example of maths presentation

Math Presentation Templates

Explain and illustrate mathematical concepts, principles and problem-solving techniques in a clear, concise and visually engaging manner with Venngage’s selection of free math presentation templates.

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Browse Course Material

Course info, instructors.

• Prof. Haynes Miller
• Dr. Nat Stapleton
• Saul Glasman

Departments

• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics, presentations.

Next: Practice and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for presentations and the components of the presentation workshop.

Criteria for Good Presentations

Effective presentations provide motivation, communicate intuition, and stimulate interest, all while being mathematically accurate and informative. As is true with their experience with mathematical writing, many students do not enter the course in possession of the tools to do much more than present the facts. For example, students often come to practice presentations with the mistaken belief that a mathematical presentation must be extremely formal throughout, every term must be rigorously defined, all facts must be proven, and pictures are too infantile for this level of presentation. We try to counter these preconceptions and urge flexibility and a sense of appropriateness: sometimes things need to be presented rigorously and formally, but sometimes a picture, conceptual explanation, or example is much more effective.

Characteristics of an Effective Undergraduate Research Talk (PDF)

Presentation Workshop

For the presentation workshop, which typically lasts 50 to 80 minutes, we begin by having the two co-instructors each give a short mock presentation. These presentations are designed to address common student misconceptions about mathematics presentations. For example, to help students realize that presentations should not be relentlessly formal, the first presentation might be good in every way except that it is dull and difficult to follow because it is unnecessarily formal throughout. In contrast, the second presentation might cover the same material but use examples and figures to introduce some concepts informally, while reserving rigorous formality as a strategy for clarifying and solidifying the most subtle or important concepts.

To help students recognize the value of the second presentation relative to the first, after each presentation we ask the students a question designed to check their understanding of the content. The goal is to allow students to discover their natural tendency to overlook weaknesses in presentations. When they try to answer questions about it, they may discover that they got less from it than they had thought. The second presentation is then intended to offer a more understandable approach to the same material. Of course it’s the second time students will have heard this material, so they will naturally understand it better. But this serves a pedagogical purpose too, as it reinforces our point.

We follow the presentations with a class discussion on how to give a good presentation. Carefully designing two mock presentations has the virtue of drawing attention to key learning objectives, but doing so is challenging. In Spring 2013, each mock presentation was delivered by a different instructor and so had different advantages and disadvantages, as is stressed by Haynes’ comments on the workshop (PDF) . In the past we have reduced accidental differences between the presentations by having a single instructor present both, and we may return to that approach in the future.

After the mock presentations, the class discusses the characteristics of a good presentation. Questions we discuss often include the following:

• What are the reasons to include a proof in a presentation?
• What other strategies are available for achieving these goals?
• What strategies can be used to make a math presentation engaging for the target audience of math majors?

In Spring 2013, the mock presentations ran long, and the class session was shorter than we had originally planned because of scheduling disruptions at MIT. Thus, the subsequent discussion was rushed. The presentation workshop works best when there is ample time for discussion.

We hope that students come away from this workshop with an appreciation for some of the complexities in designing a good presentation. Pretty much every choice involved has both pros and cons.

• Download video

This video features the presentation workshop from Spring 2013. The co-instructors deliver mock presentations, which are followed by a brief class discussion comparing the two presentations.

Chalk Talks versus Slide Presentations

Different instructors have set different expectations for the presentations. Some have insisted on slide presentations. More typically, students are encouraged to use media suited to the demands of the presentation.

When discussing slide presentations in mathematics, we usually make the following points:

• When slides contain large amounts of text (or equations), the audience cannot read and listen at the same time, so strategies are needed either to reduce the content on the slides or to guide the audience through the content.
• The audience needs time to absorb math concepts, but it is very easy to click through slides too quickly, especially when the presenter is nervous, so strategies are needed to give the audience time to think.
• The audience cannot refer to past slides to remind themselves of the meaning of new notation or of the purpose of details being presented, so strategies are needed to help the audience remember important points.

A Note about Scheduling

In the course, roughly one group presents each week. Experience has shown that the first team to present sets the bar for the rest of the semester. It is important that the first team be chosen carefully and be guided well so that they give a strong presentation.

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[Updated 2023] 20 Best Math PowerPoint Templates To Fall In Love With Numbers

Malvika Varma

Have you ever thought about the huge influence Math has on our daily lives? We are not talking about completing math worksheets given by the teacher back in school days. We are talking about math in the form of problem-solving and logic which we encounter on a daily basis. From home to school, school to work, and all the places in between, math is everywhere. Even those who suffer from fear of math cannot escape the everyday existence of math in their lives. It plays such a vital role that whenever we want to answer questions such as "How many?", we have to use math. 

“Go down deep enough into anything and you will find mathematics.” — Dean Schlicter

Mathematics has become the companion of man, a great aide since the emergence of human existence on earth. Be it time tracking, driving, cooking, measurements, banking, rates, wages, tenders, discounts, claims, supplies, jobs, stocks, contracts, taxes, money exchange, consumption, etc., the use of math can be found everywhere. Without numbers, formulas, and mathematical evidence, we cannot fix any issues in our daily lives. The laws of mathematics are evident everywhere including in nature. Scientists and engineers use it for analyzing data, pattern recognition, and evidence seeking. In recent times, to sustain in the competitive 21st-century, business circles lay emphasis on the global economy fields of science, technology, engineering, and mathematics (STEM).

Highlight the significance of mathematics in different aspects of life by downloading these 20 Best Math PowerPoint Templates designed by SlideTeam professionals. These pre-designed versatile Math PowerPoint Templates can be used for various purposes and customized as per your needs.

Let us dive into the world of numbers!

20 Best Math PowerPoint Templates To Download 

Download Math Symbols with Round and Curly Brackets Icons Template

Here is a symbolic PPT Template to introduce the algebraic signs and to discuss their essence. Symbols identified in this PPT Slide are +,-,*,÷, {}, <,>,etc. This PPT Design is great at educating primary level students where the presenter can step-by-step explain each of these mathematical symbols. Without any ado, download it now!

Download Data Driven Scatter Chart Mathematical Diagram PowerPoint Slide

Elaborate the benefits and explain the working of an important mathematical element i.e. graphs, in particular, scatter charts with this PPT Layout. Explain its functions like identifying anomalies, correlation, patterns, etc using this PPT Layout. Download this editable, multi-variable PPT Chart now!

Education can be fun too, and so you can download our attractive math PowerPoint templates for classroom sessions. There’s an increasing trend in education of using visual techniques to help students learn concepts that can be met by incorporating this editable mathematics PowerPoint layout. This pre-designed math PowerPoint background can be employed for education websites also. Math coaching institutes can employ this attractive math PowerPoint background for promotional purposes.

Illustrations usually have a good visual impact which makes this math PowerPoint template essential for your next class. Students can be taught about numbers in an engaging manner by downloading our customizable math PowerPoint templates. The color palette used here is pleasant, and they combine to perfection with the graphic elements in this template. Topics that are related to algebra, trigonometry, formulas, and complex numbers can be explained to students effectively by utilizing this pre-designed math PowerPoint background.

Download our math PowerPoint template which focuses on design, so you can turn a lesson into an easy teaching experience. Teachers can incorporate this attention-grabbing math PPT layout to teach about numbers and their significance in everyday life. The history of great mathematicians can also be effectively communicated with the help of this editable math PowerPoint theme.

Paying attention to a lesson is very important, and our math PowerPoint template makes it easy for your students to keep their eyes on the screen. Incorporate this customizable math PowerPoint layout to discuss the various math symbols and their applications in an engaging manner. Students can include this professionally designed math PowerPoint layout for their math projects and seminars.

You can use this Math PowerPoint template in presentations for math subjects at school or University. The color palette used here gives a very appealing look to the overall presentation and hence serves the purpose of elucidating math concepts to students in an engaging manner. The various topics such as geometry, algebra, calculus, etc. can be taught by utilizing this attention-grabbing mathematics PPT theme.

Business calculations are possible only because of knowledge of mathematics which can be conveyed using our math PowerPoint templates. The various aspects where math is essential can be highlighted by incorporating this visually appealing mathematical PowerPoint background. Sales professionals can also employ this pre-designed math PowerPoint theme for presenting the sales results of an organization. 

The cost allocation concept and the mathematical techniques used can be discussed by utilizing this math PowerPoint template. Accountants can also download this professionally designed math PowerPoint theme for their business meetings and conferences. The new financial policies can also be explained with the help of this editable math PowerPoint theme. Teachers can also utilize this math PowerPoint background for explaining the applications of mathematics to students.

