Inspirations: Dan issued a challenge, Fawn rocked it months ago, and I tried this once before.

I dug around a little and found this beauty: 

gardens.png

Nothing special. Part a takes all the fun out of it and immediately abstracts the situation into a math problem. No one got a chance to build a garden.

How I would modify it: 

  • Give each student a couple of drinking straws (the length of which would replace the 40 ft. noted in the problem)
  • Take a page in their notebook and draw a line as the fence
  • Give them 10-15 minutes to build a couple gardens/playgrounds/squares, offering no hints as to how they might make the biggest one
  • Compare gardens with their table members, determine which person at the table made the biggest based on sight
  • Calcuate the actual area of their gardens
  • Plot our numbers of width vs. area

From there it could get complex in a number of different ways depending on what you wanted to do.

  • Can we get the same area from two different widths?
  • Is there a definitive "biggest" garden? 
  • Can we generalize the shape of this fence with variables? 
  • What if I added another condition: x fencing and y sod? 
  • What if the existing fence wasn't there? 

And with the idea properly motivated, I might present a scenario like #53 and have them jump right to the function. In fact, a series of problems like that might be the classwork.  If you want a technology angle, I might have them generate something like this:

garden.png

I've had numerous problems trying to jump right in with things like #53 because students don't think in terms of functions. 

This was a fun thought exercise and fun to do with Algebra II. Pre-Cal is proving to be a bit more difficult but I will try. 

 

Posted
AuthorJonathan Claydon