Resource Overview Quantile® Measure: 530Q Skill or Concept: Recognize the 2‐dimensional elements of 3‐ dimensional figures. (QT‐G‐52) Use manipulatives, pictorial representations, and appropriate vocabulary (e.g., face, edge, vertex, and base) to identify and compare properties of solid figures. (QT‐G‐175) Excerpted from: Gourmet Learning 1937 IH 35 North Suite 105 New Braunfels, TX 78130 www.gourmetlearning.com © Gourmet Learning This resource may be available in other Quantile utilities. For full access to these free utilities, visit www.quantiles.com/tools.aspx. The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 skills and concepts (called QTaxons) taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content across the strands. By matching a student’s Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs to learn supporting concepts first, or has already learned it. For more information and to use free Quantile utilities, visit www.Quantiles.com. 1000 Park Forty Plaza Drive, Suite 120, Durham, North Carolina 27713 METAMETRICS®, the METAMETRICS® logo and tagline, QUANTILE®, QUANTILE FRAMEWORK® and the QUANTILE® logo are trademarks of MetaMetrics, Inc., and are registered in the United States and abroad. The names of other companies and products mentioned herein may be the trademarks of their respective owners. 3rd Grade Geometry Student Expectation: Students will identify, classify, and describe two- and threedimensional geometric figures by their attributes using formal geometric vocabulary Unit 1 – Lesson 1 The student uses formal geometric vocabulary. The student is expected to identify, classify, and describe two- and three-dimensional geometric figures by their attributes. The student compares two-dimensional figures, three-dimensional figures, or both by their attributes using formal geometric vocabulary. Study the TEKS . . . Prior Knowledge In 2nd grade, the students describe, compare, and identify two- and three-dimensional figures using attributes such as number of vertices, faces, edges, and sides, but they are not required to use formal geometric vocabulary. Next Steps 3rd In 4th grade, the students will continue to use formal geometric language, but the number of attributes will increase to include identifying and describing different types of angles as well as parallel and intersecting (including perpendicular) lines. Grade In third grade . . . Introducing formal geometric language will better prepare the students for learning more complex terms used in later grades. Many of the terms taught in this unit appear on the TAKS test. As the teacher, it is important, to model this using the geometric terms and equally as important to require students to use the terms, so they will become a part of the students’ math vocabulary. Gourmet Curriculum Press, Inc.© 1 Unit 1 – Lesson 1 Geometry Student Expectation: Students will identify and classify three-dimensional objects using their attributes Focus Activity Attributes of Geometric Figures K C Ap Teacher note: Although Focus Activities are not normally “homework,” this particular activity requires each student to identify and classify solid objects found in his/her home’s pantry or refrigerator as geometric figures. Therefore, this assignment will need to be sent home several days prior to beginning this unit. The information gathered from this Focus Activity will be used in Initial Instruction–Part II. Group size: individual Materials: parent involvement letter, page 3; “What’s in Your Pantry or Refrigerator?” chart, page 4; access to a pantry/refrigerator Before class: Make a copy of the parent involvement letter, page 3, for each student. Directions: • Discuss this homework assignment with students. Explain how they will search their pantry and/or refrigerator at home for items that can be listed under each heading on the “What’s in Your Pantry or Refrigerator?” chart. • Set a specific day for the homework assignment to be completed and returned. • Once the homework has been completed and returned, allow students to share the different items they found for each figure. • Challenge the students to think about and discuss why some figures were found more frequently in pantries and refrigerators. 