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Polyhedrons, Part 2 Objective To provide opportunities to explore the characteristics of prisms. c www.everydaymathonline.com ePresentations eToolkit Algorithms Practice EM Facts Workshop Game™ Teaching the Lesson Key Concepts and Skills • Compare faces on prisms. [Geometry Goal 2] • Identify the faces of polyhedrons. [Geometry Goal 2] • Identify and name prisms. [Geometry Goal 2] • Identify the faces, edges, and vertices of prisms. [Geometry Goal 2] Family Letters Assessment Management Common Core State Standards Ongoing Learning & Practice 1 2 4 3 Playing Beat the Calculator (Multiplication) Math Journal 1, p. 156 Student Reference Book, p. 279 per group: calculator Children practice multiplication facts. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 398). [Operations and Computation Goal 3] Key Activities Math Boxes 6 12 Children identify the bases, faces, and vertices of various prisms. They classify prisms according to the shapes of their bases. Math Journal 1, p. 154 Children practice and maintain skills through Math Box problems. Key Vocabulary Home Link 6 12 rectangular prism triangular prism hexagonal prism Math Masters, p. 199 Children practice and maintain skills through Home Link activities. Materials Curriculum Focal Points Interactive Teacher’s Lesson Guide Differentiation Options READINESS Illustrating Prefixes Student Reference Book, p. 103 paper Children illustrate prefixes used to name polygons. ENRICHMENT Solving Geometric Riddles Math Masters, pp. 200 and 201 Student Reference Book, pp. 112–114 scissors slate Children solve geometric riddles. Math Journal 1, p. 153 Student Reference Book, p. 115 Home Link 611 pattern-block prism cereal box per group: 4 of each pattern-block shape (square, triangle, trapezoid, hexagon), transparent tape paper Advance Preparation For Part 1, place a cereal box near the Math Message. Construct a prism by taping 3 or 4 of the same pattern-block shapes together. For the optional Enrichment activity in Part 3, copy a set of geometry riddle cards (Math Masters, page 201) on cardstock for each small group. Teacher’s Reference Manual, Grades 1–3 pp. 144–146 468 Unit 6 Geometry 468_EMCS_T_TLG1_G3_U06_L12_576809.indd 468 2/23/11 11:46 AM Getting Started Mental Math and Reflexes Math Message Write decimals on the board. Children read them aloud. Encourage them to exaggerate the th sound so that decimal numbers are not confused with whole numbers. What kind of shape is the cereal box? How many faces does it have? How many edges? How many vertices? What is the shape of its faces? Write your answers on paper and discuss them with a partner. Suggestions: 0.42 forty-two hundredths 1.34 one and thirty-four hundredths 6.09 six and nine-hundredths 0.5 five-tenths 2.4 two and four-tenths Home Link 6 11 Follow-Up 20.50 twenty and fifty-hundredths 5.813 five and eight hundred thirteen-thousandths 45.030 forty-five and thirty thousandths 80.102 eighty and one hundred two-thousandths Ask questions like Which digit is in the tenths place? What is the value of the digit x? How many hundredths are there? Have children share some of the 3-D objects and pictures that they brought to school. Encourage them to use geometry vocabulary to name the objects and pictures. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Briefly go over the answers regarding the cereal box. rectangular prism; 6 faces; 12 edges; 8 vertices; rectangular Identifying the Bases of a WHOLE-CLASS DISCUSSION Rectangular Prism Explain that this lesson further explores the characteristics of prisms. Review the characteristics of the bases of prisms: They are flat, opposite each other, and parallel. They are the same shape and the same size, so they are congruent. Have children discuss which faces are the bases of the cereal box. Ask: Does each face have an opposite face that is parallel and congruent to it? Yes How many pairs of parallel faces does the box have? 3 pairs In a rectangular prism, any pair of opposite faces can be the bases of the prism. Choose a pair of opposite faces to be the bases. Once you have made a choice, the other two pairs of faces are not considered the bases. Lesson 6 12 EM3cuG3TLG1_469-473_U06L12.indd 469 469 1/20/11 9:12 AM Student Page Date 6 12 䉬 Constructing Pattern-Block Time LESSON Pattern-Block Prisms SMALL-GROUP ACTIVITY Prisms and Tracing Their Faces Work in a group. 