Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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TIME: approximately 60 minutes INSTRUCTIONAL GROUPING: individuals, pairs 1 2 ABOUT THE LEARNING ACTIVITY MATERIALS • interlocking cubes (3 per student) • 3D6.BLM1: 2 cm Grid Paper (2 sheets per student) • 3D6.BLM2: Isometric Dot Paper, cut into half sheets (2 half sheets per student) • overhead projector • 3D6.BLM3: Sketching Climbing Structures (1 per student) • 3D6.BLM4: Sketching Isometric Perspectives (1 per student) • 3D6.BLM5a–b: Teach an Adult to Sketch (1 per student) MATH LANGUAGE • congruent • orthographic sketches or views (top, front, side) • rotate • mirror image • two-dimensional representation INSTRUCTIONAL SEqUENCING Geometry and Spatial Sense, Grades 4 to 6 • three-dimensional figure • isometric dot paper • isometric perspective or view • vertical line segment • diagonal line segment • horizontal line segment • edge This learning activity focuses on the relationships between two-dimensional drawings and three-dimension figures. Prior to this lesson, students should be familiar with building three- dimensional solids from top, front, and side views. ABOUT THE MATH In Grade 6, students learn to draw different views (i.e., top, front, side) and sketch isometric perspectives of three-dimensional figures. They also require opportunities to build three- dimensional models, given isometric sketches or different views of a structure. These experiences will help students develop an understanding of the relationship between three-dimensional figures and their two-dimensional representations. Students have opportunities to represent their thinking concretely and through two different types of drawings. They also have opportunities to make connections between two-dimensional sketches of three- dimensional figures in the classroom and the use of these types of two-dimensional sketches in the real world (e.g., in assembly instructions for toys, furniture, model cars or planes). Isometric diagrams use an isometric grid. An isometric grid shows three axes instead of the two found in a rectangular grid. One axis runs vertically; the other two axes run “down” at 30° angles to the left and right.
GETTING STARTED Distribute three interlocking cubes and one sheet of 3D6.BLM1: 2 cm Grid Paper to each student. Show students the following L-shaped structure built from interlocking cubes: Ask students to build a congruent structure with their three interlocking cubes. Have them place the structure on the 2 cm grid paper so that the single cube is facing them. Instruct students to label the front, back, left side, and right side of the structure on the paper. (Circulate as they do so to ensure that all students have the structure oriented in the same way.) Ask students what they see when they look at the structure from the front view. (Suggest that students look from the level of their desks to get the complete front view.) Students should see a vertical rectangle divided in half: Have students draw the front view next to the “Front” label on their page. Next, have students rotate their page 90º clockwise so they are looking at the right side view. Again, ask what they see (mirror image of an “L”). Have students draw this view next to the “Right Side” label on their page: Continue having the students rotate their pages 90º clockwise to record the back and left side views. Finally, have them look down on the structure to see the top view. They should notice that the top view could be drawn by tracing around the base of the structure. Explain that the views they have drawn are called orthographic views and that they are two-dimensional representations of the three-dimensional structure. Ask students to write “Orthographic Sketches” at the top of the page on which they have just completed the views. Explain that orthographic sketches are only one type of two-dimensional representation of a three-dimensional figure. Isometric sketches, or perspective drawings, are also two-dimensional representations of three-dimensional figures. Make connections to students’ previous experiences with orthographic and/or isometric sketches/representations. Ask, “When might you see/use this? How might this kind of sketch be used in the real world?” Provide examples like floor plans and elevations that architects and designers would use. You may wish to have some examples for the students to view on the overhead projector. Grade 6 Learning Activity: Three-Dimensional Figures – Sketching Climbing Structures 1
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Geometry and Spatial Sense, Grades
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Every effort has been made in this
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4 References 73 Learning Activities
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6 make personal connections to thei
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8 Some of the ways in which teacher
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10 Modified Program What It Means E
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12 Addressing the needs of Junior L
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14 thE BIG IdEAS In GEoMEtry And SP
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16 These big ideas are conceptually
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18 • Technology: Drawing programs
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20 IDENTIFYING, SORTING, AND CLASSI
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22 The study of geometry presents s
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24 PROPERTIES OF POLYhEDRA In the p
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26 In order to prepare students for
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28 In the junior grades, students d
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0 Another example of using interloc
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2 Junior students extend their unde
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4 USING GEOMETRIC TRANSFORMATIONS T
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6 Although translations represent t
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8 LEArnInG ABout tWodIMEnSIonAL ShA
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40 The sections that follow offer t
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42 Important benchmark angles inclu
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44 CONSTRUCTING ANGLES Students gai
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46 Size of angles Junior students l
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48 When a square is rotated about i
