This activity is intended to develop a concrete understanding of addition and multiplication of irrational and rational numbers, using the most ubiquitous of the irrational numbers: √2.
While this lesson is most closely connected to the Common Core Standard: Use Properties of Rational and Irrational Numbers, it also reinforces and builds upon (and for some students introduces) an often overlooked Common Core Standard: Solve real world and mathematical problems involving perimeters of polygons, including finding …same perimeter and different areas or with the same area and different perimeters.
This activity is perfect for tactile learners.
I have included student pages and teacher pages with suggestions/script.
You know your students best. Add to or delete whatever you need to for their needs based on where they are in their math journey.
If they are already familiar with Tangrams, you can probably skip some of the first part. If they are struggling with the Pythagorean Theorem, slow down at that part and put in a few more examples for discussion.
If they grab onto these, have them make up some for each other and challenge each other! This lesson can be as shallow or as deep as you need.