Campus: Lacy Author(s): Amy McNairy, Trina Perkins, Michelle McCord Date Created / Revised: July 28, 2015 Six Weeks Period: 5th Grade Level & Course: Kindergarten Math Timeline: 15 days Unit Title: Unit 12: Geometry – ThreeDimensional Solids Stated Objectives: TEK # and SE K.1 K.1A K.1C K.1E Lesson # 1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: Apply mathematics to problems arising in everyday life, society, and the workplace. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. Create and use representations to organize, record, and communicate mathematical ideas. K.1F Analyze mathematical relationships to connect and communicate mathematical ideas. K.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. K.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and threedimensional solids to develop generalizations about their properties. The student is expected to: K.6A Identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles. K.6B Identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world. K.6C Identify two-dimensional components of three-dimensional objects. K.6D Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably. K.6E Classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size. K.8 Data analysis. The student applies mathematical process standards to collect and organize data to make it useful for interpreting information. The student is expected to: K.8A Collect, sort, and organize data into two or three categories. See Instructional Focus Document (IFD) for TEK Specificity Key Understandings Geometric and spatial reasoning are necessary to describe and analyze art, objects, structures, and the environment. How does visualization of various figures help in understanding the world around us? Geometric figures are distinguished by attributes. Misconceptions Why is it important to distinguish the attributes of various geometric figures? Some students may think a three-dimensional figure can be named using the name of one of its two-dimensional faces rather than realizing each three-dimensional figure has its own name (e.g., a student may refer to a cube as a square, etc.). Some students may think orientation, size, texture, and/or color are defining attributes of geometric figures rather than realizing that these features do not identify or define a shape. Key Vocabulary Attributes of two-dimensional figures – characteristics that define a geometric figure (e.g., outer edges [sides], corners [vertices], etc.) Classify – applying an attribute to categorize a sorted group Irregular figure – a figure with outer edges (sides) and/or corners that appear to be different or unequal Properties of two-dimensional figures – relationship of attributes within a geometric figure (e.g., a square has 4 outer edges [sides] that appear to be the same length and 4 square corners, etc.) and between a group of geometric figures (e.g., a square and a rectangle both have 4 outer edges [sides] and 4 square corners; however, a square has 4 outer edges [sides] that appear to be the same length but a rectangle has only opposite outer edges [sides] that appear to be the same length; etc.) Regular figure – a figure with outer edges (sides) and corners that appear to be the same or equal Side – a straight outer boundary between two vertices (line segment) of a twodimensional figure Sort – grouping objects or figures by a shared characteristic or attribute Three-dimensional figure – a solid figure Two-dimensional figure – a flat figure Vertex (vertices) in a two-dimensional figure – a corner where two outer edges (sides) of a two-dimensional figure meet Suggested Day 5E Model Instructional Procedures (Engage, Explore, Explain, Extend/Elaborate, Evaluate) Materials, Resources, Notes Day 1- Engage, Explore and Explain Calendar. 18.1 Identify Cylinders Have students tell you what they know about two-dimensional shapes. Ask students, “What are some of the shapes we have learned about?” “What circles do you see around the classroom?” “What things in the classroom are round?” Use the digital lesson for 18.1. Distribute objects to model the trash can shape and ask children to identify the attributes of the shape. Lead students Calendar Workbook pages 615616. eTeacher resourcethree dimensional shapes. Digital Lesson 18.1. toward understanding attributes of cylinders. Ask the students, “What does Scout wonder?” “What words does Scout use to describe the shape of the object” “What two-dimensional shape does the object remind you of?” Display the three-dimensional shapes, cylinder, cube, cone and sphere. Tell the students, “The circle, triangle, rectangle, and square you have learned about are two-dimensional shapes. They are flat.” Ask the students, “How are these