Monday, November 24, 2014

Module 12

TCM Article – Rulers

I enjoyed this article. I think that the lesson outlined was a great way to introduce different units of measurement. I was very impressed that the students were able to figure out that their rulers are the same size without being told. One point the article made that I did not think about was the difficulty students can have actually using a ruler correctly. Not all the students knew to start at the very end of the ruler (before 1).


Angles Video and Case Studies

One thing that I took away from the case study was that many children focus more on the line segments than the actual angles when they are learning about angles. It was interesting to read the varied understandings that were taking place in one classroom. This held true in the video as well. Many of the students could demonstrate what an angle would look like. They made angles using their arms and imaginary lines. They had difficulty, though, explaining what exact part of their example was the angle.


Annenberg Angles Module

Use two or more polygons to illustrate the angles below, and explain how you would justify that some of the angles are congruent:
a. 
Vertical angles (the angles formed when two lines intersect; in the figure above, ad, cb, eh, and fg are pairs of vertical angles, and the angle measures in each pair are equal)
b. 
Corresponding angles (the angles formed when a transversal cuts two parallel lines; in the figure above, ae, bf, cg, and dh are pairs of corresponding angles, and the angle measures in each pair are equal)
c. 
Alternate interior angles (the angles formed when a transversal cuts two parallel lines; in the figure above, cf and de are pairs of alternate interior angles, and the angle measures in each pair are equal)
 
Problem B6
Solution  
Find one or more polygons you can use to see examples of the following angles:
a. 
Central angles (for regular polygons, the central angle has its vertex at the center of the polygon, and its rays go through any two adjacent vertices)
b. 
Interior or vertex angles (an angle inside a polygon that lies between two sides)
c. 
Exterior angles (an angle outside a polygon that lies between one side and the extension of its adjacent side):



I had a little trouble with each of these problems. It has been a while since I have done these kinds of problems so this module was a good refresher. After playing around with the shapes a bit and reading the solutions it became clearer.

TCM Article – How Wedge you Teach?

I could not get this article to load!


Exploring Angles with Pattern Blocks

Green Triangle: For this shape I know that all three angles add up to 180. I also recognize that this is an equilateral triangle so all of the angles are the same. 180/3=60

Blue Rhombus: I can remember that on a rhombus, the opposite angle are congruent so there was going to be two different angles. The smaller of the angles looked similar to the angles in the green triangle so I matched them up and they fit. I know that all the angles of a rhombus add up to 360. Two of the angles are 60 which add up to 120. That would mean that the remaining two angles would be 120 each.

Red Trapezoid: Going in I know that all of the angles would add up to 360. I used the 60 degree angle from the triangle to confirm that the smaller angles were 60 degrees. that would leave the two larger angles to be 120.

Tan Rhombus: I found this shape to be very difficult. I could see that there were two very obtuse angles and two acute. Because it is a quadrilateral, I know that all the angles add to 360. I played around with this for a bit and could not find  a way to get an answer.

Yellow Hexagon:  I know that all of the angles in a hexagon add up to 720 degrees. All of the angles looked to be the same size so I divided 720 by 6 to get 120 for each angle.

Challenge:
By connecting two triangles by their base you get two 120 degree, obtuse, angles.

Combining a triangle and trapezoid created a straight angle.

Combining tow hexagons created a 240 degree angle

I agree with Mai. Using the shapes we have I could not find a way to create an acute angle.

For further discussion

When I think of nonstandard measurements, I immediately think of cooking. You will often times see a pinch/ dash/ splash of a certain ingredient. I have found that these terms are used when it does not matter if there is an exact measure. It is usually an ingredient meant for flavor and left to your preference. You will never see a cake recipe using a non standard measurement on flour, baking power, or baking soda because those ingredients are critical to the cake and must be exact. The example "I'll be there shortly" also falls into this category. It lets the person know that you are probably on the way and will be there soon, but you don't say an exact time. If you were to say "I'll be there in five minutes" but it actually took ten, then it seems like you were late! You use nonstandard measurement when you don't need to be exact.


5 comments:

  1. Hi Sarah,
    I just uploaded a copy of the article though it's always available online through our library system.

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  2. I really enjoyed reading the approach the teacher used in the Rulers article also. I feel like it really gave students a chance to explore using tools to measure without worrying so much about the numbers associated with those measurements. Like you shared, the students did struggle a bit with identifying where to start measuring at the zero mark to count as 1 and so on. Since the teacher had students working in groups to discuss their findings, I think the students would be able to learn from each other in that case to help each other understand where to start measuring. I was also very surprised that some students realized that when comparing objects they had to compare them with the same units. I think that by using the non standard tools the students were able to focus more on the comparisons of "unit" sizes in terms of the different tools they used. I could not agree more with the example you shared about using non standard measurements. I feel like I say "I'll be there soon" or "See you in a bit" almost daily, but it truly does not express how long it will be until I get to the destination. Thank you for sharing your great ideas Sarah!

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  3. Hey Sarah,
    I enjoyed reading your post.

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  4. ...I had never really thought about how difficult it can be to use a ruler for the first time. It seems if maybe we give them directions, like my dad taught me, then it would be easier for students to grasp the idea.

    I liked your examples of non-standard measurement. I, too, referenced cooking--a pinch, dash, etc. But, I hadn't thought about the phrases we say, like "I'll be there shortly." That was good. :)

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  5. I could not get this Article to load either You have an awesome post this week and it is very informative. I also have never thought about how difficult it was to use a ruler either, it seems so easy now that I thought it was always easy. Great job on the Challenge cause I had a hard time with that, I am not very good at puzzle like activities.

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