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Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Unit 10: Geometry (7 days) Possible Lesson 01 (4 days) Possible Lesson 02 (3 days) POSSIBLE LESSON 01 (4 days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Students use various materials to create and describe the attributes of two-dimensional figures. Students use geometric solids to investigate and describe the attributes of three-dimensional figures. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148 5.7 Geometry and spatial reasoning.. The student generates geometric definitions using critical attributes. The student is expected to: 5.7 Identify essential attributes including parallel, perpendicular, and congruent parts of two- and three-dimensional geometric figures. Supporting Standard Underlying Processes and Mathematical Tools TEKS: 5.14 Underlying processes and mathematical tools.. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 5.14A Identify the mathematics in everyday situations. page 1 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days 5.14D Use tools such as real objects, manipulatives, and technology to solve problems. 5.15 Underlying processes and mathematical tools.. The student communicates about Grade 5 mathematics using informal language. The student is expected to: 5.15A Explain and record observations using objects, words, pictures, numbers, and technology. 5.15B Relate informal language to mathematical language and symbols. 5.16 Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to: 5.16A Make generalizations from patterns or sets of examples and nonexamples. 5.16B Justify why an answer is reasonable and explain the solution process. Performance Indicator(s): Grade 05 Mathematics Unit 10 PI 01 Create a mobile (e.g., a decorative structure that is suspended so as to turn freely in the air) that displays models of 4 different three-dimensional figures. The mobile should include 1 prism, 1 pyramid, and 2 curved surfaced figures. Use the provided die-cuts or nets (cube, rectangular prism, triangular prism, cone, cylinder, triangular pyramid, and square pyramid) to represent the three-dimensional figures selected. On each net, if applicable, use different map pencil colors to highlight parallel lines and perpendicular and to shade the congruent faces of each figure. Construct each selected net to create a three-dimensional model. Using geometric attributes, create a description card for each model that includes the following: (1) the formal geometric name; (2) a description of each of the two-dimensional faces or curved surfaces; (3) the number of faces/curved surfaces; (4) the number of vertices, if applicable; and (5) the number of edges, if applicable. Complete the mobile by using yarn or string to attach each description card to the appropriate three-dimensional model and then to a clothes hanger. The completed mobile should be similar to the sample below: page 2 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Observe the created mobile, and write a journal entry for each of the following: (1) describe the difference between the number of faces, edges, and vertices of the prism and the pyramid; (2) determine examples of real-world situations/objects in which each three-dimensional model created could be found; and (3) justify how the two-dimensional attributes define each three-dimensional model. Standard(s): 5.7 , 5.14A , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B ELPS ELPS.c.1C , ELPS.c.5F page 3 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Grade 05 Mathematics Unit 10 PI 02 Answer each of the following questions regarding the playhouse, using appropriate geometric language and labels: 1. identify the geometric figure that represents the roof, column, house, and top of the column; 2. identify the number of vertices, edges, and faces or curved surfaces on each of the figures identified in step (1); and 3. name all vertices, edges, and faces for the roof and house. Write a paragraph comparing and contrasting the attributes of the roof, column, house, and top of the column using formal geometric language. Standard(s): 5.7 , 5.14A , 5.15A , 5.15B ELPS ELPS.c.5B Key Understanding(s): page 4 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Two- and three-dimensional figures occur in architecture, fabric, art, street maps, and many other real world settings. Polygons are two-dimensional figures with specific attributes. Formal geometric vocabulary is used to identify and describe the position and attributes of two- and three- dimensional geometric figures. The orientation of a two- or three- dimensional figure does not affect its congruency or its symmetry. Three-dimensional figures consist of two-dimensional figures and are defined and distinguished by their attributes, which include faces, edges, and vertices, which can be generalized to find examples and non-examples. Two- and three-dimensional figures consist of essential attributes including parallel, perpendicular, and congruent parts. Underdeveloped Concept(s): Some students have difficulty understanding that more than one description may be needed to describe intersecting lines (such as perpendicular lines). Some students confuse the size of an angle with the length of its sides. Some students may struggle with naming all possible figures with the given characteristics or struggle with identifying a distinguishing attribute between two figures, such as the square is a special rhombus with four right angles or a cube is a special rectangular prism with all square faces. Some students may have difficulty visualizing where right angles are on three-dimensional figures. Vocabulary of Instruction: adjacent attribute intersecting lines one-dimensional figure parallel lines perpendicular lines three-dimensional figure two-dimensional figure Materials List: cardstock (2 sheets per 2 students) cardstock (2 sheets per 2 students) cardstock (4 sheets per 2 students) cardstock (4 sheets per 2 students) cardstock (optional) (9 sheets per 4 students) clothes hanger (wire) (1 per student) geometric figures or solids (1 set per 4 students, 1 set per teacher) index card (4” x 6”) (4 per student) page 5 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days math journal (1 per student) plastic zip bag (sandwich sized) (1 per 2 students) plastic zip bag (sandwich sized) (1 per 2 students) plastic zip bag (sandwich sized) (1 per 2 students) plastic zip bag (sandwich sized) (1 per 2 students) scissors (1 per student,1 per teacher) tape (clear) (1 roll per student) tape (clear) (optional) (1 roll per teacher) yarn (6 inch strip) (4 per student) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Lines, Angles, and Congruency Cards Two-Dimensional Geometric Definitions Notes Two-Dimensional Attribute Cards Two-Dimensional Figures Graphic Organizer Polygon Attributes KEY Polygon Attributes Two-Dimensional Figures Visual Graphic Organizer Polygon Table Faces, Edges, Vertices, Bases, and Curved Surfaces Cards page 6 of 74 Enhanced Instructional Transition Guide Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Three-Dimensional Geometric Definitions Notes Three-Dimensional Geometric Patterns Three Dimensional Attribute Cards Three-Dimensional Figures Graphic Organizer Attributes of Three-Dimensional Figures KEY Attributes of Three-Dimensional Figures Naming Geometric Figures KEY Naming Geometric Figures Geometric Logic Two- and Three-Dimensional Figure Practice KEY Two- and Three-Dimensional Figure Practice GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested Day 1 Suggested Instructional Procedures Notes for Teacher Topics: Spiraling Review Lines, angles, and congruency page 7 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher ATTACHMENTS Engage 1 Card Set: Lines, Angles, and Students use logic and reasoning skills to review examples and definitions of lines, angles, and congruency in order Congruency Cards (1 set per 2 to recognize them as attributes of two-dimensional figures. students) Teacher Resource: Lines, Instructional Procedures: 1. Prior to instruction, create a card set: Lines, Angles, and Congruency Cards for every 2 students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag. 2. Place students in pairs and a distribute card set: Lines, Angles, and Congruency Cards to each pair. 3. Instruct student pairs to match each card with its appropriate definition. Allow time for students to complete their Angles, and Congruency Cards (1 set per teacher) Teacher Resource: TwoDimensional Geometric Definitions – Notes (1 per teacher) matches. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the terms and the figures that model them. Verify student matches are correct. MATERIALS Ask: cardstock (2 sheets per 2 What is the difference between parallel lines and perpendicular lines? Answers may vary. Parallel students) lines never intersect, and perpendicular lines intersect at a right angle; etc. scissors (1 per teacher) Are there examples that could represent perpendicular lines in the alphabet? Explain. (yes) plastic zip bag (sandwich sized) Answers may vary. A “T” or “L” could represent perpendicular lines because the letters demonstrate right (1 per 2 students) angles (90º); etc. Are all intersecting lines perpendicular? Explain. (no) Answers may vary. Not all lines that intersect have to intersect at a right angle; etc. TEACHER NOTE If you create two lines and have them intersect like a cross, what kind of lines are these? A line is the set of all points that form a (perpendicular lines) straight path that goes in opposite page 8 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher If two lines are perpendicular, what angle measure is created by the intersecting lines? (90º) directions without ending. If the arrows Is an acute angle greater than or less than a right angle? (less than a right angle) on the end of the line were to be What do you call an angle larger than a right angle (90º) but less than a straight line (180º)? (obtuse replaced with dots or two endpoints angle) indicating a definite beginning and What are parallel, perpendicular, right, acute, and obtuse attributes that could be used to describe ending to the line, then that part of a two-dimensional figures? Explain. (yes) Answers may vary. The sides of two-dimensional figures can be described as parallel and/or perpendicular; whereas, right, acute, and obtuse are attributes that could be used to describe angles of two-dimensional figures; etc. line is called a line segment. If only one of the arrows on a line were to be replaced with an endpoint and the other end of the line continues without end in 4. Display the “Congruent” card from teacher resource: Lines, Angles, and Congruency Cards. Instruct student pairs to discuss what they think the hash marks on each side of the rectangle and the small boxes at each angle of the rectangle represent. Invite student volunteers to share their findings. Ask: the opposite direction, then that part of the line is called a ray. A vertex is the common endpoint of two rays that form an angle. A vertex of a two-dimensional What do the hash marks represent on the rectangle? Answers may vary. The hash marks represent figure is the point (corner) of intersection congruency, sides that are equal; etc. of two sides in a two-dimensional figure. Why do some sides have one hash mark and other sides have two hash marks? Answers may vary. The sides with one hash mark indicate one set of congruent sides, while the sides with two hash marks TEACHER NOTE indicate different set of congruent sides; etc. Grade 4 introduces formal and symbolic What do the small boxes at each angle of the rectangle represent? Answers may vary. The small geometric language for lines, line boxes at each angle represent sides that are perpendicular, meaning the angles are right angles with segments, rays, and angles. measures of 90º; etc. What do you notice about all the angles of the rectangle? Answers may vary. All the angles of the TEACHER NOTE page 9 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures rectangle are right angles with measures of 90º; etc. Is congruency another attribute that could be used to describe two-dimensional figures? Explain. (yes) Answers may vary. The sides and angles of two-dimensional figures can be described as congruent; etc. Notes for Teacher Many students have difficulty classifying an angle when it does not have a horizontal side. Allow these students to use a “moveable” right angle such as the corner of an index card (or their 5. Explain to students that they will be investigating the attributes of two-dimensional figures using the formal geometric terms. STAAR Grade 5 Mathematics Reference Materials) to place at the vertex of any angle. It should be easy to see if the angle is less than, equal to, or greater than a right angle. TEACHER NOTE Teacher Resource: Two-Dimensional Geometric Definitions – Notes may be used to verify student responses to the matching activities outlined in the instruction. Topics: Attributes of two-dimensional figures ATTACHMENTS Card Set: Two-Dimensional Attribute Cards (1 set per 2 students) Explore/Explain 1 Teacher Resource: Two- Students use logic and reasoning skills to investigate, compare and contrast examples and definitions of two- Dimensional Figures Graphic page 10 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures dimensional figures. Notes for Teacher Organizer (1 per teacher) Handout: Two-Dimensional Instructional Procedures: 1. Prior to instruction, create a card set: Two-Dimensional Attribute Cards for every 2 students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag. 2. Place students in pairs and distribute a card set: Two-Dimensional Attribute Cards to each pair. 3. Instruct students to work with their partner to match each card with its appropriate definition. Allow time for students to complete their matches. Monitor and assess student pairs to check for understanding. 4. Facilitate a class discussion about the terms and the figures that model them. 5. Once all matches have been verified, instruct students to organize their cards into a tree-like diagram showing how all the figures are related. For teacher reference, see teacher resource: Two-Dimensional Figures Graphic Organizer as a sample of how the cards could be arranged. Do not display this graphic to students at Figures Graphic Organizer (1 per student) Teacher Resource: Polygon Attributes KEY (1 per teacher) Handout: Polygon Attributes (1 per student) Handout (optional): TwoDimensional Figures Visual Graphic Organizer (1 per student) Handout (optional): Polygon Table this time. If needed, demonstrate what a tree diagram looks like using the model below. Explain to students that the cards are not necessarily in the correct position. MATERIALS Sample: cardstock (4 sheets per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) TEACHER NOTE page 11 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher Polygons with all sides and angles Allow time for students to organize their cards. Monitor and assess student pairs to check for understanding. congruent are called regular polygons. Facilitate a class discussion about the diagrams they created. Allow students to adjust their graphic For example, a hexagon with all sides organizers based on the class discussion. equal in length and all angles equal in Ask: angle measure, are considered regular Are all two-dimensional figures polygons? How do you know? (no) Answers may vary. Some twodimensional figures have curved sides (e.g. circles); etc. Are all polygons two-dimensional figures? How do you know? (yes) Answers may vary. All polygons have length and width; etc. hexagons. However, all hexagons are not regular hexagons. These figures are referred to as irregular figures. There are many examples of irregular hexagons in Are all polygons quadrilaterals? How do you know? (no) Answers may vary. Some polygons are the real world where all of the sides are triangles; etc. not equal in length, and all angles are Are all quadrilaterals polygons? How do you know? (yes) Answers may vary. All quadrilaterals are not equal in measure. enclosed figures with 4 straight sides; etc. Are all quadrilaterals parallelograms? How do you know? (no) Answers may vary. Quadrilaterals only TEACHER NOTE have to have four sides, and those sides do not have to all be parallel and/or congruent; etc. Teacher resource: Two-Dimensional Are all parallelograms quadrilaterals? How do you know? (yes) Answers may vary. Parallelograms Figures Graphic Organizer may be must have four sides; etc. posted in the classroom. The graphic organizer does not include all 4- sided 6. Display teacher resource: Two-Dimensional Figure Graphic Organizer. Distribute handout: Two- figures such as a “kite.” A kite would be Dimensional Figure Graphic Organizer to each student. Facilitate a class discussion to summarize the another branch off of the quadrilateral relationships between the two-dimensional figures. because of its attributes. A kite has two Ask: sets of congruent sides, but the page 12 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures How do the attributes change when comparing the quadrilateral to the parallelogram, then to the rectangle, and finally to the square? Explain. Answers may vary. For these connected figures, the figure beneath contains the attributes of the figure above it, meaning the figure’s attributes move from general to more specific if looking down the tree; etc. Notes for Teacher congruent sides are adjacent to each other, not opposite of each other. A kite’s opposite angles are congruent. The purpose of this graphic organizer is to help students visually organize the Explain to students that the attributes of a quadrilateral (a four-sided polygon) are included in the attributes of geometric figures based on their a parallelogram (a quadrilateral with opposite sides congruent, opposite sides parallel, and opposite angles common and distinguishing attributes. congruent). The attributes of a quadrilateral and a parallelogram are included in the attributes of a rectangle (a quadrilateral with four right (90o) angles (meaning opposite angles are congruent), opposite sides congruent, TEACHER NOTE opposite sides parallel, and adjacent sides are perpendicular because of the four right angles.). The attributes Handout (optional): Polygon Table is of a quadrilateral, parallelogram, and a rectangle are included in the attributes of a square (a quadrilateral with available to assist students in all sides congruent (meaning opposite sides congruent), opposite sides parallel, four right (90o) angles understanding the different types of (meaning opposite angles are congruent), and adjacent sides are perpendicular because of the four right polygons. angles.). 