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Heads Up! Linear Measurement Misconception!

While working with 5th graders today, I was reminded  about the misconceptions they have when measuring with a ruler.  Normally students are asked to measure to the nearest half or fourth of an inch.  First of all, what does nearest really mean?  We assume that 10 and 11 year old children know what nearest means…but do they?  Our number one mistake as educators–especially new educators is that we assume students know the meaning of things they often do not…only as a reflective experienced teacher do we figure this out. (had to take that rabbit trail!)  Back to measurement–once students are taught that nearest means closest we think we are in the clear, but, NOPE, we still have another problem.  When you as the teacher say, “measure to the nearest half.”  Students think that the only halves are the numbers that have halves written in them.  For example, students think that the answer has to be 1/2, 1 1/2, 2 1/2, 3 1/2 and so on.  They fail to bring their fraction understanding of wholes being two halves with them.  Students can understand that measuring to the nearest half could mean the measurement  might be a whole number (which is made up of halves) when they compare a linear ruler to wholes of a fraction like 2/2.  This same misconception occurs when students are asked to measure to the nearest 1/4.  Students think you are literally asking them to measure to only the nearest one-fourth.  Even if a measurement is 2 inches, students will say that the measurement is 2 1/4 because they hear the phrase literally.

In the example below, students who have misconceptions measuring to the nearest 1/4 will, for example, say that this marker measures to be 5 1/4 because they are looking for the number 1/4 instead of the nearest 1/4 increment.  In actuality, the marker measures to be 5 1/2 in., and students will only understand that this is the same as 2/4 through work with equivalent fractions.  Please excuse the insurance advertisement on the ruler :/.   This was the only ruler I had available at the time.

 

I will be posting more soon about teaching linear measurement :).  Come back soon!

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