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Monday, April 27, 2015

Comparing Surface Area and Volume

A great activity for those "talented students" that you are urging to think about ideas on their own.

Give the student sentence strips that contain the above phrases.  In small groups, they create the Venn Diagram.  Then, challenge them to create their own Double Venn Diagrams that compare two mathematical concepts.  

Have the students generate a list of pairs of mathematical concepts that they could compare, and then confer with their teacher
 for final approval of their basic idea.

Lately, I've been thinking about this poem.

Perhaps we need to let our "Talented Learners"  FLY?


Wednesday, March 25, 2015

Fractions: Why Numerator and Denominator?

Numerator comes from the Latin word meaning number.

Denominator comes from the Latin word meaning name. 

Don't you just wish early mathematicians would have used 
number and name?

 It would have been so much easier to teach 3rd Graders
 to read and write number and name than numerator and denominator :)

Friday, March 20, 2015

Fraction Progress: Referring to the Same Whole

I've been doing some personal professional development about the fraction progression in the Common Core Standards.  

I was thinking about this standard:
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

When I came upon this task at Illustrative Mathematics.
If you were to choose the two pictures that best compares 2/3 and 2/5, which two illustrations would you choose?

Your first reaction would be that students could choose either illustration 3 or 4 to represent 2/3.  That is true, but why must you select illustrations 4 and 5 together?

This question highlights the fact that in order to compare two fractions, they must refer to the same whole. 
Do we spend enough time on the fact that both fractions must refer to the same wholes?
     When we use pre-made worksheets that compare fractions, they usually have a pre-drawn "Whole."  

Using this task from Illustrative Mathematics, in a small group format, could lead to an amazing discussion of the importance of the "same whole."

Here at home, I think I will give my soon-to-be Third Grader 
a cookie like this and ask her to share 1/2 of the cookie
 with me. 

I will promise to share 1/2 of my (unseen ) cookie with her.

My cookie will look like this:
What do you think her reaction will be?  Will our discussion lead to the importance of the "same whole?"
P.S.  If I had a multi-grade 2/3 classroom, would this still be an appropriate lesson, using cookies instead of a worksheet?  What questions would I ask of a 2nd Grader versus a 3rd Grader? 

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!


Wednesday, December 17, 2014

Using Multiplication Comparisons to Convert Measurements

I made these bookmarks for a teacher to illustrate  how multiplication comparisons are used when converting measurements.  

Would you like a copy?  I can put them in my Google Docs file and add a link if you think you would use them.


Freeze and Dance While Learning Number Sequencing

Active kids love activities like this!
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