Roberta's Blog

Pythagorean Puzzles

Posted on: February 23, 2010

Puzzle #1

When I started this puzzle I thought about how students would enjoy doing this activity with actual pieces. I also thought about how many students no longer do puzzles at home. When I was growing up we always had a puzzle up on a card table in the living room. When I looked at the square and realized that the sides were equal to the long side (hypotenuse) of the triangle I knew that I would rotate each triangle so that hypotenuse was matching with the sides of the square. Once all the triangles were used, I just needed to rotate the blue square to fit in the middle. The other white shape (located on the right) seemed just as easy to me. I knew that the section labeled B matched that small leg of the triangle and that one of them would have to be rotated to fit there. Once that was in place I could tell that an inverted triangle needed to be placed on top of that triangle. Once these two shapes were in place the blue square fit into the top right area exactly. The remaining white space was a rectangle which I knew could be created by placing two triangles together.

Puzzle #2

When I started this puzzle I immediately thought of all the quilting patterns I have constructed in the past. The square with one square was exactly like the one in puzzle #1. I did it exactly the same way. The square with two square was also easy because there is a quilt pattern exactly like it. I knew that the two squares when placed side by side would complete the side of the square. I knew from the previous puzzle that two triangles could be place together to create a rectangle. I place the large square in the bottom right corner of the white square and the small square in the top left corner of the white square. This left 2 rectangles (one going vertically along the left side of the square under the small square and one going horizontally above the large square.)

Preferred Manipulatives

As a technology person I really do like the virtual manipulatives but I also know the value of students actually moving the pieces with their own hands. One of the advantages of virtual pieces is that students cannot lose them or drop them on the floor when they should to be working. Another advantage of virtual pieces is that the pieces are the exact size that they are meant to be for the activity. Physical pieces can be lost easily. If the students are responsible for creating their own pieces and they have poor fine motor skills, the resulting shapes may not be accurate. If the shapes are not cut correctly then the puzzles do not always work out correctly.  An advantage of the physical pieces is that no additional supplies or skills are needed. When students use virtual manipulatives they must know how to move and rotate the shape using the mouse or the keyboard in order to complete the activity. Another advantage of the physical objects is they can be taken anywhere and virtual shapes can only be used wherever a computer is located. If I had to select one over the over I would have to say the physical objects win but I really do like the technology tools too.

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2 Responses to "Pythagorean Puzzles"

Roberta,

You bring up a great point – if students are creating their own manipulatives, fine motor skills will be a concern. I know many middle school students who are not neat when cutting those math manipulatives.

Both types of manipulatives have advantages as you mentioned. I think we need to realize that using both types of manipulatives are important and we need work on incorporating both into our lessons.

We always had a puzzle on a card table growing up, too. I still love puzzles today and am always buying them for my grandkids!! 🙂

Judy

I love puzzles too! I liked your comments about quilting patterns. It’s awesome when we see math in the things we choose to do with our free time. I work at a bike shop and have for many years and one of the things we do is build custom bike frames and concepts like the Pythagorean theorem come into play all the time.

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  • Judy: Roberta, The Transformational Golf is a new site for me. I haven't seen this one and can't wait to share it with others. Many students struggle w
  • bkgeary: I like the idea of letting the student pick the material. Students never fail to amaze me with the great ideas that they come up with. I think that
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