![5/10 + 1/4 + 2/8 = 1/2 + 1/4 + 1/4 = 1/2 + 2/4 = 1/2 + 1/2 = 2/2
= 1.
This is one means of initiating a child intuitively into the
operations used for the reduction of fractions to their lowest terms.
Improper fractions also interest them very much. They come to
these by adding a number of sectors which fill two, three, or four
circles. To find the whole numbers which exist under the guise of
fractions is a little like putting away in their proper places the circular
insets which have been all mixed up. The children manifest a desire
to learn the real operations of fractions. With improper fractions they
originate most unusual sums, like the following:
[8 + (7/7 + 18/9 + 24/2) + 1] =
8
[8 + (1 + 2 + 12) + 1] =
8
8 + 15 + 1 = 24/8 = 3.
8
We have a series of commands which may be used as a guide for
the child's work. Here are some examples:
—Take 1/5 of 25 beads
—Take 1/4 " 36 counters
—Take 1/6 " 24 beans
—Take 1/3 " 27 beans
—Take 1/10 " 40 beans
—Take 2/5 " 60 counters](https://image.slidesharecdn.com/32628-250517185216-aec67184/85/Vaccinia-Virus-and-Poxvirology-Methods-and-Protocols-2nd-Edition-Stuart-N-Isaacs-Auth-34-320.jpg)
Vaccinia Virus and Poxvirology Methods and Protocols 2nd Edition Stuart N. Isaacs (Auth.)
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- 5. ME T H O D S I N MO L E C U L A R BI O L O G Y ™ Series Editor John M. Walker School of Life Sciences University of Hertfordshire Hatfield, Hertfordshire, AL10 9AB, UK For further volumes: http://www.springer.com/series/7651
- 7. Vaccinia Virus and Poxvirology Methods and Protocols Second Edition Edited by Stuart N. Isaacs UniversityofPennsylvaniaandthePhiladelphiaVAMedicalCenter, Philadelphia,PA,USA
- 8. Editor Stuart N. Isaacs Department of Medicine Division of Infectious Disease University of Pennsylvania and the Philadelphia VA Medical Center 502 Johnson Pavilion Philadelphia, PA, USA ISSN 1064-3745 ISSN 1940-6029 (electronic) ISBN 978-1-61779-875-7 ISBN 978-1-61779-876-4 (eBook) DOI 10.1007/978-1-61779-876-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2012937882 © Springer Science+Business Media, LLC 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Humana Press is a brand of Springer Springer is part of Springer Science+Business Media (www.springer.com)
- 9. Dedication To my Mom and Dad; and to my wife and children—Lauren and Jordan—who tolerate the crazy hours I work.
- 11. vii Preface Nine years ago, the chapters for the first edition of Vaccinia Virus and Poxvirology were submitted for publication in the Methods in Molecular Biology Series. This second edition does not replace the first edition since essentially every chapter in this volume represents a protocol not covered in the first edition. To allow new readers to be aware of what topics were covered in the first edition, I include the following list of chapters from the first edi- tion of Vaccinia Virus and Poxvirology, Methods and Protocols (Volume 269 in the Methods in Molecular Biology Series): 1. Working Safely with Vaccinia Virus: Laboratory Technique and the Role of Vaccinia Vaccination (Stuart N. Isaacs) 2. Construction and Isolation of Recombinant Vaccinia Virus Using Genetic Markers (María M. Lorenzo, Inmaculada Galindo, and Rafael Blasco) 3. Construction of Recombinant Vaccinia Virus: Cloning into the Thymidine Kinase Locus (Chelsea M. Byrd and Dennis E. Hruby) 4. Transient and Inducible Expression of Vaccinia/T7 Recombinant Viruses (Mohamed R. Mohamed and Edward G. Niles) 5. Construction of Recombinant Vaccinia Viruses Using Leporipoxvirus Catalyzed Recombination and Reactivation of Orthopoxvirus DNA (Xiao-Dan Yao and David H. Evans) 6. Construction of cDNA Libraries in Vaccinia Virus (Ernest S. Smith, Shuying Shi, and Maurice Zauderer) 7. Construction and Isolation of Recombinant MVA (Caroline Staib, Ingo Drexler, and Gerd Sutter) 8. Growing Poxviruses and Determining Virus Titer (Girish J. Kotwal and Melissa Abraham) 9. Rapid Preparation of Vaccinia Virus DNA Template for Analysis and Cloning by PCR (Rachel L. Roper) 10. Orthopoxvirus Diagnostics (Hermann Meyer, Inger K. Damon, and Joseph J. Esposito) 11. An In Vitro Transcription System for Studying Vaccinia Virus Early Genes (Steven S. Broyles and Marcia Kremer) 12. An In Vitro Transcription System for Studying Vaccinia Virus Late Genes (Cynthia F. Wright) 13. Studying Vaccinia Virus RNA Processing In Vitro (Paul D. Gershon) 14. Methods for Analysis of Poxvirus DNA Replication (Paula Traktman and Kathleen Boyle) 15. Studying the Binding and Entry of the Intracellular and Extracellular Enveloped Forms of Vaccinia Virus (Mansun Law and Geoffrey L. Smith) 16. Pox, Dyes, and Videotape; Making Movies of GFP Labeled Vaccinia Virus (Brian M. Ward)
- 12. viii Preface 17. Interaction Analysis of Viral Cytokine-Binding Proteins Using Surface Plasmon Resonance (Bruce T. Seet and Grant McFadden) 18. Monitoring of Human Immunological Responses to Vaccinia Virus (Richard Harrop, Matthew Ryan, Hana Golding, Irina Redchenko, and Miles W. Carroll) 19. Vaccinia Virus as a Tool for Immunologic Studies (Nia Tatsis, Gomathinayagam Sinnathamby, and Laurence C. Eisenlohr) 20. Mouse Models for Studying Orthopoxvirus Respiratory Infections (Jill Schriewer, R. Mark L. Buller, and Gelita Owens) 21. Viral Glycoprotein-Mediated Cell Fusion Assays Using Vaccinia Virus Vectors (Katharine N. Bossart and Christopher C. Broder) 22. Use of Dual Recombinant Vaccinia Virus Vectors to Assay Viral Glycoprotein-Mediated Fusion with Transfection-Resistant Primary Cell Targets (Yanjie Yi, Anjali Singh, Joanne Cutilli, and Ronald G. Collman) 23. Poxvirus Bioinformatics (Chris Upton) 24. Preparation and Use of Molluscum Contagiosum Virus (MCV) from Human Tissue Biopsy Specimens (Nadja V. Melquiot and Joachim J. Bugert) In this second edition of poxvirus protocols, there are multiple new chapters covering various approaches for the construction of recombinant viruses. Other chapters focus on methods to isolate the various forms of infectious virus, methods to study the entry of poxviruses into cells, and various protocols covering in vivo models to study poxvirus pathogenesis. There are also chapters on studying cellular immune responses and genera- tion of monoclonal antibodies to poxvirus proteins. This book also contains chapters to cover methods in poxvirus bioinformatics as well as various ways to study poxvirus immu- nomodulatory proteins. The protocols are designed to