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Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Unit 08: Geometry (15 days) Possible Lesson 01 (4 days) Possible Lesson 02 (6 days) Possible Lesson 03 (5 days) POSSIBLE LESSON 02 (6 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 districtapproved 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 classify two- and three-dimensional figures according to the defining attributes and use formal geometric language to describe the 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 4.8 Geometry and spatial reasoning.. The student identifies and describes attributes of geometric figures using formal geometric language. The student is expected to: 4.8A Identify and describe right, acute, and obtuse angles.... Supporting Standard 4.8B Identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models. Supporting Standard 4.8C Use essential attributes to define two- and three-dimensional geometric figures. Readiness Standard page 1 of 75 Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Underlying Processes and Mathematical Tools TEKS: 4.14 Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 4.14A Identify the mathematics in everyday situations. 4.15 Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The student is expected to 4.15A Explain and record observations using objects, words, pictures, numbers, and technology. 4.15B Relate informal language to mathematical language and symbols. 4.16 Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to: 4.16A Make generalizations from patterns or sets of examples and nonexamples. 4.16B Justify why an answer is reasonable and explain the solution process. Performance Indicator(s): Grade 04 Mathematics Unit 08 PI 02 Create two 4-flap books where one booklet models 4 different two-dimensional figures (e.g., rectangle, pentagon, triangle, octagon, etc.), and the other booklet models 4 different three-dimensional figures (e.g., cube, triangular pyramid, cone, sphere, etc.) that must include a prism, a pyramid, and two curved surfaced figures. For the figures in the two-dimensional booklet, record the following: (1) a sketch of the two-dimensional figure; (2) the most specific formal geometric name of the twodimensional figure; (3) number of sides, vertices, and other attributes, including description of sides (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure; and (4) a written justification describing how the attributes define the figure. For the figures in the three-dimensional booklet, record the following: (1) a sketch of the three-dimensional figure; (2) the formal geometric name of the three-dimensional figure; (3) number of faces, bases, edges, vertices, curved surfaces, and other attributes, including description of edges and faces (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure; and (4) a written justification describing how the attributes define the figure. Standard(s): 4.8A , 4.8B , 4.8C , 4.14A , 4.15A , 4.15B , 4.16A , 4.16B ELPS ELPS.c.1C , ELPS.c.1E Key Understanding(s): Polygons are two-dimensional figures with specific attributes. page 2 of 75 Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days 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. Misconception(s): Some students may think that the size of an angle can be determined by the length of its sides. It may help to show how extending the side of the angle does not change the “measure” of the angle. Differently sized angle cutouts (pie shapes) can be used to demonstrate this concept. Vocabulary of Instruction: acute angle attribute base cone congruent curved surface edges equilateral triangle face hexagon isosceles triangle obtuse octagon one-dimensional figure parallel parallelogram pentagon perpendicular plane polygon prism pyramid quadrilateral rectangle right scalene triangle side sphere square symmetry three-dimensional figure trapezoid triangle two-dimensional figure vertex Materials List: box (tissue box) (1 per teacher) cardstock (1 sheet per 2 students) cardstock (1 sheet per 2 students) page 3 of 75 Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days cardstock (7 sheets per 2 students) cardstock (optional) (7 sheets per 4 students) construction paper (9” x 12”) (2 sheets per student) dry erase marker (1 per student) geometric figures or solids (1 set per 4 students, 1 set per teacher) math journal (1 per student) paper (plain) (1 sheet per teacher) plastic zip bag (sandwich sized) (3 per 2 students) scissors (1 per teacher, 1 per student) sticky notes (optional) (2 per student) straw (drinking, flexible) (24 per student, 12 – 32 per 2 students) straw (drinking, flexible) (9 per student) tape (clear) (optional) (1 roll per teacher) tape (painter’s) (1 roll per 2 students) whiteboard (student-sized) (1 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. Polygon Cards Polygon Names Chart KEY Polygon Names Chart Figure Search KEY Figure Search Dot Paper page 4 of 75 Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Quadrilateral Descriptions KEY Quadrilateral Descriptions Quadrilateral Cards Triangle and Quadrilateral Practice KEY Triangle and Quadrilateral Practice Building Figures and Solids with Straws Two-Dimensional Figures Graphic Organizer Quadrilaterals Graphic Organizer Guess the Figure Three-Dimensional Attributes - Part 1 - KEY Three-Dimensional Attributes - Part 1 Three-Dimensional Attributes - Part 2 - KEY Three-Dimensional Attributes - Part 2 Three-Dimensional Figure Practice KEY Three-Dimensional Figure Practice Three-Dimensional Figures Graphic Organizer Three-Dimensional Geometric Patterns Two- and Three-Dimensional Attribute Cards page 5 of 75 Enhanced Instructional Transition Guide Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Geometric Definitions - Notes Geometric Logic Geometric Logic Practice KEY Geometric Logic Practice Two- and Three-Dimensional Figures KEY Two- and Three-Dimensional Figures 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 One-dimensional figures Two-dimensional figures Engage 1 Students discuss the difference between one-dimensional and two-dimensional figures. MATERIALS whiteboard (student-sized) (1 per student) dry erase marker (1 per student) Instructional Procedures: TEACHER NOTE 1. Distribute a whiteboard and dry erase marker to each student. Remind students that A plane is a flat surface that goes on forever in all directions. page 6 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures they have learned the special names for different types of lines and angles. Instruct students to record their responses to each of the following questions on their whiteboard using pictures and/or words. Ask: What are some examples of lines in the classroom? Answers may vary. The line created by the tiles on the floor; a pencil; the line along one side of a desk top; the line created where two cabinet doors meet; etc. What are some flat objects in the classroom? Answers may vary. A desk top; book cover; chalkboard; the face of the clock; etc. Notes for Teacher A plane figure is also called a two-dimensional figure with two basic units of measure, usually length and width. A polygon is a closed two-dimensional figure with 3 or more straight sides. TEACHER NOTE A circle is a two-dimensional figure whose length and width can be measured through the center of the circle (diameter). 2. Explain to students that the lines they just named are all examples of onedimensional figures, and the flat surfaces they just named are all examples of twodimensional figures. 