A \emph{simple} $n$-\emph{Venn diagram} is a collection of $n$ simple intersecting closed curves in the plane where exactly two curves meet at any intersection point; the curves divide the plane into $2^n$ distinct open regions, each defined by its intersection of the interior or exterior of each of the curves. A Venn diagram is \emph{reducible} if there is a curve that, when removed, leaves a Venn diagram with one less curve and \emph{irreducible} if no such curve exists. A Venn diagram is \emph{extendible} if another curve can be added, producing a Venn diagram with one more curve. Currently it is not known whether every simple Venn diagram is extendible by the addition of another curve. We show that all simple Venn diagrams with $5$ curves or less are extendible to another simple Venn diagram. We also show that for certain Venn diagrams, a new extending curve is relatively easy to produce. We define a new type of diagram of simple closed curves where each curve divides the plane into an equal number of regions; we call such a diagram a \emph{face-balanced} diagram. We generate and exhibit all face-balanced diagrams up to and including those with $32$ regions; these include all the Venn diagrams. Venn diagrams exist where the curves are the perimeters of polyominoes drawn on the integer lattice. When each of the $2^n$ intersection regions is a single unit square, we call these \emph{minimum area polyomino Venn diagrams}, or \emph{polyVenns}. We show that polyVenns can be constructed and confined in bounding rectangles of size $2^r \times 2^c$ whenever $r, c \ge 2$ and $n=r+c$. We show this using two constructive proofs that extend existing diagrams. Finally, for even $n$, we construct polyVenns with $n$ polyominoes in $(2^{n/2} - 1) \times (2^{n/2} + 1)$ bounding rectangles in which the empty set is not represented as a unit square. / Graduate / 0405 / 0984 / bbultena@uvic.ca

Title: Text properties as a factor in solving word problems with the use of Venn diagrams Author: Bc. Daniela Návarová Department: Department of Mathematics and Mathematical Education Supervisor: doc. RNDr. Jarmila Novotná, CSc. Supervisor's e-mail address: Jarmila.Novotna@pedf.cuni.cz This diploma thesis deals with the word problems where Venn diagrams can be used. The word problems are studied as texts and their specific text properties are scrutinised in the first, theoretical, part of the thesis. The second part describes an experiment that focuses on the importance of text properties of word problems for the problem solvers. The main aims of this diploma thesis are to show the possibility of textual examination of the chosen texts and to unfold some connections between the mathematical and linguistic views on the area of word problems. Keywords: text, word problem, Venn diagram

The purpose of this thesis is to develop a toolkit to visualize bag calculations for teaching. We take full advantage of interaction techniques in Computer Science to achieve it, which could lead to a modern and impressive way for teaching.   In this thesis, the developed toolkit is going to show the bag calculations and corresponding animations interactively and aesthetically which make new learners easier to acquire the concept of multiset.

