#STEM lesson seed: 3D printer + Math = Tangram

I am looking for 3D Printing lesson plans for my 4th graders. I want to go beyond just having them replicate the online models. I just received my 3D printer for the fall school year. I hope that you remember me. You always have fantastic workshops. -- former workshop attendee

Happy new school year! The following is the lesson seed I created for this teacher. It is aligned with her district's requirements for the Minnesota standards. If you can use it with your newly acquired 3D printer, please feel free. If you would like to share with us, we can post so other teachers can use.

prosthetic foot, image by Pongratz Engineering

Tangrams Lesson Seed

Activity Overview

1. Have students play Tangrams 
2. Use CAD to model your own Tangram set 
3. Use 3D printer to create the Tangram pieces 

By completing this activity, students will demonstrate:

Standard	Activity	Extension
5.3 I can measure angles in geometric figures and in real world objects with a protractor	Measure the angles of Tangram shapes to model on paper/cardboard and then in CAD	Complete the triangle game: start off with different angles and different leg lengths. Then have students complete the triangle and see what type of angles are made. Can you ever have two or more acute angles in a triangle? Right angles? Obtuse angles?  How many different triangles can you make with 3 specific side lengths?  Use drawing triangles to see how angles “add” together. The 30-60-90 and 45-45-90 triangles together can make angles from 0 to 180 in increments of 15. Obviously, you can do 30, 45, 60, 90 just using the triangles themselves. This shows you how to do 15 and 75 which completes the 0-90 degrees. Then you simply do the same on the other side of 90 for 90-180
(earlier standard: ability to measure with ruler)	Measure the lengths to create exact replicas  Learn how to extrude in CAD  Measure the height of the pieces to extrude piece in CAD for 3D printing	Scale the pieces (smaller or larger)  Play-Doh Fun Factory extrusion machine might be good demo for kids who don’t know what extrusion is.  Shaped notepad (e.g. circular, elephant, fruit) may be way to show how 3D printing will extrude the shape one layer at a time
5.7 I can identify and apply translations (slides), reflections (flips), or rotations (turns) to figures	Use cardboard then CAD to figure out how to arrange pieces tightly together for faster printing	How can you arrange everyone’s pieces to get maximum number of pieces per sheet when printing?

By playing Tangrams, students will demonstrate

Standard	Activity	Extension
5.4 I can compare angles according to size	Try / develop different strategies using the angles (adding them together by laying next to each other) to figure out which pieces could be used to crease the shape in the challenge card
5.6 I can find the area of different geometric figures and real-world objects	Try the strategy of figuring out where the biggest pieces have to go. Then see how they can be combined with the other pieces to create the shapes in the challenge card	Calculate the area of the challenge shape and see that it should always add up to the total area of the pieces if all pieces are used
5.7 I can identify and apply translations (slides), reflections (flips) or rotations (turns) to figures	See if transforming the shape through reflections, rotations can help give insight into the pieces that might be used to create parts of the challenge shape	Swish game helps students practice this

Levels of Tangrams:

• Tangram Tales: 3 pieces 
• Tangram Calendar or Tangoes Game: 7 pieces 

Extension:

• See how you can make quadrilaterals from triangles 
• 5.5 I can find the area of common quadrilaterals (squares and rectangles) 
• Make your own challenge cards 
• 5.6 I can find the areas of different geometric figures and real-world objects 
• 5.7 I can identify and apply translations (slides), reflections (flips), or rotations (turns) to figures 
• Make your own solution video/instructions (to help others “get it”) 
• 5.7 I can identify and apply translations (slides), reflections (flips), or rotations (turns) to figures 
• Make your own Tangram pieces and related challenge cards: can you use non-right triangles or non-square or rectangular pieces? 
• 5.1 I can identify and describe different types of triangles in various contexts 
• 5.2 I can draw and describe quadrilaterals in various contexts 
• 5.3 I can measure angles in geometric figures and in real-world objects with a protractor 
• 5.4 I can compare angles according to size 
• Design a case for your pieces and challenge cards