3. Facilitate a class discussion about the differences between one- and twodimensional figures: Ask: Using the examples on your whiteboard, how could you describe the difference between a one-dimensional figure and a two-dimensional figure? Answers may vary. A one-dimensional figure can be a straight or curved line that does not form a closed figure. A two-dimensional figure is formed by straight or curved lines that form a closed figure; etc. 4. Explain to students that a dimension is a measure in one direction. A one- page 7 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Notes for Teacher dimensional figure has only one dimension, length. Straight and curved lines are examples of one-dimensional figures. 5. Explain to students that a plane is a flat surface that goes on forever in all directions. A plane figure is a two-dimensional figure with two basic units of measure, usually length and width. Two-dimensional figures are comprised of onedimensional figures, which can have straight or curved lines. Topics: Attributes of polygons Explore/Explain 1 Students define a polygon as a closed figure with straight sides. Students examine and name polygons by identifying the number of sides and types of angles within each figure. Instructional Procedures: 1. Prior to instruction, create a card set: Polygon Cards for every 2 students by copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag. ATTACHMENTS Card Set: Polygon Cards (1 per 2 students) Teacher Resource: Polygon Names Chart KEY (1 per teacher) Teacher Resource: Polygon Names Chart (1 per teacher) Handout: Polygon Names Chart (1 per student) Teacher Resource: Figure Search KEY (1 per teacher) Handout: Figure Search (1 per student) 2. Facilitate a class discussion about attributes. Ask: MATERIALS What is an attribute? Can you give examples? Answers may vary. A characteristic that helps define a figure; etc. 3. Explain to students that they will be investigating the attributes of geometric figures, cardstock (1 sheet per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 page 8 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures beginning with two-dimensional figures. 2. Place students in pairs. Distribute a card set: Polygon Cards to each group. Instruct student pairs to sort the figures into 2 or more groups and be ready to explain how they sorted the figures. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief the possible groupings. Ask: What are the groups you created from the sort? Answers may vary. Groups of polygons with right angles and those without; groups of polygons by the number sides (3, 4, or more than 4, etc.); etc. Notes for Teacher students) TEACHER NOTE An attribute is a characteristic that helps define a figure. A two-dimensional figure is comprised of at least 3 onedimensional figures and has two basic units of measurement (usually length and width). TEACHER NOTE On handout: Polygon Names Chart, students may only provide the specific name of each quadrilateral, such as square, rectangle, parallelogram, or trapezoid. The 3. Explain to students that each figure from their card set: Polygon Cards is a polygon. Ask: relationships between the multiple ways to name each quadrilateral will be discussed in Explore/Explain 2. How do you know that each figure is a polygon? Answers may vary. Each figure is a closed figure; each figure has straight sides; etc. 4. Explain to students that one way to sort polygons is by number of sides. 5. Distribute handout: Polygon Names Chart to each student. 6. Display teacher resource: Polygon Names Chart. Ask: page 9 of 75 Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Notes for Teacher How many sides does each of these polygons have? (3, 4, 5, 6, and 8 sides) 7. Demonstrate recording the number of sides on the displayed teacher resource: Polygon Names Chart. Instruct students to replicate these numbers on their handout: Polygon Names Chart. 8. Explain to students that polygons are named by their sides. Ask: What are polygons with 3 sides called? 4 sides? 5 sides? 6 sides? 8 sides? (triangles; quadrilaterals; pentagons; hexagons; and octagons) 9. Instruct students to examine the figures on their handout: Polygon Names Chart, determine the number of angles in each, and record the number of angles and polygon name for each figure. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. 10. Collect handout: Polygon Names Chart to be redistributed in Explore/Explain 2. 11. Distribute handout: Figure Search to each student as independent practice and/or homework. 2 Topics: Spiraling Review Triangles page 10 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Quadrilaterals Explore/Explain 2 Students identify, describe, and build triangles and quadrilaterals using straws. Instructional Procedures: 1. Prior to instruction, create a card set: Quadrilateral Cards for every 2 students by copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag. 2. Facilitate a class discussion to debrief the previously assigned handout: Figure Search. 3. Place students in pairs. Distribute 9 flexible drinking straws, a pair of scissors, and handout: Dot Paper to each student. Remind students of the terms acute, right, and obtuse angles. Facilitate a class discussion about how the straws can be used to create triangles. Ask: How many triangles can you make with 9 straws? How do you know? (3; because each triangle has three sides and 3 x 3 = 9.) 4. Instruct students to use their flexible drinking straws to create triangles with different types of angles, record the triangles they made on their handout: Dot Paper, and list the different combinations of acute, obtuse, and right angles that can make a triangle. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student Notes for Teacher ATTACHMENTS Handout: Dot Paper (1 per student) Teacher Resource: Quadrilateral Descriptions KEY (1 per teacher) Teacher Resource: Quadrilateral Descriptions (1 per teacher) Card Set: Quadrilateral Cards (1 per 2 students) Handout: Quadrilaterals Graphic Organizer (1 per student) Teacher Resource: Triangle and Quadrilateral Practice KEY (1 per teacher) Handout: Triangle and Quadrilateral Practice (1 per student) Handout (optional): Building Figures and Solids with Straws (1 per student) Handout (optional): Two-Dimensional Figures Graphic Organizer (1 per student) Teacher Resource (optional): Guess the Figure (1 per teacher) MATERIALS cardstock (1 sheet per 2 students) page 11 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures solutions and for students to share their findings. Ask: Can a triangle have more than one right angle? Explain. (No, there can only be one right angle in a triangle because the other two have to be less than a right angle to close the figure.) Can a triangle have more than one obtuse angle? Explain. (No, there can only be one obtuse angle in a triangle because the other two have to be less than a right angle to close the figure.) Can a triangle have more than one acute angle? Explain. (Yes, a triangle can have all three acute angles or two acute angles and the third angle either obtuse or right.) Notes for Teacher scissors (1 per teacher, 1 per student) plastic zip bag (sandwich sized) (1 per 2 students) straw (drinking, flexible) (9 per student) math journal (1 per student) TEACHER NOTE Handout (optional): Building Figures and Solids with Straws may be used to assist students with creating the triangles in this lesson. TEACHER NOTE 5. Instruct student pairs to create an example of each type of triangle: one with a right angle, one with an obtuse angle, and one with all acute angles on their handout: Dot Paper. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. 6. Facilitate a class discussion about classifying triangles by their sides. Ask: Can a triangle have three sides of the same length? Explain. (Yes and no, because a triangle can have three sides of equal measure, at least two sides of equal measure, or no sides of equal measure.) Could you describe a triangle based on its sides? Explain. (yes) Answers may vary. If a triangle has 3 sides that are equal in length, then it is an Students identified triangles as equilateral, isosceles, or scalene in Grade 3 (TEKS 3.8). TEACHER NOTE Although the word “trapezoid” has been used at previous grade levels, Grade 4 is the first grade where students are held accountable for the attributes of a trapezoid. TEACHER NOTE Polygons with all sides and angles congruent are called regular polygons. For example, a hexagon with all sides equal in length and all angles equal in angle measure, are page 12 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures equilateral triangle; if a triangle has at least 2 sides equal in length then it is an isosceles triangle; if a triangle does not have any sides that are equal in length, then it is a scalene triangle; etc. Notes for Teacher considered regular hexagons. However, all hexagons are not regular hexagons. There are many examples of hexagons in the real world where all of the sides are not equal in length and all angles are not equal in measure. 7. Explain to students that they have learned how to identify and classify triangles based on their sides and that now they will be looking at the attributes of quadrilaterals to identify and classify them as well. Ask: TEACHER NOTE Teacher resource (optional): Guess the Figure and handout (optional): Two-Dimensional Figures Graphic Organizer are available to assist students in understanding What is the same about all polygons that are quadrilaterals? (They all have 4 sides and 4 angles.) the different types of polygons and quadrilaterals. The graphic organizer can be posted in the classroom and/or individual copies can be made for students, as necessary. 8. Display teacher resource: Quadrilateral Descriptions. 9. Distribute a card set: Quadrilateral Cards to each pair. Instruct student pairs to find a quadrilateral to match each description from the displayed teacher resource: Quadrilateral Descriptions and record the quadrilateral and description in their math journal. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. 10. Invite a student volunteer to draw an example of the figure that matches the first description from the displayed teacher resource: Quadrilateral Descriptions for the class to see. Facilitate a class discussion about how the figure drawn has only one pair of parallel sides. Explain to students that the special name for this quadrilateral is “trapezoid.” The graphic organizer does not include all four-sided figures such as a “kite.” A kite would be another branch off of the quadrilateral because of its attributes. A kite has two sets of congruent sides, but the congruent sides are adjacent to each other, not opposite of each other. A kite’s opposite angles are congruent. This graphic organizer is as a tool designed to help students to begin organizing the attributes polygons have or do not have in common. State Resources page 13 of 75 Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Notes for Teacher MTR 3 – 5: Two-Dimensional Figures Important Book 11. Repeat the activity for the next 4 descriptions on the displayed teacher resource: Quadrilateral Descriptions. Explain the special names for each quadrilateral as a “parallelogram,” “rectangle,” “rhombus,” and “square.” TEXTEAMS: Rethinking Elementary Mathematics Part II: Developing Deep and Complex Geometric Knowledge; Sorting Shapes; Missing Shapes 12. Facilitate a class discussion about the characteristics of the quadrilaterals. Ask: What characteristics do you look at when comparing quadrilaterals? Answers may vary. The lengths of the sides, angles, and if the sides are parallel or not; etc. Is it possible for a quadrilateral to have a right angle and an obtuse angle? How do you know? (Yes; a trapezoid can have both a right angle and an obtuse angle.) Is a trapezoid a parallelogram? Explain. (No; because a trapezoid has only 1 set of parallel lines and a parallelogram has 2 sets of parallel lines.) Is it possible for a quadrilateral to have no pairs of parallel sides? Explain. (yes) Answers may vary. 13. Instruct student pairs to hold up the card from their card set: Quadrilateral Cards that they think represents a quadrilateral with no parallel sides. Ask: What do you think this quadrilateral is called? Answers may vary. 14. Explain to students that because this it is a four-sided figure with no pairs of parallel sides, it is called an “irregular quadrilateral.” page 14 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Notes for Teacher 15. Display teacher resource: Quadrilateral Graphic Organizer. Redistribute previously completed handout: Polygon Names Chart to each student. Facilitate a class discussion about the relationship that exists among different types of quadrilaterals, as well as the different names for each type of quadrilateral. Instruct students to add additional names that describe the quadrilaterals on their handout: Polygon Names Chart. 16. Distribute handout: Triangle and Quadrilateral Practice to each student as independent practice and/or homework. 3 Topics: Spiraling Review Two-dimensional figures Three-dimensional figures Explore/Explain 3 Students identify, describe, and build two- and three-dimensional figures using straws. ATTACHMENTS Teacher Resource Three-Dimensional Attributes (Part 1) KEY Handout: Three-Dimensional Attributes page 15 of 75 Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Notes for Teacher Instructional Procedures: (Part 1) Handout (optional): Building Figures and Solids with Straws (1 per student) 1. Display a sheet of paper and a tissue box. Ask: What are the two dimensions of the paper you can measure with a ruler? (length and width) How many dimensions of the box can you measure? (3; length, width, and height) MATERIALS paper (plain) (1 sheet per teacher) box (tissue box) (1 per teacher) straw (drinking, flexible) (24 per student, 12 – 32 per 2 students) tape (painter’s) (1 roll per 2 students) scissors (1 per teacher, 1 per student) sticky notes (optional) (2 per student) 2. Remind students that when they were finding the area of a figure, they were working in two dimensions—length and width. Additionally, when they were finding the volume of a figure, they were working with three dimensions—length, width, and height. 3. Place students in pairs. Distribute a roll of painter’s tape to each pair and a pair of scissors and 24 flexible straws to each student. Remind students that they have used the straws to make triangles. 4. Instruct students to make a square with their flexible drinking straws. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Ask: TEACHER NOTE Handout (optional): Building Figures and Solids with Straws may be used to assist students with creating the figures in this lesson. TEACHER NOTE Approximate number of straws needed to construct each How could you change this two-dimensional figure into a three- figure: page 16 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Notes for Teacher dimensional figure? Answers may vary. 5. Instruct students to make 5 more squares with their flexible drinking straws. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Ask: Are these figures two-dimensional or three-dimensional? How do you know? (Two-dimensional; because they can only be measured by length and width.) Could you connect these figures to create a three-dimensional figure? Explain. (yes) Answers may vary. Taping each square together could create a cube; etc. TEACHER NOTE For students who have difficulty drawing a three- 6. Instruct students to lay the squares on their desk and use the tape to connect the sides of the polygon faces together to create edges as shown below. Allow time for students to complete the activity. Monitor and assess students to check for understanding. dimensional figure, allow them to use dot paper and demonstrate by drawing a cube starting with overlapping squares and then connecting the corners of both squares. TEACHER NOTE For students who need a stronger visual for the terms face, edge, and vertex, have them trace a square the same size as the square face of their cube onto a sheet of paper. Then, have them write the word “face” onto the paper and tape it to the front face of their cube. Instruct them to use Ask: small stickynotes labeled “edge” and “vertex” to tape to one of the edges and one of the vertices on their cube. page 17 of 75 Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Notes for Teacher How does a two-dimensional square differ from a three-dimensional cube? (It has another dimension.) How many squares do you need to make the cube? (6 squares) Explain to students that each square represents a face of the cube. 7. Instruct students to fold the faces of the figure up to create the cube, tape each edge together, and also tape each vertex of the figure. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Ask: A cube has how many vertices? (8 vertices) A cube has how many edges? (12 edges) 8. Distribute handout: Three-Dimensional Attributes (Part 1) to each student. Instruct students to complete the row for the cube by recording the number of faces, vertices, and edges. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion for students to name the two-dimensional figures that make-up the faces of the threedimensional figure. page 18 of 75 Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Notes for Teacher Ask: What are the names of the faces for the cube? (squares) 9. Assign each student pair one of the remaining 4 three-dimensional figures from handout: Three-Dimensional Attribute (Part 1). Distribute 12 – 32 straws to each pair, depending on the assigned figure. Instruct student pairs to use their flexible drinking straws to create their assigned three-dimensional figure. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate individual group discussions about the three-dimensional models. Ask: How will the model of the rectangular prism be like the model of the cube? How will it be different? Answers may vary. The cube has 6 congruent faces that are squares, while the rectangular prism has 6 faces, 2 of which are rectangular faces (bases) and 4 other rectangular faces. The cube has 12 edges of equal length, while the rectangular prism has 12 edges some of which are different length; etc. How are these two types of pyramids different? How are they alike? Answers may vary. They are different because the shapes of their bases are different and the number of edges is different. They are alike in that they both have some triangular-shaped faces; etc. 10. Facilitate a class discussion for students to share the models they have built. Instruct students to complete their handout: Three-Dimensional Attributes (Part page 19 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Notes for Teacher 1) based on the models shared. 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, as needed. 4 Topics: Spiraling Review Three-dimensional figures Explore/Explain 4 Students identify and describe three-dimensional figures by their attributes. Instructional Procedures: 1. Place students in groups of 4. Distribute a set of geometric figures or solids to each group. Ask: Why are all of these figures called three-dimensional figures? Answers may vary. The figures all take up space and have another dimension besides just length and width; etc. 2. Instruct students to sort the three-dimensional figures and be prepared to describe the attributes they used to do so. Allow time for students to complete the activity. Monitor and assess student groups to check for understanding. Facilitate a class discussion about the sorting activity. Ask: ATTACHMENTS Teacher Resource: Three-Dimensional Attributes (Part 2) KEY (1 per teacher) Teacher Resource: Three-Dimensional Attributes (Part 2) (1 per teacher) Handout: Three-Dimensional Attributes (Part 2) (1 per student) Teacher Resource: Three-Dimensional Figure Practice KEY (1 per teacher) Handout: Three-Dimensional Figure Practice (1 per student) Class Resource (optional): ThreeDimensional Geometric Patterns (1 set per 4 students) Handout (optional): Three-Dimensional Figures Graphic Organizer (1 per student) page 20 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures How did your group sort the geometric figures? Why? Answers may vary. Grouping spheres, cones, and cylinders together because they have curved surfaces; grouping prisms and pyramids because they all are composed of faces; etc. 3. Display all of the prisms, except the rectangular prism, from a set of geometric figures for the class to see. Ask: What are the flat surfaces of each geometric figure called? (faces) What type of two-dimensional figures are these faces? (polygons) Why are these threedimensional figures called “prisms”? (They are three-dimensional figures that have 2 congruent parallel faces (bases) and sides that are polygonal faces.) How do you determine the special name for each prism? (You look at that shape of the 2 congruent parallel faces (bases) to determine and name the type of prism.) Explain to students that the shape of the base of the prism names the prism. Notes for Teacher MATERIALS geometric figures or solids (1 set per 4 students, 1 set per teacher) cardstock (optional) (7 sheets per 4 students) scissors (optional) (1 per teacher) tape (clear) (optional) (1 roll per teacher) TEACHER NOTE If geometric solids are unavailable, use class resource (optional): Three-Dimensional Geometric Patterns to create a set of solids for every 4 students. TEACHER NOTE Pyramids and Cones A pyramid is a polyhedron (a three-dimensional figure with faces and edges). The attributes of a pyramid include faces, edges, and the “point” where the edges meet, which is 4. Display the rectangular prism from a set of geometric solids for the class to see. Ask: defined as a “vertex.” As the number of faces on the pyramid approach infinity, the surface becomes curved, creating a page 21 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Is this figure a prism? How do you know? (yes) Answers may vary. It is a three-dimensional figure with at least two congruent faces (bases) and sides that are polygonal faces; etc. How would you name this prism? Answers may vary. Notes for Teacher cone. Since a cone consists of a curved surface, it is not considered a polyhedron. When you talk about a cone the terms “face,” “edge,” and “vertex,” as defined by a polyhedron, do not apply. A wide variety of resources modify these definitions when referencing non-polyhedrons. It is possible to refer to the “vertex” of a cone as a “point” in 5. Instruct students to examine the square bases of the prism. Because a rectangular prism could have two square faces (bases), the student may refer to this figure as a square prism. Ask: What do you know about squares and rectangles? (All squares are rectangles.) elementary math. Therefore, for elementary, TEA only lists 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 three-dimensional figure is 6. Explain to students that because all squares are rectangles, it can be inferred that this is a rectangular prism even though some of the faces are “squares.” 