1. Each person chooses a different pattern-block shape. 2. Each person then stacks 3 or 4 of the shapes together to make a prism. Use (Math Journal 1, p. 153) small pieces of tape to hold the blocks together. 3. Below, carefully trace around each face of your prism. Then trace around each face of 2 or 3 more prisms on a separate sheet of paper. Ask someone in your group for help if you need it. Share prisms with other people in your group. See children’s work. Give each group 16 pattern blocks (four each of triangles, squares, trapezoids, and hexagons). Draw a square on the board. Ask: Why is the drawing not a prism? The drawing is a 2-dimensional figure. It has no thickness. Hold up a square pattern block and ask the class why it is a prism. The pattern block is a 3-dimensional object because it has thickness. Hold up a pattern-block prism that you taped together. (See Advance Preparation.) Each group will make different pattern-block prisms by taping together 3 or 4 congruent pattern blocks. Each child in a group should make a different prism. Children in each group then share their pattern-block prisms to complete journal page 153. Discussing the Shapes of Math Journal 1, p. 153 WHOLE-CLASS DISCUSSION the Faces of Prisms (Student Reference Book, p. 115) When most children have completed their tracings on the journal page, discuss children’s work as a class. Ask several children to name the shape of the bases of their prisms. Ask: What is the shape of the faces that are not bases? rectangles Prisms are named after the shapes of their bases. For example, the bases of a rectangular prism are rectangles. A prism whose bases are triangles is a triangular prism. The bases of a hexagonal prism are hexagons. Student Page Geometry Polyhedrons A polyhedron is a solid whose surfaces are all flat and formed by polygons. It does not have any curved surfaces. The faces of a regular polyhedron are all formed by copies of one regular polygon that have the same size. Three important groups of polyhedrons are shown below. These are pyramids, prisms, and regular polyhedrons. Many polyhedrons do not belong to any of these groups. Discuss the shapes on page 115 in the Student Reference Book. Point out that pyramids, as well as prisms, are named after the shape of their bases. Children should also notice that there are other polyhedrons besides pyramids and prisms. Some children might count the number of edges or vertices on the five polyhedrons at the bottom of the page. Ask: What kind of pyramid is the tetrahedron? Triangular pyramid Adjusting the Activity Pyramids triangular pyramids rectangular pyramids pentagonal pyramid hexagonal pyramid Prisms triangular prisms rectangular prisms hexagonal prism A U D I T O R Y Regular Polyhedrons regular tetrahedron (pyramid) (4 faces) cube (prism) (6 faces) regular octahedron (8 faces) regular dodecahedron (12 faces) Have children name a prism with a 5-sided base, pentagonal prism 7-sided base, heptagonal prism 8-sided base, octagonal prism 9-sided base, nonagonal prism and 10-sided base. decagonal prism Write the names on the board. Ask children how the names are related to the names of 2-dimensional shapes. Pentagonal is related to pentagon, which is the shape of the base of the pentagonal prism; heptagonal is related to heptagon, which is the shape of the base of the heptagonal prism, and so on. K I N E S T H E T I C T A C T I L E V I S U A L regular icosahedron (20 faces) Student Reference Book, p. 115 470 Unit 6 Geometry EM3cuG3TLG1_469-473_U06L12.indd 470 1/20/11 9:12 AM Student Page 2 Ongoing Learning & Practice Playing Beat the Calculator Date Time LESSON Math Boxes 6 12 2. Draw all the lines of symmetry. , parallel to line 1. Draw a line, _AB segment, CD. Draw a ray, EF , that intersects the ray, GH . A PARTNER ACTIVITY B C (Multiplication) D G E F There are (Math Journal 1, p. 156; Student Reference Book, p. 279) lines of symmetry. 