Math Manipulatives

Part 1: EXPLORING TANGRAMS

The tangram puzzle was created (so the story goes) in ancient China. It is a 7-piece puzzle that can be assembled into a square. Supposedly, an ancient Chinese king had a square mirror on his wall that he used to like to look at every morning. One day, he bumped into it, and the mirror fell to the floor and broke into 7 pieces. He had to put it back together, and supposedly the tangram puzzle was invented. We may never know what really happened!

Click on the following link to find an online tangrams game: http://www.abcya.com/tangrams.htm (Links to an external site.)

You will have to “subscribe” to access the games, but the subscription just takes a minute and is free.

The child’s voice that narrates the game can be irritating but is attractive to children using the site! You can choose from three levels of difficulty and then virtually drag, rotate, and drop tangram pieces to form a variety of shapes. Take some time to try several from each difficulty level to get a sense of what we want children to be able to do with these manipulatives.

Open a new Word document and type up what you did, including:

How successful were you with filling the shapes using the tangram pieces? In some detail, describe your experience with solving the puzzles – what you tried, things you noticed, etc.
What might be the value of doing this type of exploration with children in the elementary grades (i.e., what do they gain, mathematically, from doing this type of exploration)?
(1 page)

Part 2: OTHER VIRTUAL MANIPULATIVES

There are many websites that feature online versions of manipulatives that are often found in classrooms but can be accessed “virtually” on the computer. Use of virtual manipulatives means that children have access to an unlimited number of materials, that they won’t drop them on the floor or lose them, and that they can be used in conjunction with other tools, from timers to measuring devices. One manipulative producer, Didax, has developed a site of online manipulatives that can be used from primary grades into high school but is very appropriate for Grades 3-6. Go to the site at https://www.didax.com/math/virtual-manipulatives.html (Links to an external site.) and, note that many choices are available. Take some time to “play” and explore the geometry-related virtual manipulatives – specifically, (1) base ten blocks, (2) math balance, (3) geoboards, (4) spinners, (5) pattern blocks, and (6) fraction tiles. Research has shown that when children interact with this type of virtual manipulative, significant achievement gains tend to result. Be forewarned: Use of these online manipulatives and thinking of ways to use them in a classroom can be fun and addicting!

After your exploration, choose any three (3) of the six (6) virtual manipulatives listed above that you believe would be particularly useful in the classroom. For each of these three, write two paragraphs that explain specifically (a) what the manipulative is (and what it can do at this site), (b) what you might have children do with it, and (c) why you believe it could be valuable in your teaching of number, algebra, or geometry. For example, you could have children investigate area or perimeter by using the base ten blocks, etc.
(2 pages)

Part 3: A LANDMARK ARTICLE

Back in 1999, Pierre Van Hiele, who had originally published his work some 40 years prior, wrote an article for the National Council of Teachers of Mathematics journal Teaching Children Mathematics. This article, entitled “Developing Geometric Thinking Through Activities That Begin With Play” took off in popularity and is now commonly used for the activities described in it and cited for the information it provides about teaching and learning geometry.

Download and read this 6.5 page article (which includes lots of pictures and diagrams!). Then, in your Word document, spend one page summarizing the main ideas made by Van Hiele in the article. On a second page, write a reaction to the article. What stood out in your mind? Will the ideas of this article be useful in your planning for teaching geometry? Explain.

After you have completed the three Activities on this page, you will have a Word document that is about 5-6 pages in length (1-2 pages for Part 1, about 2 pages for Part 2, and 2 pages for Part 3)