7. Display the pyramids from a set of geometric figures for the class to see. Ask: defined as a flat surface in the shape of a two-dimensional figure. Since the circular bases of a cylinder and cone are flat surfaces in the shape of a two-dimensional 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, CSCOPE uses these What are these three-dimensional figures called? (pyramids) 8. Explain to students that like prisms, the shape of the base of a pyramid names the pyramid. The difference is that a pyramid has only one base and a prism has two bases. Ask: attributes in alignment with TEA. TEACHER NOTE Handout (optional): Three-Dimensional Figures Graphic Organizer is available to assist students in understanding the different types of polygons. This graphic organizer can page 22 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Excluding the face of the pyramid that is the base, what type of polygons are the other faces of the triangular pyramid? (triangles) Are these faces of a pyramid always a triangle? How do you know? (yes) Answer may vary. No matter what the base of the pyramid, the faces connect to the edges of base and one common endpoint at the top of the pyramid, which creates a triangular face; etc. What do you notice about the shape of the base and the name of the pyramid? How do you know? (The shape of the base names the pyramid.) Answers may vary. A square pyramid has a square for a base; a triangular pyramid has a triangle for a base; etc. Notes for Teacher be posted in the classroom and/or individual copies can be made for students, as needed. 9. Distribute handout: Three-Dimensional Attributes (Part 2) to each student. 10. Display teacher resource: Three-Dimensional Attributes (Part 2). Facilitate a class discussion about the attributes of spheres, cones, and cylinders. Instruct students to record the attributes as they are discussed on their handout: ThreeDimensional Attributes (Part 2). 11. Distribute handout: Three-Dimensional Figure Practice to each student as independent practice and/or homework. 5 Topics: Spiraling Review Two-dimensional figures Three-dimensional figures Geometric logic ATTACHMENTS page 23 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Elaborate 1 Students extend concepts of two- and three-dimensional figures by formalizing geometric definitions of these figures. Students determine common characteristics and attributes of a set of figures. Instructional Procedures: 1. Prior to instruction create a card set: Two- and Three-Dimensional Attribute Cards for every 2 students by copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag. 2. Place students in a pairs and distribute a card set: Two- and Three-Dimensional Attribute Cards to each pair. Instruct student pairs to separate the picture cards from the attribute cards into 2 piles, shuffle each pile, spread the picture cards face up on the desk, and place the attribute cards in a stack face down on the desk. 3. Explain to students that they will take turns drawing an attribute card from the pile and trying to match it with the correct picture card. Instruct students to begin the game. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. 4. Distribute handout: Geometric Definitions—Notes to each student. Instruct students to verify their matched cards with the definitions. The student with the most correct pairs of cards wins. Notes for Teacher Card Set: Two-and Three-Dimensional Attribute Cards (1 per 2 students) Handout: Geometric Definitions – Notes (1 per student) Teacher Resource: Geometric Logic (1 per teacher) Teacher Resource: Geometric Logic Practice KEY (1 per teacher) Handout: Geometric Logic Practice (1 per student) Teacher Resource: Two- and ThreeDimensional Figures KEY (1 per teacher) Handout: Two- and Three-Dimensional Figures (1 per student) MATERIALS cardstock (7 sheets per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) 5. Display teacher resource: Geometric Logic. Instruct students to examine the figures. Ask: page 24 of 75 Enhanced Instructional Transition Guide Suggested Day Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Suggested Instructional Procedures Notes for Teacher What do these figures have in common? (They are either squares or triangles; they are all shaded; they all have a single white dot in them.) 6. Explain to students that special made-up words such as roopeets are used to name sets of examples, and that they can apply what they know about two-dimensional figures to determine the characteristics a set of figures have in common. 7. Distribute handout: Geometric Logic Practice to each student. Instruct student pairs to list the characteristics each of the figures has in common. 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. 8. Distribute handout: Two- and Three-Dimensional Figures to each students as independent practice and/or homework. 6 Evaluate 1 Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. MATERIALS construction paper (9” x 12”) (2 sheets per student) scissors (1 per student) Performance Indicator(s): page 25 of 75 Enhanced Instructional Transition Guide Suggested Day Suggested Instructional Procedures Grade 4/Mathematics Unit 08: Suggested Duration: 6 days Notes for Teacher Grade 04 Mathematics Unit 08 PI 02 Create two 4-flap books where one booklet models 4 different two-dimensional figures (e.g., rectangle, pentagon, triangle, octagon, etc.), and the other booklet models 4 different threedimensional figures (e.g., cube, triangular pyramid, cone, sphere, etc.) that must include a prism, a pyramid, and two curved surfaced figures. For the figures in the two-dimensional booklet, record the following: (1) a sketch of the twodimensional figure; (2) the most specific formal geometric name of the two-dimensional figure; (3) number of sides, vertices, and other attributes, including description of sides (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure; and (4) a written justification describing how the attributes define the figure. For the figures in the three-dimensional booklet, record the following: (1) a sketch of the threedimensional figure; (2) the formal geometric name of the three-dimensional figure; (3) number of faces, bases, edges, vertices, curved surfaces, and other attributes, including description of edges and faces (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure; and (4) a written justification describing how the attributes define the figure. Standard(s): 4.8A , 4.8B , 4.8C , 4.14A , 4.15A , 4.15B , 4.16A , 4.16B ELPS ELPS.c.1C , ELPS.c.1E 04/22/13 page 26 of 75 Grade 4 Mathematics Unit: 08 Lesson: 02 Polygon Cards ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Polygon Names Chart KEY Figure ©2012, TESCCC Number of Sides and Angles Polygon Name 3 sides 3 angles Triangle 3 sides 3 angles Triangle 3 sides 3 angles Triangle 4 sides 4 angles Quadrilateral/Square/ Rectangle/Parallelogram 4 sides 4 angles Quadrilateral/Rectangle/ Parallelogram 4 sides 4 angles Quadrilateral/Parallelogram 4 sides 