Sunday, January 29, 2012

Complex Fractions in Algebra 2

I just came up with this warm up to spice up my lesson on simplifying complex fractions:

Suppose a mother and daughter decide to make a pie. 

(a)   A pecan pie to be specific.  The slave over it all day, and they are so engrossed by their pie baking that they forget to eat.  By the time the pie is ready, they’re both starving.  Suppose the mom eats twice as much as her daughter.  They’re both so hungry that they eat the whole pie.  There is 1 pie to be divided by 1 adult appetite and the little girl has ½ of an adult appetite. 

      (1)     Write a fraction that represents this situation
      (2)       How much of the pie will the mom get?  How much of the pie will the little girl get?

(b)  On another day, the mother daughter pair make an apple pie.  The father LOVES apple pie.  He comes home and shares in the eating with his wife and daughter.  So now there’s 1 pie, 2 adult appetites and a ½ an adult appetite.

   (1)       Write a fraction that represents this situation
   (2)       How much of the pie will the mom get?  How much will the dad get?  How much will the little girl get?

(c)   The mom and the dad have decided to have another baby.  This time, it’s a baby boy.  The baby boy also loves pie, but because he’s growing, the fraction of the pie that he can eat keeps changing, so let’s just let the fraction that he can eat be represented by 1/x.  The mom and the daughter again go back to pie baking and one day, they make a blueberry pie.  All four family members split the pie to match their appetites.

        (1)      Write a fraction that represents this situation
        (2)        Write an expression for how many pieces they’ll need to cut the pie into.

I like this warm up in that I think it shows pretty clearly why we would want to simplify complex fractions, but I'm thinking that it's going to be pretty time consuming, and won't even begin to address how to simplify complex fractions.  I so badly want to show students the why of math, but the how of math is all we have time for and that's what they're tested on.  

Note: I know this problem is a little sexist.  I thought I could insert students actual names when it came to teaching this so that it's not so blatantly- mom and daughter bake while father and son eat.

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