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0 Note that the concept of similari
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2 In the early junior grades, stude
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4 By the end of Grade 4, students w
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6 Perpendicularity Perpendicularity
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8 representing three-dimensional Fi
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60 When planning activities that in
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62 By the end of Grade 4, students
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64 In the grid on page 63, point O
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66 relationships in transformationa
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68 The software also enables studen
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0 Once students fundamentally under
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2 An effective means of investigati
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Learning Activities
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8 ASSESSMENT: This section provides
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TIME: approximately 60 minutes INST
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82 REFLECTING AND CONNECTING This a
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84 LEARNING CONNECTION 2 quadrilate
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2D4.BLM2 86 Angle Search Dear Paren
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2D4.BLM4 88 quadrilateral Twister C
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2D4.BLM6 0 qUADRILATERALS RULE SORT
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INSTRUCTIONAL GROUPING: whole class
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4 Ask the students to compare the 2
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6 ASSESSMENT Observe students to as
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8 explain why or why not. When stud
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3D4.BLM2a 100 What Figures Can You
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3D4.BLM3 102 Constructing Skeletons
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3D4.BLM5 104 6-Cube Rectangular Pri
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3D4.BLM7a 106 Identify the Nets Det
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Grade 4 Learning Activity: Location
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110 WORKING ON IT Have the class wo
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112 This game builds on the concept
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Loc4.BLM1a 114 Game Boards Your Sha
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Loc4.BLM2 116 Game Instructions Ins
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Loc4.BLM4 118 Instructions and Game
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INSTRUCTIONAL GROUPING: pairs 120 M
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122 ASSESSMENT Observe students as
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Mov4.BLM1 124 Design Reflection Geo
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Mov4.BLM3 126 Scavenger Hunt Dear P
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Mov4.BLM5 128 Carmen’s Carpets Ca
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TIME: approximately 60 minutes INST
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1 2 Have student pairs read their d
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1 4 This activity is a game to be p
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2D5.BLM2 1 6 Triangle Sketching Cha
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2D5.BLM4 1 8 GSP Angles Instruction
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Grade 5 Learning Activity: Three-Di
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Page 146 and 147: Assessment Opportunity As students
Page 148 and 149: 146 Once students have created thei
Page 150 and 151: 3D5.BLM1 148 Pyramid Packages An el
Page 152 and 153: 3D5.BLM3 1 0 Six Nets of a Square P
Page 154 and 155: 3D5.BLM5a 1 2 Net Characters Most o
Page 156 and 157: 3D5.BLM6a 1 4 Complete the Nets 1.
Page 158 and 159: Grade 5 Learning Activity: Location
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Page 162 and 163: 160 HOME CONNECTION Send home Loc5.
Page 164 and 165: Loc5.BLM1 162 City Treasure Hunt Ma
Page 166 and 167: Loc5.BLM3 164 City Treasure Hunt An
Page 168 and 169: Loc5.BLM5 166 What’s on My Mind?
Page 170 and 171: Grade 5 Learning Activity: Movement
Page 172 and 173: 1 0 • “What strategies did you
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Page 178 and 179: Mov5.BLM4 1 6 Translations in the H
Page 180 and 181: Grade 6 Learning Activity: Two-Dime
Page 182 and 183: 180 GETTING STARTED This part of th
Page 184 and 185: 182 ADAPTIONS/EXTENSIONS During the
Page 186 and 187: 2D6.BLM1 184 Angle Cards 45 ˚ 90
Page 188 and 189: 2D6.BLM3 186 Measuring Angles and L
Page 190 and 191: 2D6.BLM5 188 Rotating Polygons Geom
Page 192 and 193: 2D6.BLM7 1 0 What’s My Line Place
Page 196 and 197: 1 4 Distribute one half-sheet of 3D
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Page 200 and 201: 1 8 LEARNING CONNECTION 3 Sketches
Page 202 and 203: 3D6.BLM1 2 cm Grid Paper 200 Geomet
Page 204 and 205: 3D6.BLM3 202 Sketching Climbing Str
Page 206 and 207: 3D6.BLM5a 204 Teach an Adult to Ske
Page 208 and 209: 3D6.BLM6a 206 Drawing Views in The
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Page 216 and 217: INSTRUCTIONAL GROUPING: pairs 214 M
Page 218 and 219: 216 ADAPTATIONS/EXTENSIONS Groups o
Page 220 and 221: Loc6.BLM1 218 Blank 10 10 Grid 10
Page 222 and 223: Loc6.BLM3 220 Name My Shapes 10 9 8
Page 224 and 225: Loc6.BLM5 222 Coordinate Challenge
Page 226 and 227: INSTRUCTIONAL GROUPING: individual
Page 228 and 229: 226 ADAPTATIONS/EXTENSIONS Groups c
Page 230 and 231: 228 LEARNING CONNECTION 3 quadrilat
Page 232 and 233: Mov6.BLM1b 2 0 Logos (Reverse side)
Page 234 and 235: Mov6.BLM3a 2 2 Rotating Regular Sha
Page 236 and 237: Mov6.BLM3c 2 4 Geometry and Spatial
Page 238 and 239: Mov6.BLM4 2 6 Rotating the Alphabet
Page 241 and 242: APPEndIx: GuIdELInES For ASSESSMEnt
Page 243 and 244: Assessment Profile An assessment pr
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Glossary acute angle. An angle whos
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integer. Any one of the numbers …
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quadrilateral. A polygon with four
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Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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