This study aims to analyze and evaluate three non-profit organizations regarding how their sustainability accounting reports have changed and developed between year 2017 and year 2019. The study analyzes how parameters in the sustainability index have been taken into consideration to perceive which parameters are the three non-profits organization’s focal points. In addition, the study will analyze how sustainability accounting reports meet the stakeholder's information needs. Given the prevailing issues and purpose of the study, a qualitative method is relevant to this study. The selection of organizations is based on organizations' availability of sustainability reports for the assessment period. In this study, non-probability selection was chosen, where the selection was made through a preliminary investigation. The study is based on a secondary data method which is a flexible and appropriate approach.   This thesis consists of empirical studies that will help strengthen the quality of the study. The data collected in the empirical data have been analyzed on the basis of the theoretical frame of reference. Frame of reference in this thesis is based on sustainable development, sustainability accounting, Venn diagram of sustainable development, triple bottom line and stakeholder theory. The empirical data in this thesis consists of Red Cross Sweden, Save the Children Sweden and WWF.   Based on the result of this thesis, the parameters under dimensions, environmental responsibility, social responsibility and financial responsibility in each organization have similarities. For example, the environmental requirements for purchasing and procurement are seen in both the Red Cross' and Save the Children's sustainability reports. Another example of similarity that can be seen in all three organizations' sustainability reports is gender equality and diversity. The organization's focus for different parameters in sustainability reports depends on the type of business they have. The development of each organization's sustainability reports in 2017 has been remarkable. Prior to 2017, Save the Children was a pioneer in presenting sustainability reports. While the Red Cross and WWF began to present sustainability reports in 2017. According to their stakeholder analysis, all three respective organizations have included all parameters that are important to their stakeholders. Through their dialogues with both internal and external stakeholders, the respective organizations meet the stakeholders' need for information. / Syfte: Denna studie syftar till att analysera och utvärdera tre ideella organisationer och hur deras hållbarhetsredovisning rapporter har förändrats och utvecklats mellan åren 2017 och2019. Studien analyserar hur parametrar i hållbarhetsredovisning rapporter har beaktats. Studien kommer också att analysera hur hållbarhetsredovisning rapporter möter intressenternas informationsbehov.   Metod: Med hänsyn till uppsatsens syftet och frågeställningar har studien en kvalitativ ansats. Studien utgår ifrån en sekundärdata metod som är ett flexibelt och lämpligt tillvägagångssätt. Studien består också av empiriska studier som kommer att bidra till att stärka studiens kvalitet. Den insamlade datan i empirin har analyserats med underlag av den teoretiska referensramen. Teoretiska perspektiv: Den teoretiska referensram som uppsatsen bygger på är hållbarutveckling, hållbarhetsredovisning, triple bottom line och intressentteori.  Empiri: De tre ideella organisationer som har undersökts i denna uppsats är Röda Korset, Rädda barnen och WWF.  Resultat: Parametrarna under dimensioner, miljöansvar, socialt ansvar och ekonomiskt ansvar i respektive organisation har likheter. Till exempel ses miljökraven för inköp och upphandling i både Röda korsets och i Rädda barnens hållbarhetsrapporter. Ett annat exempel på likhet som kan ses i alla de tre organisationernas hållbarhetsrapporter är jämställdhet och mångfald. Organisationens fokus för olika parametrar i hållbarhetsrapporter beror på vilken typ av verksamhet de har. Utvecklingen av respektive organisations hållbarhetsrapporter under 2017har varit anmärkningsvärt. Före 2017 var Rädda barnen en pionjär när det gäller att presenterahållbarhetsrapporter. Medan Röda Korset och WWF började presentera hållbarhetsrapporter först år 2017. Alla de tre respektive organisationerna har enligt sin intressentanalys inkluderat alla parametrar som är viktiga för deras intressenter. De respektive organisationerna försöker genom sina dialoger med både interna och externa intressenter möter intressenternas behov av information.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-11T12:47:20Z No. of bitstreams: 2 Dissertação - Paula Daniele Borges dos Santos - 2017.pdf: 1755533 bytes, checksum: 6efac4df89f983ce6e59731acd88d41a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-11T12:47:44Z (GMT) No. of bitstreams: 2 Dissertação - Paula Daniele Borges dos Santos - 2017.pdf: 1755533 bytes, checksum: 6efac4df89f983ce6e59731acd88d41a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-11T12:47:44Z (GMT). No. of bitstreams: 2 Dissertação - Paula Daniele Borges dos Santos - 2017.pdf: 1755533 bytes, checksum: 6efac4df89f983ce6e59731acd88d41a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-21 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / The present work intends to show an illustrative approach to calculate and understand Greater Common Divisor and Least Common Multiple, seeking a greater assimilation and concretization of the learning of this content. This methodology is presented in a chromological order following the evolution of mathematical concepts. Therefore, this text, aiming to produce a meaningful approach of the subject, seeks to expose in a simple way what comes to be the Prime Numbers according to Numbers Theory and Venn Diagram according to the Set Theory, in order to visualize and obtain the Relation between Greater Common Divisor, Least Common Multiple, and Venn Diagram. / O presente trabalho pretende mostrar uma abordagem ilustrativa para se calcular e entender Máximo Dividor Comum e Mínimo Múltiplo Comum, buscando uma maior assimilação e concretização da aprendizagem desse conteúdo. Esta metodologia é apresentada numa ordem cronológica seguindo a evolução dos conceitos matemáticos. Logo, este texto, visando produzir uma abordagem significativa do assunto, busca expor de forma simples o que vem a ser os Números Primos segundo a Teoria dos Números e Diagrama de Venn segundo a Teoria dos Conjuntos, para que assim se consiga visualizar e obter a Relação entre Máximo Divisor Comum, Mínimo Múltiplo Comum e o Diagrama de Venn.

This thesis focuses on the teaching of mathematics using the CLIL method. The topic is Venn diagrams and learning how to solve problems using these diagrams. The language chosen for the CLIL method is English. First, the CLIL method is described, and later I introduce sets and Venn diagrams. The aim of the thesis is to prepare and implement two lessons using the CLIL method in English, and two lessons in Czech, followed by preparing a test in both languages for a third lesson. The thesis was realized by conducting a teaching experiment, which took place in two classes of multi- year grammar school (in the Quintas - the first year of secondary school). I have compiled and tested four worksheets - two with Czech tasks, two with English tasks, a presentation for the lesson using the CLIL method, and tests for both language versions. Both the tasks and solutions are part of the thesis. Before the preparation of the thesis, the following two research questions were identified: 1. What needs to be taken into consideration when preparing for the Venn diagrams lesson using the CLIL method, and what needs to be added to this lesson compared to the Czech lesson? 2. At what success rate will pupils learn using the CLIL method in English and pupils using Czech, with regard to equation building and answers to...