2 Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will identify and classify three-dimensional objects using their attributes Focus Activity—Parent Involvement Letter Attributes of Geometric Figures Dear Parents: The following is an introductory activity for our unit on Geometry. Your student has been given the assignment of searching the pantry and/or refrigerator in your home for objects that match the shapes at the top of the attached chart. Students will follow the instructions below: • Search in the pantry and/or refrigerator for boxes, containers, jars, cans, food items, etc., that match the geometric shapes on the chart. • Once an object has been identified as having the characteristics of one of the given shapes, write the name of the object in the appropriate column on the chart. For example, an orange is a round shape and would be listed under the column labeled “Spheres.” • Try to locate several examples for each shape listed on the chart. • If you are unable to find an object in the pantry or refrigerator for one of the given shapes, list objects you know that have the characteristics of the shape. This assignment must be completed and the chart returned to class on . Thank you for your help with this assignment. Gourmet Curriculum Press, Inc.© 3 Unit 1 – Lesson 1 Geometry Student Expectation: Students will identify and classify three-dimensional objects using their attributes Focus Activity—”What’s in Your Pantry or Refrigerator?” Chart Attributes of Geometric Figures Spheres 4 Rectangular Prisms Cubes Cylinders Gourmet Curriculum Press, Inc.© Cones Square Pyramids Unit 1 – Lesson 1 Geometry Student Expectation: Students will use formal geometric vocabulary Initial Instruction—Part I—Vocabulary Attributes of Geometric Figures K attribute: the specific characteristics and qualities that define each geometric figure plane figures: a figure in a plane that is formed by lines that are curved, straight, or both—(A plane is a flat surface that goes on and on in all directions.) Plane figures are 2-dimensional and flat. There is no depth. An example of a plane figure is a square, a triangle, a circle. solid figures (or space figures): a figure that has length, width and height—Solid figures are 3-dimensional and actually take up “space.” An example of a solid figure is a ball, a box of Kleenex, a a can of soup, etc. polygon: a plane figure consisting of three or more connected line segments octagon: a polygon with 8 sides hexagon: a polygon with six sides pentagon: a polygon with five sides side: Side has two definitions. One definition is for a plane figure, and one definition is for a solid figure. • If you are referring to the side of a plane figure, it is the line segments that go all around the figure. For example, there are 3 sides in a triangle, 8 in an octagon. • The side of a solid figure is a plane figure. For example, there are 6 sides of a box of cereal. All 6 sides are rectangles of various sizes. line segment: a section of a line bound by two endpoints continued on page 6 Gourmet Curriculum Press, Inc.© 5(T) Unit 1 – Lesson 1 Geometry Student Expectation: Students will use formal geometric vocabulary Initial Instruction—Part I—Vocabulary Attributes of Geometric Figures vertex: Vertex has two definitions. One definition is for a plane figure, and one definition is for a solid figure. • If you are referring to the vertex of a plane figure, it is the point where the two line segments meet going around the outside of the figure. This is often referred to as a corner. corner vertex • If you are referring to the vertex of a solid figure, it is the point where three or more edges of a solid come together. corner vertex curve: a line segment that is not straight edge: the line segment where two faces of a solid figure meet edge face: the flat surface on a solid figure pyramid: a solid figure in which the base can be any polygon and the faces are triangles—A pyramid will always come to a pointed top. prism: a solid figure in which the top and bottom (or left and right sides if placed horizontally) are parallel and congruent—All other faces are rectangles. parallel: lines or planes that are the same distance apart and never intersect (cross) 6(T) Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe three-dimensional figures using formal geometric vocabulary Initial Instruction—Part II Attributes of Geometric Figures K Teacher note: Students will use the information gathered in the Focus Activity homework assignment “What’s in Your Pantry or Refrigerator?” to describe objects using geometric vocabulary. Group size: whole group Materials: Instructional Strategy, page 8; “What’s in Your Pantry or Refrigerator?” homework assignment (from Focus Activity); solid shapes or real-life objects that represent solid shapes; large piece of butcher paper; marker Before class: Divide the butcher paper into 5 sections, and label them “Solid Figure,” “Number of Sides,” “Number of Edges,” “Number of Vertices,” and “Number of Faces” to resemble the chart below; gather solid shapes. Solid Figure # of Sides # of Edges # of Vertices # of Faces Directions: • Review geometric vocabulary. • Explain how the students can use their homework assignment to practice using geometric language. • Distribute “What’s in Your Pantry or Refrigerator?” homework collected previously, and follow the Instructional Strategy on the following page. Gourmet Curriculum Press, Inc.