Tangram Polygons: Composing and Decomposing

In my last post, Tangrams: A World of Geometry, Part Two, I talked about the thirteen convex polygon shapes that can be formed with the seven tangram pieces. In the video, I showed how to make five of them, and then I left a challenge for you to look for the remaining eight convex shapes. By way of encouragement, I provided downloads of two of the eight shapes, but left it to you to put the puzzle pieces together to form these two shapes.

In the following video, I review putting together the five shapes. You’ll see that I’ve made the tangram pieces in two different colors. I think it makes it easier to notice patterns and relationships between the shapes and the way the pieces go together to form the shapes.

Now we’ve reviewed putting the five shapes together, and you’ve seen how the colors help us think about the different ways the pieces can be put together. The next video will start by showing those two shapes for which I provided you with downloads in my previous post. Then we follow that up with finding the remaining six shapes. For some of these shapes, there may be multiple ways they can be put together. I don’t claim to have exhausted all of those ways.

Below are several attachments that you can download. The first shows all of the convex polygon shapes that are possible; the second shows one way to put the pieces together to form each shape. Then, there are three pages that have templates for all 13 of the shapes, and finally there are two pages of multiple copies of the tangram pieces in case you want to run them off on two different colors of cardstock.

It is my hope that many of you will find ways to use the tangrams as way to challenge students to look at composing and decomposing shapes. Each of these quadrilaterals, pentagons, and hexagons are composed of the same pieces and so have the same area.

For students in seventh and eighth grade it might be interesting to look at the perimeters of these thirteen shapes. If we took a side of the square tangram piece as the unit of length measure, what would be the lengths of the sides of each of the pieces? Then we could ask about the perimeters of each of the shapes.

Well, maybe that will be a future post.

ConvexPolygon  Pieces  Templates

4 Responses to Tangram Polygons: Composing and Decomposing

  1. Dr. T,

    On the Macintosh, hold down the Command Key (Open apple) + the left shift key and press 4,

    You’ll get a crosshairs cursor that you can click on the upper left corner of the area (hold the mouse button down) you want to capture, drag down and to the right to creature a capture box, release the mouse button a screenshot will be saved to your desktop.

    Double-clcik on the screenshot icon and an edit menu will open. Click on Select all, and then click on copy. Open your Word document and paste (control-v) the screenshot into your document. Once in the document, the screenshot can be resized.

    Do this a few times and you’ll never forget it.

    On the PC, in the Accessories folder, there is a program called ‘Snipping Tool’ that lets you do the same thing in Windows.

    It’s easy to go into the Scratch program and change the colors. I’ll do this and send you the file. Any particular color?


  2. Jim,
    Thanks for your comment about scratch. I just went there and quickly constructed a couple of the shapes. It works great. The thing I’m wondering is whether there is a way to copy the shape once it’s built and then be able to paste on a blank word document. In that way a student could keep a record of the shapes as she/he built them.

    The other thing I thought of was the possibility of the two large triangles being a different color from that of the five smaller shapes.

  3. Dr. T.
    There is a great Scratch tangram project that lets you manipulate the pieces to solve the puzzle shape.
    This is the web address for the project which can be played online.

    You can also download the project from this address.
    If you search Scratch on ‘tangram’ you will find two or three pages of tangram projects. It’s obviously been a favorite of Scratch programmers, which are mostly students.

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