Ask A Scientist Mathematics Archive

Question: I am currently in a teaching program.  Last week I began a part 
of my practicum that has us teaching one lesson per week in the assigned 
school.  My cooperating teacher asked me to introduce circle graphs to her 
sixth graders.  She told me the students were familiar with the process of 
converting fractions to decimals and vice versa.  One third of the way through
my lesson, I realized the majority of the students had no concept of how to do 
this.  I retaught the conversion process and then again had them look at 
circle graphs, yet they still remained confused.  How can I better illustrate 
the circle graph concept and even the fraction to decimal conversion so my 
future students will understand?  Any suggestions will be greatly appreciated.  
Thank you for your time, and I apologize for the lengthy scenario before my 
question.
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I believe a circle graph is just a pie chart showing a fraction  
so a pie cut once through the middle demonstrates 1/2 = 0.5, etc. As for the 
fraction to decimal conversion, I cannot think of any methods other than the 
plain old fashioned long division.  Of course, once you know that 1/8 = 0.125, 
then you know that 3/8 = 3 * 0.125 = 0.375 without having to do the long 
division.  Hope this helps!
John Hawley
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Hawley's hint about how to use 1/8 to get 3/8 is a nice use of 
pattern matching.  But fundamentally, how will the students understand the 
"circle graph" idea?  Basically, it is better to describe it as a pie chart 
because then students can visualize cutting it up just as if it were a pie.  
One way to get the concept across might be to cut up some cardboard "pies" 
into pieces; cut up one into thirds, one into fourths, fifths, eighths, and so 
forth...another would be to split up into groups of 5, hand each group a pie, 
and tell them to draw a piece of paper from a hat. One piece of paper would 
say 3/8 and the rest would say 1/8.  Or, better yet, one could say 0.375 and 
the others 0.125.  Then have them divide up the pie (or pizza) according to 
the numbers they drew.  Hope this helps.
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Topper
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