© 7 Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe three-dimensional figures using formal geometric vocabulary Initial Instruction—Part II Attributes of Geometric Figures Questioning Technique Instructional Strategy Say: When we describe a figure it is important to use geometric vocabulary. Ask: Why would this be important? (If everyone uses the same words, then we are able to understand what is being described. It also will help us when we are older to understand more complex geometry skills.) Say: Let’s use the objects you found in your pantry or refrigerator to practice talking like 3rd grade geometry students. Say: Let’s look at this chart and write the name of the shape in this first column (write “sphere,” “rectangular prism,” etc). One way to describe this object using geometric vocabulary would be to tell about its attributes or characteristics. Attributes include the number of sides, number of edges, number of vertices, and number of faces. Select a solid shape, and hold it up for students to inspect. Say: Identify one attribute for this object. (Accept any of the attributes from the chart, and write the information in the correct column.) Say: Now let’s fill in the rest of the attributes for this object. (Write the correct information in the remaining columns. When complete, have a student read the description of the object using the information on the chart. Continue adding other objects to the chart in the same manner. Be sure to use different shapes, so students can practice describing a variety of figures.) Teacher note: The following is a sample of what the chart may look like. Solid Figure 8 # of Sides # of Edges # of Vertices # of Faces rectangular prism 6 12 8 6 sphere 0 0 0 0 Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will compare figures by their attributes Initial Instruction—Part III Attributes of Geometric Figures C Teacher note: Students will compare two-dimensional and three-dimensional figures, or both, using formal geometric vocabulary to create a T-chart. Group size: whole class Materials: Comparison T-charts, transparency pages 10-12; completed chart from Initial Instruction–Part II; solid objects or real-life objects that represent solid objects (optional) Before class: Tape the chart from Initial Instruction–Part II on the board or wall; gather remaining materials. Directions: • Review the chart from Initial Instruction–Part II. Place the Comparison T-chart, transparency page 10, on the overhead. Explain how students are going to compare two- and three-dimensional figures. They can use the information from the Initial Instruction chart to help them. • Locate the information about a cube from the large chart. Have students give statements about a cube using that information, and write each statement as a bullet under the appropriate title. An example of the bullet statements for a cube include: • a three-dimensional object • has 6 sides • has 12 edges • has 8 vertices • Ask students to identify a two-dimensional object that is similar to a cube (square). Now have students give bullet statements that describes the attributes of a square, such as the following: • a two-dimensional figure • has 4 sides • has 0 edges • has 4 vertices (corners) • Write the bullet statements under the second column. Discuss similarities and differences of these two shapes. • Follow the same procedure for transparency page 11, comparing circles and spheres, and transparency page 12, comparing cylinders and cones. Teacher note: Bullet points must cross-correlate between columns. If a bullet on one side does not have a matching point in the other column, then space is skipped on the corresponding side of the other column. Gourmet Curriculum Press, Inc.© 9 Unit 1 – Lesson 1 Geometry Student Expectation: Students will compare figures by their attributes Initial Instruction—Part III—Comparison T-chart Attributes of Geometric Figures Cube 10 ( T ) Square Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will compare figures by their attributes Initial Instruction—Part III—Comparison T-chart Attributes of Geometric Figures Circle Sphere Gourmet Curriculum Press, Inc.