SPACE AND SHAPE Grade 9 Math

VISUALIZING AND MODELING E5 Solve problems using 3D shapes using visualization, reasoning and geometric modeling

TO REVIEW FOR THIS LESSON…  What is a _____________:  A 2D shape, with angles and straight sides  Regular polygons have all the same side lengths and angle measures  Irregular polygons do not have all the same side lengths and angle measures.  What is a _____________:  A 3D shape made of polygons  What makes a _____________unique:  “Regular polyhedrons” have all identical faces  There are only 5 of them

CATEGORIES OF 3D SHAPES  SOME of the different categories of 3D shapes:  _____________: See previous notes  _____________: Similar to platonic, but 2 or more shapes and meet at a vertex  _____________: 2 ends are identical, but the separating sides are rectangles  _____________: Regular polygon base, with triangular sides that slope to meet at a common top point  _____________: The 2 top and bottom are the same shape ( any shape) but the sides are alternating triangles

ACTIVITY #1  Everyone will be given their own 3D net to make into a shape.  During the creation of the shape you will need to record some observations (see the right).  Before you begin, make a rough sketch of what you think your shape could look like. 1. What is the name of your shape? 2. How many faces will your shape have? 3. Predict how many faces will meet at a vertex. Make the shape. 1. Does your shape have vertex regularity? 2. Are the sides all uniform? If yes, what shape are they. If no, how many/what shapes do you have? 3. Based on what you observe, what category of shape do you have? Explain why you believe that.

ARCHIMEDEAN VS PLATONIC While watching the video, answer the following questions: 1.How many ARC solids are there? 2.Rule for faces? 3.Rule for vertices? 4.What is “truncation”? 5.What is the connection between platonic and ARC solids? 6.

PRACTICE QUESTIONS 1.Compare and contrast Archemedean and Platonic. Describe the rules they follow, what they have in common, and how they are connected. 2. Use the shape on the right to answer the following questions. 3.Use calculations of height and slant height to determine if this shape could be cut out and folded into a closed 3D shape. 4.If you cut out 2 of the same shape and folded them into a single shape, what kind of shape would it be? Describe the shape in terms of vertices, faces shape category. Shape details: The triangles are all equilateral triangles, with a base measure of 5 cm. The “radius” of the hexagon (from a vertex to the center is also 5 cm