Frameworks math manipulative by Rob Lovell Frameworks math

Frameworks math manipulative by Rob Lovell

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

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

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

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

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

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)

The End. Questions?

!!Bonus Content!!

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

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

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

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

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

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

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

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