be easy to follow and the Note sections include both additional explanatory information and important insights into the protocols. Since the last edition of this book, a number of important events related to poxvirology have occurred. Examples include the FDA approval of a culture-based live smallpox vaccine and the vaccination of large numbers of US military and relatively large numbers of US civilians. Novel anti-poxvirus therapeutics have been developed and have been used in emergency settings. I will not even attempt to summarize the scientific advances in poxvi- rology that have been made over this time period. Since the last edition of this book, there have been a number of retirements of prominent poxvirologists. So I would like to acknowl- edge the retirements of Joseph J. Esposito (Centers for Disease Control and Prevention, Atlanta), Richard (Dick) W. Moyer (University of Florida, Gainesville), and Edward G. Niles (SUNY School of Medicine, Buffalo). These fine scientists ran outstanding labs, made countless contributions to the poxvirus field, and throughout their careers helped create the community that those of us in poxvirology have enjoyed. While no longer lab-based, we are fortunate that they all remain active and continue to contribute to the scientific com- munity. Since the last edition of this book, the poxvirus community sadly marked the deaths of colleagues. So I would like to acknowledge the passing of Riccardo (Rico) Wittek (April 26, 1944 to September 19, 2008) and Frank J. Fenner (December 21, 1914 to November 22, 2010). Their contributions to our field will not be forgotten. Philadelphia, PA, USA Stuart N. Isaacs
- 13. ix Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 Working Safely with Vaccinia Virus: Laboratory Technique and Review of Published Cases of Accidental Laboratory Infections. . . . . . . . . 1 Stuart N. Isaacs 2 In-Fusion® Cloning with Vaccinia Virus DNA Polymerase. . . . . . . . . . . . . . . . 23 Chad R. Irwin, Andrew Farmer, David O. Willer, and David H. Evans 3 Genetic Manipulation of Poxviruses Using Bacterial Artificial Chromosome Recombineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Matthew G. Cottingham 4 Easy and Efficient Protocols for Working with Recombinant Vaccinia Virus MVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Melanie Kremer, Asisa Volz, Joost H.C.M. Kreijtz, Robert Fux, Michael H. Lehmann, and Gerd Sutter 5 Isolation of Recombinant MVA Using F13L Selection . . . . . . . . . . . . . . . . . . 93 Juana M. Sánchez-Puig, María M. Lorenzo, and Rafael Blasco 6 Screening for Vaccinia Virus Egress Inhibitors: Separation of IMV, IEV, and EEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Chelsea M. Byrd and Dennis E. Hruby 7 Imaging of Vaccinia Virus Entry into HeLa Cells . . . . . . . . . . . . . . . . . . . . . . 123 Cheng-Yen Huang and Wen Chang 8 New Method for the Assessment of Molluscum Contagiosum Virus Infectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Subuhi Sherwani, Niamh Blythe, Laura Farleigh, and Joachim J. Bugert 9 An Intradermal Model for Vaccinia Virus Pathogenesis in Mice . . . . . . . . . . . . 147 Leon C.W. Lin, Stewart A. Smith, and David C. Tscharke 10 Measurements of Vaccinia Virus Dissemination Using Whole Body Imaging: Approaches for Predicting of Lethality in Challenge Models and Testing of Vaccines and Antiviral Treatments . . . . . . . . . . . . . . . . . . . . . . 161 Marina Zaitseva, Senta Kapnick, and Hana Golding 11 Mousepox, A Small Animal Model of Smallpox . . . . . . . . . . . . . . . . . . . . . . . . 177 David Esteban, Scott Parker, Jill Schriewer, Hollyce Hartzler, and R. Mark Buller 12 Analyzing CD8 T Cells in Mouse Models of Poxvirus Infection. . . . . . . . . . . . 199 Inge E.A. Flesch, Yik Chun Wong, and David C. Tscharke 13 Generation and Characterization of Monoclonal Antibodies Specific for Vaccinia Virus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Xiangzhi Meng and Yan Xiang
- 14. x Contents 14 Bioinformatics for Analysis of Poxvirus Genomes. . . . . . . . . . . . . . . . . . . . . . . 233 Melissa Da Silva and Chris Upton 15 Antigen Presentation Assays to Investigate Uncharacterized Immunoregulatory Genes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Rachel L. Roper 16 Characterization of Poxvirus-Encoded Proteins that Regulate Innate Immune Signaling Pathways . . . . . . . . . . . . . . . . . . . . . . . . . 273 Florentina Rus, Kayla Morlock, Neal Silverman, Ngoc Pham, Girish J. Kotwal, and William L. Marshall 17 Application of Quartz Crystal Microbalance with Dissipation Monitoring Technology for Studying Interactions of Poxviral Proteins with Their Ligands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Amod P. Kulkarni, Lauriston A. Kellaway, and Girish J. Kotwal 18 Central Nervous System Distribution of the Poxviral Proteins After Intranasal Administration of Proteins and Titering of Vaccinia Virus in the Brain After Intracranial Administration. . . . . . . . . . . . . . . . . . . . . 305 Amod P. Kulkarni, Dhirendra Govender, Lauriston A. Kellaway, and Girish J. Kotwal Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
- 15. xi Contributors RAFAEL BLASCO • Departamento de Biotecnología, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Madrid, Spain NIAMH BLYTHE • Department of Microbiology and Infectious Diseases, Cardiff Institute of Infection and Immunity, Cardiff, UK JOACHIM J. BUGERT • Department of Microbiology and Infectious Diseases, Cardiff Institute of Infection and Immunity, Cardiff, UK R. MARK BULLER • Department of Molecular Microbiology and Immunology, St. Louis University Health Sciences Center, St. Louis, MO, USA CHELSEA M. BYRD • SIGA Technologies, Inc., Corvallis, OR, USA WEN CHANG • Academia Sinica, Institute of Molecular Biology, Taipei, Taiwan, ROC MATTHEW G. COTTINGHAM • The Jenner Institute, University of Oxford, Oxford, UK MELISSA DA SILVA • Biochemistry and Microbiology, University of Victoria, Victoria, BC, Canada DAVID ESTEBAN • Biology Department, Vassar College, Poughkeepsie, NY, USA DAVID H. EVANS • Department of Medical Microbiology and Immunology, Li Ka Shing Institute of Virology, University of Alberta, Edmonton, AB, Canada LAURA FARLEIGH • Department of Microbiology and Infectious Diseases, Cardiff Institute of Infection and Immunity, Cardiff, UK ANDREW FARMER • Clontech Laboratories, Inc., Mountain View, CA, USA INGE E.A. FLESCH • Research School of