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Understanding Units

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Inches, Square Inches, Cubic Inches     In high school, geometry was my nemesis too, so I completely understand how easy it is for my students to be confused when it comes to labeling answers.  We spent a lot of time early in the year learning about area and surface area.  I think this made it difficult for my class to then understand a linear unit.  When they would have to count the length of a side of a polygon draw on a grid, they would often incorrectly count the squares inside along the length.  To try to help students differentiate between linear, square, and cubic units, I broke out a set of pipe cleaners.     Although a bit floppy, the pipe cleaners served as a good way to model the three different units of measure.  Students went around the room and found various objects to measure and the most appropriate unit with which to measure.  This activity helped students to use the correct unit of measure and led to productive ...
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Surface Area and Nets

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          I always enjoy teaching surface area because there are so many great ways to make it concrete for my students.  In order to build conceptual understanding, students need to be able to physically touch and build polyhedra.  In sixth grade math, we focus on the surface area of rectangular and triangular prisms (http://www.corestandards.org/Math/Content/6/G/A/4/).          The lesson began with a video from Andrew Stadel's Estimation 180 collection called "File Cabinet." (http://www.101qs.com/518-file-cabinet--act-1) I warned students that it might seem strange, but Mr. Stadel was going to cover the cabinet with sticky notes.  They would have to figure out how many sticky notes it would take to cover the cabinet.  Source: Andrew Stadel http://mr-stadel.blogspot.com/2012/04/file-cabinet.html       My students' reaction was priceless - despite the somewhat silliness of the task!  Th...
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Intervention Groupings

     Each year I teach a math intervention course.  This course runs for about 25 minutes, so I don't get very much time to work with my students.  I have to make every minute matter, so each day is very carefully structured.  But this can be very hard to do!  What skills should I cover? Do I have time to get out the manipulatives?  Are number talks worth the time it takes to do them?     I have found a few things do help to make the intervention time successful.  First of all, keep the number of students relatively small.  Less than 20 students is ideal, but under 16 is even better.  When the class is too big, it is very difficult for every student to have a voice.  I need to make sure that I have an opportunity to interact with every student, so keeping the numbers small is important.      Secondly, ditch the worksheets!  The drill and kill approach to reviewing material is ineffective.  S...
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Math Specialist

   I had the opportunity to participate in a year-long study at Saginaw Valley State University in a Mathematics Specialist program sponsored by the Great Lakes Bay Regional Alliance.  During my year of studies, I had spent a lot of time learning how to look at student work.  We teachers learned to ask ourselves, "What does this student know and understand?"  This is good advice.  In order to guide instruction, it is important for teachers to understand their students' thinking.  Spending time conducting student interviews and looking at student work can be an effective way to better understand the thoughts of a middle schooler (or any student).      Although answers can sometimes seem very random and unrelated, students often have some sort of reason for offering a particular solution.  Teachers can ask clarifying questions to help them understand the thought process of their students.  I saw this in action this year when I w...
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