Saturday, April 12, 2014

“Geometry [and all areas of mathematics for that matter] is more than definitions; it is about describing relationships and reasoning” (NCTM 2000, p. 41)

Tangram Discoveries (Solution) 

Even though I did not get any of the jargon right, I did get both of these problems correct. ♥‿♥

Coordinate Grids 

What websites did you explore and which ones would you use in your own classroom?  What are the advantages and disadvantages of using online programs in the classroom? 

I looked at all the links.  Bellow I listed a few of my favorites.  I believe the advantages of using online programs out way the disadvantages.  Students who need extra help can play he games and go through different activities to gain an understanding of the topic.  Students who have mastered the topic can do extended activities that the teacher assigns to further their knowledge.

A disadvantage that sticks out to me would be a student who is struggling, skipping over questions or parts of the lesson and the teacher not being aware. This would be counter-productive and no one benefits.

Em, do you feel students are likely to skip over the problems they are having trouble with instead of asking for help?

Billy Bug 2 - Move the bug to help him feed. Uses all four quadrants, four 5x5 grids.

Graphing Ordered Pairs- Lesson with interactive practice on graphing and locating ordered pairs on a grid.

Ordered Simple Plot - Input a series of (x,y) ordered pairs and plot them in the order the pairs are inputted, either connected or as unconnected data points.

Whats the Point? - Play a coordinate plane game from Funbrain.com. (use the hardest level)

Stock the Shelves - You have two minutes to put the soda bottles in their correct places on the coordinate plane.

Em, I have high hopes of using technology immensely in my classroom. How do you feel about that?

Miras and Reflections 


Have you ever used a Mira before? Did you find any part of this problematic? How did this build on your understanding of transformations? 


I have never used a Mira before and it was easy to use once I figured out the lighting and the shadow my hand casts.  It opened my eyes to symmetry.  Objects that I could see 2 or four lines turned out had 6 or 8. 







Letters with No Lines of Symmetry:     E, F, G, J, K, L, N, P, Q, R, S, Z
Letters with One Line of Symmetry:     A, B, C, D, H, M, T
Letters with Two Lines of Symmetry:     I, U, V, W, Y
Letters with More than Two Lines of Symmetry:      O


If we were to change the font or style it would change the line of symmetries because of the differences in the print of the font. Ie: A is different from A

Challenge: Find a word that has line symmetry 

BOX   OX  DOC

Em, were you able to find a word?

Kaleidoscopes Article



On page 81 in this article the author states, “Throughout the study of mathematics, students need to develop and apply geometric reasoning, visualization, and spatial reasoning skills.”  This is best done in my opinion through hands on discovery and investigations.  The activities along with the making of the kaleidoscopes help the students connect concepts with physical objects.  Below I listed the websites mentioned in the article.  I played around with them and saved them to show Alexander. 

Kaleidoscopes



Em, this was a very hands on moduel. I feel I do better the more hands on an activity is. How about you?

Annenberg Measurement Module

Like in other modules, the lack of the proper tools made this one harder to participate in. I relied on my past experiences in chemistry to help me envision doing the exercises. I have learned that measurement is only as precise as the tool being used to measure and the ability of the user to use that tool effectively.

Problem B1: How could you use the tinfoil to find the surface area of the rock?  Why would you use this technique?  

I have never hear of measuring this way before but it made perfect sense as soon as I read it. I went out side to look for a large rock so I could do this activity. 

I wrapped to rock in foil. ( there is no way this method will be exact)
 Unwrapped the foil and transferred to the graph paper.

Outside perimeter   75 cm²
Inside perimeter      56 cm²
Average perimeter   65.1 cm²




Then I switch to a smaller graph paper. 0.5 cm

Outside perimeter   70.25 cm²
Inside perimeter       59 cm²
Average perimeter   64.625 cm²

The smaller the measurement the more precise the measurement.


Case Studies

Summarize your reflection questions and make connections to the other activities and measurement PowerPoint.  

Students come to school with a cloudy version of non-standard types of measurement.  They have a hard time with the realization that a larger measured number means a smaller unit or item was used to measure it. They still believe big = big.  Slowly through teaching and practice, students start to make these connections. In the upper primary grades, students learn how to use different measuring devices properly. They realize that in order to get a proper measurement they must use the tool correctly and be consistent in their technique.  

For further discussion

A fellow teacher says that he cannot start to teach any geometry until the students know all the terms and definitions and that his fifth graders just cannot learn them. What misconceptions about teaching geometry does this teacher hold?  

For me I learn better, when I have something visual to attach words a definitions with.  I can honestly say that I had little problems with this module but I would still struggle with terms and technical definitions.  I realize that math terminology is important but I am more worried about the concept and skills to achieve comprehension of the subject matter.

Em, will you focus on skills and comprehension first or vocabulary and mathematical jargon?


Now that you’ve had some time to explore the world of geometry, how has your view of the key ideas of geometry that you want your students to work though changed?

I can say that it is a little less scary.  It was reassuring for me to hear that Dr. Higgins still struggles with different concepts. I am looking forward to teaching geometry in my classroom because of the hands on possibilities it have to offer.

1 comment:

  1. Em, do you feel students are likely to skip over the problems they are having trouble with instead of asking for help?

    Absolutely, I have on several occasions gotten frustrated with a problem and gave up moving on to a less difficult problem. I feel as if this is the same for younger students especially if a teacher or an adult is not walking around giving assistance.

    Em, I have high hopes of using technology immensely in my classroom. How do you feel about that?

    Again, absolutely! Before enrolling in school I felt that technology would impede learning in the classroom as it could be distracting. However, I now know better. When used in conjunction to what they are learning in the classroom it allows students to expand on this knowledge. I wonder, isn’t it mandated that all classroom have technology capability.

    Em, were you able to find a word?

    Apparently, I skipped over this challenge but, I know I would have if I actually tried… 

    Em, this was a very hands on module. I feel I do better the more hands on an activity is. How about you?

    Absolutely, I learn by doing. Some people learn from seeing and some from reading. This class meets the needs of all the above don’t you think?
    I commend you on the work with the tin foil…great job..I gave up!

    Em, will you focus on skills and comprehension first or vocabulary and mathematical jargon?

    To be honest my immediate response would be skills and comprehension. However, this would depend on the learning abilities of the students in my classroom. For instance, in some cases I might be able to teach all of these together and sometimes one area at are time.

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