Monday, January 30, 2017

Linear Interpolation

Graphic, Progress, Chart, Representation
I am teaching a new math class this semester called the Mathematics of Animation.  It is based off of and uses much of the material from Pixar in a Box at Khan Academy.  Normally I would use most of the material but our bandwidth sucks and I cannot get all the students online to do everything online.  To make it count as a math credit, I choose one or two topics per unit and go into more detail.

So in this case, the topic is linear interpolation which is a way to fill in values you might not have otherwise.  It involves finding the slope and using that to help find your next number.  I would use it to find the value between the 2nd and 3rd dots.  Assuming the x value of the 2nd dot is 9.5 and the 3rd dot is 13.90, I can use it to find the value for x = 11.

 So far, the linear interpolation is being used in the context of the frame and time associated with the animation of a ball.   I began by teaching it in a general sense of the steps needed in the process.  I used the chart which connected the viscosity of water to its temperature.  I wanted to give it to them in several different contexts so they might see how it applied to different situations.

The second context was population growth between two different years.  Same process but a different context.  I was able to show the slope as the population increase each year.  This context worked out much better because they could relate to population growth much better than the viscosity of water. 

For the third context, I took them back to their original context.  The final context was the easiest as it is what they saw when creating animation but they still struggled with the process.  Since I'm a bit frustrated, I looked on the web for ideas on ways to teach this topic but I didn't find anything other than what I was doing. 

I found lots of worksheets, a few videos, and other materials but no articles on ways to teach it effectively.  I did find a super mathematical article on it but nothing I could use with my students.

So I am wondering is there a better way to teach this topic or is it have them find the slope between the two points, find the distance between the original x value and the new x value to find the amount of increase before adding it to the original y value. 

Does anyone have any suggestions?  I'd love to hear from anyone on this topic.  Thank you.