122 123 100 101 4. Write the numerals. 3. Number of days for one revolution around the sun: Children develop automaticity with multiplication facts by playing Beat the Calculator. Have children keep a record of the facts for which they get the product first when playing the role of the Brain by making a check mark on their Fact Power Table, journal page 156. For Fact Power Table directions, see Lesson 4-5. For game directions, see page 279 in the Student Reference Book. Remind children to fill in the product on their Fact Power Table when they have 3 check marks for a fact. Which planet takes the fewest days to revolve around the sun? Mercury 88 Venus 225 Earth 365 Mars 687 A. Mercury C. Venus B. Earth D. Mars Exit Slip 5 _ or 0.05 _ or 0.3 five-hundredths 100 3 10 three-tenths 3 _ three-hundredths 100 33 34 6. Divide. triangle. Label the points. 5 3 30 ÷ 6 = B 12 ÷ 4 = 4 20 ÷ 5 = A 2 3 C C or 0.03 79 5. Connect 3 points to make a right Sample answer: 5 _ 10 or 0.5 five-tenths Fill in the circle for the best answer. Which letter names the right angle? Ongoing Assessment: Recognizing Student Achievement 5 H 106 107 = 14 ÷ 7 =9÷3 52 53 Math Journal 1, p. 154 EM3MJ1_G3_U06_128-156.indd 154 Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward demonstrating automaticity with multiplication facts through 10 × 10. Children record the facts from the Fact Power Table for which they recorded at least one check mark. Children are making adequate progress if they record all of the facts from the unshaded portion of the table. Some children may record additional facts from the shaded portion. 1/18/11 3:31 PM NOTE For practice identifying congruent figures, go to www.everydaymathonline.com. [Operations and Computation Goal 3] Math Boxes 6 12 INDEPENDENT ACTIVITY (Math Journal 1, p. 154) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-10. The skill in Problem 6 previews Unit 7 content. Home Link Master Name HOME LINK 6 12 Family Note Home Link 6 12 INDEPENDENT ACTIVITY (Math Masters, p. 199) Date Time Making a Solid Shape Our class has been exploring the characteristics and parts of various 3-dimensional shapes— especially prisms. The pattern on this page can be used to make one type of prism. Prisms are named for the shapes of their bases. 117 Please return this Home Link to school tomorrow. Cut on the dashed lines. Fold on the dotted lines. Tape or paste each TAB inside or outside the shape. Discuss the following questions with someone at home: pentagonal prism pentagon What is the shape of the bases? rectangle What is the shape of the other faces? 15 edges How many edges does the shape have? 10 vertices How many vertices does the shape have? 1. What is this 3-D shape called? Home Connection Children cut out a pattern and make a pentagonal prism. Then they talk about the shape with someone at home. 2. 3. 4. 5. B TA TAB TAB TAB TA B TAB TAB TA B TAB Math Masters, p. 199 EM3MM_G3_U06_167-205.indd 199 1/18/11 1:44 PM Lesson 6 12 EM3cuG3TLG1_469-473_U06L12.indd 471 471 1/22/11 1:37 PM 3 Differentiation Options PARTNER ACTIVITY READINESS Illustrating Prefixes 15–30 Min (Student Reference Book, p. 103) To explore polygon names, have children discuss prefixes used to name polygons and relate the prefixes to other words they know. Children refer to the chart of prefixes on page 103 in the Student Reference Book. They fold a blank page into 4 boxes and illustrate 4 or more (use the back of the page) of the prefixes with pictures that will help them remember the prefix meanings. Examples: Tricycles have three wheels like a triangle has three angles and sides. A dollar is made of four quarters like a quadrangle is made of four angles and sides. The Pentagon building in Washington, D.C. is in the shape of a pentagon. The x in hexa- is like the x in six. An