Which is the best deal? Gatorade Introduction to Algebra Problem

Here is a Grocery Store problem.  I went to the store and video taped all the different Gatorade options.  (And yes, I did get some looks at the store)  My student's will have to decide which is the best deal.  I want my students to try to use problem solving skills to get at the best deal.  I want them to struggle a little bit with the complexity of the problem.  They will somehow need to get all of the 5 different options on the same unit measure playing field.   I have given a couple of answers below.  I was looking for students to justify their work with equations, diagrams or graphs.  They are not bound by any particular method.  However, they must show their work and give their answer in complete sentences.  In the video their is an example of what kind of work I expect.  I debated on whether to include this.  My end thinking was that I wanted them to see that their needed to be some work shown and a complete sentence answer. So I showed them a couple of solutions in the video.  But the exemplar solutions are NOT in the worksheet.

Click Here to Get the PDF Worksheet  (see below)

Of course I loved the traditional approach of figuring out the price per oz.  However, if you notice she also write that the Large Can was equal to 3 of the Smaller cans.  (24qts = 3(8qrts))  I love it.

This was a different student's paper.  This was another favorite answer because she wrote a diagram of two of the smaller bottles equaling the larger bottle.



All this really makes me realize how different we think.  I have to get myself out of teaching a certain method and saying that is the only way to do it.  It just is not right.  Think of your choice of cars.  Why are there so many cars choices out there?  It is because we all are different and like different things.  In math, it is the same way.  The plain and simple truth is that understanding our method of choice thoroughly first, then branching out to understanding other answer methods will benefit us.  I know I will forever be learning how to teach better.  This is exciting and daunting at the same time.  I will keep on trying to get better.

Let me know your thoughts?
Dave

Will Froggy get to the other side of the Lake? Solving Trig Equations.

WILL FROGGY GET ACROSS THE LAKE?

Froggy is a mechanical toy Frog.  He follows a sine wave path surfacing every 12 feet.  He dives down 7 feet from the surface along his path.  He is trying to get across Lake Tad which is 120 feet wide..  There is one problem, actually two.  There are two shallow places in the lake that if Froggy hits will break.  That's right.  Froggy will not make it if he hits those shallow spots.   The first low spot is 24 feet from the starting spot.  The second low spot is 51.5 feet from the ending spot.  The video actually will tell you a possible way of solving and the answer.  This is definitely not the only way to solve this question.
Click Here to get the Frogger Worksheet

This activity helps students put a few skills and concepts together.  They need to know how to build a trig equation.  They need to know how to graph a trig equation.  They need to recognize the periodic nature of the trig equation to spot the answer farther out on the graph.  

I had my students make a video of their answer.  I checked out the iPad cart for the day and had students make their videos on the app called DOCERI.  We then uploaded them to our content management system called CANVAS.  At the bottom of this blog, I am giving you an example of one of the solutions.

STUDENT SOLUTION

All the best,
Dave