## Unit 1

### Section 1

• XY plane, X and Y axes, their orientation
• Coordinates of points in the XY plane
• Quadrants Q1, Q2, Q3 and Q4
• Constructive Solid Geometry (CSG)
• Make squares, rectangles and circles
• Assign colors to objects
• Display objects

### Section 2

• Distance between points
• Width and height of planar objects
• 2D and 3D objects are sets of points
• Sets and basic set operations
• Make rings, arcs, triangles and quadrilaterals
• Display multiple objects together
• Create unions and intersections of objects
• Subtract objects

### Section 3

• Size (diameter) of objects
• Distance between objects
• Area of planar objects
• Create regular polygons
• Make prisms based on squares, rectangles, regular polygons, circles, planar rings, triangles and quadrilaterals
• Combine multiple prisms to create a large variety of 3D objects
• Make hollow objects by subtracting prisms of different heights
• Eliminate random color mixing on overlapping surfaces
• Erase parts of planar and 3D objects
• Intersect 3D objects with planes parallel to the XY, XZ and YZ planes

### Section 4

• Vectors in the XY plane
• Vector as the difference of two points
• Basic vector operations
• Move points and objects by adding vectors to them
• Combine X an Y translations

### Section 5

• Split planar (2D) objects along lines parallel to the X and Y axes
• Split 3D objects along planes parallel to the XY, XZ and YZ planes
• Move (translate) objects in the Z direction
• Mirror planar objects about lines parallel to the X and Y axes
• Mirror 3D objects about planes parallel to the XY, XZ and YZ planes
• Scale (stretch and shrink) objects in the X, Y and Z directions

## Unit 2

### Section 6

• Learn how to rotate objects in the XY plane by playing Tetris
• Positive and negative rotation
• Rotation about the origin (0, 0)
• Rotation about an arbitrary point in the XY plane:
• Center of rotation inside the object
• Center of rotation on object’s boundary
• Center of rotation outside of object

### Section 7

• Practice 2D rotations and translations by building Tangram puzzles

### Section 8

• Learn first 3D objects and build simple 3D models
• Create spheres, cubes, cylinders and cones

### Section 9

• Create pipe-like objects (tubes, pipes, 3D rings etc.)
• Create boxes and toruses

### Section 10

• Learn how to rotate and translate objects in the 3D space by playing Tetris 3D
• There are six possible rotations in the 3D space
• Z-axis rotations are the same as XY-plane rotations
• Right-hand rule
• Special cases of rotations discussed separately:
• Rotation point is inside the object
• Rotation point is on object’s boundary
• Rotation point is outside of object

## Unit 3

### Section 11

• Practice 3D rotations and translations by creating a variety of 3D objects related to sports
• Create truncated cones and arcs

### Section 12

• Learn how to exploit axial and planar symmetry to simplify designs
• Mirror 2D objects about lines parallel to the X or Y axes
• Mirror 3D objects about planes that are perpendicular to the X, Y or Z axes
• Exploit multiple symmetries in one design

### Section 13

• Learn how to exploit rotational symmetry to simplify designs
• Combine axial / planar and rotational symmetries

### Section 14

• Solve spatial puzzles in order to develop spatial reasoning skills

### Section 15

• Practice previously learned concepts by building advanced 3D models related to movies
• Scale (shrink or stretch) 2D and 3D objects
• Erase parts of objects

## Unit 4

### Section 16

• Curved surfaces are represented via straight triangles, and how to take advantage of this fact to create new shapes
• More accurate surface representation leads to larger data files and increased memory and computing time
• Make computations faster by reducing the number of sides in cylinders and cones
• Create elbows (elbow = part of a torus)
• Create new objects by reducing the number of facets on elbows and spheres
• Create intersections of objects
• Boolean operations are more efficient when objects have fewer facets

### Section 17

• Create spirals by revolving a given 2D object in the XY plane about the Y axis with a given angle of revolution, and elevation gain per one complete turn
• Create a rail to a staircase
• Create helical screw blades for a meat grinder
• Create a nut with thread, and a double-helix DNA model
• Create a minigolf obstacle
• Complete a freeway intersection
• Build a slide for children’s playground

### Section 18

• Identify repeating patterns and exploit them to simplify models
• Python for-loop

### Section 19

• Use Python for-loop to automate simpler designs
• Create color bars with changing colors, stars of gradually increasing heights
• Create a pyramid by stacking rectangular prisms of gradually decreasing diameter
• Create a round staircase

### Section 20

• Use design automation for advanced projects
• Build a railroad with many wooden ties
• Build a spoked wheel, and a snowflake
• Build a flower with many petals
• Build a clock with minute marks
• Build a sophisticated double-helix DNA model using balls and sticks