4 angles Quadrilateral/Trapezoid 4 sides 4 angles Quadrilateral/Trapezoid 4 sides 4 angles Quadrilateral 5 sides 5 angles Pentagon 6 sides 6 angles Hexagon 8 sides 8 angles Octagon 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Polygon Names Chart Figure ©2012, TESCCC Number of Sides and Angles 11/09/12 Polygon Name page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Figure Search KEY Use the descriptions below to write the letters of the figures that fit that description. You may use each figure more than once. Hint: some figures are polygons, some are not. B C A E I F J G H K L (1) A figure with at least one pair of parallel lines B, E, F, G, H, I, J, L (2) A quadrilateral E, G, I (3) A hexagon H, L (4) A polygon with more than 3 sides B, E, G, H, I, K, L (5) A figure with at least one right angle A, F, G, I (6) A triangle A, D (7) A figure with at least one obtuse angle B, E, H, K, L (8) A figure that is not a polygon C, F, J (9) A figure with more than 4 vertices B, H, K, L (10) A figure with at least one acute angle A, D, E ©2012, TESCCC 11/09/12 D page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Figure Search Use the descriptions below to write the letters of the figures that fit that description. You may use each figure more than once. Hint: some figures are polygons, some are not. B C A E I F J D G H K L (1) A figure with at least one pair of parallel lines_______________________ (2) A quadrilateral ____________________________________________________ (3) A hexagon _______________________________________________________ (4) A polygon with more than 3 sides _____________________________________ (5) A figure with at least one right angle ___________________________________ (6) A triangle ________________________________________________________ (7) A figure with at least one obtuse angle _________________________________ (8) A figure that is not a polygon _________________________________________ (9) A figure with more than 4 vertices _____________________________________ (10) A figure with at least one acute angle __________________________________ ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Dot Paper ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Quadrilateral Descriptions KEY (1) Only 1 pair of parallel sides (2) Four right angles; only 2 sides the same length (3) Four right angles; all sides the same length (4) Two pairs of parallel sides; no right angles (5) Opposite sides parallel; all sides the same length (6) No pairs of parallel sides Possible answers: (1) (2) (3) (4) Trapezoid Rectangle Square Parallelogram (for it to be a rhombus, all sides have to be congruent) (5) Rhombus (for it to be a square, all angles must be right angles) (6) Irregular Quadrilateral ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Quadrilateral Descriptions (1) Only 1 pair of parallel sides (2) Four right angles; only 2 sides the same length (3) Four right angles; all sides the same length (4) Two pairs of parallel sides (5) Opposite sides parallel; all sides the same length (6) No pairs of parallel sides ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Quadrilateral Cards Trapezoid Square ©2012, TESCCC Rectangle Rhombus Parallelogram Quadrilateral 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Triangle and Quadrilateral Practice KEY Draw a sketch and name each triangle in the space provided. 1. Has 3 sides All three angles are acute. Sketches may vary. Acute triangle 2. Has 3 sides One angle is a right angle. Sketches may vary. Right triangle 3. Has 3 sides One angle is an obtuse angle. Sketches may vary. Obtuse triangle Draw a sketch and name each quadrilateral in the space provided. 4. Has 4 sides Sketches may vary. Opposite sides are congruent. Opposite sides are parallel. Rectangle, Rhombus, Opposite angles are congruent. Parallelogram, Square 5. Has 4 sides All sides are congruent. Opposite sides are parallel. All angles are right angles. ©2012, TESCCC Sketches may vary. Square 05/14/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Triangle and Quadrilateral Practice KEY Draw a sketch and name each quadrilateral in the space provided. 6. Has 4 sides Sketches may vary. Opposite sides are congruent. Opposite sides are parallel. Rectangle, Square All angles are right angles. 7. Has 4 sides Only 2 sides are parallel. Sketches may vary Trapezoid 8. Has 4 sides All sides are congruent. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Sketches may vary. Rhombus (9) Can a figure be both a rectangle and a rhombus? Explain. Yes, a square is both a rectangle and a rhombus. (10) Does a trapezoid and a rectangle have anything in common? Explain. Yes, both are quadrilaterals and both have at least one pair of parallel sides. (11) Can a right triangle be classified as an acute triangle? Explain. No; Answers may vary; An acute triangle must have all angles less than 90º. So, a right triangle cannot be an acute triangle because it has a 90º angle; etc. (12) What kind of angles are the other two angles on a right triangle? acute angles ©2012, TESCCC 05/14/13 page 2 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Triangle and Quadrilateral Practice Draw a sketch and name each triangle in the space provided. 1. Has 3 sides All three angles are acute. 2. Has 3 sides One angle is a right angle. 3. Has 3 sides One angle is an obtuse angle. Draw a sketch and name each quadrilateral in the space provided. 4. Has 4 sides Opposite sides are congruent. Opposite sides are parallel. Opposite angles are congruent. 5. Has 4 sides All sides are congruent. Opposite sides are parallel. All angles are right angles. ©2012, TESCCC 05/14/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Triangle and Quadrilateral Practice Draw a sketch and name each quadrilateral in the space provided. 6. Has 4 sides Opposite sides are congruent. Opposite sides are parallel. All angles are right angles. 7. Has 4 sides Only 2 sides are parallel. 8. Has 4 sides All sides are congruent. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. (9) Can a figure be both a rectangle and a rhombus? Explain. (10) Does a trapezoid and a rectangle have anything in common? Explain. (11) Can a right triangle be classified as an acute triangle? Explain. (12) What kind of angles are the other two angles on a right triangle? ©2012, TESCCC 05/14/13 page 2 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Building Figures and Solids with Straws Materials: flexible drinking straws masking tape scissors Procedure: To create a polygon Use scissors to slice the short end of the straw up to the bend in the straw (see dotted line on diagram) Slice along dotted line To make the geometric figures, squeeze the short end together and insert it into the long end of the straw. Always insert a short/sliced end into a long end. Continue inserting until you have created the desired polygon. To create a solid Use the polygons you have created to serve as the face of each solid figure. Example: a cube would need six square faces. Lay the polygon faces on a table to create a net. Use masking tape to tape the edges of the polygon faces together to create the net. Bring the faces of the net up to create the 3-dimensional figure. Tape the remaining edges together. A good idea is to have the students put tape on each edge and vertex as reference “touching points.” ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Two-Dimensional Figures Graphic Organizer ©2012, TESCCC 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Quadrilaterals Graphic Organizer Quadrilaterals Parallelogram Rectangle Trapezoid Rhombus Square ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Guess the Figure Materials: 1 set of quadrilateral pieces per student or pair of students Procedure: Teacher selects one piece from his/her set of pieces and hides it. In order to determine which piece the teacher has hidden, the groups take turns asking “yes/no” questions about which piece they think is hidden, or they can make an actual guess as to which piece is hidden. This is a good strategizing game and the teacher should take advantage of opportunities that arise to discuss these strategies. Some questions, the teacher may ask are: What is the best question to ask first? Why? Is there another question that is equally as good? Why or why not? If you were left with a square, a rhombus, and a rectangle, what would be a good question to ask? ©2012, TESCCC 05/14/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Guess the Figure ©2012, TESCCC 05/14/13 page 2 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Attributes (Part 1) KEY Figure Name Cube Rectangular Prism Sketch Number of Faces Number of Vertices Number of Edges Names of Faces 6 8 12 Squares 12 Rectangles OR Rectangles and Squares 6 8 Triangular Prism 5 6 9 Triangles and Rectangles Triangular Pyramid 4 4 6 Triangles 8 Square and Triangles Square Pyramid ©2012, TESCCC 5 11/09/12 5 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Attributes (Part 1) Figure Name Sketch Number of Faces Number of Vertices Number of Edges Names of Faces Cube Rectangular Prism Triangular Prism Triangular Pyramid Square Pyramid ©2012, TESCCC 11/0912 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Attributes (Part 2) KEY Figure Name Model Attributes All points are the same distance from its center Sphere Cone Cylinder ©2012, TESCCC 11/09/12 1 circular base 1 curved surface two congruent circular bases that are parallel 1 curved surface page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Attributes (Part 2) Figure Name Sketch Attributes Sphere Cone Cylinder ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Figure Practice KEY These groups show different types of three-dimensional figures. Name the group in which the following items should be placed. Then name the 3-dimensional figure the item best represents. (1) Baseball: Group C; Sphere (5) Basketball: Group C; Sphere (2) Funnel: Group C; Cone (6) Can of soup: Group C; Cylinder (3) Cereal box: Group A; Rectangular prism (4) Refrigerator: Group A; Rectangular prism (7) The moon: Group C; Sphere (8) Egyptian pyramid: Group B; Pyramid Describe and write 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. (B) Triangular Prism (A) Cube 6 square faces (2 square faces (bases) and 5 faces (2 triangular faces (bases) and 3 4 other square faces), 12 edges, 8 vertices rectangular faces), 9 edges, 6 vertices (C) Triangular Pyramid (D) Cone 4 triangular faces (1 triangular face (base) and 3 other triangular faces), 6 edges, and 1 circular base, 1 curved surface 4 vertices (E) Sphere (F) Cylinder 1 curved surface 2 circular bases, 1 curved surface ©2012, TESCCC 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Figure Practice These groups show different types of three-dimensional figures. Name the group in which the following items should be placed. Then name the 3-dimensional figure the item best represents. (1) Baseball: (5) Basketball: (2) Funnel: (6) Can of soup: (3) Cereal box: (7) The moon: (4) Refrigerator: (8) Egyptian pyramid: Describe and write 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. (A) Cube (B) Triangular Prism (C) Triangular Pyramid (D) Cone (E) Sphere (F) Cylinder ©2012, TESCCC 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Figures Graphic Organizer Triangular Prism Rectangular Prism Square Pyramid Triangular Pyramid Cylinder Cone Sphere Cube ©2012, TESCCC 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Cube ©2012, TESCCC 11/09/12 page 1 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Rectangular Prism ©2012, TESCCC 11/09/12 page 2 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Triangular Prism ©2012, TESCCC 11/09/12 page 3 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Square Pyramid ©2012, TESCCC 11/09/12 page 4 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Triangular Pyramid ©2012, TESCCC 11/09/12 page 5 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Cone ©2012, TESCCC 11/09/12 page 6 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Three-Dimensional Geometric Patterns Cylinder ©2012, TESCCC 11/09/12 page 7 of 7 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute 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 (90º) to each other Right angle an angle that measures 90º; lines that are perpendicular to each other Acute angle an angle with a measure less than a right angle (90º) Obtuse angle an angle that measures greater than a right angle (90º) but less than a straight line (180º) ©2012, TESCCC 05/14/13 page 1 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Polygon a closed twodimensional figure with 3 or more straight sides Quadrilateral any four-sided polygon Congruent Figures figures that are the same size, same shape Two-dimensional figure a figure with two basic units of measure, usually length and width four-sided (quadrilateral) polygon with • opposite sides congruent • opposite sides parallel • opposite angles congruent Parallelogram ©2012, TESCCC 05/14/13 page 2 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Rectangle four-sided polygon (quadrilateral) with • 4 right (90°) angles • opposite sides congruent • opposite sides parallel • adjacent sides perpendicular Square 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 05/14/13 page 3 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Triangle a polygon with • 3 sides • 3 angles • 3 vertices 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 and lie in the same plane C ©2012, TESCCC 05/14/13 page 4 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards 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 Edge a line segment where two faces meet on a threedimensional figure the point (corner) of intersection of two sides in a two-dimensional figure and the point (corner) of intersection of three or more edges of a threedimensional figure Vertex Face ©2012, TESCCC the flat surface of a three-dimensional figure 05/14/13 page 5 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Three-dimensional figure a figure with three units of measure: • • • length width (depth) height • prisms Base of a threedimensional figure — 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 — Prism circular base three-dimensional figure with • • two congruent, parallel faces (bases) sides that are polygonal faces three-dimensional figure with Rectangular prism • 6 rectangular faces — 2 rectangular faces (bases) — 4 other rectangular faces • • ©2012, TESCCC 05/14/13 12 edges 8 vertices page 6 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Cube three-dimensional figure with 6 square faces • — 2 square faces (bases) — 4 other square faces 12 edges 8 vertices • • Triangular prism three-dimensional figure with 5 faces • — 2 triangular faces (bases) — 3 rectangular faces 9 edges 6 vertices • • Pyramid three-dimensional figure with • • Square pyramid 1 face (base) sides that are triangular faces three-dimensional figure with • 5 faces —1 square face (base) — 4 triangular faces • • ©2012, TESCCC 05/14/13 8 edges 5 vertices page 7 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three- Dimensional