7. Distribute handout: Polygon Attributes to each student as independent practice and/or homework. TEACHER RESOURCE The handout (optional): TwoDimensional Figures Visual Graphic Organizer provides a visual representation of two-dimensional figures along with the names in a treelike graphic organizer. 2 Topics: Spiraling Review Faces, edges, vertices, bases, and curved surfaces page 13 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher ATTACHMENTS Engage 2 Card Set: Faces, Edges, Students use logic and reasoning skills to review examples and definitions of faces, edges, vertices, bases, and Vertices, Bases, and Curved curved surfaces in order to recognize them as attributes of three-dimensional figures. Surface Cards (1 set per 2 students) Instructional Procedures: Teacher Resource: ThreeDimensional Geometric 1. Prior to instruction, create a card set: Faces, Edges, Vertices, Bases, and Curved Surface Cards for every 2 students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag. 2. Facilitate a class discussion to debrief the previously assigned handout: Polygon Attributes, as needed. 3. Place students in pairs and distribute a card set: Faces, Edges, Vertices, Bases, and Curved Surface Cards to each pair. Instruct student pairs to match each card with its appropriate definition. Allow time for students to Definitions – Notes (1 per teacher) Class Resource (optional): Three-Dimensional Geometric Patterns (1 set per 4 students) complete their matches. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the terms and the figures that model them. Verify student matches are correct. MATERIALS Ask: cardstock (2 sheets per 2 How is an edge on a three-dimensional figure like a side on a two-dimensional figure? Answers students) may vary. They are both line segments where parts of the figure meet; etc. scissors (1 per teacher) How is a vertex on a three-dimensional figure different from a vertex on a two-dimensional figure? plastic zip bag (sandwich sized) Answers may vary. Although they both show a point of intersection, the three-dimensional figure shows (1 per 2 students) where 3 or more edges intersect, whereas a two-dimensional figure shows where 2 sides intersect; etc. geometric figures or solids (1 set per teacher) 4. Display a triangular prism, hexagonal prism, and cube for the class to see. Use these prisms to discuss the terms face and base. Explain to students that the base of a figure defines the name of the prism. Begin with the cardstock (optional) (9 sheets per 4 students) page 14 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher displayed triangular prism. tape (clear) (optional) (1 roll per Ask: teacher) This figure has how many faces? (5 faces) How could you describe the faces of this figure? (2 triangular faces and 3 rectangular faces) TEACHER NOTE If the bases of a prism are the two unique faces that are congruent and parallel to each other, If geometric figures or solids are which faces are the bases? (the triangular faces) unavailable, use class resource Demonstrate that the bases of a triangular prism are parallel by placing the triangular prism in the palm of one hand and placing the palm of your other hand on top. Discuss how the two triangular faces (and your palms) are parallel to each other. What is the name of this figure? (a triangular prism) (optional): Three-Dimensional Geometric Patterns to create a set of figures for every 4 students. TEACHER NOTE Teacher Resource: Three- Refer to the displayed hexagonal prism and use the same discussion above to determine that the two hexagons are the bases of the figure; therefore, the figure is called a hexagonal prism. Next, discuss the displayed cube. Discuss how the cube has six congruent faces that are all squares; therefore, any two of the squares that are parallel to one another could be considered the bases. Explain to students that this figure Dimensional Geometric Definitions – Notes may be used to verify student responses to the matching activities outlined in the instruction. has a unique name, a cube. 5. Display a square pyramid and triangular pyramid. Use these pyramids to discuss the terms face and base. Explain to students that a pyramid has only one base, and the base defines the name of the pyramid. Begin with the displayed square pyramid. Ask: A pyramid has how many bases? (1 base) This figure has how many faces? (5 faces) page 15 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher How could you describe the faces of this figure? (triangles and a square) Since there is only one square face, what do you think is the name of this pyramid? (a square pyramid) Notice, the non-base faces are all triangles. Next, refer to the displayed triangular pyramid. Ask: This figure has how many faces? (4 faces) How could you describe the faces of this figure? (all triangles) Since all of the faces are triangles, are all of the faces congruent? Answers may vary. If the faces of the triangular prism are all equilateral triangles, then any of the faces could be the base. If one of the triangles is not congruent to the other triangles, then the non-congruent triangle is the base. What is the name of this figure? (a triangular pyramid) 6. Display the cylinder, the cone, and the sphere to distinguish the difference between circular surface and circular base. Ask: Do all of these figures have a base? (No, the sphere has no base.) Since the sphere has no base, the sphere is described as a curved surface. How many bases does the cylinder have? (2 bases) How could you describe the bases of a cylinder? (2 circular bases) How could you describe the other surface of the cylinder? (a curved surface) page 16 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher The cone has how many bases? (1 base) How could you describe the other surface of the cone? (a curved surface) 7. Explain to students that they will be investigating the attributes of three-dimensional figures using the formal geometric terms. Topics: Attributes of three-dimensional figures ATTACHMENTS Card Set: Three-Dimensional Attribute Cards (1 set per 2 students) Explore/Explain 2 Teacher Resource: Three- Students use logic and reasoning skills to investigate, compare and contrast examples and definitions of three- Dimensional Figures Graphic dimensional figures. Organizer (1 per teacher) Handout: Three-Dimensional Instructional Procedures: 1. Prior to instruction, create a card set: Three-Dimensional Attribute Cards for every 2 students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag. 2. Place students in pairs and distribute a card set: Three-Dimensional Attribute Cards to each pair. 3. Instruct student pairs to match each card with its appropriate definition. Allow time for students to complete their matches. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the terms and the figures that model them. Figures Graphic Organizer (1 per student) Teacher Resource: Attributes of Three-Dimensional Figures KEY (1 per teacher) Handout: Attributes of ThreeDimensional Figures (1 per student) 4. Once all matches have been verified, instruct students to organize their cards into a tree-like diagram showing how all the figures are related. For teacher reference, see teacher resource: Three-Dimensional Figures MATERIALS page 17 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Graphic Organizer as a sample of how the cards could be arranged. Do not display this graphic to the students at this time. If needed, demonstrate what a tree diagram looks like using the model below. Explain to students that the cards are not necessarily in the correct position. Sample: Notes for Teacher cardstock (4 sheets per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) geometric figures or solids (1 set per 4 students, 1 set per teacher) Allow time for students to organize their cards. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the diagrams they created. Allow students to adjust their graphic organizers based on the class discussion. Ask: TEACHER NOTE Pyramids and Cones A pyramid is a polyhedron (a threedimensional figure with faces and edges). The attributes of a pyramid Are all three-dimensional figures prisms? How do you know? (no) Answers may vary. Some three- include faces, edges, and the “point” dimensional figures are pyramids or have curved surfaces; etc. where the edges meet, which is defined Are all prisms three-dimensional figures? How do you know? (yes) Answers may vary. All prisms have as a “vertex.” As the number of faces on length, width, and height (or depth); etc. the pyramid approaches infinity, the Are all prisms rectangular? How do you know? (no) Answers may vary. Some prisms are triangular, surface becomes curved, creating a pentagonal, etc. cone. Since a cone consists of a curved Are all pyramids three-dimensional figures? How do you know? (yes) All pyramids have length, width, surface, it is not considered a and height (or depth); etc. polyhedron. When you talk about a cone the terms “face,” “edge,” and page 18 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures 5. Display teacher resource: Three-Dimensional Figure Graphic Organizer. Distribute handout: ThreeDimensional Figure Graphic Organizer to each student. Facilitate a class discussion to summarize the relationships between the figures. Ask: Notes for Teacher “vertex,” as defined by a polyhedron, do not apply. A wide variety of resources modify these definitions when referencing non-polyhedrons. It is Are all cubes rectangular prisms? How do you know? (yes) Answers may vary. All cubes have 6 square possible to refer to the “vertex” of a cone (rectangular) faces, 12 edges, and 8 vertices; etc. as a “point” in elementary math. Therefore, for elementary, TEA only lists 6. Distribute handout: Attributes of Three-Dimensional Figures to each student as independent practice and/or homework. the curved surface and circular base as the attributes of a cone and do not reference “vertex” as a defining attribute. So, CSCOPE uses these attributes in alignment with TEA. Cones and Cylinders According to TEA, a face of a threedimensional figure is defined as a flat surface in the shape of a twodimensional figure. Since the circular bases of a cylinder and cone are flat surfaces in the shape of a twodimensional figure, they could also be considered “faces.” However, for elementary, TEA only lists curved surface and circular base(s) as the attributes of a cylinder and cone. So, page 19 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher CSCOPE uses these attributes in alignment with TEA. TEACHER NOTE The faces of some rectangular prisms are all rectangles and the faces of some rectangular prisms are rectangles and squares. However, recall all squares are rectangles, so refer to this prism as a rectangular prism. 3 Topics: Spiraling Review Naming attributes of two- and three-dimensional figures ATTACHMENTS Explore/Explain 3 Teacher Resource: Naming Students investigate and name the attributes of two- and three-dimensional figures. Geometric Figures KEY (1 per teacher) Teacher Resource: Naming Instructional Procedures: 1. Distribute handout: Naming Geometric Figures to each student. Display the top part of page 1 of teacher resource: Naming Geometric Figures. Facilitate a class discussion regarding how to name the attributes of a labeled geometric figure. Emphasize when naming line segments that the order of the letters within one segment does not matter. For example, is the same line segment as . Also explain that when naming Geometric Figures (1 per teacher) Handout: Naming Geometric Figures (1 per student) faces of figures, the order of the letters naming one face should be clockwise; however, the beginning vertex of page 20 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures the face does not matter. For example, the following all name the same face: ABCD, BCDA, CDAB, and DABC. 2. Place students in pairs and instruct students to work together to complete the handout. Allow time for students to complete the activity. Monitor and assess students to check for understanding. When student pairs have completed the handout, invite student volunteers to display their answers. Facilitate a class discussion encouraging students to determine all the possible ways attributes can be named. Notes for Teacher TEACHER NOTE When naming faces, some resources will name faces using a counterclockwise order. However, the answer keys provide sample answers in clockwise order. TEACHER NOTE It is customary to name an angle with a single capital letter or an interior number when there is no possibility of confusion. Angles can also be named with three letters with the middle letter representing the vertex of the referenced angle. page 21 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Topics: Attributes of two- and three-dimensional figures Notes for Teacher ATTACHMENTS Teacher Resource: Geometric Logic (1 per teacher) Teacher Resource: Two- and Elaborate 1 Three-Dimensional Figure Students extend concepts of geometric attributes of two- and three-dimensional figures. Practice KEY (1 per teacher) Handout: Two- and Three- Instructional Procedures: 1. Display teacher resource: Geometric Logic for the class to see. Explain to students that special made-up Dimensional Figure Practice (1 per student) words such as hulops can be used to name sets of examples. Although these are made-up names for the sets, you can still apply what you know about two-dimensional figures to determine the characteristics a set of figures have in common. Ask: What do these figures have in common? Answers may vary. The first figure is a triangle with a square inside it, the second figure is a rectangle with a pentagon inside of it, and the third figure is a pentagon with a hexagon inside of it; they are polygons inside of polygons; etc. What pattern do these shapes seem to be following? Answers may vary. The inside figure has one more side and one more vertex than the outside figure; etc. 2. Distribute handout: Two- and Three-Dimensional Figure Practice to each student. Instruct students to complete the handout independently. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief student solutions. page 22 of 74 Enhanced Instructional Transition Guide Suggested Day 4 Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Evaluate 1 Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned Notes for Teacher ATTACHMENTS Handout: Three-Dimensional Geometric Patterns (1 per student) to this lesson. Performance Indicator(s): MATERIALS Grade 05 Mathematics Unit 10 PI 01 clothes hanger (wire) (1 per Create a mobile (e.g., a decorative structure that is suspended so as to turn freely in the air) that displays models of 4 student) different three-dimensional figures. The mobile should include 1 prism, 1 pyramid, and 2 curved surfaced figures. yarn (6 inch strip) (4 per student) Use the provided die-cuts or nets (cube, rectangular prism, triangular prism, cone, cylinder, triangular pyramid, and index card (4” x 6”) (4 per square pyramid) to represent the three-dimensional figures selected. On each net, if applicable, use different map student) pencil colors to highlight parallel lines and perpendicular and to shade the congruent faces of each figure. tape (clear) (1 roll per student) Construct each selected net to create a three-dimensional model. Using geometric attributes, create a description card scissors (1 per student) for each model that includes the following: (1) the formal geometric name; (2) a description of each of the two- math journal (1 per student) dimensional faces or curved surfaces; (3) the number of faces/curved surfaces; (4) the number of vertices, if applicable; and (5) the number of edges, if applicable. Complete the mobile by using yarn or string to attach each description card to the appropriate three-dimensional model and then to a clothes hanger. The completed mobile should be similar to the sample below: page 23 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher Observe the created mobile, and write a journal entry for each of the following: (1) describe the difference between the number of faces, edges, and vertices of the prism and the pyramid; (2) determine examples of real-world situations/objects in which each three-dimensional model created could be found; and (3) justify how the twodimensional attributes define each three-dimensional model. Standard(s): 5.7 , 5.14A , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B ELPS ELPS.c.1C , ELPS.c.5F Evaluate 2 Instructional Procedures: page 24 