Biology, The Australian National University, Canberra, ACT, Australia ROBERT FUX • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany HANA GOLDING • Division of Viral Products, Center for Biologics Evaluation and Research, Food and Drug Administration, Bethesda, MD, USA DHIRENDRA GOVENDER • Faculty of Health Sciences, Division of Anatomical Pathology, Department of Clinical Laboratory Sciences, University of Cape Town, South Africa HOLLYCE HARTZLER • Department of Molecular Microbiology and Immunology, St. Louis University Health Sciences Center, St. Louis, MO, USA DENNIS E. HRUBY • SIGA Technologies, Inc., Corvallis, OR, USA CHENG-YEN HUANG • Academia Sinica, Institute of Molecular Biology, Taipei, Taiwan, ROC CHAD R. IRWIN • Department of Medical Microbiology and Immunology, Li Ka Shing Institute of Virology, University of Alberta, Edmonton, AB, Canada STUART N. ISAACS • Division of Infectious Diseases, Department of Medicine, University of Pennsylvania and the Philadelphia VA Medical Center, Philadelphia, PA, USA SENTA KAPNICK • Division of Viral Products, Center for Biologics Evaluation and Research, Food and Drug Administration, Bethesda, MD, USA
- 16. xii Contributors LAURISTON A. KELLAWAY • Division of Anatomical Pathology, Department of Clinical Laboratory sciences, Faculty of Health Sciences, University of Cape Town, South Africa GIRISH J. KOTWAL • Kotwal Bioconsulting, LLC, Louisville, KY, USA; InFlaMed Inc, Louisville, KY, USA; Department of Microbiology and Biochemistry, University of Medicine and Health Sciences, Saint Kitts, West Indies JOOST H.C.M. KREIJTZ • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany; Department of Virology, Erasmus MC, Rotterdam, The Netherlands MELANIE KREMER • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany AMOD P. KULKARNI • Division of Anatomical Pathology, Department of Clinical Laboratory sciences, Faculty of Health Sciences, University of Cape Town, South Africa MICHAEL H. LEHMANN • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany LEON C.W. LIN • Research School of Biology, The Australian National University, Canberra, ACT, Australia MARÍA M. LORENZO • Departamento de Biotecnología, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Madrid, Spain WILLIAM L. MARSHALL • Division of Infectious Disease, Department of Medicine, University of Massachusetts School of Medicine, Worcester, MA, USA XIANGZHI MENG • Department of Microbiology and Immunology, University of Texas Health Science Center at San Antonio, San Antonio, TX, USA KAYLA MORLOCK • Division of Infectious Disease, Department of Medicine, University of Massachusetts School of Medicine, Worcester, MA, USA SCOTT PARKER • Department of Molecular Microbiology and Immunology, St. Louis University Health Sciences Center, St. Louis, MO, USA NGOC PHAM • Division of Infectious Disease, Department of Medicine, University of Massachusetts School of Medicine, Worcester, MA, USA RACHEL L. ROPER • Department of Microbiology and Immunology, Brody School of Medicine, East Carolina University, Greenville, NC, USA FLORENTINA RUS • Division of Infectious Disease, Department of Medicine, University of Massachusetts School of Medicine, Worcester, MA, USA JUANA M. SÁNCHEZ-PUIG • Departamento de Biotecnología, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Madrid, Spain JILL SCHRIEWER • Department of Molecular Microbiology and Immunology, St. Louis University Health Sciences Center, St. Louis, MO, USA SUBUHI SHERWANI • Department of Microbiology and Infectious Diseases, Cardiff Institute of Infection and Immunity, Cardiff, UK NEAL SILVERMAN • Division of Infectious Disease, Department of Medicine, University of Massachusetts School of Medicine, Worcester, MA, USA STEWART A. SMITH • Research School of Biology, The Australian National University, Canberra, ACT, Australia GERD SUTTER • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany DAVID C. TSCHARKE • Research School of Biology, The Australian National University, Canberra, ACT, Australia
- 17. xiii Contributors CHRIS UPTON • Biochemistry and Microbiology, University of Victoria, Victoria, BC, Canada ASISA VOLZ • Institute for Infectious Diseases and Zoonoses, University of Munich LMU, Munich, Germany DAVID O. WILLER • Department of Microbiology, Mt. Sinai Hospital, Toronto, ON, Canada YIK CHUN WONG • Research School of Biology, The Australian National University, Canberra, ACT, Australia YAN XIANG • Department of Microbiology and Immunology, University of Texas Health Science Center at San Antonio, San Antonio, TX, USA MARINA ZAITSEVA • Division of Viral Products, Center for Biologics Evaluation and Research, Food and Drug Administration, Bethesda, MD, USA
- 19. 1 Stuart N. Isaacs (ed.), Vaccinia Virus and Poxvirology: Methods and Protocols, Methods in Molecular Biology, vol. 890, DOI 10.1007/978-1-61779-876-4_1, © Springer Science+Business Media, LLC 2012 Chapter 1 Working Safely with Vaccinia Virus: Laboratory Technique and Review of Published Cases of Accidental Laboratory Infections Stuart N. Isaacs* Abstract Vaccinia virus (VACV), the prototype orthopoxvirus, is widely used in the laboratory as a model system to study various aspects of viral biology and virus–host interactions, as a protein expression system, as a vaccine vector, and as an oncolytic agent. The ubiquitous use of VACVs in the laboratory raises certain safety concerns because the virus can be a pathogen in individuals with immunological and dermato- logical abnormalities, and on occasion can cause serious problems in normal hosts. This chapter reviews standard operating procedures when working with VACV and reviews published cases on accidental laboratory infections. Key words: Vaccinia virus, Biosafety Level 2, Class II Biological Safety Cabinet, Personal protective equipment, Smallpox vaccine, Complications from vaccination, Laboratory accidents Poxviruses are large DNA viruses with genomes of nearly 200 kb. Their unique site of DNA replication and transcription (1), the fascinating immune evasion strategies employed by the virus (2, 3), and the relative ease of generating recombinant viruses that express foreign proteins in eukaryotic cells (4, 5) have made pox- viruses an exciting system to study and a common laboratory tool. Variola virus, the causative agent of smallpox, is the most 1. Introduction * The views expressed in this chapter are solely those of the author and do not necessarily reflect the position or policy of the Department of Veterans Affairs or the University of Pennsylvania.
