Drill bit fractions

Act One:  Drill bits are measured by the diameter of the bit in inches. The drill bits below are ordered left to right in increasing size. The numerators in the fractions have been blacked out.  What could the numerators be?  Explain your reasoning. 

Act Two:  Useful info:  Fraction Strip Diagram up to 1/16 for exploring equivalent fractions.  Note: You could have students work in groups to make their own fraction strips up to 1/64.  Technology: supplement this lesson with this interactive equivalent fraction app from NCTM Illuminations.  Finally, consider this video on Visualizing Equivalent Fractions from Khan Academy. 

Act Three:  Click here to see the actual numerators. 

Extension: Create up your own set of drill bits.  Give them fractional lengths and order them from least to greatest going left to right.  Be sure to use at least three different denominators in the lengths of your drill bits. 

Extension Two: Lets go back to the original picture.  What if we black out the 1 in the numerator from the first and last drill bits as pictured here?  Remember that the bits increase in size from left to right.  Thinking about all of the drill bits, what numerators or sets of numerators are possible?

Task notes: These pics can be used to think about, compare and order fractions. They give students a real life context to consider as they think about fractions.  When we ask students to think about what the numerators could be we assume students are thinking in whole numbers.  If appropriate for your class or particular students you could open the numerator to all rational numbers.