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. Performance Indicator(s): Grade 05 Mathematics Unit 10 PI 02 Answer each of the following questions regarding the playhouse, using appropriate geometric language and labels: 1. identify the geometric figure that represents the roof, column, house, and top of the column; 2. identify the number of vertices, edges, and faces or curved surfaces on each of the figures identified in step (1); and 3. name all vertices, edges, and faces for the roof and house. page 25 of 74 Enhanced Instructional Transition Guide Suggested Day Grade 5/Mathematics Unit 10: Suggested Duration: 4 days Suggested Instructional Procedures Notes for Teacher Write a paragraph comparing and contrasting the attributes of the roof, column, house, and top of the column using formal geometric language. Standard(s): 5.7 , 5.14A , 5.15A , 5.15B ELPS ELPS.c.5B 05/17/13 page 26 of 74 Grade 5 Mathematics Unit: 10 Lesson: 01 Lines, Angles, and Congruency Cards Parallel lines lines that lie in the same plane, never intersect, and are the same distance apart Perpendicular lines lines that intersect at right angles (90°) to each other Right angle an angle that measures 90°; lines that are perpendicular to each other Acute angle an angle with a measure less than a right angle (90°) ©2012, TESCCC 05/14/13 page 1 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Lines, Angles, and Congruency Cards Obtuse angle an angle whose measure is greater than a right angle (90°) but less than a straight line (180°) Congruent figures with the same size, same shape ©2012, TESCCC 05/14/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Geometric Definitions - Notes Angle: two rays that meet at a common endpoint Acute angle: an angle with a measure less than a right angle (90°) Circle: the set of all points that lie the same distance from the center and lie in the same plane Congruent: figures with the same size, same shape Equilateral Triangle: a triangle with 3 congruent sides and 3 congruent angles Hexagon: a polygon with 6 sides, 6 angles, and 6 vertices Irregular figure: a figure with at least 2 sides not congruent or at least 2 angles not congruent Isosceles Triangle: a triangle with at least 2 congruent sides and 2 congruent angles Line: a set of points that form a straight path that goes in opposite directions without ending Line segment: part of a line between two endpoints Obtuse angle: an angle whose measure is greater than a right angle (90°) but less than a straight line (180°) Octagon: a polygon with 8 sides, 8 angles, and 8 vertices Parallel lines: lines that lie in the same plane, never intersect, and are the same distance apart Parallelogram: four-sided (quadrilateral) polygon with opposite sides congruent, opposite sides parallel, and opposite angles congruent Perpendicular lines: lines that intersect at right angles (90°) to each other Pentagon: a polygon with 5 sides, 5 angles, and 5 vertices Plane: a flat surface that goes on forever in all directions Point: an exact location in space, represented by a dot Polygon: a closed two-dimensional figure with three or more straight sides ©2012, TESCCC 05/17/13 page 1 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Geometric Definitions - Notes Quadrilateral: any four-sided polygon Ray: part of a line that has one endpoint and continues without end in one direction Rectangle: four-sided polygon (quadrilateral) with 4 right (90°) angles, opposite sides congruent, opposite sides parallel , and adjacent sides perpendicular Regular figure: a figure with all sides congruent and all angles congruent Right angle: an angle that measures 90°; lines that are perpendicular to each other Rhombus: four-sided polygon (quadrilateral) having all four sides congruent, opposite sides parallel, and opposite angles congruent Scalene Triangle: a triangle with no congruent sides and no congruent angles Square: four-sided polygon (quadrilateral) with 4 right (90°) angles, all sides congruent, opposite sides parallel, and adjacent sides perpendicular Trapezoid: four-sided polygon (quadrilateral) with exactly one pair of parallel sides Triangle: a polygon with 3 sides, 3 angles, and 3 vertices Two-dimensional figure: a figure with two basic units of measure, usually length and width Vertex (plural – vertices): the point (corner) of intersection of two sides in a two-dimensional figure ©2012, TESCCC 05/17/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Attribute Cards Polygon Congruent Sides Noncongruent Sides a closed two-dimensional figure with three or more straight sides Quadrilateral any four-sided polygon Two-dimensional figure a figure with two basic units of measure, usually length and width Parallelogram four-sided (quadrilateral) polygon with • • • ©2012, TESCCC 05/13/13 opposite sides congruent opposite sides parallel opposite angles congruent page 1 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Attribute Cards Rectangle four-sided polygon (quadrilateral) with • • • • Square 4 right (90°) angles opposite sides congruent opposite sides parallel adjacent sides perpendicular four-sided polygon (quadrilateral) with • • • • 4 right (90°) angles all sides congruent opposite sides parallel adjacent sides perpendicular Rhombus four-sided polygon (quadrilateral) with • • • all sides congruent opposite sides parallel opposite angles congruent Trapezoid four-sided polygon (quadrilateral) with exactly one pair of parallel sides ©2012, TESCCC 05/13/13 page 2 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Attribute Cards Triangle a polygon with • 3 sides • 3 angles • 3 vertices Equilateral Triangle a triangle with • 3 congruent sides • 3 congruent angles Isosceles Triangle a triangle with • 2 congruent sides • 2 congruent angles Scalene Triangle a triangle with • no congruent sides • no congruent angles ©2012, TESCCC 05/13/13 page 3 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Attribute Cards Pentagon a polygon with • 5 sides • 5 angles • 5 vertices Hexagon a polygon with • 6 sides • 6 angles • 6 vertices Octagon a polygon with • 8 sides • 8 angles • 8 vertices Circle the set of all points that lie the same distance from the center (C) and lie in the same plane C ©2012, TESCCC 05/13/13 page 4 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Figures Graphic Organizer Two Dimensional Figures Polygons Triangle Equilateral Isosceles Quadrilateral Pentagon Hexagon Octagon Scalene Parallelogram Rectangle Circles Trapezoid Rhombus Square ©2012, TESCCC 05/14/13 page 1 of 1 Grade 03 Mathematics Unit: 05 Lesson: 01 Polygon Attributes KEY Describe the number of sides and vertices of each of the polygons (1) – (10). Use the attributes parallel, perpendicular, right angles, congruent angles, and congruent sides, where appropriate. Then match each description to the polygon figures in the boxes below. Label each polygon figure with the number(s) that matches its description. (1) Hexagon (6) Square 4 sides and 4 vertices with all sides 6 sides and 6 vertices congruent, adjacent sides perpendicular, and 4 right (90º) angles (2) Pentagon (7) Trapezoid 4 sides and 4 vertices with exactly one pair of 5 sides and 5 vertices parallel sides (3) Scalene triangle (8) Rhombus 4 sides and 4 vertices with all sides 3 sides and 3 vertices with no congruent congruent, opposite sides parallel, and sides or angles opposite angles congruent (4) Octagon (9) Rectangle 4 sides and 4 vertices with opposite sides 8 sides and 8 vertices congruent, adjacent sides perpendicular, and 4 right (90º) angles (5) Equilateral Triangle (10) Isosceles Triangle 3 sides and 3 vertices with all sides and 3 sides and 3 vertices with at least 2 angles congruent congruent sides and 2 congruent angles 3 2 4 9 10 ©2012, TESCCC 2 8 7 5 1 4 1 6, 8, 9 6, 8, 9 8 05/17/13 3 page 1 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Polygon Attributes KEY Use the information from the table on the previous page and handout: Two-Dimensional Figures Graphic Organizer to help answer these questions. (11) What attributes do a square and a rectangle have in common? How are these figures different? Both are quadrilaterals with opposite sides parallel and congruent, adjacent sides perpendicular, and 4 right (90o) angles. The difference between these figures is that a rectangle need not have all sides congruent, and a square must have all sides congruent. (12) Can a figure be both a rectangle and a rhombus? Explain. Yes, a square is both a rectangle and a rhombus. A square is special type of a rectangle because both have 4 right (90o) angles, adjacent perpendicular sides, and opposite sides congruent. In fact, the square has all sides congruent. A square is a special type of a rhombus because both have 4 congruent sides and opposite angles congruent. In fact, the square has 4 right (90o) angles. (13) Do a trapezoid and a rectangle