- 20. 2 S.N. Isaacs famous member of the poxvirus family. It was eradicated as a human disease by the late 1970s and now work with the virus is confined to only two World Health Organization-sanctioned sites under Biosafety Level 4 conditions. Thus, vaccinia virus (VACV) is more widely studied and has become the prototype member of the orthopoxvirus genus. VACV was used as the vaccine to confer immunity to variola virus and helped in the eradication of small- pox. In the USA, routine vaccination with the smallpox vaccine ended in the early 1970s. Since then, the Advisory Committee on Immunization Practices (ACIP) and the CDC have recommended that people working with poxviruses continue to get vaccinated (6–10). This recommendation for those working with VACV is based mainly on the potential problems that an unintentional infection due to a laboratory accident may cause. Rationale for this recommendation is furthered by the understanding that the strains of VACV used in the laboratory setting (e.g., Western Reserve (WR); see Note 1) are more virulent than the vaccine strain. Also, lab workers frequently handle virus at much higher titers than the dose given in the vaccine (see Note 2). There have been reports of laboratory accidents involving VACV (discussed later in this chapter), but a much greater number of such incidents likely go unreported. The total number of people working with VACV and the frequency with which they work with the virus is also unknown. Thus, for laboratory workers, both the full extent of the problem and potential benefit from the vaccine are not known. This chapter discusses laboratory procedures, personal safety equipment, and published laboratory accidents, all of which will serve as aides in preventing accidental laboratory infections, and highlights the need to work safely with the virus. 1. Class II Biological Safety Cabinet (BSC). 2. Personal protective equipment. 3. Autoclave. 4. Disinfectants: 1% sodium hypochlorite, 2% glutaraldehyde, formaldehyde, 10% bleach, Spor-klenz, Expor, 70% alcohol. 5. Sharps container disposal unit. 6. Centrifuge bucket safety caps. 7. Occupational medicine access to the smallpox vaccine (see Note 3). 2. Materials and Equipment
- 21. 3 1 Working Safely with Vaccinia Virus… The following section describes safety practices when working with fully replication-competent live VACV. Table 1 summarizes some published cases of laboratory accidents and will be used to highlight various aspects of working safely with the virus. In addition to fully replication-competent VACVs, there are very attenuated strains of VACV (e.g., MVA and NYVAC) that are unable to replicate and form infectious progeny virus in mammalian cells. These highly attenuated, non-replicating VACVs are considered BSL-1 agents (25). With that said, labs that work with both replication-competent and non-replicating viruses should be wary of potential contamina- tion of stocks of avirulent virus with replication-competent poxvi- ruses. This could result in an accidental laboratory infection as highlighted in Case 19 in Table 1. Since unintentional VACV infec- tions most commonly occur through direct contact with the skin or eyes, the most important aspect of working safely with VACV is to use proper laboratory and personal protective equipment to help prevent accidental exposure to the virus. One of the first lines of defense against an accidental exposure is to always work with infec- tious virus in a BSC. A BSC is a requirement when working with VACV. The cabinet not only confines the virus to a work area that is easily defined and cleaned, but the glass shield on the front of the BSC also serves as an excellent barrier against splashes into the face. A BSC draws room air through the front grille, circulates HEPA- filtered air within the cabinet area, and HEPA filters the air that is exhausted. Thus, working in a BSC protects the worker and the room where VACV is being handled from the unlikely event of aero- solization of the virus (see Note 4). An equally important line of defense against accidental expo- sure to the virus is wearing proper personal protective equipment. This includes gloves, lab coat, and eye protection. VACV does not enter intact skin, but gains access through breaks in the skin. Thus, gloves are critical (see Note 5). Accidental infections due to breaks in skin are highlighted by Cases 1, 5–7, 18, and 19 in Table 1 (see Figs. 1–3). Some of these accidents could have been prevented by use of personal protective equipment. While the front shield of the BSC serves as a first line of protection against splashes into the eye, it is also recommended that safety glasses with solid side shields be worn when working with VACV. Depending upon the work being done (e.g., handling high-titer purified stocks of VACV), one should consider additional eye protection like goggles or a full-face shield. This is important to consider because, as an immunologi- cally privileged site (26), the eye can be susceptible to a serious infection even in those previously vaccinated (27). Finally, a lab coat or some other type of outer protective garment decreases the chance of contaminating clothing. If such a contamination occurs, 3. Methods 3.1. Laboratory and Personal Protective Equipment
- 28. 10 S.N. Isaacs Fig. 1. Photograph of non-needlestick infection of fingers ~5 to 7 days after the onset of symptoms. (a) Right hand and (b) left hand. Reprinted by permission from Macmillan Publishers Ltd.: The Journal of Investigative Dermatology, see ref. 15, copyright © 2003. Fig. 2. Photographs of primary and secondary lesions 18 days after the onset of symptoms. (a) Primary lesion on finger at the site of a prior cut and (b) lesion on chin developing a few days after the finger lesion. Reprinted from the Journal of Clinical Virology, see ref. 17, copyright © 2004, with permission from Elsevier. an outer garment can be quickly removed and decontaminated. Furthermore, a lab coat will prevent accidentally carrying the virus out of the laboratory environment. Since the virus can be stable in the environment, after protective equipment is removed, good hand washing with soap and water is important (28). Cases 1, 5–9, 16, 18, and 19 in Table 1 (see Figs. 1–4) represent potentially pre- ventable accidents if proper biosafety practices were followed.
