As we have continued our conversation about shapes and shape properties one activity that I found particularly engaging was the fold and cut activity. The premise of this activity is that any shape can be made by folding a piece of paper and making one cut. The challenge we were given was to make as many different quadrilaterals as we could by doing this our self. I started doing this activity by making a square, and after realizing that it was difficult to visualize where the lines of the shape would be after I had folded it a few times, I began by drawing the shape with a sharpie so that I could see the lines on the front and the back sides of the paper. After doing this step I was quickly able to come up with the square by seeing the lines that could be overlapped by folding. From this I knew I could get to a rectangle by folding the long sides of the rectangle on top of themselves in an accordion fold until it resembled a square, then following the same steps as a square to end up with the rectangle. Using this same type of process I was able to first find the folding pattern to create the rhombus and then made the accordion folds in a parallelogram to make it resemble the rhombus, and cut to create the parallelogram. After these shapes I found that other quadrilaterals were more difficult. One that I found after a few tries was the isosceles trapezoid. I think that this shape was easier to find because it had a line of symmetry. By being able to fold it down the center and have then lines that immediately overlapped, this helped make the other folds more natural. I also think that this is one of the reasons I was not able to figure out how to make the right trapezoid. In this shape there was not a line of symmetry that could be folded down and other lines just line up on top of each other. Because of this I found myself trying to make awkward fold that would not go through the entire length of the paper, however I do not think that this would end up being the correct way to create this shape.
Personally I really enjoyed this activity because it was very easy to fold a piece of paper, make a cut, and then unfold it to see what I had come up with. It was quick to see if you had done it correctly and if you didn’t, I could try again right away. I also thought that this activity challenged my understanding of shape properties. As I was folding these shapes, in order to create the shapes correctly, it was necessary for me to understand different shape properties such as symmetry, angles, right angles, and parallel sides. For these reasons I think that this activity would be beneficial for elementary students. First off, it also allows for quick selfassessment. Students are able to try one way that they think that they could correctly create the shape, unfold, and see if they were correct. This is a great way for students to begin to see that this is a critical aspect of math. Very often when we are trying to find an answer, we will try one way and see if that leads us to the correct answer, but if it doesn’t, that is ok, we can try again. Another aspect of this activity that I thought was beneficial for students was the fact that students would be challenged in their shape properties as they would complete this activity. It is imperative that students understand lines that are parallel to each other, lines that are perpendicular, or if they are on a different angle, how they could fold the paper so that these lines would overlap. Because this activity was a bit challenging even for me when I tried this with quadrilaterals, I wonder if this could be used in an elementary classroom with different triangles or even if they were just challenged to make a square and rectangle. I think that only having three different lines to worry about or making familiar shapes like squares and rectangles could make the activity a bit simpler. However, overall I think that some form of this activity could help extend student’s thinking and help further their geometric thinking.
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AuthorMy name is Chelsea VanderZwaag, I am a senior at Grand Valley State University majoring in Mathematics and Elementary Education. Archives
December 2015
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