Geometry

What are the key ideas of geometry that you want your students to work through during the school year?

I would want my students to become familiar with vocabulary needed to understand geometry. I would like them to understand that there is so much more to a shape than its outer appearance. For example: A square is a square because that is what we were told. 

A Square is a flat shape with 4 equal sides and every angle is a right angle (90°).

Van Hiele levels and Polygon Properties Article

The van Hiele levels are built sequentially upon one another.  I know we all start out at the visualization level.  That is we see a shape for what it is.  A square is a square because it looks like one. One masters each level depending on the quality of instruction they have.  The van Hieles mention 5 phases of learning.  I can remember geometry in school and I always felt I was good at it until college. I do not remember my instruction getting much further than the information stage. 
I do like how the article and the power point stressed that if the teacher is not thinking at the child’s level little to no learning will occur.  I think this to be true in many cases.  “The teacher needs to remember that although the teacher and the student may both use the same word; they may interpret it quite differently”.  We need to be mindful of our students and ask questions to make sure our students understand.  They may be just memorizing what they think they want them to say and retain little knowledge of the topic.

Em, I feel like I am barely a two on the van Hiele scale.  What about you? I think my 8 year old knows more about this that I do.

How did you do with the activity in the PowerPoint?  Knowing what you now know, what do you think about geometric instruction and how will this impact you’re planning in your own future classroom?

I was slightly nervous as there were many shapes and I did not know what to expect.  I did manage to get them all right and do plan to show Alexander to see how he does. I did not realize how important manipulatives were until my tutoring experience last semester.  In the classroom I am in now, I have seen many times where the use of base ten rods would have helped with comprehension.  I will work to give my students the opportunity to use hands on activities to enhance their learning. 


Em, how important is it for you to use maniplitives in your future classroom?

Annenberg Triangle and Quadrilaterals Module

Linkage strip: Problem B1

I don’t think I fully understood this problem.  I could tell if the units formed a triangle but I was unsure what they meant by “Can it be deformed?”  I did figure it out in the end by noticing the note given. 

Em, did you have a problem with this?

Building Towers: Problem C1


I did not have the necessary materials to try this activity but I have played a virtual game like it.  In order to make it to the next level you had to build a bridge across hole of some sort.  You have a limited amount of materials so you have to choose you construction carefully.  I had more success when building with triangles than any other shape. 

Thinking about Triangles: PowerPoint activity

Look around the room and find some triangles? 
 Sadly, there are no triangles in this room.  I could split a square shape in half diagonally and make a few. 

What do these shapes have in common? I
f I did have a triangle in my room, I would say that they all have 3 sides and 3 angles

Where do you think the word triangle comes from? 
Tri- means three

What other words I know that start with tri: 
Trifold, trilogy, tripod… that’s all I got

How are they similar to the word triangle and how are the different? 
The all have three of something.

What is the definition of a polygon? 
 I said they had straight lines and were closed figures. 

Is it possible to make a three-sided polygon that is not a triangle?
No, because any polygon that has three sides is some kind of a triangle.

Is it possible for a triangle to have two right angles?
No, In order for me to make a triangle I only have the option for one right angle.

How many different right triangles can be made on the geoboard? 
This was hard for me for some reason.  I could only rap my head around 10.  I wish there was an example on the power point.  I Googled it and found a picture but I guess I would have helped me if I was shown.

How many different types of triangles can you find?  
To be honest I don’t know triangle types very well and I had to look this up.  After I looked them up, I was able to make them all. Correction, all but one the Equilateral Triangle.

Em, please tell me I am not the only one who had to look this up!  So much for the future of our children!

1. How would you structure this lesson for students in an elementary classroom?  I would definitely demonstrate what was expected first.  My students will not all be on the same level and everyone will know exactly what is expected.  
2. What parts did you have issues with? This question should state, what parts did you not have trouble with.  I Felt I struggled with a lot and I am a little embarrassed.  I should have done this assignment after the Annenberg.
3. Did you need to revisit some vocabulary words to remind yourself of their meanings? If so, which ones?

• Acute triangle: A triangle for which all interior angles are acute.
• Acute Angle: An angle that has measure less than 90°.
• Obtuse triangle: A triangle that has an obtuse angle as one of its interior angles.
• Obtuse Angle: An angle that has measure more than 90° and less than 180°
• Equilateral Triangle: A triangle with three congruent or equal sides or angles.
• Scalene triangle: A triangle in which all three sides are a different length.
• Isosceles triangle: A triangle with two equal sides and two equal angles.

Em, I had to look almost every triangle up.  I am going to have to take some time to memorize this.  How did you do?