shapes different?” Read aloud this problem as children listen. “Michael has four shapes. One is a cylinder. How can Michael describe the cylinder? Have the students use a cylinder, a cube, a cone, and a sphere to complete workbook page 615. Hold up a cylinder and ask children to hold up a shape that is like it. Introduce the name of the shape, “cylinder”. Read the labels on the sorting mat to students. Ask the students “Which three-dimensional solid is the cylinder?” Have students place the shape on the sorting mat under the word cylinder. Have the students sort the rest of the shapes on the sorting mat. Explain to students what a flat surface is. Show one flat surface of the cylinder. Tell students, “This is a flat surface on the cylinder.” “What shape is this flat surface?” “What can you tell about the surfaces of a cylinder?” Have students match a picture of each shape (see eTeacher resources) to the shapes on the sorting mat and glue them on the page to show how they are sorted. Reread the problem about Michael, from the beginning of the lesson. Ask students, “How can Michael describe his cylinder”. Have students look at workbook page, 616. For exercise 1, ask students to name the yellow shape at the top of the page. Elicit that the shape is a cylinder. Read the word cylinder with the students. Read the words next to the cylinder. Instruct students to circle the words that describe a cylinder. For exercise 2, show students a real-world cylinder, such as a can, and a geometric solid cylinder. Point out that the flat surfaces on the top and bottom of the shape. Ask the students, “How can you describe the flat surfaces of the cylinder?” “What word can you use to describe the surface of a cylinder that is not flat?” Demonstrate how to count the flat surfaces of a cylinder. Ask the students, “How many flat surfaces does a cylinder have?” Instruct student to write the number 2 on the worksheet. Day 2 – Elaborate and Evaluate Calendar. 18.1 Identify Cylinders Cont’d. Review cylinders, and re-state that cylinders have two flat surfaces. Give students workbook page 617, and instruct students to look at exercise 3. Ask the students, “What do you see?” Have the students take turns naming the objects on the shelf. A tuna can, a basketball, a block, a can of tennis balls, a packing box, a candle, an orange, a mailing tube, a horn. Ask the students, “Which objects are shaped like a cylinder?” “How do you know they are cylinders?” Have students mark an X on each object shaped like a cylinder. Encourage children to name other objects they know that are shaped like a cylinder. Have students look at workbook page 618. Read students the riddle for exercise 4. “I have two flat surfaces that are circles. Which shape am I?” Ask students, “Which shape is the answer to the riddle?” Have students mark an X on that shape. Read exercise 5 aloud to children. “How can you sort, classify, and Calendar Workbook pages 617618. identify cylinders?” Direct students to fill in the bubble for the correct answer. Day 3 –Engage, Explore Day 4 –Explain, Elaborate, and Evaluate Calendar. 18.2 Identify Cones Lead students to recall what they have learned about cylinders. Draw a circle, a triangle, a rectangle, and a square on the board. Ask students to point out straight and curved lines. Ask the students, “What are some words we can use to describe the parts of shapes?” Choose or draw an item with a flat surface and one with a curved surface and ask children to tell which type of surface each has. Use the digital lesson 18.2. Give the children manipulatives to demonstrate the shape of the traffic cones and ask them about the attributes of this shape. Help children to understand the properties of cones. Ask the students, “What does Scout know about the name of the object?” Where has Scout seen the object before?” “What would Scout like to learn?” Read the problem aloud as children listen. “Dennis has four shapes to sort. He wants to sort them into two sets: cone and not a cone. What will the sets look like?” Put out a cone, cube, cylinder, and sphere. Hold up the cone. Tell students, “This three-dimensional shape is called a cone.” Show students the sorting mat on page, 621. Read the labels on the sorting mat. Tell students to place the three-dimensional shapes on the page. Ask the students, “Which shape is the cone?” “How can you describe a cone?” Instruct students to sort the shapes on the sorting mat. Ask the students, “What can you tell about the surfaces of a cone?” Tell students to “Notice that the cone has a point, and a cylinder does not.” Have children match a picture of each shape to the shapes on the sorting mat, using eTeacher resource). Have the students glue the shape pictures on the sorting mat. Reread the problem about Dennis, from the beginning of the lesson. Discuss what Dennis’ two sets will look like. Calendar. 