Template 10

This math educational PowerPoint template can be a useful resource for professors, teachers, or math students to study binary digits. The history of numbers can be illustrated effectively by incorporating this attention-grabbing math PowerPoint theme. Computer teachers can also employ this pre-designed math PowerPoint background to teach binary language and make them understand the process by which a computer performs the calculation.

Template 11

Incorporate this amazingly designed math PowerPoint template to discuss the role of mathematics in budget forecasting of organization. The formulas and mathematical techniques required for excelling in the career of mathematics can also be illustrated with the help of our customizable math PowerPoint background. The finance policies of a company can be elucidated in business meetings by utilizing this pre-designed math PowerPoint layout.

Template 12

Illustrate the mathematical formulas and theorems to clear the concepts of students with the help of our awe-inspiring math PowerPoint template. Education websites can easily incorporate this editable math PowerPoint theme. Coaching institutes can download this attractive math PowerPoint template for math online course advertisements.

Template 13

Math is essential in almost every profession and this can be effectively portrayed by employing this aesthetically appealing math PowerPoint template. By downloading this editable math PPT theme, HR can present the method of calculating the full-time equivalent of the employees of the company. The various formulas can be illustrated with the help of this pre-designed mathematics PowerPoint background.

Template 14

Financial calculation of the business expenses of an enterprise can be presented in an effective manner by downloading this math PowerPoint template. The professionally crafted financial calculation PPT icon uses graphics of calculating equipment like a calculator that clearly depicts the topic which needs to be addressed with the audience. The different uses of mathematical calculations can also be illustrated by utilizing this customizable math PowerPoint template.

Template 15

When it comes to educating kids about math and calculations, it’s smarter to take a fun way. Incorporate our attention-grabbing math PowerPoint template to explain the significance of geometry in everyday life. You can discuss the geometrical instruments with kids and explain their usage by utilizing this professionally designed math PowerPoint background.

Template 16

Download Graphical Representation Of Business KPI PowerPoint Template 

Companies can download this customizable business KPI PowerPoint template to elucidate the enterprise results. The applications of mathematics can also be discussed by utilizing this engaging math PowerPoint theme. Elucidate the company graphs to the employees by incorporating this pre-designed math PowerPoint background.

Template 17

When it is fun to learn, education becomes more effective and this purpose is rightly served by this attention-grabbing math PowerPoint template. The mathematical formulas can be demonstrated along with sample problems by utilizing this professionally designed math PowerPoint background. Online classes and courses can also be promoted by employing this editable math PowerPoint layout.

Template 18

If creating fun worksheets every now and then is getting tiring in your packed schedule, download this editable math PowerPoint template. Teachers can easily download this pre-designed math PowerPoint to explain mathematical formulas to students and also its practical application. Accountants can also employ this visually appealing math PowerPoint background for business meetings.

Template 19

The insurance claim procedure can be effectively communicated with the help of this professionally designed math PowerPoint template. The application of mathematics in different careers can also be portrayed by utilizing this math PowerPoint theme. This editable math PowerPoint layout can also be used for conferences and seminars to present statistics of an organization.

Template 20

Coaching institutes can incorporate this attractive math PowerPoint template for advertisement purposes. Educational websites and blogs can also download this pre-designed math PowerPoint to elaborate on the courses available and the various details regarding it. NGOs can incorporate this math PowerPoint background to create awareness regarding the importance of education at every stage of life.

Math is a strong foundation of organized life and it is all around us. It is extremely significant in our lives and, even without understanding it, we use concepts of math in several fields. Download these 20 Best Math PowerPoint Templates and showcase the importance of math. A life devoid of math is difficult to imagine.

“Mathematics is, in its way, the poetry of logical ideas.” –Albert Einstein

Enjoy the language of numbers!

FAQs on Math

What is math.

Mathematics, or math, is a field of study concerned with the properties and relationships of numbers, quantities, and shapes. It involves the study of abstract concepts such as numbers, quantity, space, and change, and how they relate to each other.

This is an essential subject that is used in a wide variety of fields, including science, engineering, finance, and technology. It provides a framework for understanding the natural world, developing new technologies, and solving complex problems. Math is also a subject that encourages critical thinking, problem-solving skills, and logical reasoning, which are valuable skills in many areas of life.

Mathematics can be divided into several subfields, including algebra, geometry, trigonometry, calculus, and statistics, each with its own set of concepts, principles, and methods. Math is also closely related to other subjects such as physics, chemistry, and computer science, and it is used extensively in these fields to solve problems and develop new theories and applications.

Who invented math?

Mathematics, as a subject, was not invented by any one individual or culture. Instead, it has developed over thousands of years across various civilizations around the world.

The origins of mathematics can be traced back to ancient civilizations such as the Babylonians, Egyptians, and Greeks, who developed mathematical systems to solve practical problems in areas such as astronomy, engineering, and trade. The ancient Greeks, in particular, made significant contributions to the development of mathematics, including the concepts of geometry, arithmetic, and algebra.

Later, during the medieval period, Arab mathematicians made important contributions to the development of algebra and trigonometry, which were later incorporated into the European mathematical tradition.

In modern times, mathematics has continued to evolve and develop, with significant contributions from individuals such as Isaac Newton, Gottfried Leibniz, and Leonhard Euler, among others. Today, mathematics is a vast and diverse field of study that continues to advance our understanding of the world around us and provide solutions to complex problems in science, engineering, finance, and technology.

What are the 4 types of math?

Mathematics can be divided into various subfields, each with its own set of concepts, principles, and methods. Here are four main branches of mathematics:

• Arithmetic: Arithmetic is the study of numbers and the basic operations of addition, subtraction, multiplication, and division. It is the foundation of all other branches of mathematics and is essential in everyday life for tasks such as counting, measuring, and calculating.
• Algebra: Algebra is the study of mathematical symbols and the rules for manipulating them. It involves the use of variables and equations to solve problems, including linear equations, quadratic equations, and systems of equations.
• Geometry: Geometry is the study of shapes, sizes, and positions of objects in space. It involves the study of points, lines, angles, shapes, and spatial relationships, and is used in areas such as architecture, engineering, and art.
• Calculus: Calculus is the study of change and rates of change. It involves the study of limits, derivatives, integrals, and differential equations, and is used in areas such as physics, engineering, and economics to solve problems related to rates of change and optimization.

Other important branches of mathematics include number theory, statistics, probability theory, and combinatorics. Each of these branches has its own unique set of concepts and methods, and they all play a vital role in advancing our understanding of the world around us.

Who is the father of maths?

If we consider the foundations of mathematics, the ancient Greek philosopher and mathematician Pythagoras is often referred to as the "father of mathematics."

Pythagoras and his followers, known as the Pythagoreans, made significant contributions to the development of mathematics in the areas of geometry, arithmetic, and number theory. They are credited with discovering the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Although Pythagoras lived over 2,500 years ago and his work may not have survived in its original form, his contributions to the development of mathematics have had a lasting impact and continue to influence mathematical thinking and education to this day.

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Free Templates for Math for PowerPoint and Google Slides

Make your presentations and lessons stand out with these free Math templates.  

Download them to use with PowerPoint or edit them in Google Slides and start creating!

Transport Your Audience Back to the 90s with This Groovy Template for PowerPoint and Google Slides. Relive the nostalgia of the 1990s with this free and creative PowerPoint template and Google Slides theme. This vibrant design is packed with fun icons, geometric shapes, and bright colors that will transport your audience back to […]

90’s Vibes free creative Powerpoint template and Google Slides theme.

Geometrical shapes and volume formulas free PowerPoint Template and Google Slides Theme Ready to dive into geometry and volume? This template is perfect for this type of Math. Paper like backgrounds, highlighters, pen, ruler and a compass are featured in this free theme, along with some geometric shapes and their […]

Geometrical Shapes and Volume, free school template.

Free template with a retro interface look for Google Slides and PowerPoint. This template has a retro style with a grid background, featuring a colorful interface with geometric shapes. The pink, blue and yellow tones create a vibrant and dynamic look that will catch your audience’s attention. Whether you want […]

Simple retro interface free ppt and slides template.

Free PowerPoint template and Google Slides theme. Jones is a simple presentation template for marketing, school or to present your next business idea. Even though I used black and yellow as their main colors, you can edit the theme and change its look with just a few clicks. DOWNLOAD POWERPOINT […]

Jones, simple presentation template with hand drawn doodles

Free template for Google Slides and PowerPoint. Thena features fresh colors and geometric shapes. It can be used for a number of different topics, such as a presentation about modern art or a geometry lesson. I’ve used theme colors, so if you wish to change its accents, follow this tutorial. […]

Thena, fun template with geometric shapes.

