Category Archives: Geometric Measure and Dimension

Honey, I Shrunk the Kids #MTBoS30 Post 15

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Many years ago, when I first began teaching, students compiled portfolios in their mathematics classes.  In the beginning it was a waste of time.  But as they adjusted them, I felt they could be useful learning tools.  About the time they got them just right, (students were making claims and supporting with reasoning /evidence, not just a bulleted list of steps to solve an equation)…well, they did away with them.

A colleague shared a task during my last year of portfolios.  I ran across it a couple of years ago in a file some where.  Once again, I forgot about it until I found this DVD:

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The task was simply for students to devise a plan to confirm or dispute Disney’s claim that the kids were shrunk to 1/4 inch tall.  Most would collect some measurements from the movie screen and support their conclusions with proportional reasoning.

Kind of interesting to determine if they held the same ratios throughout all of the scenes or if some seemed more to scale than others.

What other movies could be offered in a similar task?

Mindset #MTBoS30 Post 6

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A bit sad when I read Fawn’s post here but true.

Yes our students may come to us broken down and have given up on learning math.  But that’s when we have an opportunity to give them a chance…

By using open tasks, anyone can play with the math…not just “the smart kids” who have memorized all the steps and procedures. 

The thing I appreciated most about the staircases task was there were no rights/wrongs as we began.  Only a what do you think?  And why?  Students ordered the staircases, discussed with classmates, supported their claims with reasoning or critiqued the thinking of others. 

Then, they had to devise a measure that confirmed their claim.  In 2 years, this is one of my favorite lessons.

I will continue to search for rich, thoughtful tasks that allow ALL of my students participate and move forward. 

They may arrive at a zero love for math, but when they leave, they will know they are quite able…

Enticing Students to Think with Food

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What better way to end our semester than a few tasks involving food?  Sometimes the last weeks of school can be filled with multiple distractractions.  In hopes of holding my students’ attention while they’re in class, I am bribing them to think with food.  Yes, I have fallen to enticing them with external rewards.

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With the Oreo Mega Stuff,  A Recursive Process offers some research by Chris & Chris.  My plan is to follow the QFT model outlined here.  I just recently became aware of the Question Formulation Technique which I shared in this post.  The Q-Focus is simply to display my package of Mega Stuf Oreos, wondering what questions they have – recording all of their comments as questions …and follow the process allowing them to determine their own questions, lead their own learning.  Though I would hope they would approach this from a volume stand-point – letting them design their own questions may lead to other ideas and I am fine, so long as they are thinking and talking math, yes they may eat their research tools once they’ve answered their chosen question.  The final product will be a 30-second pro/con commercial Mega vs. Original supported by their mathematical findings.

Offering several stations to review surface area and volume formulas utilizing various candies as they are packaged as well as the infamous pouring water from a pyramid to a cube / cylinder to a cone will be modeled as one of the station activities.

Finally, using the  Ice Cream Cone  found at Illustrative Mathematics.

ICE CREAM prompt and file

As a “reward” for successfully completing this task, I think a class Ice Cream Party would be appropriate.  I just need to know how much ice cream I should purchase to ensure everyone has plenty to enjoy without too many leftovers.  Assuming the cones are filled with ice cream with a “spherical” scoop atop – sounds like a great homework practice problem to me…

Geometric Measurement and Dimension (GMD)  Explain volume formulas and use them to solve problems
  • G-GMD.1 – Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
  • G-GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  • G-MG.A.3 : Modeling with Geometry- Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Several times this year, I’vfe gotten the GMD (geometric measureme and dimension) and MG (modeling with geometry)domains mixed up, I am slowly beginning to internalize the new notations. 🙂

I also like this prompt: Doctor’s Appointment for GMD-A.3.

On a side note – Reading an article in MT the other night – I wondered, “Was I supposed to know that?”

The derivative of area of a circle is the circumference?  The derivative of volume of a sphere is surface area?  Similarly…derivative of area of square is half the perimeter, derivative of volume of cube is half surface area…  How/Why did I miss that? Or did I know it at some point but just pushed it aside years ago?  Interesting…made me wonder and I started looking at other figures – will share more later.