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Invitations to Mathematics

Investigations in Geometry:

"Net Quest" 3 rd

Edition

Suggested for students

at the

Grade 6 level

An activity of

The CENTRE for EDUCATION

in MATHEMATICS and COMPUTING

Faculty of Mathematics, University of Waterloo

Waterloo, Ontario, Canada N2L 3G1

© 2010 The Centre for Education in Mathematics and Computing

Copyright © 1996, 2000, 2010

The Centre for Education in Mathematics and Computing

Faculty of Mathematics

University of Waterloo

Waterloo, Ontario Canada N2L 3G1

Limited reproduction permission:

1. The Centre for Education in Mathematics and Computing grants permission

to individual teachers to reproduce the Black Line Masters as needed for use with thei r own students.

2. The Centre for Education in Mathematics and Computing grants permission

to an educator providing a professional development workshop to make up to 35 copies of the Black Line Masters for any individual activity for use once with one group. Reproduction of text pages for an entire school or school district or fo r commercial use is prohibited. i

Investigations in Geometry

Grade 6: Net Quest

Preface

The Centre for Education in Mathematics and Computing at the University of Waterloo is dedicated to the development of materials and workshops that promote effective learni ng and teaching of mathematics. This unit is part of a project designed to assist teachers of Grades 4, 5, an d 6 in stimulating interest, competence, and pleasure in mathematics, among their students. While the activities are appropriate for either individual or group work, the latter is a particular focus of this effort. Students will be engaged in collaborative activities which will enable them to construct their own mathematical meaning and u nderstanding. This emphasis, plus the extensions and related activities included, provide ample scope for all students' interests and ability levels. Related “Family Math" activities which may be used to involve the students' parents are also suggested. Each unit consists of a sequence of activities intended to occupy about one week of daily classes; however, teachers may choose to take extra time to explore the activitie s and extensions in more depth. The

Investigations in Geometry is comprised of activities to enhance the students' geometry and spatial sense

abilities, as well as creativity and problem-solving skills. Geometry c oncepts are easily integrated with other subject areas, providing ways to demonstrate that mathematics pervades e veryday life. Due to their nature, geometry activities depend heavily on manipulative materials. Every effort has been made to use materials readily available in most classrooms/schools, and a number of Black-Line Masters (BLMs) are provided to add further manipulatives.

Preface

ii

Grade 6: Net Quest

Investigations in Geometry

Contributing Authors

Contributing Authors

Anne Cirillo (MSSB)

Craig Fleming (WCBE)

Jackie Harris (MSSB)

Kathy Kubota-Zarivnij (MSSB)

Kelly Lantink (WCBE)

Bev Marshman (University of Waterloo)

Brian McCudden, MSSB

Mary Morabito, WCBE

Lorna Morrow (Mathematics Consultant)

Ron Sauer, WCBE

Editors

Bev Marshman

Lorna Morrow

We wish to acknowledge the support of the Centre for Education in Mathematics and Computing, and in particular the efforts of Ron Scoins, Barry Ferguson, Larry David son, and Patty Mah, and, for the second edition, Bonnie Findlay.

Acknowledgements

iii

Investigations in Geometry

Grade 6: Net Quest

Preface ........................................................................ Contributing Authors ........................................................................ ......................................ii Table of Contents ........................................................................ Overview ........................................................................ COMMON BELIEFS ........................................................................ ESSENTIAL CONTENT ........................................................................ CURRICULUM CONNECTIONS ........................................................................ ASSESSMENT ........................................................................ PREREQUISITES ........................................................................ LOGOS ........................................................................ MATERIALS ........................................................................ LETTER TO PARENTS ........................................................................ Activity 1: Nets Of Cubes ........................................................................ ..............................6 Activity 2: Constructing Three-Dimensional Figures From Nets .................................8 Activity 3: Recognizing Nets........................................................................ ........................10

Activity 4: The Jolly Postman (Two Periods) ...................................................................12

BLM 1: Cube Nets 1 ........................................................................ BLM 2: Cube Nets 2 ........................................................................ BLM 3: Cube Nets 3 ........................................................................ BLM 4: Cube Nets 4 ........................................................................ BLM 5: Geopaper ........................................................................ BLM 6: 3D Figures ........................................................................ BLM 7: 3D Figures ........................................................................ BLM 8: 3D Figures ........................................................................ BLM 9: Mystery Figures ........................................................................ ................................23 BLM 10: Net Matching 1 ........................................................................ ...............................24 BLM 11: Net Matching 2 ........................................................................ ...............................25 BLM 12: Net Matching 3 ........................................................................ ...............................26 BLM 13: Cube Problems ........................................................................ .................................27 BLM 14: Cube Problems ........................................................................ .................................28 BLM 15: The Jolly Postman ........................................................................ ..........................29 Solutions & Notes ........................................................................

Suggested Assessment Strategies ........................................................................

..........32 Other Resources ........................................................................

Table of Contents

Contents

Overview Page 1

Investigations in Geometry

Grade 6: Net Quest

Overview

COMMON BELIEFS

These activities have been developed within the context of certain belie fs and Geometry is best learned through a combination of active exploration and reasoning, through a cycle of concrete investigations which leads to con jecture, of geometric objects they can manipulate in order to discover the geomet ric relationships and develop their spatial sense by constructing, drawing, measuring, visualizing, comparing, transforming, and classifying geometr ic Geometry uses a formal language to describe objects and their interrelat ionships formal language of geometry is not as important as helping them to ident ify geometric properties and principles and to use pictures or everyday lang uage to Geometry provides ample opportunity for the development of divergent thi nking

ESSENTIAL CONTENT

During this unit, the student will:

Page 2 Overview

Grade 6: Net Quest

Investigations in Geometry

Overview

ACTIVITY

Activity 1

Nets of Cubes

Activity 2

Constructing

Three-

Dimensional

Figures from

Nets

Activity 3

Recognizing

Nets

Activity 4

The Jolly

Postman

(2 periods)

DESCRIPTION OF THE

ACTIVITY

given nets for cubes pyramids, and other 3D to describe the nets and in justifying their choices that meet post requirements and constructing, the packages

CURRICULUM

EXPECTATIONS

from nets pyramids using grid and isometric paper from nets describe geometric ideasquotesdbs_dbs11.pdfusesText_17