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Tuesday, January 27, 2015

Manipulatives that Assist Students in Thinking about Similar and Congruent

I have several sets of these  32 MiniRelational GeoSolids. 

 I mix them all together when we do an activity in which students sort the shapes into groups that illustrate the characteristics of similar and congruent.  There are very few concrete materials that help students think about the difference between the properties of these two concepts. 

In grades 4-6 you can also introduce the mathematical symbols for congruent and similar:

congruent Congruent (same shape and size)

similar Similar (same shape, different size)

How about having that mathematically talented group of students in your class create an anchor chart for the class that compares the properties of congruent and similar.  

Here is an interesting anchor chart that I found on Google Images. Let student research the meanings of the markings on the triangles and explain the definitons of the words proportional and adjacent. (Don't worry about the calculations at the bottom, just use the illustrations.)

What do you think about this idea?  I had 3 very mathematically talented boys in my 3rd/4th grade class one year that kept me up at night thinking of challenging activities for them to do or investigate. (They loved geometry concepts, and I heard that one of the boys later became an engineer :) )When we would cover our "grade level" material, I would meet with them 8 minutes before class and discuss the lesson. Then using white boards or concrete materials, they would show me that they understood those concepts. 

 Next, I would give them their assignment, discuss the quality of work that I was looking for, and they would work and write in their math journals at the reading table in the back of the room.  I can only tell you that the quality of work that came from those boys was worth the sleepless nights and extra work.  


Sunday, January 25, 2015

3 -Dimensional Sort

This afternoon at our house was a lazy, snowy day. I decided to challenge my granddaughter, who is in 2nd Grade, to a 3-Dimensional Sort Challenge. 
This a great activity to do with a small group of students during Guided Math. 

 Using a set of 32 MiniRelational GeoSolids

and a set of cards labeled: cone, pyramid, prism, and  cylinder.

Earlier in the weekend, we built prisms and pyramids out of toothpicks and playdough.
We talked about what made 3-D shapes 
either a prism or pyramid.  

So when I gave her the bag of 32 shapes and asked her to categorize them, I did not review any concepts... 
she was just given the task. 

The first time around she made 2 common errors:
1) she categorized the hexagonal prisms as a cylinders.
2) she categorized the triangular prisms as a pyramids.

Why?  Probably because she was never exposed to these shapes before and did not deeply understand the "the characteristics" of the different types of 3-D shapes.  As we reviewed each category 
of 3- D shapes, we again talked about what she looked for when she was looking at each shape.

Cone- "Only 1 face at the bottom, and a vertex at the top of the shape."
Cylinder- "2 faces with curved sides. No vertex at all."
Prism - Faces- there can be a different number of them, and vertices."
Pyramid - " One vertex at the top, straight sides, and a bottom."

After our discussion I place all the shapes back into a plastic bag and asked her if she wanted to try again.  WITH THE INCENTIVE OF EARNING A DOLLAR IF SHE COULD CATEGORIZE THEM ALL CORRECTLY!

She is now $1.00 richer!


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