Free education templates for Google Slides and PowerPoint. 17 different layouts. Utilize them in PowerPoint or Google Slides. Or customize them, save them as JPEG and use them in Google Jamboard or Microsoft Whiteboard. – Or print them out! – This bundle includes: – Frayer model– Weekly planner– Station rotation– […]

School Bundle 06. Templates for education.

Free PowerPoint template and Google Slides theme. Spilsbury free slides theme can be used in the classroom or for a presentation about psychology, mental health, education and more. I used theme colors, so you can edit the master (theme) and change the accent colors for any colors you like. I’ve […]

Spilsbury, puzzle slides theme. Updated Template.

Free PowerPoint template and Google Slides theme. Free multipurpose template for PowerPoint and Google Slides presentations. Lane is a formal template with beautiful tiles made with shapes and lines. Since it’s a multipurpose template, you can use it for different topics. If you need this template to match the colors […]

Lane, free theme with blue tiles.

Free PowerPoint template and Google Slides theme. Free fun template to celebrate we are back to school! Ready to start school? We are almost there! You can use this fun template to welcome your students! Not only it’s great as a Back to School theme, but also works for Math […]

Welcome back to School! Fun slides theme.

Free PowerPoint template and Google Slides theme. Free interactive gameboard template for the little ones (and for the not so little too!) If you are thinking on creating some fun end of the year activities, this template is perfect! To set it up, simply add your questions, activities or challenges […]

Frogtastic! Fun free digital board game template.

Get a copy of this template here.

Jamboard for Equivalent Fractions

Free PowerPoint template and Google Slides theme. Unbox your lesson with this template! It comes with an agenda slide. Are you ready to unbox your ideas? This template is perfect to get them out of your head and share them with your colleagues or classmates! And not only you can […]

Unbox your ideas presentation template.

Free PowerPoint template and Google Slides theme. Buying groceries and counting money template. If you are teaching your students how to count money, this Market template can come quite handy! Go to the market and start adding your list items into the shopping cart! – To modify prices, go to […]

Market, interactive template for counting money.

Free PowerPoint template and Google Slides theme. A classic Bauhaus-inspired free presentation slides. Morris is a free multi-purpose template, its geometric shapes and editable colors make it perfect for many different topics. To customize the colors to fit your topic or brand, go to Slide > Edit Theme, click on […]

Morris, Bauhaus presentation template.

Free PowerPoint template and Google Slides theme. Black and yellow slides theme with shapes. Taxi free template has basic shapes to put all focus on your content. It has a simple memphis style with lots of space to add text, images and infographics! If you wish to change its accents, […]

Taxi, simple memphis presentation template.

Presenting to learn: learning math by talking about it

Undergraduate, secondary school, elementary school, using communication to help reduce math anxiety, professional development opportunities and teacher training, research on the effectiveness of various modes of active learning.

Most of this site is about “learning to communicate” math; this page is about “communicating to learn” math. In other words, students can improve their understanding of math by communicating about it. The following resources describe or illustrate how giving presentations or talking about math can help students to learn math. There’s another page about writing to learn math .

Many of these resources advocate group work. Information about teaching teamwork (including forming teams, teaching teamwork strategies, and grading teamwork) is available on the page about teaching informal communication . Many of the following resources were found by undergraduate researcher Noor Doukmak.

In many educational models, students teach themselves some (or all) of the math rather than solely listening to lectures. Such learner-based models often involve communication in the form of  collaboration, in which students discuss math with each other, and/or presentation, in which students demonstrate what they’ve learned &/or teach it to other students. The specific names applied to these learner-based strategies vary over time (and space). See below for some examples.

• “Inquiry-based learning refers to any pedagogy that replaces traditional lectures and textbooks with some form of student-centered activities… The Journal of Inquiry-Based Learning in Mathematics (JIBLM) publishes university-level course notes that are freely downloadable, professionally refereed, and classroom-tested.”
• The Academy of Inquiry-Based Learning provides videos, workshops, mentoring, small grants, etc.
• “the development and implementation of inquiry-based learning at all educational levels in the United States, particularly in the fields of mathematics and science, and
• “the preservation and dissemination of the inquiry-based learning methodology inspired by Dr. R. L. Moore…”
• The website The Legacy of R.L. Moore provides demonstrations, a quick-start guide, and literature about the method R.L. Moore used with graduate students. In the Moore method, selected students worked individually to prove theorems and presented their work to each other.
• To enable the Moore method to be successfully used in undergraduate classes, modifications have been made that include having students work together in small groups rather than individually, and meetings with the instructor in which the instructor can guide inquiry. See these articles about the Modified Moore Method .
• The Moore method and inquiry-based learning often center around tasks that are “small” enough for several solutions or proofs to be presented in one class session. In contrast, in some undergraduate seminars, students give the lectures and only one or two students lecture in each class session. See the page about Undergraduate Seminars ; some articles are listed at the end of the page.

Myriad other courses replace or supplement lecture with active modes of learning that involve student communication. Some resources and specific examples follow:

• A Practical Guide to Cooperative Learning in Collegiate Mathematics , by N.L. Habelgans et al. , MAA Notes #37, 1995.
• Readings in Cooperative Learning for Undergraduate Mathematics , edited by E. Dubinsky, D. Mathews, and B. E. Reynolds, MAA Notes #44.
• GoodQuestions Project , Department of Mathematics, Cornell University This website includes concept questions for checking understanding and generating discussion in calculus classes. From the website: “The GoodQuestions project seeks to improve calculus instruction by adapting two methods developed in physics instruction — ConcepTests and Just-in-Time-Teaching. GoodQuestions is a pedagogical strategy that aims to raise the visibility of the key concepts and to promote a more active learning environment.”
• “From Calculus to Topology: Teaching Lecture-Free Seminar Courses at All Levels of the Undergraduate Mathematics Curriculum,” by D. L. King, PRIMUS , Vol 11, No 3, Sep 2001, pp. 209-227. From the abstract: “The paper discusses the author’s experiences teaching mathematics courses in a lecture-free, discussion-based seminar format at all levels of the traditional undergraduate mathematics curriculum. These seminars replace the traditional lecture with classroom discussion of course readings and exercises prepared by students in advance of class.”
• “Mathematics Through Workshops Based on Collaborative Learning,” by A. B. Kasturiarachi, PRIMUS , Vol 7, No 2, Jan 1997, pp. 147-163. Abstract: “…The goal in this article is to demonstrate, based on the Academic Mastery Program (AMP) at Occidental College, how to incorporate collaborative learning into the mathematics curriculum. AMP is a program…[for]…freshman undergraduates…The structure of the program, we believe, minimizes the isolation of women, minorities, and borderline students by transforming each student’s contribution into the success of a group. We will describe in detail the format of the weekly two hour workshops, which are supervised by student facilitators. Issues such as student recruitment, hiring facilitators, and designing worksheets will also be discussed.”
• “ A Handbook for Mathematics Teaching Assistants ” by Tom Rishel, The MAA This handbook includes brief but helpful guidance on cooperative learning, writing assignments, and the active classroom, as well as links to further resources.
• “ Models in Algebra and Rhetoric: A New Approach to Integrating Writing and Mathematics in a WAC Learning Community ” by Ronald J. Heckelman and Will-Matthis Dunn III, Language and Learning Across the Disciplines 6(3) August 2003. This paper describes the integration of college algebra with rhetoric & writing in a team-teaching situation. “We make no claims that learning to do algebra or to write becomes “easier” as a result of the focus on models…Nevertheless, our students have demonstrated that yoking the two disciplines by focusing on models provides a powerful critical instrument…”
• “ The IMPlementation Center: Interactive Mathematics Program Resource Center “, The Interactive Mathematics Program (IMP) , Key Curriculum Press This website presents a “four-year program of problem-based mathematics that replaces the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus sequence…”
• “ Complex Instruction: Raising Achievement Through Group Worthy Tasks ,” NRICH enriching mathematics This website provides strategies for including groupwork in math classes successfully. Provides strategies for encouraging all members of the team to contribute, including choosing group-worthy tasks, assigning group roles, rewarding diverse contributions to groupwork, and enabling quieter students to contribute by raising their status within the group. Videos demonstrate these techniques. A workshop summary and discussion about Complex Instruction is on the blog Math Mama Writes… by Sue VanHattum.
• Engel, J. S., “ Students Questioning Students (SQS): a Technique to Invite Students’ Involvement ,”  Gifted Education International , September 1988, Vol. 5, No. 3, pp. 179-185. Secondary students teach the classes not via lecturing but via questioning their classmates. A video about SQS is also available.
• Huang, J. and B. Normandia, Students’ Perceptions on Communicating Mathematically: A Case Study of a Secondary Mathematics Classroom , The International Journal of Learning , 2009, Vol. 16, No. 5, pp.1-22.
• Huang, J. et al., “Communicating Mathematically: Comparison of Knowledge Structures in Teacher and Student Discourse in a Secondary Math Classroom,” Communication Education , Jan 2005, Vol. 54, No. 1, pp. 34-51. This is a study about students in a pre-calculus class whose teacher had them spend much of class time talking to one another about math content. Each student explains to his peers how he solved a math problem and then listens to his peers do the same.
• Improving Writing and Speaking Skills Using Mathematical Language ( ERIC record ) From the abstract: “A study investigated the effectiveness of an intervention for improving adolescent writing and speaking using mathematical language… [The intervention consisted of] journal writing, cooperative learning, and portfolio assessment. Results indicated that: (1) students’ attitudes toward writing and mathematics improved; (2) students’ understanding of mathematics improved; and (3) students showed an increase in their ability to talk mathematically.” Includes reviews of literature about including communication in math classrooms. Includes appendices with sample writing prompts for prealgebra and algebra.
• “Integrating Oral Presentation into Mathematics Teaching and Learning: An Exploratory Study with Singapore Secondary Students” by Fan Lianghuo & Yeo Shu Mei, from The Montana Mathematics Enthusiast , Monograph 3, October 2007 Festschrift in Honor of Guenter Toerner’s 60th Birthday , pp. 81-98.
• Johnson, D. W., & Johnson, R. T. (1990). “Using Cooperative Learning in Math.” In N. Davidson (Eds.) Cooperative Learning in Mathematics: A Handbook for Teachers . (pp. 103-125). Addison-Wesley Publishing.