© 11 ( T ) Unit 1 – Lesson 1 Geometry Student Expectation: Students will compare figures by their attributes Initial Instruction—Part III—Comparison T-chart Attributes of Geometric Figures Cylinder 12 ( T ) Cone Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe and identify two-dimensional figures using formal geometric vocabulary Initial Instruction—Part IV Attributes of Geometric Figures S Optional Reading Activity Teacher note: After reading Patchwork Quilt by Valerie Flournoy, students will have the opportunity to create a quilt square incorporating shapes they have studied in class. Group size: whole class Materials: a copy of Patchwork Quilt by Valerie Flournoy; 6” x 6” square (construction paper works best); markers/crayons; index cards; glue; poster boards; scissors; yarn Before class: Obtain a copy of the book; cut paper into 6” x 6” squares. Gather remaining materials. Directions: • Introduce the book Patchwork Quilt. Have students predict what the story will be about based on the title. Also allow them to share personal stories or experiences with quilts. • Read the story aloud taking notice of different shapes and patterns throughout the story. Remind students that patchwork quilts are made up of many different shapes and patterns. • Give each student a square piece of paper and explain how they will make a square for a class patchwork quilt. They must create a quilt square that has at least 3 different shapes from the ones studied in class. • Students should first plan their design before sketching it in pencil onto the square paper. Once the design has been sketched, students can use markers/crayons to color their design. • When students are finished with their square, give them an index card. Each student will write a description of his/her quilt square by using geometric vocabulary to describe his/her design. In order to keep track of matching quilt squares and descriptions, write a corresponding number on each. • Collect all squares and glue them onto the poster board(s) to resemble a quilt. Collect the index card descriptions. • Display the quilt, so all students can see it. Read each description, and allow students to determine which quilt square is being described. Use yarn to connect the quilt squares with the corresponding description. Gourmet Curriculum Press, Inc.© 13 Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe and identify two-dimensional figures using formal geometric vocabulary Initial Instruction—Part V Attributes of Geometric Figures Optional Reading Activity K S Teacher note: After hearing the story Captain Invincible and the Space Shapes by Stuart J. Murphy, students will use geometric vocabulary to describe different plane figures to create a new story. Group size: whole class Materials: Captain Invincible and the Space Shapes by Stuart J. Murphy; white paper; markers or crayons; writing tool Before class: Obtain a copy of Captain Invincible and the Space Shapes; gather paper (1 piece per student) and other materials. Directions: • Read the story aloud to the class. • Discuss the space shapes mentioned in the story. Explain how each student will create a page for a new book by describing a plane shape using geometric vocabulary. • Assign each student a plane figure (more than one student can have the same figure). Each student will draw a picture using the characters and setting of the book. He/She will incorporate the assigned plane shape into the picture. • Following the story line of the book, students will write a short new situation for Captain Invincible to escape from and what or how the given plane shape could be used for to help in his escape. Students must also follow the story format and describe their plane shape using geometric vocabulary just as Captain Invincible does in the book. • Collect finished pictures and collate them together to make a book. As a class, write an introduction and conclusion for the new version. Share the new story with the class. 14 Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe figures using formal geometric vocabulary Initial Instruction—Guided Practice Attributes of Geometric Figures Ap Teacher note: Use this Guided Practice as a whole-group discussion to assess students’ ability to use vocabulary from the Initial Instruction. Group size: whole group Materials: shapes, pages 16-17; real-life or wooden solid shapes; answer key, page 45 Before class: Make 1 copy of the shapes, pages 16-17, and cut out each shape; gather reallife objects or wooden solid shapes. Directions: • Display each plane and space shape. • Allow students to give oral descriptions of the attributes of each shape using correct geometric vocabulary. • Possible sample responses: • square—4-sided figure; all sides are equal length • pentagon—a polygon with five sides and five corners Gourmet Curriculum Press, Inc.© 15 Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe figures using formal geometric vocabulary Initial Instruction—Guided Practice—Shapes Attributes of Geometric Figures 16 Gourmet Curriculum Press, Inc.© Unit 1 – Lesson 1 Geometry Student Expectation: Students will describe figures using formal geometric vocabulary Initial Instruction—Guided Practice—Shapes Attributes of Geometric Figures Gourmet Curriculum Press, Inc.© 17
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