- 29. 11 1 Working Safely with Vaccinia Virus… Fig. 3. Photograph of the right hand of a woman 11 days after contact with a raccoon rabies vaccine bait in Pennsylvania in 2009. Fig. 4. Vaccinia virus infection of eye. (a) Left eye 5 days after the onset of symptoms. The primary pox lesion is located at the inner canthus. (b) Satellite lesion on lower conjunctiva developing 7 days after the onset of symptoms. Photographs by E. Claire Newbern. Figures and legend reproduced from ref. 18. These published materials are in the public domain. Also note that in some published accidents, prompt interven- tions may have prevented potential infections. In Case 9, prompt flushing of the eye with water after a splash exposure may have prevented infection. In Case 14, disinfecting the site of inocula- tion, as well as active smallpox vaccination on the day of the acci- dent may have prevented the infection. In addition to VACV being handled at Biosafety Level-2 (29), as with all biohazardous agents, routine good laboratory safety 3.2. Laboratory Safety
- 30. Another Random Document on Scribd Without Any Related Topics
- 31. The diameter from 0° to 180° is outlined heavily and extends beyond the circumference, in order to facilitate the adjustment of the angle to be measured and to give a strict exactness of position. This is done also with the radius which marks 90°. The child places a piece of an inset in such a way that the vertex of the angle touches the middle of the diameter and one of its sides rests on the radius marked 0°. At the other end of the arc of the inset he can read the degrees of the angle. After these exercises, the children are able to measure any angle with a common protractor. Furthermore, they learn that a circle measures 360°, half a circle 180°, and a right angle 90°. Once having learned that a circumference measures 360° they can find the number of degrees in any angle; for example, in the angle of an inset representing the seventh of the circle, they know that 360° ÷ 7 = (approximately) 51°. This they can easily verify with their instruments by placing the sector on the graduated circle. These calculations and measurements are repeated with all the different sectors of this series of insets where the circle is divided into from two to ten parts. The protractor shows approximately that: 1/3 circle=120°and360°÷3 =120° 1/4 " =90° " 360°÷4 =90° 1/5 " =72° " 360°÷5 =72° 1/6 " =60° " 360°÷6 =60° 1/7 " =51° " 360°÷7 =51° 1/8 " =45° " 360°÷8 =45° 1/9 " =40° " 360°÷9 =40° 1/10 " =36° " 360°÷10=36° In this way the child learns to write fractions: 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 He has concrete impressions of them as well as an intuition of their arithmetical relationships.
- 32. The material lends itself to an infinite number of combinations, all of which are real arithmetical exercises in fractions. For example, the child can take from the circle the two half circles and replace them by four sectors of 90°, filling the same circular opening with entirely different pieces. From this he can draw the following conclusion: 1/2 + 1/2 = 1/4 + 1/4 + 1/4 + 1/4. He also may say that two halves are equal to four fourths, and write accordingly: 2/2 = 4/4. This is merely the expression of the same thing. Seeing the pieces, he has done an example mentally and then has written it out. Let us write it according to the first form, which is, in reality, an analysis of this example: 1/2 + 1/2 = 1/4 + 1/4 + 1/4 + 1/4. When the denominator is the same, the sum of the fractions is found by adding the numerators: 1/2 + 1/2 = 2/2; 1/4 + 1/4 + 1/4 + 1/4 = 4/4.
