1. Frameworks math manipulative by Rob Lovell

2. Frameworks math manipulative Rob Lovell Contents What are Frameworks? How can a teacher use them? Why would a teacher use them? Questions?

3. Frameworks math manipulative Rob Lovell What Are Frameworks? Math manipulative Plastic geometric shapes Edges snap together Make 3D solids –Called “polyhedra”

4. Frameworks math manipulative Rob Lovell How? Euler’s Formula Student’s discover Euler’s Formula!! F + V = E + 2

5. Frameworks math manipulative Rob Lovell How? Euler’s Formula Choose a polyhedron, build it, fill out chart Pyramid (tri.)Prism (tri.)Cube (rect.) Pyramid (rect.)Prism (rect.)Octahedron NameSketchFacesVerticesEdges F + V = E + 2 Triangular Prism 5 6 9

6. Frameworks math manipulative Rob Lovell Why Use Frameworks? Why should a math teacher use Frameworks? Think on own for 20 seconds Pair with neighbour for 1 minute Share with class

7. Frameworks math manipulative Rob Lovell Summary What? –Manipulatives to build polygons and polyhedra How? –Explore Euler’s Formula Why? –Hands-on experience (to construct knowledge)

8. The End. Questions?

9. !!Bonus Content!!

10. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids “platonic solid” = 3D analog of regular polygon = regular polyhedron 2D3D Regular polygon (ex. square) Regular polyhedron (ex. cube) Identical sidesIdentical faces Identical angles (radians) Identical solid angles (steradians)

11. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Build a 4-faced regular polyhedron –{equilateral triangle} –{equilateral triangle, square, pentagon} –{all shapes} Tetrahedron (4 faces) Tetrahedron

12. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Build a 6-faced regular polyhedron –Tetrahedron (4 faces) –Hexahedron (6 faces) Hexahedron

13. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Build a 8-faced regular polyhedron –Tetrahedron (4 faces) –Hexahedron (6 faces) –Octahedron (8 faces) Octahedron

14. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Build a 12-faced regular polyhedron –Tetrahedron (4 faces) –Hexahedron (6 faces) –Octahedron (8 faces) –Dodecahedron (12 faces) Dodecahedron

15. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Build a 20-faced regular polyhedron –Tetrahedron (4 faces) –Hexahedron (6 faces) –Octahedron (8 faces) –Dodecahedron (12 faces) –Icosahedron (20 faces) Icosahedron

16. Frameworks math manipulative Rob Lovell Activity 1: Platonic Solids Platonic Solids –Tetrahedron (4 faces) –Hexahedron (6 faces) –Octahedron (8 faces) –Dodecahedron (12 faces) –Icosahedron (20 faces) Questions? Icosahedron

17. Frameworks math manipulative Rob Lovell Activity 3: Nets “But I already know how to do Nets!” –Paper, scissors, glue –Virtual Nets Teacher: Faster! Easier! Student: Tangible! Control!