Classroom Discussions: Using Math Talk to Help Students Learn, Grades K–6 , Second Edition by Suzanne H. Chapin, Catherine O’Connor, and Nancy Canavan Anderson “This best seller offers an unparalleled look at the significant role that classroom discussions can play in teaching mathematics and deepening students’ mathematical understanding.”

Communication assignments are often used as part of a strategy to reduce math anxiety, thus indirectly improving learning of mathematics. See the page of resources and research about using communication to reduce math anxiety .

Many teacher workshops address active forms of learning that involve students communicating about math. See, for example, the following opportunities:

• Academy of Inquiry-Based Learning workshops
• Park City Math Institute
• Please recommend additions to this list.

Although the various modes of active learning described above provide students with the opportunity to communicate mathematics, their effectiveness for learning mathematics likely depends on a variety of factors. Some relevant research is listed below.

• Prince, M., “ Does Active Learning Work? A Review of the Research ,” Journal of Engineering Education , July 2004, pp. 223-231.
• Laursen, S., et al., “ Evaluation of the IBL Mathematics Project: Student and Instructor Outcomes of Inquiry-Based Learning in College Mathematics : A Report Prepared for the Educational Advancement Foundation and the IBL Mathematics Centers,” Assessment and Evaluation Center for Inquiry Based Learning in Mathematics, April 2011. This study conducted by the Assessment and Evaluation Center for Inquiry Based Learning included over 100 course sections at four campuses across two academic years. “The approaches implemented at the IBL Mathematics Centers benefited students in multiple, profound, and perhaps lasting ways. Learning gains and attitudinal changes were especially positive for groups that are often under-served by traditional lecture-based approaches, including women and lower-achieving students. First-year and less mathematically experienced students also benefited particularly. Yet there was no evidence of negative consequences of IBL for men, high-achieving students, older and more experienced students: these groups too made gains greater than their non-IBL peers.” More publications from this study are available from the website of Ethnography and Evaluation Research at the University of Colorado, Boulder .
• Kirschner, P. A., et al., “ Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching ,” Educational Psychologist 41(2), 75-86, 2006. Abstract: “Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional designmodels that support guidance during instruction are briefly described.”
• Bressoud, D. M., “ The worst way to teach ,” Launchings , July 2011. This blog post summarizes some of the research that supports Halmos’ quote, “The best way to learn is to do; the worst way to teach is to talk,” or as Bressoud puts it, “Shut up and teach.”
• Brickman, P., et al., “ Effects of Inquiry-based Learning on Students’ Science Literacy Skills and Confidence ,” International Journal for the Scholarship of Teaching and Learning , Vol 3, No. 2, July 2009. From the abstract: “In this study, we demonstrated greater improvements in students’ science literacy and research skills using inquiry lab instruction. We also found that inquiry students gained self-confidence in scientific abilities, but traditional students’ gain was greater – likely indicating that the traditional curriculum promoted over-confidence. Inquiry lab students valued more authentic science exposure but acknowledged that experiencing the complexity and frustrations faced by practicing scientists was challenging, and may explain the widespread reported student resistance to inquiry curricula.”

Please suggest good research to add to this bibliography . Of greatest interest are literature reviews, meta-analyses, and studies of multiple courses and institutes, but any relevant research is welcome.

What is Math Comm

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Accessibility

8. Appendices

In the appendices you should include any data or material that supported your research but that was too long to include in the body of your paper. Materials in an appendix should be referenced at some point in the body of the report.

Some examples:

• If you wrote a computer program to generate more data than you could produce by hand, you should include the code and some sample output.

• If you collected statistical data using a survey, include a copy of the survey.

• If you have lengthy tables of numbers that you do not want to include in the body of your report, you can put them in an appendix.

Sample Write-Up

Seating unfriendly customers, a combinatorics problem.

By Lisa Honeyman February 12, 2002

The Problem

In a certain coffee shop, the customers are grouchy in the early morning and none of them wishes to sit next to another at the counter.

1. Suppose there are ten seats at the counter. How many different ways can three early morning customers sit at the counter so that no one sits next to anyone else?

2. What if there are n seats at the counter?

3. What if we change the number of customers?

4. What if, instead of a counter, there was a round table and people refused to sit next to each other?

Assumptions

I am assuming that the order in which the people sit matters. So, if three people occupy the first, third and fifth seats, there are actually 6 (3!) different ways they can do this. I will explain more thoroughly in the body of my report.

Body of the Report

At first there are 10 seats available for the 3 people to sit in. But once the first person sits down, that limits where the second person can sit. Not only can’t he sit in the now-occupied seat, he can’t sit next to it either. What confused me at first was that if the first person sat at one of the ends, then there were 8 seats left for the second person to chose from. But if the 1 st person sat somewhere else, there were only 7 remaining seats available for the second person. I decided to look for patterns. By starting with a smaller number of seats, I was able to count the possibilities more easily. I was hoping to find a pattern so I could predict how many ways the 10 people could sit without actually trying to count them all. I realized that the smallest number of seats I could have would be 5. Anything less wouldn’t work because people would have to sit next to each other. So, I started with 5 seats. I called the customers A, B, and C.

With 5 seats there is only one configuration that works.

As I said in my assumptions section, I thought that the order in which the people sit is important. Maybe one person prefers to sit near the coffee maker or by the door. These would be different, so I decided to take into account the different possible ways these 3 people could occupy the 3 seats shown above. I know that ABC can be arranged in 3! = 6 ways. (ABC, ACB, BAC, BCA, CAB, CBA). So there are 6 ways to arrange 3 people in 5 seats with spaces between them. But, there is only one configuration of seats that can be used. (The 1 st , 3 rd , and 5 th ).

Next, I tried 6 seats. I used a systematic approach to show that there are 4 possible arrangements of seats. This is how my systematic approach works:

Assign person A to the 1 st seat. Put person B in the 3 rd seat, because he can’t sit next to person A. Now, person C can sit in either the 5 th or 6 th positions. (see the top two rows in the chart, below.) Next suppose that person B sits in the 4 th seat (the next possible one to the right.) That leaves only the 6 th seat free for person C. (see row 3, below.) These are all the possible ways for the people to sit if the 1 st seat is used. Now put person A in the 2 nd seat and person B in the 4 th . There is only one place where person C can sit, and that’s in the 6 th position. (see row 4, below.) There are no other ways to seat the three people if person A sits in the 2 nd seat. So, now we try putting person A in the 3 rd seat. If we do that, there are only 4 seats that can be used, but we know that we need at least 5, so there are no more possibilities.

Possible seats 3 people could occupy if there are 6 seats

Once again, the order the people sit in could be ABC, BAC, etc. so there are 4 * 6 = 24 ways for the 3 customers to sit in 6 seats with spaces between them.

I continued doing this, counting how many different groups of seats could be occupied by the three people using the systematic method I explained. Then I multiplied that number by 6 to account for the possible permutations of people in those seats. I created the following table of what I found.