- 33. The two halves make an entire circle, as do the four fourths. Now let us fill a circle with different pieces: for example, with a half circle and two quarter circles. The result is 1 = 1/2 + 2/4. And in the inset itself it is shown that 1/2 = 2/4. If we should wish to fill the circle with the largest piece (1/2) combined with the fewest number of pieces possible, it would be necessary to withdraw the two quarter sectors and replace them by another half circle; result: 1 = 1/2 + 1/2 = 2/2 = 1. Let us fill a circle with three 1/5 sectors and four 1/10 sectors: 1 = 3/5 + 4/10. If the larger pieces are left in and the circle is then filled with the fewest number of pieces possible, it would necessitate replacing the four tenths by two fifths. Result: 1 = 3/5 + 2/5 = 5/5 = 1. Let us fill the circle thus: 5/10 + 1/4 + 2/8 = 1. Now try to put in the largest pieces possible by substituting for several small pieces a large piece which is equal to them. In the space occupied by the five tenths may be placed one half, and in that occupied by the two eighths, one fourth; then the circle is filled thus: 1 = 1/2 + 1/4 + 1/4 = 1/2 + 2/4. We can continue to do the same thing, that is to replace the smaller pieces by as large a sector as possible, and the two fourths can be replaced by another half circle. Result: 1 = 1/2 + 1/2 = 2/2 = 1. All these substitutions may be expressed in figures thus:
- 34. 5/10 + 1/4 + 2/8 = 1/2 + 1/4 + 1/4 = 1/2 + 2/4 = 1/2 + 1/2 = 2/2 = 1. This is one means of initiating a child intuitively into the operations used for the reduction of fractions to their lowest terms. Improper fractions also interest them very much. They come to these by adding a number of sectors which fill two, three, or four circles. To find the whole numbers which exist under the guise of fractions is a little like putting away in their proper places the circular insets which have been all mixed up. The children manifest a desire to learn the real operations of fractions. With improper fractions they originate most unusual sums, like the following: [8 + (7/7 + 18/9 + 24/2) + 1] = 8 [8 + (1 + 2 + 12) + 1] = 8 8 + 15 + 1 = 24/8 = 3. 8 We have a series of commands which may be used as a guide for the child's work. Here are some examples: —Take 1/5 of 25 beads —Take 1/4 " 36 counters —Take 1/6 " 24 beans —Take 1/3 " 27 beans —Take 1/10 " 40 beans —Take 2/5 " 60 counters
- 35. In this last there are two operations: 60 ÷ 5 = 12; 12 X 2 = 24; or 2 X 60 = 120; 120 ÷ 5 = 24, etc. Reduction of Common Fractions to Decimal Fractions: The material for this purpose is similar to that of the circular insets, except that the frame is white and is marked into ten equal parts, and each part is then subdivided into ten. In these subdivisions the little line which marks the five is distinguished from the others by its greater length. Each of the larger divisions is marked respectively with the numbers, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 0. The 0 is at the top and there is a raised radius against which are placed the sectors to be measured. To reduce a common fraction to a decimal fraction the sector is placed carefully against the raised radius, with the arc touching the circumference of the inset. Where the arc ends there is a number which represents the hundredths corresponding to the sector. For
- 36. example, if the 1/4 sector is used its arc ends at 25; hence 1/4 equals 0.25. Page 275 shows in detail the practical method of using our material to reduce common fractions to decimal fractions. In the upper figure the segments correspond to 1/3, 1/4, and 1/8 of a circle are placed within the circle divided into hundredths. Result: 1/3 + 1/4 + 1/8 = 0.70.
- 37. The lower figure shows how the 1/3 sector is placed: 1/3 = 0.33. If instead we use the 1/5 sector we have: 1/5 = 0.20, etc. Numerous sectors may be placed within the circle; for example:
- 38. 1/4 + 1/7 + 1/9 + 1/10. In order to find the sum of the fraction reduced to decimals, it is necessary to read only the number at the outer edge of the last sector. Using this as a basis, it is very easy to develop an arithmetical idea. Instead of 1, which represents the whole circle, let us write 100, which represents its subdivisions when used for decimals, and let us divide the 100 into as many parts of a circle as there are sectors in the circle, and the reduction is made. All the parts which result are so many hundredths. Hence: 1/4 = 100 ÷ 4 = 25 hundredths: that is, 25/100 or 0.25. The division is performed by dividing the numerator by the demoninator: 1 ÷ 4 = 0.25. Third Series of Insets: Equivalent Figures. Two concepts were given by the squares divided into rectangles and triangles: that of fractions and that of equivalent figures. There is a special material for the concept of fractions which, besides developing the intuitive notion of fractions, has permitted the solution of examples in fractions and of reducing fractions to
- 39. decimals; and it has furthermore brought cognizance of other things, such as the measuring of angles in terms of degrees. For the concept of equivalent figures there is still another material. This will lead to finding the area of different geometric forms and also to an intuition of some theorems which heretofore have been foreign to elementary schools, being considered beyond the understanding of a child. Material: Showing that a triangle is equal to a rectangle which has one side equal to the base of the triangle, the other side equal to half of the altitude of the triangle. In a large rectangular metal frame there are two white openings: the triangle and the equivalent rectangle. The pieces which compose the rectangle are such that they may fit into the openings of either the rectangle or the triangle. This demonstrates that the rectangle and the triangle are equivalent. The triangular space is filled by two pieces formed by a horizontal line drawn through the triangle parallel to the base and crossing at half the altitude. Taking the two pieces out and putting them one on top of the other the identity of the height may be verified.
- 40. Already the work with the beads and the squaring of numbers has led to finding the area of a square by multiplying one side by the other; and in like manner the area of a rectangle is found by multiplying the base by half other. Since a triangle may be reduced to a rectangle, it is easy to find its area by multiplying the base by half the height. Material: Showing that a rhombus is equal to a rectangle which has one side equal to one side of the rhombus and the other equal to the height of the rhombus. The frame contains a rhombus divided by a diagonal line into two triangles and a rectangle filled with pieces which can be put into the rhombus when the triangles have been removed, and will fill it completely. In the material there are also an entire rhombus and an entire rectangle. If they are placed one on top of the other they will be found to have the same height. As the equivalence of the two figures is demonstrated by these pieces of the rectangle which may be used to fill in the two figures, it is easily seen that the area of a rhombus is found by multiplying the side or base by the height.
- 41. Material: To show the equivalence of a trapezoid and a rectangle having one side equal to the sum of the two bases and the other equal to half the height. The child himself can make the other comparison: that is, a trapezoid equals a rectangle having one side equal to the height and the other equal to one-half the sum of the bases. For the latter it is only necessary to cut the long rectangle in half and superimpose the two halves. The large rectangular frame contains three openings: two equal trapezoids and the equivalent rectangle having one side equal to the sum of the two bases and the other side equal to half the height. One trapezoid is made of two pieces, being cut in half horizontally at the height of half its altitude; the identity in height may be proved by placing one piece on top of the other. The second trapezoid is composed of pieces which can be placed in the rectangle, filling it completely. Thus the equivalence is proved and also the fact that the area of a trapezoid is found by multiplying the sum of the bases by half the height, or half the sum of the bases by the height.
- 42. With a ruler the children themselves actually calculate the area of the geometrical figures, and later calculate the area of their little tables, etc. Material: To show the equivalence between a regular polygon and a rectangle having one side equal to the perimeter and the other equal to half of the hypotenuse. The analysis of the decagon. In the material there are two decagon insets, one consisting of a whole decagon and the other of a decagon divided into ten triangles.