18.2 Identify Cones Cont’d. Give each student workbook page 622. Find exercise 1, and instruct students to look at the red shape. Ask, “What is it?” “Which words can you use to describe the surfaces of a cone?” Read the words next to the cone. Instruct children to circle the words that describe a cone. Have students look at exercise 2. Show children a real world cone, such as a party hat, and a geometric solid cone. Point out the flat surface on the bottom. Ask the students, “How can you describe the shape of the flat surface on a cone?” “What word can you use to describe the surface of a cone that is not a flat surface?” “How many flat surfaces does a cone have?” Instruct students to write the number one, on workbook page 622. Give students workbook page 623, and call on volunteers to name the objects going across each shelf of the bookshelf in order. Ask the students, “Which objects are shaped like a cone?” “How do you know” Instruct students to mark each cone-shaped object with an X. Focus the student’s attention to exercise 4, on workbook page 624. Read the riddle aloud to children. “I have a curved surface and one flat surface. Which shape am I?” Children should make an X on the cone. Calendar 18.2 Digital Lesson eTeacher resource-three dimensional shapes. Workbook page 621. Calendar Workbook pages 622, 623, and 624. Read exercise 5 aloud to the children. “How do you sort, classify, and identify cones?” Direct children to fill in the bubble for the correct answer. Day 5 – Engage, and Explore, Explain Calendar. 18.3 Identify Spheres Have students discuss with you what they know about cones. Draw a cone for students to see. Ask students, “Does a cone have a curved surface?” Draw a circle, a triangle, a rectangle and a square. Ask students, “Which shapes have parts that are flat?” “Which shapes have parts that are curved?” Use Digital Lesson 18.3 Have students use objects to model different shapes that a ball can be and ask them which shapes might be best. Guide students toward recognizing and identifying a sphere. Ask students, “What do Scout and Rafferty find?” “What does Scout want to know?” “Do the balls have curved surfaces or flat surfaces?” Read aloud this problem as students listen. “Ray has four shapes. One is a sphere. How can Ray describe the sphere?” Have students use a cube, a cylinder, a cone, and a sphere to complete workbook page 627. Hold up a sphere and ask children to hold up a shape that is like it. Introduce the name of the shape—sphere. Ask students, “How can you describe a sphere?” “What can you tell about the surface of a sphere?” Read the labels on the sorting mat (page 627) to the students. Have students place the three dimensional shapes on the page and sort the shapes. Then have students match a picture of each shape to the shapes on the sorting mat. Have them glue the shape pictures on the page. Then say to students, “I am thinking of a shape that does not have any flat surfaces. What shape am I thinking of?” Reread the problem about Ray from the beginning of the lesson. Ask students, “How can Ray describe his sphere?” “Name some things that are shaped like a sphere.” “How are they alike?” Three dimensional shapes eTeacher resource three dimensional shapes Digital lesson 18.3 Workbook page 627 & 628 Have students use workbook pg. 628. For exercise 1, ask students to name the red shape at the top of the page. Read the label, “sphere”, with children. Explain that the surface of an object is all of the outside, or the outer parts. Rub your hands around the surface of the sphere to demonstrate the word. Talk about the spheres curved surface. Ask students, “How many curved surfaces does a sphere have?” (none) “What word could you use to describe the surface of a sphere?” (curved) Read the descriptions next to sphere. Instruct students to circle the correct description. Instruct students to look at exercise 2. Ask, “How many spheres do you see?” “Why are the other shapes not called spheres?” Have students color the spheres. Day 6 –Elaborate and Evaluate Calendar. 