Next I tried to come up with a formula. I decided to look for a formula using combinations or permutations. Since we are looking at 3 people, I decided to start by seeing what numbers I would get if I used n C 3 and n P 3 .

3 C 3 = 1   4 C 3 = 4   5 C 3 = 10   6 C 3 = 20

3 P 3 = 6   4 P 3 = 24   5 P 3 = 60   6 P 3 = 120

Surprisingly enough, these numbers matched the numbers I found in my table. However, the n in n P r and n C r seemed to be two less than the total # of seats I was investigating. 

Conjecture 1:

Given n seats at a lunch counter, there are n -2 C 3 ways to select the three seats in which the customers will sit such that no customer sits next to another one. There are n -2 P 3 ways to seat the 3 customers in such a way than none sits next to another.

After I found a pattern, I tried to figure out why n -2 C 3 works. (If the formula worked when order didn’t matter it could be easily extended to when the order did, but the numbers are smaller and easier to work with when looking at combinations rather than permutations.)

In order to prove Conjecture 1 convincingly, I need to show two things:

(1) Each n – 2 seat choice leads to a legal n seat configuration.

(2) Each n seat choice resulted from a unique n – 2 seat configuration.

To prove these two things I will show

And then conclude that these two procedures are both functions and therefore 1—1.

Claim (1): Each ( n – 2) -seat choice leads to a legal n seat configuration.

Suppose there were only n – 2 seats to begin with. First we pick three of them in which to put people, without regard to whether or not they sit next to each other. But, in order to guarantee that they don’t end up next to another person, we introduce an empty chair to the right of each of the first two people. It would look like this:

We don’t need a third “new” seat because once the person who is farthest to the right sits down, there are no more customers to seat. So, we started with n – 2 chairs but added two for a total of n chairs. Anyone entering the restaurant after this procedure had been completed wouldn’t know that there had been fewer chairs before these people arrived and would just see three customers sitting at a counter with n chairs. This procedure guarantees that two people will not end up next to each other. Thus, each ( n – 2)-seat choice leads to a unique, legal n seat configuration.

Therefore, positions s 1 ' s 2 ', and s 3 ' are all separated by at least one vacant seat.

This is a function that maps each combination of 3 seats selected from n – 2 seats onto a unique arrangement of n seats with 3 separated customers. Therefore, it is invertible.

Claim (2): Each 10-seat choice has a unique 8-seat configuration.

Given a legal 10-seat configuration, each of the two left-most diners must have an open seat to his/her right. Remove it and you get a unique 8-seat arrangement. If, in the 10-seat setting, we have q 1 > q 2 , q 3 ; q 3 – 1 > q 2 , and q 2 – 1 > q 1 , then the 8 seat positions are q 1 ' = q 2 , q 2 ' = q 2 – 1, and q 3 ' = q 3 – 2. Combining these equations with the conditions we have

q 2 ' = q 2 – 1 which implies q 2 ' > q 1 = q 1 '

q 3 ' = q 3 – 2 which implies q 3 ' > q 2 – 1 = q 2 '

Since q 3 ' > q 2 ' > q 1 ', these seats are distinct. If the diners are seated in locations q 1 , q 2 , and q 3 (where q 3 – 1 > q 2 and q 2 – 1 > q 1 ) and we remove the two seats to the right of q 1 and q 2 , then we can see that the diners came from q 1 , q 2 – 1, and q 3 – 2. This is a function that maps a legal 10-seat configuration to a unique 8-seat configuration.

The size of a set can be abbreviated s ( ). I will use the abbreviation S to stand for n separated seats and N to stand for the n – 2 non-separated seats.

therefore s ( N ) = s ( S ).

Because the sets are the same size, these functions are 1—1.

Using the technique of taking away and adding empty chairs, I can extend the problem to include any number of customers. For example, if there were 4 customers and 10 seats there would be 7 C 4 = 35 different combinations of chairs to use and 7 P 4 = 840 ways for the customers to sit (including the fact that order matters). You can imagine that three of the ten seats would be introduced by three of the customers. So, there would only be 7 to start with.

In general, given n seats and c customers, we remove c- 1 chairs and select the seats for the c customers. This leads to the formula n -( c -1) C c = n - c +1 C c for the number of arrangements.

Once the number of combinations of seats is found, it is necessary to multiply by c ! to find the number of permutations. Looking at the situation of 3 customers and using a little algebraic manipulation, we get the n P 3 formula shown below.

This same algebraic manipulation works if you have c people rather than 3, resulting in n - c +1 P c

Answers to Questions

• With 10 seats there are 8 P 3 = 336 ways to seat the 3 people.
• My formula for n seats and 3 customers is: n -2 P 3 .
• My general formula for n seats and c customers, is: n -( c -1) P c = n - c +1 P c

_________________________________________________________________ _

After I finished looking at this question as it applied to people sitting in a row of chairs at a counter, I considered the last question, which asked would happen if there were a round table with people sitting, as before, always with at least one chair between them.

I went back to my original idea about each person dragging in an extra chair that she places to her right, barring anyone else from sitting there. There is no end seat, so even the last person needs to bring an extra chair because he might sit to the left of someone who has already been seated. So, if there were 3 people there would be 7 seats for them to choose from and 3 extra chairs that no one would be allowed to sit in. By this reasoning, there would be 7 C 3 = 35 possible configurations of chairs to choose and 7 P 3 = 840 ways for 3 unfriendly people to sit at a round table.

Conjecture 2: Given 3 customers and n seats there are n -3 C 3 possible groups of 3 chairs which can be used to seat these customers around a circular table in such a way that no one sits next to anyone else.

My first attempt at a proof: To test this conjecture I started by listing the first few numbers generated by my formula:

When n = 6    6-3 C 3 = 3 C 3 = 1

When n = 7    7-3 C 3 = 4 C 3 = 4

When n = 8    8-3 C 3 = 5 C 3 = 10

When n = 9    9-3 C 3 = 6 C 3 = 20

Then I started to systematically count the first few numbers of groups of possible seats. I got the numbers shown in the following table. The numbers do not agree, so something is wrong — probably my conjecture!

I looked at a circular table with 8 people and tried to figure out the reason this formula doesn’t work. If we remove 3 seats (leaving 5) there are 10 ways to select 3 of the 5 remaining chairs. ( 5 C 3 ).

The circular table at the left in the figure below shows the n – 3 (in this case 5) possible chairs from which 3 will be randomly chosen. The arrows point to where the person who selects that chair could end up. For example, if chair A is selected, that person will definitely end up in seat #1 at the table with 8 seats. If chair B is selected but chair A is not, then seat 2 will end up occupied. However, if chair A and B are selected, then the person who chose chair B will end up in seat 3 . The arrows show all the possible seats in which a person who chose a particular chair could end. Notice that it is impossible for seat #8 to be occupied. This is why the formula 5 C 3 doesn’t work. It does not allow all seats at the table of 8 to be chosen.

The difference is that in the row-of-chairs-at-a-counter problem there is a definite “starting point” and “ending point.” The first chair can be identified as the one farthest to the left, and the last one as the one farthest to the right. These seats are unique because the “starting point” has no seat to the left of it and the “ending point” has no seat to its right. In a circle, it is not so easy.

Using finite differences I was able to find a formula that generates the correct numbers:

Proof: We need to establish a “starting point.” This could be any of the n seats. So, we select one and seat person A in that seat. Person B cannot sit on this person’s left (as he faces the table), so we must eliminate that as a possibility. Also, remove any 2 other chairs, leaving ( n – 4) possible seats where the second person can sit. Select another seat and put person B in it. Now, select any other seat from the ( n – 5) remaining seats and put person C in that. Finally, take the two seats that were previously removed and put one to the left of B and one to the left of C.

The following diagram should help make this procedure clear.

In a manner similar to the method I used in the row-of-chairs-at-a-counter problem, this could be proven more rigorously.

An Idea for Further Research:

Consider a grid of chairs in a classroom and a group of 3 very smelly people. No one wants to sit adjacent to anyone else. (There would be 9 empty seats around each person.) Suppose there are 16 chairs in a room with 4 rows and 4 columns. How many different ways could 3 people sit? What if there was a room with n rows and n columns? What if it had n rows and m columns?

References:

Abrams, Joshua. Education Development Center, Newton, MA. December 2001 - February 2002. Conversations with my mathematics mentor.

Brown, Richard G. 1994. Advanced Mathematics . Evanston, Illinois. McDougal Littell Inc. pp. 578-591

The Oral Presentation

Giving an oral presentation about your mathematics research can be very exciting! You have the opportunity to share what you have learned, answer questions about your project, and engage others in the topic you have been studying. After you finish doing your mathematics research, you may have the opportunity to present your work to a group of people such as your classmates, judges at a science fair or other type of contest, or educators at a conference. With some advance preparation, you can give a thoughtful, engaging talk that will leave your audience informed and excited about what you have done.

