Objective and Overview
In this lesson, students will make their own Tangram puzzle to share with their classmates. They will then take time to work on solving the puzzles created by their classmates. A variety of content connections for a range of grade-levels are described further in the lesson plan.
To introduce students to working with Tangrams on Mathigon, have them explore the Mathigon Tangram Activity and allow them to work on any of the puzzles for 5 minutes or so. As they are exploring the puzzles, ask them to note any strategies that are working well for them as well as any puzzles they are having difficulty solving. After 5 minutes or so, invite students to share some observations with the class.
Students are now going to make their own puzzle for their classmates to solve. Share this starting Polypad with them. Click here to learn how to share Polypads with students. Students will use the 7 pieces to create a custom puzzle. Once they have created the final shape, they should select all the pieces and click the "Join" option at the bottom to create a single, joined polygon.
If you like, invite students to add other elements to their puzzle:
Next, as shown in the first video, students should save a copy to their library and then copy the link to share with classmates. To allow students to share links with each other, consider creating a spreadsheet or document that all members of your class can edit. Each student can enter in their name and the enter in their Polypad link. Then, they can click on each other's link to view and solve their puzzle. When solving the puzzle, students can find the 7 Tangram pieces to use in the Geometry file panel. This entire process involves a number of steps so you may want to demonstrate it for students before having them begin their work.
This lesson will hopefully provide opportunities for creativity, problem-solving, and exploration while also providing an engaging and fun activity for students. However, below are some options for connecting this lesson to specific content standards.
Area and Perimeter
After sharing the starting Polypad, ask students to turn on the grid background and find the area and perimeter of the starting square. Then, after they have made their puzzle, ask students to find the area and perimeter of their new shape before sharing it with their classmates. If your students have studied Pythagoras' Theorem, they can use this approach for finding the perimeter. Otherwise, they can use the ruler tool on Polypad. Ask them to write down the area and perimeter of their shape. When solving classmates' puzzles, ask students to also find the area and perimeter of the puzzle they are solving. Once they have solved the puzzle, they can connect with the puzzle maker and discuss if they found the same area and perimeter. Do not be quick to reveal to students that the area stays constant. Allow them the time and space to come to this conclusion on their own. If you're interested in exploring more about the relationship between area and perimeter, view Pentomino Perimeters.
Most puzzles students create will be single polygons. If you set this as a restriction, you can use this as an entry activity into exploring the sum of interior angles of polygons. Before sharing a puzzle, ask students to use the protractor tool to find the sum of all interior angles of their polygon. Like above, have them write it down and do the same process with the puzzle they solve. After some time for students to work, gather together as a class and ask students to share the sum of the interior angles of some of the puzzles. Discuss any patterns that emerge. Hopefully some puzzles will have the same sum of interior angles. Project these puzzles to the class and ask them what they notice. Hopefully, some will notice that the polygons have the same number of side lengths. Use this as a starting point to the relationship between the number of sides of a Polygon and the sum of the interior angles.
View Tangram Coordinates for some ideas on connecting Tangrams to plotting points in the coordinate plane.
For students looking for more options in creating puzzles, invite them to create puzzles using 2 or more sets of Tangrams. Be sure to have them include text on their puzzle indicating the number of Tangram sets used in their puzzle.
Depending upon what path you took with this lesson, you can close the lesson in a variety of ways. You could have students share some puzzles they enjoyed solving, some puzzles they had trouble solving, some puzzles they found especially creative, etc. If you focus on a content standard above, you will likely want to provide some closure connected to the specific content.
If your students' puzzles are particularly creative and original, please share the puzzle via Twitter and tag @MathigonOrg or post it to community.mathigon.org.