18.3 Identify Spheres (cont’d.) Use workbook page 629. Look at exercise 3 together. Ask, “Which objects in the bookshelf are shaped like a sphere?” Have students mark an X on each object shaped like a sphere. Encourage students to find objects around them shaped like a sphere. Ask students to look at the middle shelf on the page. Have students take turns Workbook pages 629 & 630 naming each object and identify the matching three dimensional shape. Use workbook page 630. Read the riddle for exercise 4, “I have a curved surface. Which shape am I?” Instruct students to look at workbook pg. 630. “Look at the two shapes. How will you solve this riddle?” “Which shape has a curved surface?” Have students mark it with an X. Complete exercise 5, by asking students which shape is not a sphere? Instruct students to bubble in the correct response. Day 7 –Engage, Explore Calendar. Use Digital Lesson Opener 18.4 Show objects to students that share the shape of the hay bale and the bucket and ask about the properties of each. Help students understand how to identify objects shaped like a cube. Ask, “What does Scout think the hay bale looks like?” “Which object that Scout sees has a curved surface?” “Which object has straight sides?” “What would Scout like to find out?” Use Workbook pg. 633 Identify Cubes 18.4 Read aloud this problem as students listen, “Maya has four shapes. One is a cube. How can Maya describe the cube?” Have students use a cube, cylinder, cone, and sphere to complete the workbook page. Hold up a cube and ask children to hold up a shape that is like it. Introduce the name of the shape—cube. Point out the edges and vertices on the cube. Ask, “How can you describe a cube?” “What can you tell about the surface of the cube?” Read the labels on the sorting mat (pg. 633). Have students place the solid shapes on the page. Point to a cube. What is this shapes name? Have students match a picture of each shape to the solids on each page. Have them glue the pictures on the page in the correct column. Say, “I have a shape that has a curved surface. Could it be a cube? Explain.” Reread the problem about Maya. Ask, “How can Maya describe her cube?” Day 8 – Explain, Elaborate, Calendar. Use Workbook pg. 634 & 635. Instruct students to look at Exercise 1. Ask the students to name the blue shape. Elicit that the shape is a cube. Read the word cube with the students. Read the words next to cube with children. Instruct students to circle the words that can be used when they describe a cube. Say, “Name the shape of each flat surface on the cube.” “How many flat surfaces does a cube have?” Show students a real world cube, such as an alphabet block, and a geometric solid cube. Help students count the flat surfaces by counting the top and bottom and then going around the middle. Tell students that they need to keep track of which flat surface they start counting with so that they do not count any flat surface twice. Instruct students to look at Exercise 2. Sort the shapes that look like cubes and the shapes that do not look like cubes. Discuss with students how some three-dimensional figures, like cubes, are regular and some three-dimensional figures are irregular figures. Instruct students to look at Exercise 3. Have students take turns naming the objects shown on the shelves, starting with 18.4 Digital Lesson A cube shaped object, and cylinder shaped object. Workbook pg. 633 A cube, cylinder, cone and sphere. Workbook pg. 634, and 635. Real-World Cube Geometric Solid Cube the top shelf. Ask, “Which objects are shaped like a cube?” “How do you know they are cubes?” Have students mark an X on each object shaped like a cube. Day 9 –Engage, Explore, Calendar. Ask children to tell you what they know about squares and cubes. Show students a number cube. Ask, “What is the name of this shape? (cube) “What are some other things that come in the shape of a cube?” “What shape is a globe” (sphere) Have students draw a picture of the hay bale in the barn. Ask, “Is the face of the hay bale round?” (no) “How many lines does the face of the hay bale have?” (4) “How many corners does the face of the hay bale have?” (4) Use Workbook pg. 639. Read this problem aloud as students listen. “Kelly has a cone, a cube, and a cylinder. Each threedimensional shape has a flat surface shaped like a circle or a square. Which of Kelly’s shapes has a face that is a circle? Which of Kelly’s shapes has a flat surface that is shaped like a square?” Have students point to and name each three-dimensional shape on the page. Say, “Use your three dimensional solids. Look at the cone. Can a cone roll? How do you know?” “Can you roll a cone when its point is up? Why not?” Have students point to the flat surface on the cone on the page. Point out the dashed line around the flat surface. Say, “Trace the dashed line of the cone. What shape is the flat surface of a cone? Draw a line from the cone and connect it to the circle on the other side of the page.” Discuss with children the shape of the flat surfaces of the cube and the cylinder. If necessary, help children locate the dashed lines on the cube and cylinder. Have them trace the dashed lines on the shapes and draw a line matching the threedimensional shape to the two-dimensional shape. Say, “Which of Kelly’s