Planning for Your Oral Presentation

In most situations, you will have a time limit of between 10 and 30 minutes in which to give your presentation. Based upon that limit, you must decide what to include in your talk. Come up with some good examples that will keep your audience engaged. Think about what vocabulary, explanations, and proofs are really necessary in order for people to understand your work. It is important to keep the information as simple as possible while accurately representing what you’ve done. It can be difficult for people to understand a lot of technical language or to follow a long proof during a talk. As you begin to plan, you may find it helpful to create an outline of the points you want to include. Then you can decide how best to make those points clear to your audience.

You must also consider who your audience is and where the presentation will take place. If you are going to give your presentation to a single judge while standing next to your project display, your presentation will be considerably different than if you are going to speak from the stage in an auditorium full of people! Consider the background of your audience as well. Is this a group of people that knows something about your topic area? Or, do you need to start with some very basic information in order for people to understand your work? If you can tailor your presentation to your audience, it will be much more satisfying for them and for you.

No matter where you are presenting your speech and for whom, the structure of your presentation is very important. There is an old bit of advice about public speaking that goes something like this: “Tell em what you’re gonna tell ’em. Tell ’em. Then tell ’em what you told ’em.” If you use this advice, your audience will find it very easy to follow your presentation. Get the attention of the audience and tell them what you are going to talk about, explain your research, and then following it up with a re-cap in the conclusion.

Writing Your Introduction

Your introduction sets the stage for your entire presentation. The first 30 seconds of your speech will either capture the attention of your audience or let them know that a short nap is in order. You want to capture their attention. There are many different ways to start your speech. Some people like to tell a joke, some quote famous people, and others tell stories.

Here are a few examples of different types of openers.

You can use a quote from a famous person that is engaging and relevant to your topic. For example:

• Benjamin Disraeli once said, “There are three kinds of lies: lies, damn lies, and statistics.” Even though I am going to show you some statistics this morning, I promise I am not going to lie to you! Instead, . . .

• The famous mathematician, Paul Erdös, said, “A Mathematician is a machine for turning coffee into theorems.” Today I’m here to show you a great theorem that I discovered and proved during my mathematics research experience. And yes, I did drink a lot of coffee during the project!

• According to Stephen Hawking, “Equations are just the boring part of mathematics.” With all due respect to Dr. Hawking, I am here to convince you that he is wrong. Today I’m going to show you one equation that is not boring at all!

Some people like to tell a short story that leads into their discussion.

“Last summer I worked at a diner during the breakfast shift. There were 3 regular customers who came in between 6:00 and 6:15 every morning. If I tell you that you didn’t want to talk to these folks before they’ve had their first cup of coffee, you’ll get the idea of what they were like. In fact, these people never sat next to each other. That’s how grouchy they were! Well, their anti-social behavior led me to wonder, how many different ways could these three grouchy customers sit at the breakfast counter without sitting next to each other? Amazingly enough, my summer job serving coffee and eggs to grouchy folks in Boston led me to an interesting combinatorics problem that I am going to talk to you about today.”

A short joke related to your topic can be an engaging way to start your speech.

It has been said that there are three kinds of mathematicians: those who can count and those who can’t.

All joking aside, my mathematics research project involves counting. I have spent the past 8 weeks working on a combinatorics problem.. . .

To find quotes to use in introductions and conclusions try: http://www.quotationspage.com/

To find some mathematical quotes, consult the Mathematical Quotation Server: http://math.furman.edu/~mwoodard/mquot.html

To find some mathematical jokes, you can look at the “Profession Jokes” web site: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

There is a collection of math jokes compiled by the Canadian Mathematical Society at http://camel.math.ca/Recreation/

After you have the attention of your audience, you must introduce your research more formally. You might start with a statement of the problem that you investigated and what lead you to choose that topic. Then you might say something like this,

“Today I will demonstrate how I came to the conclusion that there are n ( n  – 4)( n  – 5) ways to seat 3 people at a circular table with n seats in such a way that no two people sit next to each other. In order to do this I will first explain how I came up with this formula and then I will show you how I proved it works. Finally, I will extend this result to tables with more than 3 people sitting at them.”

By providing a brief outline of your talk at the beginning and reminding people where you are in the speech while you are talking, you will be more effective in keeping the attention of your audience. It will also make it much easier for you to remember where you are in your speech as you are giving it.

The Middle of Your Presentation

Because you only have a limited amount of time to present your work, you need to plan carefully. Decide what is most important about your project and what you want people to know when you are finished. Outline the steps that people need to follow in order to understand your research and then think carefully about how you will lead them through those steps. It may help to write your entire speech out in advance. Even if you choose not to memorize it and present it word for word, the act of writing will help you clarify your ideas. Some speakers like to display an outline of their talk throughout their entire presentation. That way, the audience always knows where they are in the presentation and the speaker can glance at it to remind him or herself what comes next.

An oral presentation must be structured differently than a written one because people can’t go back and “re-read” a complicated section when they are at a talk. You have to be extremely clear so that they can understand what you are saying the first time you say it. There is an acronym that some presenters like to remember as they prepare a talk: “KISS.” It means, “Keep It Simple, Student.” It may sound silly, but it is good advice. Keep your sentences short and try not to use too many complicated words. If you need to use technical language, be sure to define it carefully. If you feel that it is important to present a proof, remember that you need to keep things easy to understand. Rather than going through every step, discuss the main points and the conclusion. If you like, you can write out the entire proof and include it in a handout so that folks who are interested in the details can look at them later. Give lots of examples! Not only will examples make your talk more interesting, but they will also make it much easier for people to follow what you are saying.

It is useful to remember that when people have something to look at, it helps to hold their attention and makes it easier for them to understand what you are saying. Therefore, use lots of graphs and other visual materials to support your work. You can do this using posters, overhead transparencies, models, or anything else that helps make your explanations clear.

Using Materials

As you plan for your presentation, consider what equipment or other materials you might want use. Find out what is available in advance so you don’t spend valuable time creating materials that you will not be able to use. Common equipment used in talks include an over-head projector, VCR, computer, or graphing calculator. Be sure you know how to operate any equipment that you plan to use. On the day of your talk, make sure everything is ready to go (software loaded, tape at the right starting point etc.) so that you don’t have “technical difficulties.”

Visual aides can be very useful in a presentation. (See Displaying Your Results for details about poster design.) If you are going to introduce new vocabulary, consider making a poster with the words and their meanings to display throughout your talk. If people forget what a term means while you are speaking, they can refer to the poster you have provided. (You could also write the words and meanings on a black/white board in advance.) If there are important equations that you would like to show, you can present them on an overhead transparency that you prepare prior to the talk. Minimize the amount you write on the board or on an overhead transparency during your presentation. It is not very engaging for the audience to sit watching while you write things down. Prepare all equations and materials in advance. If you don’t want to reveal all of what you have written on your transparency at once, you can cover up sections of your overhead with a piece of paper and slide it down the page as you move along in your talk. If you decide to use overhead transparencies, be sure to make the lettering large enough for your audience to read. It also helps to limit how much you put on your transparencies so they are not cluttered. Lastly, note that you can only project approximately half of a standard 8.5" by 11" page at any one time, so limit your information to displays of that size.

Presenters often create handouts to give to members of the audience. Handouts may include more information about the topic than the presenter has time to discuss, allowing listeners to learn more if they are interested. Handouts may also include exercises that you would like audience members to try, copies of complicated diagrams that you will display, and a list of resources where folks might find more information about your topic. Give your audience the handout before you begin to speak so you don’t have to stop in the middle of the talk to distribute it. In a handout you might include:

• A proof you would like to share, but you don’t have time to present entirely.

• Copies of important overhead transparencies that you use in your talk.

• Diagrams that you will display, but which may be too complicated for someone to copy down accurately.

• Resources that you think your audience members might find useful if they are interested in learning more about your topic.

The Conclusion

Ending your speech is also very important. Your conclusion should leave the audience feeling satisfied that the presentation was complete. One effective way to conclude a speech is to review what you presented and then to tie back to your introduction. If you used the Disraeli quote in your introduction, you might end by saying something like,

I hope that my presentation today has convinced you that . . . Statistical analysis backs up the claims that I have made, but more importantly, . . . . And that’s no lie!

Getting Ready

After you have written your speech and prepared your visuals, there is still work to be done.

