Excel Project in Calculus part 3

If you need background, see my first post:

First Excel in Calculus post.
** If you want the Word and Excel copies, @me (@robebymathdude) on Twitter **

For this third Excel project, I wanted to stress to the students how much they assume continuity, and how big an impact that assumption plays in their expectations.  I got at this by having them conjecture about important places for the function, and then go back and revise those guesses depending upon some other work. 

This was in the section where we first encountered local extrema, and had spent a good bit of time with rates of change, so I wanted to expand on those ideas.

For the first set, I had displayed some (x,y) pairs, and then had the students guess where the local max occurred after first finding Average Rates of Change (ARC) between each pair of points.  Almost all said it had to be around x=3, and no one mentioned the assumption of continuity.  I then showed them the function with the vertical asymptote (1e below).  About half of the students when answering part (g) mentioned the assumption of continuity, but the other half did not.  

IDSUM is the sum of the digits in their ID number.  This gives related but different problems. 

1.       For the function F-1 (light orange background), we will do some data analysis.

a.       For each pair, find the Average Rate of Change (ARC) between the pair. (The first row is “x” and the bottom row is “y”)

b.       Where (between what x-values) does it appear the ARC becomes zero?  Why?

c.       Find the ARC for the entire data set.  Between what pair of x-values (if anywhere) does it appear the function has the same ARC as the ARC for the entire data set?  Why?

d.       Now find the sum of the digits in your Blinn ID, and call that IDSUM.

e.       Graph the function  

 Include the graph in your write up.  (Desmos, fooplot, or some other graphing device)

f.        Now compute   f(0), f(1), f(2), f(2.5), f(3.5), f(4), f(5), f(6)

g.       How does this change your answers to parts b and c of this question?  What were you assuming about the function F-1 when you answered parts b and c?

For the next parts, I had them repeat the ARC calculations, and then make some projections for future values.  They then compared their guesses with the actual function values.  For the first, the function was

But for the last pair, the function was not linear, but instead exponential:

I then asked the students how the estimates compared to the original estimates, and what assumptions they made. 

Excel Projects in Calculus part 2

This is the second of my posts on Excel projects in Calculus.  I had two main goals with this project.  First, I wanted to explore some limits and see some limitations of technology.  Then I wanted to help explore a type of word problem and drive home the idea of always checking the end points of the interval.  If you need background, see my first post:

First Excel in Calculus post.
** If you want the Word and Excel copies, @me (@robebymathdude) on Twitter **

For question 2, I had the students explore the two limits definitions of e (going to 0 and going to infinity)  You will notice I asked them to look at the formula and then match that formula to the correct limit. 

Then in parts b, d, and d I had them explore the other thing: in Excel there is an overflow error sometimes.  (This is inspired by a twitter conversation Chris Robbins @Grallator  and I had)  There was a good bit of confusion with the students over this, and I had to walk most of them through this to finally get the idea I was aiming at.  Which is fine, but a heads up if you do this in your classes.

The other part of this project was the standard something is out in the water, and we have to decide how far down the shore to run before swimming type of problem.  I used a lifeguard in this case.

I wanted the students to have to wrestle with the boundaries, so I did four different variations on the basic problem.  I first varied the running speed, then the swimming speed, then the total distance along the shore, then the total distance out.  I also arranged the step size for increasing the speeds to make sure we got to the boundary case in most instances.  I then programmed the Excel squares with conditional formatting to highlight red when that happened.  You can see some of that on my example sheet.

This proved interesting, as there were a couple of students who had no red cells.  (It was my fault, they happened to have zeros in just the right places!)  So they asked me, and I started by asking them to compare mine and theirs, and why might I use the color red.  It was generally a good discussion. 

The case where we changed the distance was more trouble for the students, as you ended up with almost a calculus of variations type of problem.  But given they are Calculus I students, most of them gave reasonable answers about what seemed to be happening.

Excel Projects for Calculus - Part 1

Greetings, long time, no post!  Sorry about that, the legislature here in Texas really overhauled the way developmental mathematics (actually all forms) is done, and our department has been in a full scramble trying to navigate that.  (Maybe a few posts on that later, after I survive this semester)

** For the background, read the first post **
First Excel in Calculus post.

Anyway, for the upcoming AMATYC conference

https://amatyc.site-ym.com/page/2018ConfHome?

I will be presenting on Using Excel in Calculus.  (Friday from 3:10 – 4:00 if are you going) and while I have 50 minutes, I am doing five different Excel projects with my Calculus 1 students this semester, so I am blogging about the first few projects to make sure each project is discussed in some detail.

BACKGROUND:

To set the background, Blinn College is a 2 year College, and the Bryan – Villa Maria Campus is about 5 miles from Texas A&M.   Most of our students are trying to transfer to A&M, so we teach a large number of sections of Calculus (32 students each section).  Also, many of the introductory Engineering classes at Texas A&M use Excel, so I wanted to introduce the students to spreadsheets and also have them see their power.  We also have a campus agreement with Microsoft, so there is no problem with cost or access for students to Excel and Word, and I want them to show the formulas they program, so that is why we are using Excel instead of say Google sheets. 

One big thing I learned (this is semester 3 of doing these) is that most of the students had not used a spreadsheet before, and almost a third of them did not know you could program a spread sheet.  This is actually why this first project is so short, it allows the students to learn how to program a spreadsheet to calculate stuff they are already familiar with mathematically. 

On to the assignment:

When I assign this first project, I include three files in the submodule of our Learning Management System (LMS) the instructions (in Word format), the answers for my fake ID number (in PDF format), and an Excel template.  All three are posted below as images, but see the end if you want the original files for your own class.

The instructions have the students first put their own school ID number in the purple boxes, which causes all of the yellow and green cells to change value, as they are programmed off of the ID number.  This is so that each student has their own version, but I can still easily grade them.  The students then calculate some average rates of change with different descriptions of what the numbers are telling us.  (See the details in the instructions) 

When you read the instructions, you might have thought that there is more than one correct answer about the average rate of change for these questions.  Correct!  That is actually one reason I have the students define the function and provide units.  The students often are not consistent about what they program and what the write down.  This is part of the discussion we had in class about how average rate of change is more than speed, but it can apply to any function in all sorts of different contexts.

One thing about this: when I first assign the project, I open the template in class, and show the students how to program the cells.   Then, when I copy/paste, and the formulas compute the answer automatically, there is usually great excitement from the students.  Again, a good number were not aware of this ability in spreadsheets.  This is also a nice time to spend a few moments on the value of algebraic thinking.

Anyway, if you have comments, questions, etc., please let me know.  Thanks for reading.

** If you want the Word and Excel copies, @me (@robebymathdude) on Twitter **

Instructions:

Fake-Answers

With “fake” formulas

  

 Template***