have anything in common? Explain. Yes, both are quadrilaterals and both have at least one pair of parallel sides. Some trapezoids may have right angles, such as in the figure labeled 7. (14) Can a right triangle be classified as an equilateral triangle? Explain. No. Answers may vary. A right triangle has 1 right (90o) angle which means that the other two angles cannot be right (90o) angles. All sides would be square, and it would no longer be a triangle. (15) Is a rectangle a square? Explain. No, because not all sides of a rectangle are congruent. (16) Is a square a rectangle? Explain. Yes, a square is special type of a rectangle because both have 4 right (90o) angles, adjacent perpendicular sides, and opposite sides congruent. In fact, the square has all sides congruent. (17) Is a circle a polygon? Explain. No, because a circle consists of a continuous curved line, and a polygon has straight lines. (18) What is the attribute relationship between the quadrilateral, parallelogram, rhombus, and square? Explain. The attributes of a quadrilateral (a four-sided polygon) are included in the attributes of a parallelogram (a quadrilateral with opposite sides congruent, opposite sides parallel, and opposite angles congruent). The attributes of a quadrilateral and a parallelogram are included in the attributes of a rhombus (a quadrilateral with all sides congruent (meaning opposite sides are congruent), opposite sides parallel, and opposite angles are congruent). The attributes of a quadrilateral, parallelogram, and a rhombus are included in the attributes of a square (a quadrilateral with all sides congruent (meaning opposite sides are congruent), opposite sides parallel, four right (90o) angles (meaning opposite angles are congruent), and adjacent sides that are perpendicular because of the four right angles.). ©2012, TESCCC 05/17/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Polygon Attributes Describe the number of sides and vertices of each of the polygons (1) – (10). Use the attributes parallel, perpendicular, right angles, congruent angles, and congruent sides, where appropriate. Then match each description to the polygon figures in the boxes below. Label each polygon figure with the number(s) that matches its description. (1) Hexagon (6) Square (2) Pentagon (7) Trapezoid (3) Scalene triangle (8) Rhombus (4) Octagon (9) Rectangle (5) Equilateral Triangle (10) Isosceles Triangle ©2012, TESCCC 05/13/13 page 1 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Polygon Attributes Use the information from the table on the previous page and handout: Two-Dimensional Figures Graphic Organizer to help answer these questions. (11) What attributes do a square and a rectangle have in common? How are these figures different? (12) Can a figure be both a rectangle and a rhombus? Explain. (13) Do a trapezoid and a rectangle have anything in common? Explain. (14) Can a right triangle be classified as an equilateral triangle? Explain. (15) Is a rectangle a square? Explain. (16) Is a square a rectangle? Explain. (17) Is a circle a polygon? Explain. (18) What is the attribute relationship between the quadrilateral, parallelogram, rhombus, and square? Explain. ©2012, TESCCC 05/02/12 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Two-Dimensional Figures Visual Graphic Organizer Two Dimensional Figures Polygons Triangle Equilateral Isosceles Circles Quadrilateral Pentagon Hexagon Octagon Scalene Parallelogram Rectangle Trapezoid Rhombus Square ©2012, TESCCC 05/13/13 page 1 of 1 Grade 5 Mathematics Unit: 10 Lesson: 01 Polygon Table Figure Description Triangle • 3 sides • 3 vertices • 3 angles Quadrilateral • 4 sides • 4 vertices • 4 angles Pentagon • 5 sides • 5 vertices • 5 angles Hexagon • 6 sides • 6 vertices • 6 angles Octagon • 8 sides • 8 vertices • 8 angles ©2012, TESCCC Congruent Sides Regular 05/10/13 Non-Congruent Sides Irregular page 1 of 1 Grade 5 Mathematics Unit: 10 Lesson: 01 Faces, Edges, Vertices, Bases, and Curved Surface Cards Face the flat surface of a threedimensional figure Edge a line segment where two faces meet on a threedimensional figure Vertex the point (corner) of intersection of three or more edges of a threedimensional figure ©2012, TESCCC 05/14/13 page 1 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Faces, Edges, Vertices, Bases, and Curved Surface Cards Base of a threedimensional figure • prisms — the 2 unique faces (bases) that are congruent and parallel to each other unless all faces are the same shape • pyramids — the unique face (base) unless all faces are the same shape • curved-surface figures — circular base Curved Surface surface of a threedimensional figure that is curved ©2012, TESCCC 05/14/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Definitions – Notes Base of a three-dimensional figure: (1) prisms - the 2 unique faces (bases) that are congruent and parallel to each other unless all faces are the same shape; (2) pyramids - the unique face (base) unless all faces are the same shape; (3) curved-surface figures - circular base Cone: three-dimensional figure with 1 circular base and 1 curved surface Cube: three-dimensional figure with 6 square faces (2 square faces (bases) and 4 other square faces), 12 edges, and 8 vertices Cylinder: three-dimensional figure with two congruent circular bases that are parallel and 1 curved surface Curved Surface: surface of a three-dimensional figure that is curved Edge: a line segment where two faces meet on a three-dimensional figure Face: the flat surface of a three-dimensional figure Hexagonal prism: three-dimensional figure with 8 faces (2 hexagonal faces (bases) and 6 rectangular faces), 18 edges, and 12 vertices Pentagonal prism: three-dimensional figure with 7 faces (2 pentagonal faces (bases) and 5 rectangular faces), 15 edges, and 10 vertices Pentagonal pyramid: three-dimensional figure with 6 faces (1 pentagonal face (base) and 5 triangular faces), 10 edges, and 6 vertices Prism: three-dimensional figure with two congruent, parallel faces (bases) and sides that are polygonal faces Rectangular prism: three-dimensional figure with 6 rectangular faces (2 rectangular faces (bases) and 4 other rectangular faces), 12 edges, and 8 vertices Rectangular pyramid: three-dimensional figure with 5 faces (1 rectangular face (base) and 4 triangular faces), 8 edges, and 5 vertices Sphere: three-dimensional figure with all of its points the same distance from its center Square pyramid: three-dimensional figure with 5 faces (1 square face (base) and 4 triangular faces), 8 edges, and 5 vertices Three-dimensional figure: a figure with three units of measure including length, width (depth), and height ©2012, TESCCC 05/14/13 page 1 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Three-Dimensional Geometric Definitions – Notes Triangular prism: three-dimensional figure with 5 faces (2 triangular faces (bases) and 3 rectangular faces), 9 edges, and 6 vertices Triangular pyramid: three-dimensional figure with 4 triangular faces (1 triangular face (base) and 3 other triangular faces), 6 edges, and 4 vertices Vertex (plural – vertices): the point (corner) of intersection of three or more edges of a three-dimensional figure ©2012, TESCCC 05/14/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Cube ©2012, TESCCC 10/11/12 page 1 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Rectangular Prism ©2012, TESCCC 10/11/12 page 2 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Triangular Prism ©2012, TESCCC 10/11/12 page 3 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Square Pyramid ©2012, TESCCC 10/11/12 page 4 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Triangular Pyramid ©2012, TESCCC 10/11/12 page 5 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Cone ©2012, TESCCC 10/11/12 page 6 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Cylinder ©2012, TESCCC 10/11/12 page 7 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Pentagonal Prism ©2012, TESCCC 10/11/12 page 8 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Geometric Patterns Hexagonal Prism ©2012, TESCCC 10/11/12 page 9 of 9 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Attribute Cards Three-dimensional figure a figure with three units of measure • • • Cylinder length width (depth) height three-dimensional figure with • • two congruent circular bases that are parallel 1 curved surface Sphere three-dimensional figure with all of its points the same distance from its center Cone three-dimensional figure with • • Prism three-dimensional figure with • • ©2012, TESCCC 1 circular base 1 curved surface 05/14/13 two congruent, parallel faces (bases) sides that are polygonal faces page 1 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Attribute Cards Triangular prism three-dimensional figure with 5 faces • — 2 triangular faces (bases) — 3 rectangular