Attribute Cards Triangular pyramid three-dimensional figure with • 4 triangular faces — 1 triangular face (base) — 3 other triangular faces • • 6 edges 4 vertices Curved Surface surface of a threedimensional figure that is curved Cylinder three-dimensional figure with • • Cone three-dimensional figure with • • Sphere ©2012, TESCCC two congruent circular bases that are parallel 1 curved surface 1 circular base 1 curved surface three-dimensional figure with all of its points the same distance from its center 05/14/13 page 8 of 8 Grade 4 Mathematics Unit: 08 Lesson: 02 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°) 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; and (3) curved-surface figures – circular base. Circle: the set of all points that lie the same distance from the center and lie in the same plane Cone: three-dimensional figure with 1 circular base and 1 curved surface Congruent: figures that are the same size, same shape Cube: three-dimensional figure with 6 square faces (2 square faces (bases) and 4 other square faces), 12 edges, and 8 vertices Curved Surface: surface of a three-dimensional figure that is curved Cylinder: three-dimensional figure with two congruent circular bases that are parallel and 1 curved surface Edge: a line segment where two faces meet on a three-dimensional figure Equilateral Triangle: a triangle with 3 congruent sides and 3 congruent angles Face: the flat surface of a three-dimensional figure 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 parallel, opposite sides congruent, 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 ©2012, TESCCC 05/17/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Geometric Definitions—Notes Point: an exact location in space, represented by a dot Polygon: a closed two-dimensional figure with three or more straight sides Prism: three-dimensional figure with two congruent, parallel faces (bases) and sides that are polygonal faces Pyramid: three-dimensional figure with 1 face (base) with sides that are triangular faces 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, adjacent sides perpendicular, opposite sides congruent, and opposite sides parallel Rectangular prism: three-dimensional figure with 6 rectangular faces (2 rectangular faces (bases) and 4 other rectangular faces), 12 edges, and 8 vertices 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) with all sides congruent, opposite sides parallel, and opposite angles congruent Scalene Triangle: a triangle with no congruent sides and no congruent angles Sphere: three-dimensional figure with all of its points the same distance from its center Square: four-sided polygon (quadrilateral) with all sides congruent, opposite sides parallel, 4 right (90°) angles, and adjacent sides perpendicular Square pyramid: three-dimensional figure with 5 faces (1square face (base) and 4 triangular faces), 8 edges, and 5 vertices Trapezoid: four-sided polygon (quadrilateral) with exactly one pair of parallel sides Triangle: a polygon with 3 sides, 3 angles, and 3 vertices Three-dimensional figure: a figure with three units of measure including length, width (depth), and height 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 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 and the point (corner) of intersection of three or more edges of a three-dimensional figure ©2012, TESCCC 05/17/13 page 2 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Geometric Logic These are roopeets. What characteristics do these roopeets have in common? ©2012, TESCCC 11/09/12 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Geometric Logic Practice KEY List the characteristics each of these figures have in common. Each figure is made-up of a shaded quadrilateral and an unshaded triangle sharing one side (or attached on one side). Use the space below to draw another example with these same characteristics, and then to draw a non-example. Example Non-Example Drawings may vary but should adhere to characteristics listed above. Drawings may vary but should NOT adhere to characteristics listed above. ©2012, TESCCC 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Geometric Logic Practice List the characteristics each of these figures have in common. Use the space below to draw another example with these same characteristics, and then to draw a non-example. Example ©2012, TESCCC Non-Example 05/14/13 page 1 of 1 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three-Dimensional Figures KEY A description is given for each polygon. Write the name of the polygon described and then match each polygon name to the correct figure in the box below. Label the polygon with the number that matches its description and name. (1) Polygon with six sides (2) Four-sided polygon with opposite sides parallel and no right angles Hexagon Parallelogram (3) Four sided polygon with opposite sides (4) Polygon with three sides parallel, all sides congruent, and opposite angles congruent Triangle Rhombus (5) Polygon with five sides (6) Four-sided polygon with only one pair of parallel sides Pentagon Trapezoid (7) Four-sided polygon with opposite sides (8) Polygon with eight sides parallel, opposite sides congruent, and 4 right angles Octagon Rectangle (9) Polygon with four sides (10) Four-sided polygon with all sides congruent and four right angles Quadrilateral Square (11) Three-sided polygon with one right angle (12) Three-sided polygon with one obtuse angle Right Triangle Obtuse Triangle ©2012, TESCCC 05/14/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three-Dimensional Figures KEY Describe and write 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 4 triangular faces (1 triangular face (base) and 3 other triangular faces), 6 edges, and 4 vertices (3) Rectangular Prism 6 faces (2 rectangular faces (bases) and 4 other rectangular faces), 12 edges, 8 vertices (5) Cone 1 circular base, 1 curved surface (7) Sphere (2) Triangular Prism 5 faces (2 triangular faces (bases) and 3 rectangular faces), 9 edges, 6 vertices (4) Cube 6 square faces (2 square faces (bases) and 4 other square faces), 12 edges, 8 vertices (6) Square Pyramid 5 faces (1 square face (base) and 4 triangular faces), 8 edges, 5 vertices (8) Cylinder 1 curved surface ©2012, TESCCC 2 circular bases, 1 curved surface 05/14/13 page 2 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three-Dimensional Figures A description is given for each polygon. Write the name of the polygon described and then match each polygon name to the correct figure in the box below. Label the polygon with the number that matches its description and name. (1) Polygon with six sides (2) Four-sided polygon with opposite sides parallel and no right angles (3) Four-sided polygon with opposite sides (4) Polygon with three sides parallel, all sides congruent, and opposite angles congruent (5) Polygon with five sides (6) Four-sided polygon with only one pair of parallel sides (7) Four-sided polygon with opposite sides parallel, opposite sides congruent, and 4 right angles (8) Polygon with eight sides (9) Polygon with four sides (10) Four-sided polygon with all sides congruent and four right angles (11) Three-sided polygon with one right angle (12) Three-sided polygon with one obtuse angle ©2012, TESCCC 05/14/13 page 1 of 2 Grade 4 Mathematics Unit: 08 Lesson: 02 Two- and Three-Dimensional Figures Describe and write 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) Cone (6) Square Pyramid (7) Sphere (8) Cylinder ©2012, TESCCC 05/14/13 page 2 of 2