Using Fractions to Make Cookies

For a concluding lesson before winter break my students will be mixing the dry ingredients for a chocolate chip cookie lesson.  While I have done this before, I have never had the opportunity to allow every 6th grade student to participate.  This is usually due to the cost of purchasing large quantities of cookie material; however, this year I applied for a grant to use for "Hands on Math" activities that would be embedded throughout the year.  I was lucky enough to receive $500 and so the cookie's have begun.

Students were given the Nestle Toll House recipe and needed to make half the recipe, double the recipe, and quadruple the recipe.  Some of the ingredients were easy to double, half, and quadruple such as eggs, and any denomination of 1, but others they struggled with.

The recipe required 2 1/4 Cups of Flour.  To cut this in half many students were baffled.  Well do we multiple it or divide it or what? These were common questions ultimately followed by I don't get it.  Students immediately turned to procedural ways of solving the problem, but couldn't decide what would work or even make sense of a reasonable answer such as half of 2 1/4 would be 1 1/2?  There was a large gap between using common sense and a dependence on procedural methods.  I am not sure how to break this.  Once we drew a picture the students could answer the problem easily, as the math truly shouldn't have been above their level, but what does it take to link these three processes together: procedural, conceptual, and common sense?

I am starting to believe that it must be instilled at a very young age, and by 6th grade it takes lots of going backwards/re-teaching for them to be comfortably with a picture as an answer or for them to reason about mathematics.  Unfortunately I am always disheartened by only seeing students for a year and knowing that mostly they will be moved back to procedures within the following years; and ultimately we do not do enough tasks or have enough time for all students to truly get it through manipulatives.


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