faces 9 edges 6 vertices • • Rectangular prism three-dimensional figure with 6 rectangular faces • — 2 rectangular faces (bases) — 4 other rectangular faces 12 edges 8 vertices • • Cube three-dimensional figure with 6 square faces • — 2 square faces (bases) — 4 other square faces 12 edges 8 vertices • • Pentagonal prism three-dimensional figure with • 7 faces — 2 pentagonal faces (bases) — 5 rectangular faces • • Hexagonal prism 15 edges 10 vertices three-dimensional figure with • 8 faces — 2 hexagonal faces (bases) — 6 rectangular faces • • ©2012, TESCCC 05/14/13 18 edges 12 vertices page 2 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Attribute Cards Pyramid three-dimensional figure with • • Triangular pyramid 1 face (base) sides that are triangular faces three-dimensional figure with • 4 triangular faces — 1 triangular face (base) — 3 other triangular faces • • Square pyramid 6 edges 4 vertices three-dimensional figure with • 5 faces — 1 square face (base) — 4 triangular faces • • Rectangular pyramid 8 edges 5 vertices three-dimensional figure with • 5 faces — 1 rectangular face (base) — 4 triangular faces • • ©2012, TESCCC 05/14/13 8 edges 5 vertices page 3 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Attribute Cards Pentagonal pyramid three-dimensional figure with • 6 faces — 1 pentagonal face (base) — 5 triangular faces • • ©2012, TESCCC 05/14/13 10 edges 6 vertices page 4 of 4 Grade 5 Mathematics Unit: 10 Lesson: 01 Three-Dimensional Figures Graphic Organizer Three-Dimensional Figures Prisms Triangular Prism Rectangular Pentagonal Prism Prism Curved Surfaces Pyramids Cylinder Hexagonal Prism Cone Sphere Cube Triangular Pyramid ©2012, TESCCC Square Pyramid 05/14/13 Rectangular Pyramid Pentagonal Pyramid page 1 of 1 Grade 5 Mathematics Unit: 10 Lesson: 01 Attributes of Three-Dimensional Figures KEY Describe the attributes (number of faces, describe faces and bases, edges, vertices, curved surfaces, and/or circular bases, where applicable) for each figure. Then match each description to a figure in the box below. Label the figure with the number that matches its description. (1) Triangular Pyramid (6) Triangular Prism 4 triangular faces (1 triangular face (base) and 3 other triangular faces), 6 edges, 4 vertices 5 faces (2 triangular faces (bases) and 3 rectangular faces), 9 edges, 6 vertices (2) Rectangular Prism (7) Cube 6 rectangular faces (2 rectangular faces (bases) and 4 other rectangular faces), 12 edges, 8 vertices 6 square faces (2 square faces (bases) and 4 other square faces), 12 edges, 8 vertices (3) Hexagonal Prism (8) Square Pyramid 8 faces (2 hexagonal faces (bases) and 6 rectangular faces), 18 edges, 12 vertices 5 faces (1 square face (base) and 4 triangular faces), 8 edges, 5 vertices (9) Cylinder (4) Sphere 2 circular bases, 1 curved surface 1 curved surface with all of its points the same distance from its center (5) Cone (10) Pentagonal Prism 1 circular base, 1 curved surface 7 8 7 faces (2 pentagonal faces (bases) and 5 rectangular faces), 15 edges, 10 vertices 6 4 5 10 1 9 2 ©2012, TESCCC 3 05/13/13 page 1 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Attributes of Three-Dimensional Figures KEY Use the information from the table on the previous page to help answer these questions. (11) What attributes do a cube and a rectangular prism have in common? How are these figures different? A cube has all the attributes of a rectangular prism. All the faces of a cube must be squares, but all the faces of a rectangular prism do NOT have to be squares. (12) Can a figure be both a rectangular prism and a cube? Explain. Yes, a cube is both a cube and a rectangular prism. All the faces of a cube are squares, and all squares are rectangles. (13) Complete the table below to list the number of faces, edges, and vertices of a prism with a base of 8 edges. For the figure, describe each type of face and then name the figure. Number of Faces 10 Number of Edges 24 Number of Vertices Types of Faces (number and name of each) Name of Figure 16 2 octagonal faces (bases) and 8 rectangular faces Octagonal Prism (14) How is a triangular prism different than a rectangular prism? Explain. A triangular prism has 2 triangular faces (bases), and a rectangular prism has 2 rectangular faces (bases). This means that a triangular prism has fewer faces, edges, and vertices than a rectangular prism because a triangle only has 3 sides and a rectangle has 4 sides. (15) How is a triangular prism different than a triangular pyramid? A triangular prism has 2 triangular faces (bases), and a triangular pyramid has 1 triangular face (base). A triangular prism has rectangular faces, and a triangular pyramid has only triangular faces. A triangular pyramid has fewer faces, edges, and vertices than a triangular prism. (16) Name two real world objects that describe a cylinder and a cone. Describe how these two figures are alike and how they are different based on their geometric attributes. Answers may vary. Similar attributes include a circular base and a curved surface on both. Differences are that a cone has 1 circular base, and a cylinder has 2 circular bases. (17) Name two real world objects that describe a square pyramid and a cube. Describe how these two figures are alike and how they are different based on their geometric attributes. Answers may vary. Similar attributes include a square face (base). Differences are that a square pyramid has triangular faces, and a cube has square faces. The pyramid has fewer faces, edges, and vertices than the cube. (18) What is true about the side faces (not the base) of all pyramids? The side faces of all pyramids are triangular. ©2012, TESCCC 05/14/13 page 2 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Attributes of Three-Dimensional Figures Describe the attributes (number of faces, describe faces and bases, edges, vertices, curved surfaces, and/or circular bases, where applicable) for each figure. Then match each description to a figure in the box below. Label the figure with the number that matches its description. (1) Triangular Pyramid (2) Triangular Prism (3) Rectangular Prism (4) Cube (5) Hexagonal Prism (6) Square Pyramid (7) Sphere (8) Cylinder (9) Cone (10) Pentagonal Prism ©2012, TESCCC 05/14/13 page 1 of 2 Grade 03 Mathematics Unit: 05 Lesson: 01 Attributes of Three-Dimensional Figures Use the information from the table on the previous page to help answer these questions. (11) What attributes do a cube and a rectangular prism have in common? How are these figures different? (12) Can a figure be both a rectangular prism and a cube? Explain. (13) Complete the table below to list the number of faces, edges, and vertices of a prism with a base of 8 edges. For the figure, describe each type of face and then name the figure. Number of Faces Number of Edges Number of Vertices Types of Faces (number and name of each) Name of Figure (14) How is a triangular prism different than a rectangular prism? Explain. (15) How is a triangular prism different than a triangular pyramid? (16) Name two real world objects that describe a cylinder and a cone. Describe how these two figures are alike and how they are different based on their geometric attributes. (17) Name two real world objects that describe a square pyramid and a cube. Describe how these two figures are alike and how they are different based on their geometric attributes. (18) What is true about the side faces (not the base) of all pyramids? ©2012, TESCCC 05/14/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Naming Geometric Figures KEY Vertex V E X G F H B C Face T Y A The vertices in this two-dimensional figure are: T, V, X, and Y The sides in this two-dimensional figure are: D Edge The vertices in this three-dimensional figure are: A, B, C, D, E, F, G, and H The edges in this three-dimensional figure are: VX, XY, TY, and VT AB, AD, CD, CB, BE, AF, FH, EF, EG, GH, GC, and HD The face in this two-dimensional figure is: TVXY The angles in this two-dimensional figure are: ∠T , ∠V , ∠X, and ∠Y The faces in this three-dimensional figure are: ABCD, ABEF, EGHF, CGHD, AFHD, and BEGC Note: For sides and edges, VX could also be named XV. For faces, moving clockwise, faces could be named TVXY, VXYT, XYTV, or YTVX. Sample answers provided for naming edges and faces Use the geometric solids below to complete the table. U S P V T O W X N L Q R M (1) Name the faces: (5) Name the faces: QSTR, QSUW, UVXW, WXRQ, VXRT, UVTS (2) Name the edges: LONM, LPO, LPM, MPN, NPO (6) Name the edges: LM, LO, ON, NM, LP, MP, NP, and OP QR, QS, QW, SU, UW, WX, XV, UV, TV, XR, TR, and ST (3) Name the vertices: (7) Name the vertices: Q, R, S, T, U, V, W, and X (4) Name a real-world object that has this same shape. Answers may vary. ©2012, TESCCC L, M, N, O, and P (8) Name a real-world object that has this same shape. Answers may