy to integrate vectors there but easier than in Math.  Vectors are one of those topics that are much harder to teach without a context.

I had to do a bit of research so I can teach it in my College Prep math class.  I needed to know more about their use in the real world because its important to show relationships and connections.

Many of the ways vectors are used in real life are done so without using the word vector.  This is a good thing to shae with students. So on to the way vectors are used in real life.

1.  Air traffic controllers give pilots a specific heading (direction) with a specific distance (magnitude) along the planned route.Vectors are also used in flight patterns to take into account the wind blowing with or against or cross the plane's flight.

2.Vectors are used to aim cannons and other heavy artillery.

3. In baseball, any player must run in a certain direction going a certain distance in order to intercept a ball.  The player also has to predict where the ball will be to catch it, not aim for where it is now.

4. In basketball, football and golf, the player uses vectors to determine the trajectory of the ball in order to make a basket, get it to the right player to get it to the goal or in the hole.  In football, the quarterback must take his own movement into account, the receiver's movement and the path of ball, all of which can be represented by vector arrows.

5.  When someone asks for directions, they are given them via vectors such as two blocks left, then three blocks right.

6.  Many video games such as Angry Birds use vectors in the shooting of birds at objects.  The vectors include the amount of the pull used to launch the bird and  the angle of launch.  This is actually the most relevant use of vectors for my students.  Vectors are used in video game development to describe the location of an objects or physical simulations of objects.

There you have it, six different situations where vectors are used.  No one thinks of arrows or directions with speed but they use it every day instinctively.  If people want they can create a diagram of a football play off of the television or a shot from a basketball game but we know what we are doing without knowing all the proper mathematical terms.

Let me know what you think.  I'd love to hear.

6.

Orienteering, Etc and Vectors

  I wanted to find more hands on activities for my students so when I teach vectors they don't have to only use the book or worksheets.  I want them to experience a chance to experience vectors personally.  So as a continuation to yesterdays blog, I've found a few more activities that sound fun.

1.  Orienteering with vectors.  This is a lovely exercise where students orienteer around the school, keeping track of distance and direction, so they can create a scale model of their path.  This activity helps teach resultant vector.  The lesson plan gives enough information so you can set up such a course in your school.

2. Navigational Vectors is a site with 8 piloting lessons based on vectors.  These are called piloting lessons designed to help students navigate the skies.  The first lesson introduces vectors by having the student calculate the distance between their town and the state capital.  It covers displacement, reading maps, determining vectors and scalars in real situations.  Each lesson teaches more about vectors including taking into account wind and finding the arrival time.  At the end, a student can take the "Pilot Test Flight" which has the students use all their knowledge to complete this activity.

Although the lessons are just directions, they are clear and each lesson has students completing an activity that practices the application of what they are learning.  In addition, the starting point is the student's home state and it assumes there is an airport in the town so the student can do the work.  Every thing is clear and laid out in steps.

3. As a way to introduce vector addition, Mythbusters has two different videos that show a great introduction to vectors.  In addition, this video shows a truck speeding down the road with a ball being fired out the back to show vector addition.   Either of these would provide a great introduction to the topic.

4.  What about using vectors to create a dance?  At Teach Mathematics, there is a very short description talking about using vectors to show the choreography of a dance.  Imagine giving your students (the more artistic ones) a chance to use vectors to create a dance that could be performed by a small group of people as a the product for a project? 

5. Finally what about relating vectors to the game "Angry Birds"?
a. This  video that introduces vectors and scalars using angry birds before beginning the lecture.  Its short but great.
b. This PDF of an article at Mathematic Shed relates parabolas and vectors to angry birds in a fun way with precise examples. 


The last example could also be used when teaching parabolas.  I'm getting ready to teach factoring to Algebra II and  I think I'll sneak this material in there, just before I begin vectors so that I'll have a nice topic to use to tie the two topics together.

Vectors, Vectors, and More Vectors.

  Around the time I teach matrices, I also teach vectors to another class.  I'm always on the lookout for ways to teach vectors that show students they mean something other than the dry material found in the textbook.

This activity is a great way to introduce the use of vectors though a treasure hunt.  It is a seven page PDF showing how vectors are used to find the treasure using a program from the Concordia Consortium.  The material is older but it could easily be adjusted to use google earth for the map.  You could also use the original island map with annotation tools.

Teach Engineering has a lovely activity that combines history, vectors,  and geography together in an activity designed to show students how dead reckoning relates to vectors.  The lesson explains that vectors are used to show fluid movement in many branches of engineering before explaining dead reckoning to the students.

Although the lesson itself is paper based, it would be easy to scan into the computer to upload so students could use a program or app that allows them to draw or easily erase mistakes.  It has everything needed except for colored pencils.  Just download and go.

 Jen Silver's Math Bloghas a lovely activity for creating a vector maze.  The activity comes with an example to show how its done.  Then students are expected to try it themselves.  The idea is the student creates the smallest sum of lengths wins.  There are rules they have to follow about setting up the vectors but it requires thought and lots of planning.  I looked at it and immediately wanted to try it myself.

In addition, she provides a free downloadable PDF file with 8 different templates for students to use.  The starting and finishing point may be different or the walls within the maze may change so this activity can provide lots of challenges for your students.

This site has a lovely video on Vectors in Climbing which talks about how vectors are used in climbing.  It introduces using vectors in a real life situation while introducing the topic, talking about adding vectors using two different methods, decomposition of vectors, and vectors and angles.

In addition, there is a paper from a lady in Norway who made the video and refers to it in the paper.  Its a well written paper with some very good information.  It relates body geometry to vectors and climbing academically.

More tomorrow on orienteering and other activities that help students learn vectors.