Edges, Vertices, Polyhedra, Cones and Cylinders, OH MY!

Today a group of grade 3 students asked if cylinders and cones had edges (the line where the flat face meets the curved face) and if the point on a cone is a vertex.  

If you consider the textbook definition, an edge is the line where two faces meet and faces are always flat surfaces.  A vertex is the point where three edges meet.  Given these definitions, cylinders and cones have neither vertices or edges.

But I know that the point of a cone is called a vertex, because the axis of a cone is a line through the vertex and the center of the base.  If the point of a cone is a vertex, then do cones and cylinders have edges?

I looked on the web (Math Forum) and found that the textbook definitions are for polyhedra, i.e. 3D shapes made up of only flat faces.  The problem is that there is no other word to label the place where the flat face meets the curved face on either a cylinder or a cone.  Math Forum recommended extending some definitions:  edges would still be the line where two faces meet but we could have a "curved edge" (both words are necessary).  A face is flat but we could have a "curved face" (again, both words necessary).  So a cylinder would have two faces and one curved face, and two curved edges but no vertex.  A cone would have one face and one curved face, one curved edge, and a vertex.  But this seems a bit confusing for me, let alone the kids.

So does anyone else have any definitive mathematical terms or solutions to this?

Multiplication/Division Aid

     One of the "tools" we can use with our students who struggle to memorize the multiplication table and who get stopped in problem solving by their lack of math facts is "Numbers That I Hear When I Count."  On each of the strips below are the multiples of the numbers 2-9.  If a student needs to multiply 6 x 6, he/she would flip to the "Numbers That I Hear When I Count By 6's" and count down then over to the sixth number to find the answer "36."

     Likewise, if a student is trying to divide 56 by 8, he/she would flip to the "8" card and look for the number closest to "56", then count the position of "56" on the card..."56" will be the 7th number so 56 divided by 8 is 7.  For division with remainders, if a student was attempting to divide 76 by 8, they would go to the "8" card and look for the closest number to 76 without going over it.  That number would be 72 which is the 9th number.  So 76 divided by 8 is nine with a remainder of 4.

     Of course we would still want students to memorize their facts.  But in the meantime, this tool may help them solve other problems without the frustration and labor of "guess and check."

     And I just hope I got all the numbers right!

Capacity

Hi Everyone! I read this online and thought it was helpful. Many of us are familiar with the big G to help students remember what a gallon is made of. This little story helps them remember how to draw the big G. Of course, this should be used after the understanding of capacity is there.

Welcome to the Land of Gallon. In this land there are four Queens (quarts), each Queen has a Prince and a Princess (pints), each Prince and Princess has 2 children (cups).

Thanks again to the teacher who offered up the chicken crossing the road scenario to help out with rounding, I love it!

Thank you Jan! This is a wonderful tool for us to all share ideas and resources. Monday's Investigations training will be a great topic to discuss and how the resource can be useful to basic skills instruction.
I am interested in knowing how teachers feel about having an established common set of pre and post assessments that we all use as they relate to the curriculum? Thoughts are welcomed.
Nicole

Implementing Success Tracker

Hi All! I am curious to hear how everyone/anyone is implementing Success Tracker. I have given the beginning of year tests to a few students, then used the data to find common weaknesses. I am in the process now of creating problems from my list of common weaknesses to use as Do Nows when my Basic Skills students arrive. This way I can use a "spiral" approach to some of the trouble spots. In addition, some of the online interventions assigned to the students after they take the test, are valuable. However, as mentioned at yesterday's meeting, some are very rote and may not be useful. Please comment if you are using Success Tracker in a different way. I would love to hear other ideas!

Wow! I am very interested in your experience with the Success Tracker, Jan. This blog was a great idea! What a fast and easy way to share your experiences. Very helpful to me so that I know what its quirks are. I guess with any technology it has its little issues. Thanks for your thoughts. Keep posting!

Success Tracker Gd. 4 Beginning of the Year Test

What I've noticed so far....

The printed version is different from the online version in the following ways:
-the online version has a place value question for question #1; this question is not included in the pdf version,
-question 5 in the online version includes the problem question, "What is 254 rounded to the nearest ten?" This question does not appear in the pdf version,
-question 16 in the online version shows an array of 4 x 9 squares; in the pdf version the squares are in groups of 9 but not arranged in an array. Instead they are in a straight line,
-question 29 in the online test shows the fractions in a equivalency grid, in the pdf version the fractions are just listed in rows on a grid.

So I'm using the online version!