vary. 05/17/13 page 1 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Naming Geometric Figures KEY Sample answers provided for naming edges and faces Use the geometric solids below to complete the table. R E W B F D A D T N F C (9) Name two parallel faces: G S (11) Name two parallel faces: ABC to DEF SDNT to RWGF, SRFT to DWGN, SRWD to TFGN (10) Name two parallel edges: (12) Name two parallel edges: RS to WD, RW to SD, RS to FT, ST to RF, WD to GN, DN to WG, FT to GN, TN to FG AC to DF , AB to DE, BC to EF, AD to CF, BE to CF, BE to AD Use the diagram below to complete the table. A H G F (13) Name a square: B C E D (15) Name a parallelogram: BCDE ABDG or BCDE or ABEH or ACDH (14) Name a rectangle: (16) Name a trapezoid: BCDE or ABEH or ACDH ABFG or ABEG or ABFH or ACDG or FBCD or ABDH (17) In triangle AHG, which angle is the right angle? (18) ABFH is what type of quadrilateral? ∠H ©2012, TESCCC 05/17/13 Trapezoid page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Naming Geometric Figures Vertex V X E G F H B C Face T Y A The vertices in this two-dimensional figure are: T, V, X, and Y The sides in this two-dimensional figure are: D Edge The vertices in this three-dimensional figure are: A, B, C, D, E, F, G, and H The edges in this three-dimensional figure are: VX, XY, TY, and VT AB, AD, CD, CB, BE, AF, FH, EF, EG, GH, GC, and HD The face in this two-dimensional figure is: TVXY The angles in this two-dimensional figure are: ∠T , ∠V , ∠X, and ∠Y The faces in this three-dimensional figure are: ABCD, ABEF, EGHF, CGHD, AFHD, and BEGC Note: For sides and edges, VX could also be named XV. For faces, moving clockwise, faces could be named TVXY, VXYT, XYTV, or YTVX. Use the geometric solids below to complete the table. U S P V T O W X N L Q R M (1) Name the faces: (5) Name the faces: (2) Name the edges: (6) Name the edges: (3) Name the vertices: (7) Name the vertices: (4) Name a real-world object that has this same shape. (8) Name a real-world object that has this same shape. ©2012, TESCCC 05/17/13 page 1 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Naming Geometric Figures Use the geometric solids below to complete the table. R E W B F D A D T N F C G S (9) Name two parallel faces: (11) Name two parallel faces: (10) Name two parallel edges: (12) Name two parallel edges: Use the diagram below to complete the table. A H G F B C E D (13) Name a square: (15) Name a parallelogram: (14) Name a rectangle: (16) Name a trapezoid: (17) In triangle AHG, which angle is the right angle? (18) ABFH is what type of quadrilateral? ©2012, TESCCC 05/17/13 page 2 of 2 Grade 5 Mathematics Unit: 10 Lesson: 01 Geometric Logic These are hulops. What characteristics do hulops have in common? ©2012, TESCCC 10/11/12 page 1 of 1 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice KEY Use the clues to determine the geometric figures described. (1) (2) Group A Clues • • • • Figure B Clues • • • Same number of faces as vertices Most of the faces are triangles No parallel faces Most of the faces share a vertex Figure: Pyramid Fewer faces than vertices 2 congruent, parallel polygonal faces all other faces are parallelograms Figure: Prism (3) How are the three-dimensional figures in Group A different from those in Group B? The threedimensional figures in Group A have no parallel faces, but the Group B figures have at least one pair of parallel faces. Use the grouping of figures below to answer #4 and #5. A B C D E (4) Which of the figure(s) above does not belong to the set? Explain. Figure C because it is the only figure with no parallel lines. (5) Draw another figure that could be in this grouping. Drawings may vary. (6) These figures show the two different types of tops Josh created. The shaded portion in each figure shows a face shared by the two threedimensional figures that makeup each top. • • What three-dimensional figures are in Top A? Top B? Top A: rectangular prism and rectangular pyramid Top A Top B Top B: 2 square (or rectangular) pyramids Compare the number of faces in Top A to Top B (including the one shaded/shared face in each). How many more faces does Top A have than Top B? Explain. Top A has 1 additional face. Answers may vary. Top A has 10 faces (including the shaded/shared face) and Top B has 9 faces (including the shaded/shared face). 10 – 9 = 1 additional face. ©2012, TESCCC 05/14/13 page 1 of 3 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice KEY Sample answers are provided for naming edges and faces. Complete the table below based on each two-dimensional figure given. The first one is completed as an example. Sample Answers Name of Figure Use hash marks to indicate congruent sides, arcs to indicate congruent angles, and square corners to indicate square corners Vertices A Parallelogram D B A, B, C, D Parallel Sides AB to DC AD to BC Congruent Sides Perpendicular Sides Congruent Angles Right Angles AB to DC AD to BC None ∠A to ∠C ∠B to ∠D None HK to SM HS to KM HS to HK HK to KM KM to SM SM to HS C H (7) Rectangle K H, K, M, S S M HK to SM HS to KM ∠H to ∠K to ∠M to ∠S ∠H, ∠K , ∠M, ∠S M L (8) Trapezoid L, M, P, S S ©2012, TESCCC LS to MP None LS to SP MP to SP ∠S to ∠P ∠S, ∠P P 05/14/13 page 2 of 3 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice KEY Sample answers are provided for naming edges and faces. Complete the table below based on each three-dimensional figure given. The first one is completed as an example. Sample Answers Figure Faces that are Parallelograms Faces that are Triangles Faces that are Rectangles Faces that are Parallel Faces that are Congruent Faces that are Congruent and Parallel ABCH, CBDE, DGEF, GFAH, DCHG, ABEF None ABCH, CBDE, DGEF, GFAH, DCHG, ABEF ABCH to DGEF, ABEF to CDGH, AFGH to CDBE ABCH, CBDE, DGEF, GFAH, DCHG, ABEF ABCH to DGEF, ABEF to CDGH, AFGH to CDBE JKNO, JKLM, LMNO KLN, JMO JKNO, JKLM, LMNO KLN, JMO KLN to JMO KLN and JMO QRST QUT, TUS, SUR, RUQ None QUT to TUS to SUR to RUQ None D C G H E B F A L K N (9) M J O U (10) R QRST S Q T (11) Give a real-world example of a cylinder, cone, and sphere. Describe the attributes of each of these objects. Answers may vary. An example of a cylinder is a canned good, a cone is a party hat, and a sphere is a ball. The canned good has 2 circular bases and 1 curved face, the party hat has 1 circular base and 1 curved surface, and the ball has 1 curved surface. ©2012, TESCCC 05/14/13 page 3 of 3 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice Use the clues to determine the geometric figures described. (1) (2) Group A Clues • • • • Figure B Clues • • • Same number of faces as vertices Most of the faces are triangles No parallel faces Most of the faces share a vertex Figure: Fewer faces than vertices 2 congruent, parallel polygonal faces all other faces are parallelograms Figure: (3) How are the three-dimensional figures in Group A different from those in Group B? Use the grouping of figures below to answer #4 and #5. A B C D E (4) Which of the figures above does not belong in the grouping? Explain. (5) Draw another figure that could be in this grouping. (6) These figures show the two different types of tops Josh created. The shaded portion in each figure shows a face shared by the two threedimensional figures that makeup each top. • What three-dimensional figures are in Top A? Top B? Top A • Top B Compare the number of faces in Top A to Top B (including the one shaded/shared face in each). How many more faces does Top A have than Top B? Explain. ©2012, TESCCC 05/14/13 page 1 of 3 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice Complete the table below based on each two-dimensional figure given. The first one is completed as an example. Sample Answers Name of Figure Use hash marks to indicate congruent sides, arcs to indicate congruent angles, and square corners to indicate square corners Vertices Parallel Sides Congruent Sides Perpendicular Sides A Parallelogram D B A, B, C, D AB to DC AD to BC AB to DC AD to BC Congruent Angles Right Angles ∠A to ∠C None and None ∠B to ∠D C (7) Rectangle H K S M M L (8) S ©2012, TESCCC P 05/14/13 page 2 of 3 Grade 5 Mathematics Unit: 10 Lesson: 01 Two- and Three-Dimensional Figure Practice Complete the table below based on each three-dimensional figure given. The first one is completed as an example. Sample Answers Figure Faces that are Parallelograms Faces that are Triangles Faces that are Rectangles Faces that are Parallel Faces that are Congruent Faces that are Congruent and Parallel ABCH, CBDE, DGEF, GFAH, DCHG, ABEF None ABCH, CBDE, DGEF, GFAH, DCHG, ABEF ABCH to DGEF, ABEF to CDGH, AFGH to CDBE ABCH, CBDE, DGEF, GFAH, DCHG, ABEF ABCH to DGEF, ABEF to CDGH, AFGH to CDBE D C G H E B F A L K N (9) M J O U (10) R S Q T (11) Give a real-world example of a cylinder, cone, and sphere. Describe the attributes of each of these objects. ©2012, TESCCC 05/14/13 page 3 of 3