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 3D 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”
= 3D analog of regular polygon
= regular polyhedron
2D
3D
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