3D Transformations: Translations and Rotations of Geometric Figures

1. March 16, 2012 • Grab a Computation Challenge, keep it face down and put your name on the back. • Write your homework in your agenda: NONE • Take out your Error Analysis, make sure your name is on it and pass it forward. • Let’s review your test.

2. Let’s Unpack the Standards M7G4: Students will further develop their understanding of three-dimensional figures. a) Describe three-dimensional figures formed by translations and rotations of plane figures through space. b) Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.

3. Concept Map Translations Rotations 3D figures Cones Cylinders Describe Prisms Pyramids Sketch Unit 7: Slices and Shadows Cross-sections Model Describe

4. March 19, 2012 • Graph your Computation Challenge. • Write your homework in your agenda: NONE • Take out your shape chart from Friday, your KIM chart, and a piece of paper.

5. What am I learning today? 3D Transformations What will I do to show that I learned it? Identify the solid figure created by translating and rotating plane figures in space Describe, sketch and model 3D transformations Course 2

6. What do we remember about plane figures? 4 sides, 4 right angles, opposite sides are parallel and congruent Rectangle yes Prism 3 sides, can have varying lengths, angles = 180 degrees Triangle yes Pyramid 4 congruent sides, 4 congruent right angles, opposite sides are parallel Square yes Cube Prism or Pyramid 6 congruent sides; 6 congruent angles Hexagon yes Sphere Circle No sides or angles No

7. Word Bank pyramid cylinder polyhedron prism edge face vertex solid figure cone Platonic Solid sphere

8. SPACE FIGURES • Definition: • Any object that occupies three dimensions is considered a • Basic Terms: • A flat surface area of a geometric solid (space figure) is a • The intersection of two faces of a geometric solid is an • The intersection of two or more edges of a geometric solid is a • Basic Figures: • A geometric solid (space figure) with bases (ends) congruent and parallel circular regions and a curved surface joining the ends is a • A set of points in space an equidistant from a given point is a solid figure face edge vertex cylinder sphere

9. Basic Figures: • A closed surface (space figure) formed by the union of polygonal regions is a • A geometric solid (space figure) with a circular base and a curved surface that tapers to a point (apex) is a • Polyhedra: • A polyhedron with bases congruent and parallel polygonal region whose lateral faces are parallelograms is a • A polyhedron with a polygonal base and sloping triangular sides that meet at a common vertex (apex) is a • A polyhedron with each face a congruent regular polygonal region is a polyhedron cone prism pyramid Platonic solid

10. polygon polyhedron translation rotation

11. Foldable 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line.

12. The fold crease Foldable 2. Now, divide the right hand section into 4 sections by drawing 3 evenly spaced lines. 3. Use scissors to cut along your drawn line, but ONLY to the crease!

13. 2D to 3D The fold crease Foldable 4. Write 2D to 3D down the left hand side

14. 2D to 3D The fold crease Foldable 5. Fold over the top cut section and write Circle on the outside. Circle Triangle 6. Do the same for the other three folds. Label the outside: Triangle, Square, and Rectangle Square Rectangle

15. 2D to 3D Foldable 7. Open your foldable. On the left hand side, write Translation. Translation Explanation Rotation Example 8. On the right hand side write Rotation

16. March 20, 2012 • Write your homework in your agenda: Homework and Practice worksheet • Take out your foldable from yesterday and your KIM chart. • Open your CRCT wkbk to p. 31 and complete # 1- 12.

17. When you translate a circle through space, it moves a fixed distance along a straight path. What solid figure is the result of this translation? Cylinder

18. When you translate a triangle through space, it moves a fixed distance along a straight path. What solid figure is the result of this translation? Triangular Prism

19. When you translate a rectangle through space, it moves a fixed distance along a straight path. What solid figure is the result of this translation? Rectangular Prism

20. When you translate a square through space, it moves a fixed distance along a straight path. What solid figure is the result of this translation? What solid figure is the result of this translation? Prism Cube

21. Lesson Practice • A square measures 5 inches on each side. The square is translated 3 inches directly above the plane in which it lies. The two squares are connected by four line segments. What solid figure is formed? • What space figure would be created if it had been translated the same distance as the length of its side? Prism Cube

22. Lesson Practice • A circle has a diameter of 5 cm. The circle is translated 3 cm directly above the plane in which it lies. Each point of the circle is then connected by a line segment to its translated point. What three dimensional figure is formed? • What figure would be created if the diameter and the height were congruent? Cylinder Cylinder

23. Let’s Discuss these questions… • Why do translations have to be made through space in order to create a three-dimensional figure? • Every time you translate a square the result is a prism. True or False? Explain. • Can polygons other than triangles, squares and rectangles be translated? Explain.

24. line of symmetry

25. Let’s Spin and See! When you rotate a circle through space, it spins around a line of symmetry. With rotation, that circle becomes a sphere.

26. Let’s Spin and See! When you rotate a circle through space, it could also spin around a fixed point or line outside itself. With rotation, that circle becomes a torus or ring.

27. Let’s Spin and See! When you rotate a triangle through space, it can spin around a line of symmetry or around its vertex. With rotation, that triangle becomes a cone.

28. Let’s Spin and See! When you rotate a triangle through space, it could also spin around a fixed point or line outside itself. With rotation, that circle becomes a funnel or volcano.

29. Let’s Spin and See! When you rotate a rectangle or square through space, it spins around a line of symmetry. With rotation, that rectangle becomes a cylinder.

30. Let’s Spin and See! When you rotate a square or rectangle through space, it could also spin around a fixed point or line outside itself. With rotation, that rectangle or square produces a figure that is annulus washer.

31. Lesson Practice • What three dimensional shape will be formed if the right triangle shown is rotated about the line shown? • What three dimensional figure will be formed if the rectangle shown is rotated about the line shown?

32. Lesson Practice • Is there a difference in the type of solid figure created based on the line of symmetry around which a planar shape is rotated?

33. Writing in Math • Does the direction of the translation affect the final shape of the solid? Explain. • A rectangle is rotated around its vertical line of symmetry to create a cylinder. Suppose rotating the rectangle around its horizontal line of symmetry results in an identical cylinder. What can you conclude about the rectangle?