Geometry Objectives

1. Geometry Objectives • 0506.4.3 Identify a three-dimensional object from two-dimensional representations of that object and vice versa. • 0506.1.1 Given a series of geometric statements, draw a conclusion about the figure described.

2. Geometry • Groups of 3 or 4 • Share with your group what you know about geometry.

3. Let’s brainstorm • What ideas about geometry did you hear in your groups discussion? • What ideas did you have about geometry? • What kinds of shapes are studied in geometry? • What kinds of relationships are studied in geometry?

4. In your spiral • Make a KWL chart K L W What I Learned (this will be filled in as we go along) What I Know About Geometry What I want to Know

5. POLYHEDRA Make this chart in your spiral These are the classes we will be focusing on. Prisms Pyramids Cones Cylinders Prisms

6. POLYHEDRA Polyhedra are 3D shapes with faces that are polygons. Since the faces are polygons, all of the edges are straight.

7. What we know about Three Dimensional Shapes

8. Three dimensional shapes • Display the entire collection where each member of the group can see them. • What do you already know about three-dimensional shapes? • How would you describe three-dimensional shapes?

9. Discuss with group. What are the likes and differences between 2 dimensional and 3 dimensional? Use interwrite Likes Differences Analytical thinking

10. A cube 2 dimensional or 3 dimensional?

11. Which are 2 Dimensional? B A C D

12. Where do you see examples of each? • Think about your daily life. • Where do you see 2 dimensional objects? • Where do you see 3 dimensional objects? Practical thinking

13. Words to know!!! • faces • edges • vertices

14. faces • Each side is a face (the flat smooth part). • Soon we will be finding surface area. • When finding the surface area of a figure, you must measure all faces. • You must know the length and width of each face. • Once you have found those lengths, you must then find the area.

15. How many faces does the cube have? The cube

16. Edges • Where two faces meet. • The faces of polyhedra always have 3 or more edges. • The edges of polyhedra are always line segments. • The endpoints of the edges are called vertices. • There are always more edges than faces or vertices.

17. vertex • Vertex typically means a corner or a point where edges meet. • For example a square has four corners, each is called a vertex. • The plural form of vertex is vertices.

19. Sort • Sort the shapes into the classes displayed on the chart you copied into your notes. • If you are not sure about any of the shapes, set them aside. • Next, discuss the characteristics with your group.

20. Think of where you see each of these objects daily or may have seen them before. • Make a list for each under the chart or on your next clean page.

21. Life

22. Homework • No homework

23. Geometry Objectives • 0506.4.3 Identify a three-dimensional object from two-dimensional representations of that object and vice versa. • 0506.1.1 Given a series of geometric statements, draw a conclusion about the figure described.

24. POLYHEDRA Quick review Polyhedra are 3D shapes with faces that are polygons. Since the faces are polygons, all of the edges are straight.

25. Polyhedra: 3D shapes with faces that are polygons. Polygons

26. Sort into 2 groups • Group 1: shapes that are polyhedra with faces that are polygons. • Group 2: shapes that are polyhedra with faces that are not polygons. • Return all the shapes that do not have all polygons as faces to the plastic bag.

27. Analyze polyhedra • There are 12 different polyhedra. • Find the 12 different ones. • Keep only those 12 and put the rest back in the bag.

28. Name the shapes • What are the names of the shapes? • How are the names determined? • What two classes of polyhedra are represented in the set? Explain. Prisms and pyramids

29. Analyzing Polyhedra • All of the polyhedra have polygons for faces. • Polyhedra have vertices and edges. • The faces are rectangles, squares, triangles, hexagons, and octagons. • The polyhedra in the set are prisms and pyramids. • The polygons of a polyhedra always have three or more edges.

30. Investigate • Polyhedra can be analyzed in many different ways. • One way is to compare the number of faces, vertices, and edges. • In your group analyze the faces, vertices, and edges of the prisms and pyramids.

31. What did you discover about the faces, vertices, and edges of the shapes? • In what ways are the faces of the shapes alike? Different? • What are some other mathematical names we can use to describe the faces? • In what ways are the vertices of the shapes alike? Different?

32. What are some other mathematical names we can use to describe vertices? • In what ways are the edges of the shapes alike? Different? • What are some other mathematical names we can use to describe edges?

33. Faces • Prisms have 5 or more faces. • Pyramids have 4 or more faces. • The faces of polyhedra are always polygons.

34. Vertices • Vertices are points where edges meet.

35. Edges • The faces of polyhedra always have 3 or more edges. • The edges of polyhedra are always line segments. • The endpoints of the edges are called vertices. • There are always more edges than faces or vertices.

36. Based on what you observed with your group. Answer the following problem together.

37. Prisms and Pyramids • Discuss in your group how prisms and pyramids are similar and different. • Make a Venn Diagram Analytical thinking

38. Prisms and Pyramids • What are the properties of prisms? • What are the properties of pyramids? • In what ways are prisms and pyramids different? • What is true about all prisms? • What is true about all pyramids? • Does anyone have a question about either?

39. Prisms and Pyramids • Prisms are polyhedra that have two bases which are congruent. The other faces are rectangles. • Pyramids have a base that is any polygon. The other faces are triangles.

40. In what ways are prisms named? • Prisms are most often named by their bases, the two ends that are congruent, parallel polygons. • A rectangular prism has rectangles for bases. • Pyramids are also named by their base. • A square pyramid has a square base.

41. Try the following with your group.

42. POLYHEDRA Polyhedra are 3D shapes with faces that are polygons. Since the faces are polygons, all of the edges are straight Prisms Pyramids A 3D shape that has two congruent polygons for bases. The other faces are polygons that have exactly four edges A pyramid has one base which is a polygon and is used to name the pyramid. The other faces are triangles

43. Draw an example of each.

44. Try this one • In your spiral draw either a pentagonal prism or pentagonal pyramid. • Write a description of the shape (faces, vertices, and edges) • Check with a partner to see if they agree with what you wrote.

45. Wrap up • Think about our school… • What combinations of polyhedra were used in the building’s design? • Discuss with group.

46. Homework

47. Geometry Objectives • 0506.4.3 Identify a three-dimensional object from two-dimensional representations of that object and vice versa. • 0506.1.1 Given a series of geometric statements, draw a conclusion about the figure described.

48. Cones, cylinders, and spheres • Discuss with your group the ways that cones, cylinders, and spheres are alike and different.

49. Cones, cylinders, and spheres • What are the properties of cones? • Cylinders? • Spheres? • In what ways are cones, cylinders, and spheres alike? • Different? • What is true about all cones? Cylinders? Spheres? • Any questions?

50. POLYHEDRA Polyhedra are 3D shapes with faces that are polygons. Since the faces are polygons, all of the edges are straight Prisms Pyramids A 3D shape that has two congruent polygons for bases. The other faces are polygons that have exactly four edges A pyramid has one base which is a polygon and is used to name the pyramid. The other faces are triangles Cones Cylinders Spheres A 3D shape with a flat circular base and a curved surface that forms a point called an apex 3D shape with 2 congruent, flat circular bases, and a curved surface that joins them A curved surface that is shaped like a ball. Every part of the surface is the same distance from the center.