- 43. Page 281 shows a table taken from our geometry portfolio, representing the equivalence of a decagon to a rectangle having one side equal to the perimeter and the other equal to half the hypotenuse. The bead number cubes built into a tower. The photograph shows the pieces of the insets—the decagon and the equivalent rectangle—and beneath each one there are the small equal triangles into which it can be subdivided. Here it is demonstrated that a rectangle equivalent to a decagon may have
- 44. one side equal to the whole hypotenuse and the other equal to half of the perimeter. Another inset shows the equivalence of the decagon and a rectangle which has one side equal to the perimeter of the decagon and the other equal to half of the altitude of each triangle composing the decagon. Small triangles divided horizontally in half can be fitted into this figure, with one of the upper triangles divided in half lengthwise. Thus we demonstrate that the surface of a regular polygon may be found by multiplying the perimeter by half the hypotenuse. SOME THEOREMS BASED ON EQUIVALENT FIGURES A. All triangles having the same base and altitude are equal. This is easily understood from the fact that the area of a triangle is found by multiplying the base by half the altitude; therefore triangles having the same base and the same altitude must be equal. For the inductive demonstration of this theorem we have the following material: The rhombus and the equivalent rectangle are each divided into two triangles. The triangles of the rhombus are different, for they are divided by opposite diagonal lines. The three different triangles resulting from these divisions have the same base (this can be actually verified by measuring the bases of the different pieces) and fit into the same long rectangle which is found below the first three figures. Therefore, it is demonstrated that the three triangles have the same altitude. They are equivalent because each one is the half of an equivalent figure.
- 45. The decagon and the rectangle can be composed of the same triangular insets. The triangular insets fitted into their metal plates.
- 46. B. The Theorem of Pythagoras: In a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the two sides. Material: The material illustrates three different cases: First case: In which the two sides of the triangle are equal. Second case: In which the two sides are in the proportion of 3:4. Third case: General. First case: The demonstration of this first case affords an impressive induction. In the frame for this, shown below, the squares of the two sides are divided in half by a diagonal line so as to form two triangles and the square of the hypotenuse is divided by two diagonal lines into four triangles. The eight resulting triangles are all identical; hence the triangles of the squares of the two sides will fill the square of the hypotenuse; and, vice versa, the four triangles of the square of the hypotenuse may be used to fill the two squares of the sides. The substitution of these different pieces is very interesting, and all the more because the triangles of the squares of the sides are all of the same color, whereas the triangles formed in the square of the hypotenuse are of a different color.
- 47. Second case: Where the sides are as the proportion of 3:4. In this figure the three squares are filled with small squares of three different colors, arranged as follows: in the square on the shorter side, 32 = 9; in that on the larger side, 42 = 16; in that on the hypotenuse, 52 = 25. Second Case The substitution game suggests itself. The two squares formed on the sides can be entirely filled by the small squares composing the
- 48. square on the hypotenuse, so that they are both of the same color; while the square formed on the hypotenuse can be filled with varied designs by various combinations of the small squares of the sides which are in two different colors. Third case: This is the general case. The large frame is somewhat complicated and difficult to describe. It develops a considerable intellectual exercise. The entire frame measures 44 × 24 cm. and may be likened to a chess-board, where the movable pieces are susceptible of various combinations. The principles already proved or inductively suggested which lead to the demonstration of the theorem are: (1) That two quadrilaterals having an equal base and equal altitude are equivalent. (2) That two figures equivalent to a third figure are equivalent to each other. In this figure the square formed on the hypotenuse is divided into two rectangles. The additional side is determined by the division made in the hypotenuse by dropping a perpendicular line from the apex of the triangle to the hypotenuse. There are also two rhomboids in this frame, each of which has one side equal respectively to the large and to the small square of the sides of the triangle and the other side equal to the hypotenuse. The shorter altitude of the two rhomboids, as may be seen in the figure itself, corresponds to the respective altitudes, or shorter sides, of the rectangles. But the longer side corresponds respectively to the side of the larger and of the smaller squares of the sides of the triangle. It is not necessary that these corresponding dimensions be known by the child. He sees red and yellow pieces of an inset and simply moves them about, placing them in the indentures of the frame. It is the fact that these movable pieces actually fit into this white
- 49. background which gives the child the opportunity for reasoning out the theorem, and not the abstract idea of the corresponding relations between the dimensions of the sides and the different heights of the figures. Reduced to these terms the exercise is easily performed and proves very interesting. This material may be used for other demonstrations: Demonstration A: The substitution of the pieces. Let us start with the frame as it should be filled originally. First take out the two rectangles formed on the hypotenuse; place them in the two lateral grooves, and lower the triangle. Fill the remaining empty space with the two rhomboids. The same space is filled in both cases with: A triangle plus two rectangles, and then A triangle plus two rhomboids. Hence the sum of the two rectangles (which form the square of the hypotenuse) is equal to the sum of the two rhomboids. In a later substitution we consider the rhomboids instead of the rectangles in order to demonstrate their respective equivalence to the two squares formed on the sides of the triangle. Beginning, for example with the larger square, we start with the insets in the original position and consider the space occupied by the triangle and the larger square. To analyze this space the pieces are all taken out and then it is filled successively by: The triangle and the large square in their original positions. The triangle and the large rhomboid.
- 50. Showing that the two rhomboids are equal to the two rectangles. Demonstration B: Based on Equivalence. In this second demonstration the relative equivalence of the rhomboid, the rectangles, and the squares is shown outside the figure by means of the parallel indentures which are on both sides of the frame. These indentures, when the pieces are placed in them, show that the pieces have the same altitude.