• Prepare your notes on cards rather than full-size sheets of paper. Note cards will be less likely to block your face when you read from them. (They don’t flop around either.) Use a large font that is easy for you to read. Write notes to yourself on your notes. Remind yourself to smile or to look up. Mark when to show a particular slide, etc.
• Practice! Be sure you know your speech well enough that you can look up from your notes and make eye contact with your audience. Practice for other people and listen to their feedback.
• Time your speech in advance so that you are sure it is the right length. If necessary, cut or add some material and time yourself again until your speech meets the time requirements. Do not go over time!
• Anticipate questions and be sure you are prepared to answer them.
• Make a list of all materials that you will need so that you are sure you won’t forget anything.
• If you are planning to provide a handout, make a few extras.
• If you are going to write on a whiteboard or a blackboard, do it before starting your talk.

The Delivery

How you deliver your speech is almost as important as what you say. If you are enthusiastic about your presentation, it is far more likely that your audience will be engaged. Never apologize for yourself. If you start out by saying that your presentation isn’t very good, why would anyone want to listen to it? Everything about how you present yourself will contribute to how well your presentation is received. Dress professionally. And don’t forget to smile!

Here are a few tips about delivery that you might find helpful.

• Make direct eye contact with members of your audience. Pick a person and speak an entire phrase before shifting your gaze to another person. Don’t just “scan” the audience. Try not to look over their heads or at the floor. Be sure to look at all parts of the room at some point during the speech so everyone feels included.
• Speak loudly enough for people to hear and slowly enough for them to follow what you are saying.
• Do not read your speech directly from your note cards or your paper. Be sure you know your speech well enough to make eye contact with your audience. Similarly, don’t read your talk directly off of transparencies.
• Avoid using distracting or repetitive hand gestures. Be careful not to wave your manuscript around as you speak.
• Move around the front of the room if possible. On the other hand, don’t pace around so much that it becomes distracting. (If you are speaking at a podium, you may not be able to move.)
• Keep technical language to a minimum. Explain any new vocabulary carefully and provide a visual aide for people to use as a reference if necessary.
• Be careful to avoid repetitive space-fillers and slang such as “umm”, “er”, “you know”, etc. If you need to pause to collect your thoughts, it is okay just to be silent for a moment. (You should ask your practice audiences to monitor this habit and let you know how you did).
• Leave time at the end of your speech so that the audience can ask questions.

Displaying Your Results

When you create a visual display of your work, it is important to capture and retain the attention of your audience. Entice people to come over and look at your work. Once they are there, make them want to stay to learn about what you have to tell them. There are a number of different formats you may use in creating your visual display, but the underlying principle is always the same: your work should be neat, well-organized, informative, and easy to read.

It is unlikely that you will be able to present your entire project on a single poster or display board. So, you will need to decide which are the most important parts to include. Don’t try to cram too much onto the poster. If you do, it may look crowded and be hard to read! The display should summarize your most important points and conclusions and allow the reader to come away with a good understanding of what you have done.

A good display board will have a catchy title that is easy to read from a distance. Each section of your display should be easily identifiable. You can create posters such as this by using headings and also by separating parts visually. Titles and headings can be carefully hand-lettered or created using a computer. It is very important to include lots of examples on your display. It speeds up people’s understanding and makes your presentation much more effective. The use of diagrams, charts, and graphs also makes your presentation much more interesting to view. Every diagram or chart should be clearly labeled. If you include photographs or drawings, be sure to write captions that explain what the reader is looking at.

In order to make your presentation look more appealing, you will probably want to use some color. However, you must be careful that the color does not become distracting. Avoid florescent colors, and avoid using so many different colors that your display looks like a patch-work quilt. You want your presentation to be eye-catching, but you also want it to look professional.

People should be able to read your work easily, so use a reasonably large font for your text. (14 point is a recommended minimum.) Avoid writing in all-capitals because that is much harder to read than regular text. It is also a good idea to limit the number of different fonts you use on your display. Too many different fonts can make your poster look disorganized.

Notice how each section on the sample poster is defined by the use of a heading and how the various parts of the presentation are displayed on white rectangles. (Some of the rectangles are blank, but they would also have text or graphics on them in a real presentation.) Section titles were made with pale green paper mounted on red paper to create a boarder. Color was used in the diagrams to make them more eye-catching. This poster would be suitable for hanging on a bulletin board.

If you are planning to use a poster, such as this, as a visual aid during an oral presentation, you might consider backing your poster with foam-core board or corrugated cardboard. A strong board will not flop around while you are trying to show it to your audience. You can also stand a stiff board on an easel or the tray of a classroom blackboard or whiteboard so that your hands will be free during your talk. If you use a poster as a display during an oral presentation, you will need to make the text visible for your audience. You can create a hand-out or you can make overhead transparencies of the important parts. If you use overhead transparencies, be sure to use lettering that is large enough to be read at a distance when the text is projected.

If you are preparing your display for a science fair, you will probably want to use a presentation board that can be set up on a table. You can buy a pre-made presentation board at an office supply or art store or you can create one yourself using foam-core board. With a presentation board, you can often use the space created by the sides of the board by placing a copy of your report or other objects that you would like people to be able to look at there. In the illustration, a black trapezoid was cut out of foam-core board and placed on the table to make the entire display look more unified. Although the text is not shown in the various rectangles in this example, you will present your information in spaces such as these.

Don’t forget to put your name on your poster or display board. And, don’t forget to carefully proof-read your work. There should be no spelling, grammatical or typing mistakes on your project. If your display is not put together well, it may make people wonder about the quality of the work you did on the rest of your project.

For more information about creating posters for science fair competitions, see

http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

http://www.siemens-foundation.org/science/poster_guidelines.htm ,

Robert Gerver’s book, Writing Math Research Papers , (published by Key Curriculum Press) has an excellent section about doing oral presentations and making posters, complete with many examples.

References Used

American Psychological Association . Electronic reference formats recommended by the American Psychological Association . (2000, August 22). Washington, DC: American Psychological Association. Retrieved October 6, 2000, from the World Wide Web: http://www.apastyle.org/elecsource.html

Bridgewater State College. (1998, August 5 ). APA Style: Sample Bibliographic Entries (4th ed) . Bridgewater, MA: Clement C. Maxwell Library. Retrieved December 20, 2001, from the World Wide Web: http://www.bridgew.edu/dept/maxwell/apa.htm

Crannell, Annalisa. (1994). A Guide to Writing in Mathematics Classes . Franklin & Marshall College. Retrieved January 2, 2002, from the World Wide Web: http://www.fandm.edu/Departments/Mathematics/writing_in_math/guide.html

Gerver, Robert. 1997. Writing Math Research Papers . Berkeley, CA: Key Curriculum Press.

Moncur, Michael. (1994-2002 ). The Quotations Page . Retrieved April 9, 2002, from the World Wide Web: http://www.quotationspage.com/

Public Speaking -- Be the Best You Can Be . (2002). Landover, Hills, MD: Advanced Public Speaking Institute. Retrieved April 9, 2002, from the World Wide Web: http://www.public-speaking.org/

Recreational Mathematics. (1988) Ottawa, Ontario, Canada: Canadian Mathematical Society. Retrieved April 9, 2002, from the World Wide Web: http://camel.math.ca/Recreation/

Shay, David. (1996). Profession Jokes — Mathematicians. Retrieved April 5, 2001, from the World Wide Web: http://www.geocities.com/CapeCanaveral/4661/projoke22.htm

Sieman’s Foundation. (2001). Judging Guidelines — Poster . Retrieved April 9, 2002, from the World Wide Web: http://www.siemens-foundation.org/science/poster_guidelines.htm ,

VanCleave, Janice. (1997). Science Fair Handbook. Discovery.com. Retrieved April 9, 2002, from the World Wide Web: http://school.discovery.com/sciencefaircentral/scifairstudio/handbook/display.html ,

Woodward, Mark. (2000) . The Mathematical Quotations Server . Furman University. Greenville, SC. Retrieved April 9, 2002, from the World Wide Web: http://math.furman.edu/~mwoodard/mquot.html

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Math Lesson Powerpoint Template

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Math Lesson Presentation Free PowerPoint template and Google Slides theme

Math is incredibly important in our lives, and without realizing it, we use mathematical concepts and the skills we learn from math problems every day.Mathematics is one of the first subjects offered in school. If you are a teacher, need a presentation for the classroom and you want to make it more interesting for your students, this math lesson plan template is for you.

Math Lesson

Education can also be fun, which is why we decided to use a color palette for slides, including blue and cream. Illustrations are usually very visual, so we added some illustrations, but it was essential to avoid distractions during the course, so we made sure that the illustrations did not distract from the actual information. The background is pleasant and combines well with the graphical elements associated with algebra, trigonometric functions, formulas and complex Numbers. With typography, your course won’t miss anything, so let’s emphasize how powerful sans-serif fonts can be for headings. Great for large sizes, so the “teacher can’t see anything” excuse is no longer valid here! With Slidesgo’s help, there are no problems to solve, so get creative and calculate success rates!

