Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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226 ADAPTATIONS/EXTENSIONS Groups can present their design to the school administration and/or team/club members, explaining why they believe their logo should be adopted. ASSESSMENT Observe students as they work on and explain their logo designs, and assess how well they: • explain why they selected the mathematical shapes and tools to design their logos; • show their understanding of the symmetries associated with their logos; • explain the strategies they used to create line and rotational symmetry in their logos; • judge the efficiency of various strategies. Student reflections on the reverse of Mov6.BLM6 Logos can be used for diagnostic purposes, to provide information on students’ strengths and difficulties. HOME CONNECTION See Mov6.BLM1a–b: Logos for a letter to be sent home to parents as part of the Getting Started portion of the lesson. LEARNING CONNECTION 1 Regular Shapes and Rotational Symmetry MATERIALS • Mov6.BLM3a–d: Rotating Regular Shapes (1 per student) • 2 large demonstration copies of each shape on Mov6.BLM3a–d: Rotating Regular Shapes • pieces of tracing paper (4 per student) • paper fasteners (1 per student) • rulers (1 per pair of students) • protractors (1 per pair of students) Distribute copies of Mov6.BLM3a–d: Rotating Regular Shapes (one copy per student). Ask, “Why are these two-dimensional shapes called regular?” Allow students to examine the shapes in pairs to determine possible patterns. Facilitate a discussion through which students discover that all the sides and all the angles must be congruent for a shape to be called regular. Have each student trace the shapes from Mov6.BLM3a–d: Rotating Regular Shapes. Students cut out the shapes from the four pages of the blackline master and the shapes from their tracing paper. Discuss how a centre of rotation allows you to turn a regular polygon onto itself exactly. There can be no overlapping parts when this occurs. Demonstrate with the large equilateral triangles. Geometry and Spatial Sense, Grades 4 to 6
Ask students to work with a partner to see if they can find a way to mark the centre of rotation for the equilateral triangle. Allow time for experimentation, and ask for volunteers to share their findings. (The centre of rotation can be found by bisecting one angle of the triangle through folding, repeating this process with a second angle, and finding where the two fold lines meet. Bisecting a third angle will verify that the centre of rotation is correct. Demonstrate with a large equilateral triangle if none of the students discover the strategy.) Label the centre of rotation for each of the large equilateral triangles and place one triangle exactly on top of the other, using a paper fastener to hold the triangles in place. Label the angles A, B, and C. Slowly rotate the top copy until it lies exactly over the bottom triangle. Have the students tell you when each overlying occurs. Keep rotating the triangle until it returns to its original position. Ask, “How many times does one equilateral triangle lie exactly over the other?” (3) Instruct the students to work in pairs or groups of three, repeating the process with the square, the pentagon, and the regular hexagon. Students should record their findings and look for patterns. Have a discussion to see which patterns the students have found. You want them to recognize that the number of rotations corresponds to the number of sides. However, the students might discover other interesting ideas or patterns. Ask if their patterns or ideas would be true for other regular polygons. What about irregular polygons? Have the students cut out other shapes to test their conjectures. Teachers with access to The Geometer’s Sketchpad might want to let their students test their conjectures in that environment, exploring more complex regular polygons. LEARNING CONNECTION 2 Alphabet Rotations MATERIALS • Mov6.BLM4: Rotating the Alphabet (1 per student) • tracing paper (1 piece per student) Students use Mov6.BLM4: Rotating the Alphabet to discover which of the capital letters of the alphabet have rotational symmetry. Students work individually to decide on the letters that they believe have rotational symmetry. At this time they are not permitted to use any aids and must base their conjectures on perception. Students then work in pairs, checking their conjectures with tracing paper to prove which of the letters have rotational symmetry. Students could also discover, and then check, which of the numbers and the lower case letters of the alphabet have rotational symmetry. Grade 6 Learning Activity: Movement – Logo Search and Design 22
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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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142 GETTING STARTED Show students t
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Assessment Opportunity As students
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146 Once students have created thei
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3D5.BLM1 148 Pyramid Packages An el
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3D5.BLM3 1 0 Six Nets of a Square P
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3D5.BLM5a 1 2 Net Characters Most o
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3D5.BLM6a 1 4 Complete the Nets 1.
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Grade 5 Learning Activity: Location
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1 8 2) (next student) Travel 2 bloc
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160 HOME CONNECTION Send home Loc5.
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Loc5.BLM1 162 City Treasure Hunt Ma
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Loc5.BLM3 164 City Treasure Hunt An
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Loc5.BLM5 166 What’s on My Mind?
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Grade 5 Learning Activity: Movement
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1 0 • “What strategies did you
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1 2 LEARNING CONNECTION 2 How Many
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Mov5.BLM2 1 4 What Am I? Use your t
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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 194 and 195: TIME: approximately 60 minutes INST
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
Page 210 and 211: 3D6.BLM7 208 Imitator Demo Structur
Page 212 and 213: 3D6.BLM9a 210 Construction Challeng
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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 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
Page 245 and 246: Glossary acute angle. An angle whos
Page 247 and 248: integer. Any one of the numbers …
Page 249 and 250: quadrilateral. A polygon with four
Page 252: © Ministry of Education Printed on
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Geometry and Spatial Sense, Grades 4 to 6 - EduGains

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