3D

Euler’s Formula

brittgow

prisms&pyramids

Learning Intention: Students will investigate Euler’s rule that describes the relationship between the number of faces, the number of edges and the number of vertices of 3D objects.

Success Criteria: Students will create 3D shapes using toothpicks and jelly-lollies to represent edges and vertices. They will then count and record in a table the faces, edges and vertices of the shapes and investigate Euler’s Rule.

Today we are going to learn more about 3D shapes and investigate a special relationship between the number of vertices, edges and faces of such shapes. Create the following shapes using toothpicks and jubes:

  1. tetrahedron
  2. triangular prism
  3. square base pyramid
  4. cube
  5. pentagonal pyramid
  6. pentagonal prism
  7. hexagonal pyramid
  8. hexagonal prism

Now draw a table with six columns that records the name of the polyhedron, the name of the base shape, the number of sides on the base shape, the number of faces, number of vertices and number of edges. Complete the table for each of the 8 shapes listed above. Now see if you can work out any relationship between the values in your table.

 

Geometry – shapes and objects

brittgow

polyhedra

Image Source

Learning Intention:

  • Students will be able to identify and describe 2D shapes and understand the terms translation, reflection, dilation and rotation.
  • They will be able to identify and describe, draw, plan and construct 3D objects.

Success Criteria:

  • Students will complete a poster that shows various shapes undergoing transformations and construct a tessellation from appropriate 2D shapes.
  • They will identify and describe 2D and 3D shapes from photographs.
  • They will draw isometric drawings with dot paper and nets and construct 3D shapes.

So far we have learnt about the properties of polygons, especially triangles and quadrilaterals,  in terms of their sides, angles, perimeter and area. Next we will be looking at TRANSFORMATIONS – how 2D shapes are translated (moved), reflected, rotated and dilated. Your task is to create a poster that shows the letters of your name undergoing each of the following transformations – translation, reflection, rotation and dilation. Draw two copies of each of four block letters of your name and then complete a transformation with one of the letters of each pair.

Screen Shot 2013-08-20 at 10.34.49 AM

We will then learn more about 3D shapes and how they are drawn and constructed.

Polygon matching game – identifying 2D shapes.

Sort the shapes – identify and describe polygons

Polygon sorting – regular and irregular polygons.

More interactives from the Maths Zone (2D shapes)

Classifying 2D and 3D shapes – Geometric Figures Game

Drag and drop 3D shapes – Naming 3D shapes

Matching 3D shapes – identifying 3D shapes

More interactives from the Maths Zone (3D objects)