shapes have a flat surface that is a circle? Which of Kelly’s shapes has a flat surface that is a square?” Workbook pg. 639 Three-dimensional shapes. Day 10 – Explain, Elaborate Calendar. Use Workbook pg. 640. Guide students to Exercise 1. Have them analyze the given information. Say, “What shapes do you see?” “Which one of these shapes has a flat surface that is shaped like a circle?” “Trace along the edge of the flat surface with your finger.” “Color the cylinder.” Explain that on a cylinder there are two flat surfaces, one at the top and one on the bottom. Repeat for Exercise 2. Say, “Look at exercise 3. What shapes do you see?” “Which one of these shapes has a flat surface that is shaped like a square?” “How do you know your answer is correct?” “Color the cube.” Use Workbook pg. 641. Say, “What object is first in Exercise 4?” “What threedimensional shape is the block shaped like?” “What shape is a flat surface on a cube?” “Mark an X in the box under the square.” Continue in this same way for Exercises 5-8. Workbook pg. 640641. Day 11 – Day 12 – Explain/Extend/ Elaborate Calendar. Place 3 or 4 examples of each of these shapes in the sack or gift bag (Cube, Cylinder, Cone, Rectangular Prism, and Sphere). 1. Gather children to your discussion circle. Place the pieces of yellow and blue paper in the circle where you can reach them and all the students can see them. Let the children know that these are your sorting mats. Then hold up the grocery or gift sack and explain that you are going to pull out some things for them to see, one at a time. Each time you pull out a new object, you’re going to place it on either the yellow or the blue mat. Their job is to figure out how you’re sorting the objects by watching very closely. Let them know that you’re going to work in silence, and they’ll need to be very quiet as well. 2. Pull 4 or 5 objects out of the sack one at a time, placing those with flat faces on one mat and those with curved surfaces on the other. 3. Pull the next object out of the sack, hold it up, and shrug your shoulders. Then motion for children to point to the mat where they think it belongs. After a few moments, place it on the correct mat. Repeat this with another object. 4. Pull another object out, have students to point to the mat they believe is correct, and ask a few to explain their reasoning this time. After the object has been placed correctly, continue to sort silently, as students point to one of the mats each time. If many still seem puzzled by the time you’re down to the last few objects, ask for more explanations. You might also give them a few hints in the form of questions: “Am I sorting these objects by their color?” or “Am I sorting these objects by the size—small and large?” or “Am I sorting objects by their shape?” 5. Continue sorting the objects, until all objects are sorted. 6. When all the objects have been sorted onto the two mats, ask children to pair-share their observations, and then call on volunteers to share their thinking with the class. Toward the end of the discussion, confirm that you were sorting the objects by flat and curved surfaces, and then identify each of the shapes by name. Students should have brought to school, something from home that is the shape of a sphere, cone, cylinder, or cube. Prior to instruction, distribute the object(s) students have brought from home to each owner. Allow students that did not bring an object from home to find an object in the classroom to share. Label 4 sheets of chart paper: “Real World Triangles,” 1 sheet of chart paper “Real World Squares", 1 sheet of chart paper "Real World Rectangles", and 1 sheet of chart paper “Real World Circles.” Display models of a sphere, cone, cylinder, rectangular prism, and cube. As each figure is introduced, place it on a separate sheet of bulletin board paper. Invite students, one at a time, to share their object(s). Instruct students to match their object to the appropriate threedimensional model by placing their object on the corresponding bulletin board paper. Allow all students to share their object(s) and place them match them to a three-dimensional model. Collect students’ objects and retain for use on another day. Have students make and color: “My 3D Shapes Book” grocery sack or gift bag containing 15–20 different 3-D objects 2 pieces of construction paper, one yellow and one blue Models of a Sphere, Cone, Cylinder and Rectangular Prism 4 pieces of Chart Paper (pre-labeled: “Real World Triangles, Real World Rectangles, Real World Circles, and Real World Squares”.) Day 13 Explain/Extend/ Elaborate Place students in groups of 4. Distribute clay or play dough and a plate to each student. Gather clay or play dough, a plate, and plastic