Ways to Use Tangrams in Math

I have used Tangrams in my geometry classes before.  I have a worksheet where they are told to make a certain shape using specific pieces.  One of the shapes is a triangle using all seven pieces while another is a concave tangram.

I know there are other ways to use them but have never taken the time to figure that out.  I've looked for apps to use but only found ones that had pictures that students needed to recreate.  Tonight I found one called Hands-on Math Tangrams on the apple store but it costs $2.99 and I don't know if it would work for high school students.  It says it helps students develop understanding of shapes and properties, visual problem solving, basic fractions, classifying angles, symmetry, rotations and translations.  I have not tried it yet because I prefer to try light versions before I invest in a full version that costs.

However, there are ways to use regular tangrams made by students.  I had one activity that had students make their own tangram square using nothing more than written instructions with measurements.  Once they finished the square, they were asked to color in the pieces before cutting them out.  This activity is good because it makes them read rulers and that is one of the standards.

On the other hand, one can use this which has students create their own tangram using a coordinate plane and geometric line segments.  Furthermore, it helps students practice using geometric terms to create something so it reinforces vocabulary.

Tangrams can be used to help students work on estimation and percents.  Let students work in small groups.  Each person in the group creates a shape using 3 to 7 tangram pieces on a piece of graph paper.  When done, the paper is passed to the person on the drawers right.  Each person will estimate how much of the grid is covered by the shape as both a fraction and a percent.  Then they could the number of squares associated with the shape and  total number of squares so they can calculate the actual fraction and percentage.  This provides a visual way for students to see the relationship.

Another activity is to let students determine the fractional amount each piece is of the whole.  For instance, the largest triangles represent 1/4th each, the medium triangle, the square, and the parallelogram are all 1/8th and the smallest triangles represent 1/16th of the whole.  Students then create concave shapes that represent say 1/2 of the total area of the 7 pieces..  Once they figure out one shape, they try another shape made up of different pieces covering the same amount of area. Have them repeat the activity for 1/8th, 3/4th or 7/16th.  This activity is good for helping students understand equivalent fractions and area.

Let students explore how many convex polygons can be made from the all seven tangram pieces..  The question was first posed in 1930 and two Japanese mathematicians came up with 13 convex polygons are possible.  This paper addresses the question and shows the 13 convex polygons with enough lines to recreate them.

There are other activities but I'll save those for another day.  Have fun exploring these.  Let me know what you think, I'd love to hear.  Have a good day.