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22 Examples of Mathematics in Everyday Life

Let’s read further to know the real-life situations where maths is applied.

1. Making Routine Budgets

How much should I spend today? When I will be able to buy a new car? Should I save more? How will I be able to pay my EMIs? Such thoughts usually come into our minds. The simple answer to such type of question is maths. We prepare budgets based on simple calculations with the help of simple mathematical concepts. So, we can’t say, I am not going to study maths ever! Everything which is going around us is somehow related to maths only.

Application: 

• Basic mathematical operations (addition, subtraction, multiplication, and division)
• Calculation of percentage
• Arithmetic calculations

2. Construction Purpose

You know what, maths is the basis of any construction work. A lot of calculations, preparations of budgets, setting targets, estimating the cost, etc., are all done based on maths. If you don’t believe it, ask any contractor or construction worker, and they will explain as to how important maths is for carrying out all the construction work.

Application:

• Preparing budgets
• Taking measurements
• Estimating the cost and profit
• Calculus and Statistics
• Trigonometry

3. Exercising and Training

I should reduce some body fat! Will I be able to achieve my dream body ever? How? When? Will I be able to gain muscles? Here, the simple concept that is followed is maths. Yes! based on simple mathematical concepts, we can answer to above-mentioned questions. We set our routine according to our workout schedule, count the number of repetitions while exercising, etc., just based on maths.

• Basic Mathematical Operations (additions, subtraction, multiplication, and division)
• Logical and Analogical Reasoning

4. Interior Designing

Interior designing seems to be a fun and interesting career but, do you know the exact reality? A lot of mathematical concepts, calculations, budgets, estimations, targets, etc., are to be followed to excel in this field. Interior designers plan the interiors based on area and volume calculations to calculate and estimate the proper layout of any room or building. Such concepts form an important part of maths.

• Ratios and Percentages
• Mathematical Operations

5. Fashion Designing

Just like interior design, maths is also an essential concept of fashion design. From taking measurements, estimating the quantity and quality of clothes, choosing the color theme, and estimating the cost and profit, to producing cloth according to the needs and tastes of the customers, maths is followed at every stage.

• Basic Mathematical Operations
• Rations and Percentages

6. Shopping at Grocery Stores and Supermarkets

The most obvious place where you would see the application of basic mathematical concepts is your neighborhood grocery store and supermarket. The schemes like ‘Flat 50% off, ‘Buy one get one free, etc., are seen in most of the stores. Customers visit the stores, see such schemes, estimate the quantity to be bought, the weight, the price per unit, discount calculations, and finally the total price of the product, and buy it. The calculations are done based on basic mathematical concepts. Thus, here also, maths forms an important part of our daily routine.

• Ratio and Percentage

7. Cooking and Baking

In your kitchen also, the maths is performed. For cooking or baking anything, a series of steps are followed, telling us how much of the quantity is to be used for cooking, the proportion of different ingredients, methods of cooking, the cookware to be used, and many more. Such are based on different mathematical concepts. Indulging children in the kitchen while cooking anything, is a fun way to explain maths as well as basic cooking methods.

• Mathematical Algorithm
• Ratios and Proportions

Maths improves the cognitive and decision-making skills of a person. Such skills are very important for a sportsperson because by this he can take the right decisions for his team. If a person lacks such abilities, he won’t be able to make correct estimations. So, maths also forms an important part of the sports field.

• Probability
• Mathematical Operations and Algorithm
• Logical Reasoning
• Game Theory

9.  Management of Time

Now managing time is one of the most difficult tasks which is faced by a lot of people. An individual wants to complete several assignments in a limited time. Not only the management, but some people also are not even able to read the timings on an analog clock. Such problems can be solved only by understanding the basic concepts of maths. Maths not only helps us to understand the management of time but also to value it.

10. Driving

‘Speed, Time, and Distance’ are all these three things that are studied in mathematical subjects, which are the basics of driving irrespective of any mode of transportation. Maths helps us to answer the following question;

• How much should be the speed to cover any particular distance?
• How much time would be taken?
• Whether to turn left or right?
• When to stop the car?
• When to increase or decrease the speed?
• Logical reasoning
• Numerical Reasoning

11. Automobiles Industry

The different car manufacturing companies produce cars based on the demands of the customers. Every company has its category of cars ranging from microcars to luxury SUVs. In such companies, basic mathematical operations are being applied to gain knowledge about the different demands of the customers.

12. Computer Applications

Ever wondered how a computer works? How easily it completes every task in a proper series of actions? The simple reason for this is the application of maths. The fields of mathematics and computing intersect both in computer science. The study of computer applications is next to impossible without maths. Concepts like computation, algorithms and many more forms the base for different computer applications like PowerPoint, word, excel, etc. are impossible to run without maths.

Applications:

• Computation
• Coding Methods
• Cryptography

13. Planning a Trip

We all are bored with our monotonous life and we wish to go on long vacations. For this, we have to plan things accordingly. We need to prepare the budget for the trip, the number of days, the destinations, and hotels adjust our other work accordingly, and many more. Here comes the role of maths. Basic mathematical concepts and operations are required to be followed to plan a successful trip.

14. Hospitals

Every Hospital has to make the schedule the timings of the doctors available, the systematic methods of conducting any major surgery, keeping the records of the patients, records of the success rate of surgeries, number of ambulances required, training for the use of medicines to nurses, prescriptions, and scheduling all tasks, etc. All these are done based on Mathematical concepts.

• Body Mass Index

15. Video Games

Playing video games is one of the most favorite entertainment activities done all over the world, irrespective of the fact that whether you are a kid or an adult. Students usually skip their maths classes to play video games. But, do you know here also they are learning maths? Here, they learn about the different steps and techniques to be followed to win any game. Not only while playing, but the engineers who introduce different games for people also follow the different mathematical concepts.

16. Weather Forecasting

The weather forecasting is all done based on the probability concept of maths. Through this, we get to know about the weather conditions like whether it’s going to be a sunny day or rainfall will come So, next time you plan your outing, don’t forget to see the weather forecasting.

Application:    

17. Base of Other Subjects

Though maths is itself a unique subject. But, you would be surprised to know that it forms the base for every subject. The subjects like physics, chemistry, economics, history, accountancy, and statistics every subject is based upon maths. So, next time you say, “I’m not going to study this maths subject ever!” remember, this subject will not going to leave you ever.

• Operations Research
• Linear Programming

18. Music and Dance

Listening to music and dancing is one of the most common hobbies of children. Here also, they learn maths while singing and learning different dance steps. Coordination in any dance can be gained by simple mathematical steps.

19. Manufacturing Industry

The part of maths called ‘Operations Research is an important concept that is being followed at every manufacturing unit. This concept of maths gives the manufacturer a simple idea of performing several tasks under the manufacturing unit like,

• What quantity is to be produced?
• What methods are to be followed?
• How to increase production?
• How the cost of production can be reduced?
• Removing unnecessary tasks.
• Following methods like target costing, ABC costing, cost-profit budgeting, and many more.
• Ratios and Probability

20. Planning of Cities

Urban planning includes the concepts of budgeting, planning, setting targets, and many more which all forms part of mathematics. No activity is possible without maths.

21. Problem-solving skills

Problem-solving skills are one of the most important skills which every individual should possess to be successful in life. Such skills help the individual in taking correct decisions in life, let it be professional or personal. This is all done when the person has the correct knowledge of basic mathematical concepts.

• Mathematical Reasoning

22. Marketing

The marketing agencies make the proper plans as to how to promote any product or service. The tasks like promoting a product online, use of social media platforms, following different methods of direct and indirect marketing, door-to-door sales, sending e-mails, making calls, and providing several schemes like ‘Buy one get one free, ‘Flat 50% off, offering discounts on special occasions, etc. are all done based on simple mathematical concepts. Thus, maths is present everywhere.

• Percentages
• Mathematical Operations  

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16 comments.

very good and rare found examples are here to be learned here.

Really informative and knowledgeable

I never realized how much math we use every day.

Example of cost

It nice and great! Idea

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Math Lesson Infographics

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Numbers, they're all over the place! Math is the quintessential subject in school. Did you enjoy the Math Lesson template we've created some time ago? Now, to take it to the next level, you can download this set of editable infographics and turn them into new content for your presentation! Since they've been designed to be combined, the typography is the same and the variety of colors is also present. Need some thematic icons? Because we have them too!

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