knife for the teacher. Place a ball in the center of each group of students. Instruct students to make a ball using their play dough as you model the same. Facilitate a discussion regarding the attributes of a ball. Invite students to predict what shape would appear if the ball were cut in half. Carefully cut the play dough ball in half to show the inside. Allow students to speculate as to why the circle appears when the ball in cut in half. Remove each ball from the center of each group of students and replace it with a party hat. Instruct students to make the changes to their play dough as you model and discuss in detail the physical changes that are occurring. Remove each party hat from the center of each group of students and replace it with a can. Instruct students to make the changes to their play dough as you model and discuss in detail the physical changes that are occurring. Remove each can from the center of each group of students and replace it with the tissue box. Instruct students to make the changes to their play dough as you model and discuss in detail the physical changes that are occurring. Remove each tissue box from the center of each group of students and replace it with the die. Instruct students to make the changes to their play dough as you model and discuss in detail the physical changes that are occurring. Facilitate a discussion to review each of the figures created. Invite students to describe the figures using their own words. Allow students to share other real world objects that have the same attributes as the figures created with play dough. Record student suggestions on the previously created Real World Objects Charts. Clay/Play dough Paper plate Plastic knife Ball Party Hat Can Tissue Box Day 14 Explain/Extend/ Elaborate Prior to instruction, combine the previously created Shape Collection with the three-dimensional models of the following solids: rectangular prism, cube, cone, and cylinder. Place a mixed collection in a box for each group of 4 students. It is important that each tables’ collection has several examples of the various shapes and solids. Place students into groups of 4 and distribute one box of objects to each group. Explain to students that you have selected a secret shape in your mind. Explain that you are going to give clues to help students determine your secret shape. Students will sort through their collection to identify the attributes of a shape as clues are given. Present the first set of clues to students. Allow time between each clue for students to discuss the clue and search for the attribute in their collection. My secret shape can roll. If my secret shape was cut in half, you would see a circle. My secret shape has no corners. Ask: What is my secret shape? (sphere) Allow students to guess the answer before announcing the correct choice. Invite students to share the objects they selected that match the clues given. Instruct students to explain and justify their choices. Repeat with another shape. Do a shape worksheet. Models of a Sphere, Cone, Cylinder and Rectangular Prism Shape Collection – students brought from home 4 large boxes (1 per table) Shape worksheet Two and Three Dimensional Shape Walk: Teacher will take the students on a “Shape Walk” through the school and on the playground. Prior to the walk, the teacher will review using models the four geometric shape: cone, sphere, cylinder and cube. Teacher should show the students Day 15 – Explain/Extend/ Explore Models of a Sphere, Cone, Cylinder and Rectangular Prism Manila paper Crayons one shape and ask them to recall what it is and tell whether it stacks, slides or rolls. After reviewing the shapes, explain to the students that you will be taking a walk through the school and on the playground looking for these geometric shapes. Tell the students that if they find one they will need to point it out to you and then tell you which geometrical shape it is. Let students know that they will need to pay close attention to their classmates and what they find because when they return to class they will be drawing a picture of something they saw that was a : cone, sphere, cylinder and cube. Go on the SHAPE WALK. After returning from the walk, pass out a piece of manila paper and show students how to divide it into fourths using a black crayon. Once they have divided their paper tell them they will need to use their crayons to draw a picture of something they saw on their walk that was cone shaped, sphere shaped, cylinder shaped and cube shaped. Day 16 – Day 17 - Day 18 - Day 19 - Accommodations for Special Populations D Accommodations for instruction will be provided as stated on each student’s (IEP) Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.