octopus has eight legs like an octagon has eight sides. The Ns in nona- are like the Ns in nine. Decades are made of 10 years like decagons are made of 10 angles and sides. Student Page Geometry Polygons are named after the number of their sides. The prefix for a name tells the number of sides. Prefixes triangle quadrangle or quadrilateral pentagon hexagon heptagon octagon tri- 3 quad- 4 penta- 5 hexa- 6 hepta- 7 octa- 8 nona- 9 deca- 10 dodeca- 12 The flag of Nepal is the only flag in the world with 5 sides. All other flags have 4 sides. The flag of Switzerland has a white cross with an edge that is a dodecagon (12 sides). nonagon flag of Nepal flag of Switzerland 1. Name the polygon. a. 6 sides b. 4 sides d. 8 sides e. 12 sides c. 10 sides 2. Draw a pentagon whose sides are not all the same length. Check your answers on page 339. Student Reference Book, p. 103 472 Unit 6 Geometry EM3cuG3TLG1_469-473_U06L12.indd 472 1/20/11 9:12 AM SMALL-GROUP ACTIVITY ENRICHMENT Solving Geometric Riddles 15–30 Min (Math Masters, pp. 200 and 201; Student Reference Book, pp. 112–114) To apply children’s knowledge of geometric solid attributes, have them solve geometry riddles. Directions are found on Math Masters, page 200. Children may refer to the Geometric Solids pages in the Student Reference Book as needed. Planning Ahead Make the prism from Home Link 6 12 for the Home Link Lesson 6 13 Follow-Up. Have children keep Math Journal 1 accessible throughout Unit 7 as they will need to cut out the remaining Fact Triangles on Activity Sheets 3 and 4 for Lesson 7-2. Children also need to copy the Length of Day graph on journal page 125 to the graph on journal page 279. They need the data from the National High/Low Temperatures Project on journal page 43 for Lesson 7-8. Have children copy their body measures from journal page 251. They will revisit their body measures in Lesson 10-7. Teaching Master Name LESSON 6 12 Date Teaching Master Time Name Geometry Riddles Date Time LESSON 6 12 Geometry Riddles Cards 1. Work in teams of 2 to 4. 112–119 2. Cut out the Geometry Riddles cards from Math Masters, page 201 and place them facedown on the playing surface. 3. The team of readers chooses a card and silently reads all the clues. They write the answer to the riddle on a slate without showing it to the other team, the guessers. Then they read only the first clue aloud to the guessers. The guessers discuss the clue and guess the shape. If their guess is correct, the turn is over. If it is not correct, the readers read the second clue. Continue until the guessers name the shape on the card. Then switch roles. 4. Readers assign one tally mark for every clue needed. Record the tallies on the chart below. 5. If teams disagree on an answer to a riddle, they may use the Student 1. I am a geometric solid. 2. I have 2 surfaces. 2. I have only 1 surface. 3. My base is formed by a circle. 3. My 1 surface is curved. 4. I have a point at the top. 4. I have no base. What am I? What am I? A cone A sphere 1. I am a polyhedron. 1. I am a polyhedron. 2. I have 2 triangular bases. 2. I have the fewest number of 3. I have 3 other faces. Reference Book section on Geometric Solids, pages 112–119. 4. My other faces are rectangles. 6. Teams switch roles. The game ends when all the cards have been What am I? used. The team with the fewest tally marks wins. Names of Team Members 1. I am a geometric solid. A triangular prism Points 4. I come to a point at the top. What am I? A triangular pyramid Team 1: Team 2: Math Masters, p. 200 EM3MM_G3_U06_167-205.indd 200 faces of all the polyhedrons. 3. All of my faces are triangles. 1. I am a polyhedron. 1. I am a polyhedron. 2. I have 5 faces. 2. I have 6 faces. 3. Four of my faces are triangles. 3. All of my faces are congruent. 4. My base is a square. 4. All of my faces are squares. What am I? What am I? A rectangular pyramid A rectangular prism or cube Math Masters, p. 201 1/18/11 12:57 PM EM3MM_G3_U06_167-205.indd 201 2/10/10 Lesson 6 12 EM3cuG3TLG1_469-473_U06L12.indd 473 2:18 PM 473 1/20/11 9:12 AM