- 51. This is the manner of procedure: Starting again with the original position, take out the two rectangles and place them in the parallel indentures to the left, the larger in the wider indenture and the smaller in the narrower indenture. The different figures in the same indenture have the same altitude; therefore the pieces need only to be placed together at the base to prove that they are equal—hence the figures are equal in pairs: the smaller rectangle equals the smaller rhomboid and the larger rectangle equals the larger rhomboid. Starting again from the original position you proceed analogously with the squares. In the parallel indentures to the right the large square may be placed in the same indenture with the large rhomboid, which, however, must be turned in the opposite direction (in the direction of its greatest length); and the smaller square and the smaller rhomboid fit into the narrower indenture. They have the same altitude; and that the bases are equal is easily verified by putting them together; therefore here is proof that the squares and the rhomboids are respectively equivalent. Rectangles and squares which are equivalent to the same rhomboids are equivalent to each other. Hence the theorem is proved. . . . . . . .
- 52. Showing that the two rhomboids are equal to the two squares. This series of geometric material is used for other purposes, but they are of minor importance. Fourth Series of Insets: Division of a Triangle. This material made up of four frames of equal size, each containing an equilateral triangle measuring ten centimeters to a side. The different pieces should fill the triangular spaces exactly. One is filled by an entire equilateral triangle.
- 53. One is filled by two rectangular scalene triangles, each equal to half of the original equilateral triangle, which is bisected by dropping a line perpendicularly to the base. The third is filled by three obtuse isosceles triangles, formed by lines bisecting the three angles of the original triangle. The fourth is divided into four equilateral triangles which are similar in shape to the original triangle. With these triangles a child can make a more exact analytical study than he made when he was observing the triangles of the plane insets used in the "Children's House." He measures the degrees of the angles and learns to distinguish a right angle (90°) from an acute angle (<90°) and from an obtuse angle (>90°). Furthermore he finds in measuring the angles of any triangle that their sum is always equal to 180° or to two right angles. He can observe that in equilateral triangles all the angles are equal (60°); that in the isosceles triangle the two angles at the opposite ends of the unequal side are equal; while in the scalene triangle no two angles are alike. In the right-angled triangle the sum
- 54. of the two acute angles is equal to a right angle. A general definition is that those triangles are similar in which the corresponding angles are equal. Material for Inscribed and Concentric Figures: In this material, which for the most part is made up of that already described, and which is therefore merely an application of it, inscribed or concentric figures may be placed in the white background of the different inset frames. For example, on the white background of the large equilateral triangle the small red equilateral triangle, which is a fourth of it, may be placed in such a way that each vertex is tangent to the middle of each side of the larger triangle. There are also two squares, one of 7 centimeters on a side and the other 3.5. They have their respective frames with white backgrounds. The 7 centimeters square may be placed on the background of the 10 centimeters square in such a way that each corner touches the middle of each side of the frame. In like manner the 5 centimeters square, which is a fourth of the large square, may be put in the 7 centimeters square; the 3.5 centimeters square in the 5 centimeters square; and finally the tiny square, which is 1/16 part of the large square, in the 3.5 centimeters square. There is also a circle which is tangent to the edges of the large equilateral triangle. This circle may be placed on the background of the 10 centimeters circle, and in that case a white circular strip remains all the way round (concentric circles). Within this circle the smaller equilateral triangle (1/4 of the large triangle) is perfectly inscribed. Then there is a small circle which is tangent to the smallest equilateral triangle. Besides these circles which are used with the triangles there are two others tangent to the squares: one to the 7 centimeters square and the other to the 3.5 centimeters square. The large circle, 10 centimeters in diameter, fits exactly into the 10 centimeters square; and the other circles are concentric to it.
- 55. These corresponding relations make the figures easily adaptable to our artistic composition of decorative design (see following chapter). Finally, together with the other material, there are two stars which are also used for decorative design. The two stars, or "flowers," are based on the 3.5 centimeters square. In one the circle rests on the side as a semi-circle (simple flower); and in the other the same circle goes around the vertex and beyond the semi-circle until it meets the reciprocal of four circles (flower and foliage).
- 56. III SOLID GEOMETRY Since the children already know how to find the area of ordinary geometric forms it is very easy, with the knowledge of the arithmetic they have acquired through work with the beads (the square and cube of numbers), to initiate them into the manner of finding the volume of solids. After having studied the cube of numbers by the aid of the cube of beads it is easy to recognize the fact that the volume of a prism is found by multiplying the area by the altitude. In our didactic material we have three objects for solid geometry: a prism, a pyramid having the same base and altitude, and a prism with the same base but with only one-third the altitude. They are all empty. The two prisms have a cover and are really boxes; the uncovered pyramid can be filled with different substances and then emptied, serving as a sort of scoop. These solids may be filled with wheat or sand. Thus we put into practise the same technique as is used to calculate capacity, as in anthropology, for instance, when we wish to measure the capacity of a cranium. It is difficult to fill a receptacle completely in such a way that the measured result does not vary; so we usually put in a scarce measure, which therefore does not correspond to the exact volume but to a smaller volume. One must know how to fill a receptacle, just as one must know how to do up a bundle, so that the various objects may take up the least possible space. The children like this exercise of shaking the
- 57. receptacle and getting in as great a quantity as possible; and they like to level it off when it is entirely filled. The receptacles may be filled also with liquids. In this case the child must be careful to pour out the contents without losing a single drop. This technical drill serves as a preparation for using metric measures. By these experiments the child finds that the pyramid has the same volume as the small prism (which is one-third of the large prism); hence the volume of the pyramid is found by multiplying the area of the base by one-third the altitude. The small prism may be filled with clay and the same piece of clay will be found to fill the pyramid. The two solids of equal volume may be made of clay. All three solids can be made by taking five times as much clay as is needed to fill the same prism. . . . . . . . Having mastered these fundamental ideas, it is easy to study the rest, and few explanations will be needed. In many cases the incentive to do original problems may be developed by giving the children definite examples: as, how can the area of a circle be found? the volume of a cylinder? of a cone? Problems on the total area of some solids also may be suggested. Many times the children will risk spontaneous inductions and often of their own accord proceed to measure the total surface area of all the solids at their disposal, even going back to the materials used in the "Children's House." The material includes a series of wooden solids with a base measurement of 10 cm.: A quadrangular parallelopiped (10 X 10 X 20 cm.) A quadrangular parallelopiped equal to 1/3 of above A quadrangular pyramid (10 X 10 X 20 cm.)
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