7 Oct 2016
The Signal and the Noise, by Nate Silver, is a book about statistical predictions and forecasts. The primary question of the book is: how do we make predictions that capture more signal and less noise in a data set? This theme is similar to N. N. Taleb’s project in Anti-Fragile: how do we make decisions in a world we can’t fully understand? Silver’s answer to these questions involve a combination of empirical observations, statistical analysis that is appropriate to the data and question under review, and an answer that provides as precise and accurate a prediction about future events as possible. Avoiding overconfidence, over-fitting one’s model to the data set, and making too vague a prediction due to insufficient analysis are mistakes that Silver recommends we avoid.
One way to make better predictions is to use Bayes’s Theorem: (xy)/(xy+z(1-x))
f(x) = ————
xy + z(1-x)
This theorem states that the posterior probability, f(x’), which is the probability of an event, x’, occurring after we’ve considered some previous evidence, x, y, & z. x is the initial estimate of the event occurring independent of any evidence. y is the probability of an event occurring if x is true. z is the probability of an event occurring if x is false.
For example, if you find a pair of underwear in your dresser drawer that does not belong to you or your spouse, and you suspect your spouse of cheating on you, one way you could use Bayes’s Theorem to produce a probabilistic prediction about the likelihood of your spouse cheating on you is as follows:
x, the initial estimate that your spouse is cheating — 4% (which is the national average of men cheating on their wives)
y, the probability of underwear appearing if he is cheating — 50% (essentially random, even odds)
z, the probability of underwear appearing if he is not cheaing on you — 5% (is there some other, innocent explanation for the underwear’s appearance?
Using Bayes’s Theorem, our prediction that our spouse is cheating on us goes from 4% to 29%:
f(x’) = (.04 x .5) / ((.04 x .5) + .05(1-.04))
f(x’) = .02 / (.02 + .048)
f(x’) = .2941
Silver’s analysis of predictions and forecasts echoes that of Taleb in Anti-Fragile. Both claim that financial analysts are generally over confident in their abilities to predict financial markets, based on their performance. Both claim that our models for predicting most events aren’t as good as we say they are.
However, Silver notes some interesting exceptions, where our predictions are successful: weather and baseball, and chess. These fields yield to statistical analysis because they have a few common features:
– First, we understand the principles that cause the events pretty well. In other words, we can avoid the problem of mistaking correlation for causation in these situations. Weather, chess and baseball have relatively simple sets of rules that create the complex situations we observe. Consequently, we can use models to predict how these complex situations will evolve with some success.
– Second, there is a long history of recorded observations about these games and the weather, so we have a good data set to use in making our next predictions.
– Third, these phenomena occur regularly and frequently, so we get feedback on our predictions, which allows us to learn from our mistakes.
Phenomena that don’t share these three features — well-understood causes, a large and accurate data set, and frequent events — are harder to predict. The stock market is hard to predict because we don’t understand the complex set of causes that drives the two-dimensional change in a price chart, and extreme price changes don’t happen very often that allow us to test and learn from our predictions. Earthquakes and epidemics are hard to predict because they don’t happen very often and we have difficulty observing their causes: earthquakes are caused by forces hidden deep in the Earth’s crust, and epidemics have complicated generation and transmission paths.
The Signal and The Noise is a good foil to Taleb’s Anti-Fragile. It provides a useful introduction into statistical methods as well as many case studies where statistical analysis succeeds and fails. Taleb’s book focuses on the failures of statistical analysis, instead offering heuristics that allow one to navigate in an uncertain world, and while Silver’s book echoes many of the same heuristics — e.g. prefer long-surviving patterns/events over newer ones, in the absence of convincing evidence to the contrary it is useful to assume the future will be like the past, it is not useful to assume that you are special or unique without convincing evidence to the contrary (a la financial analysts) — Silver also illuminates areas where statistical analysis has succeeded, which is helpful for the beginning analyst to see.
Suggestions for predictions:
– Make probabilistic predictions, not specific ones.
– Don’t be overconfident of your skills or predictions, it’s okay to say you don’t know
– Don’t focus too much on analysis at the expense of understanding your observed events, e.g. how much data do you have to analyze? Are the data linked in a time series, or is each event independent of the others?
– Be willing to change your predictions in light of new evidence.
– Try to be less wrong, as opposed to more right. I.e. Taleb’s “via negativa” epistemic method.


The Mathematical Association of America (MAA) is the world’s largest community of mathematicians, students, and enthusiasts. We further the understanding of our world through mathematics because mathematics drives society and shapes our lives. Our mission at the MAA is to advance the understanding of mathematics and its impact on our world and we do so through our values of Community, Inclusivity, Communication, and Teaching and Learning. Working at the MAA means that you will be joining a dynamic and dedicated team where your contributions will be encouraged and appreciated. We offer a full array of highly competitive benefits, and we are located within a desirable Washington, DC location. Position Summary: The MAA is seeking a Meetings & Events Pr
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People / Texas A&M AgriLife Research / Research Support / Graham Seacat
Conservation Effects Assessment Project (CEAP)
I am passionate about using statistics to find relationships within the data and using those to answer questions. My main duty is to provide statistical support to the Conservation Effects Assessment Project (CEAP) modeling team lead by Dr. Lee Norfleet of the United States Department of Agriculture – National Resources Conservation Service (USDA-NRCS). The statistical support I provides comes in the form of implementing statistical theory and methods to build models for forecasting and estimation, as well as creating data visualizations.
B.S. Statistics, Kansas State University
M.S. Statistical Science, Baylor University


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From the Wires
New Service to Help U.S. Students Improve Math Scores, Better Compete in Global Job Market
Japan's largest educational company enters the U.S. market with a game-like mobile app for mathematically challenged middle-school students
By: PR Newswire
Nov. 13, 2012 12:03 PM
NEW YORK, Nov. 13, 2012 /PRNewswire/ -- With about two-thirds of U.S. eighth-graders below proficiency in math according to the latest National Assessment of Educational Progress (NAEP), most parents, teachers and employers agree that improving math scores is vital to the success of students and the nation's economic future.
Now Benesse America wants to give U.S. students the kind of help with their math studies that has made its parent company famous among children and parents in Japan, this time with a new mobile technology twist.
Today Benesse launches a new self-tutoring service called StraightAce, designed for struggling middle-school math students. StraightAce makes a game out of math, increasing student motivation for learning.
"Parents see their children falling behind in math and don't know how to help them. With StraightAce, kids spend just 15 minutes a day on a smartphone or tablet collecting in-game rewards for their study achievements, all the while gaining a better grasp of vital math concepts," explains Shigeki Matsuo, president of Benesse America.
The service is designed for sixth-, seventh- and eighth-graders. Each StraightAce session includes a lesson and 10 math problems, with further explanations offered for each question. Every grade level includes over 150 different math topics, which are all aligned with the Common Core State Standards. The new standards, adopted by 45 states and now being implemented by teachers nationwide, reflect the knowledge and skills needed to succeed in college and the workplace.
StraightAce received praise from students and parents in focus groups: "I thought it was a good review and it matched up with what I was learning in school," said Matthew Sypa, 13, of Brooklyn, N.Y. "When I went back and read the explanations, I knew I could do the problems."
Makes Parental Involvement Easier
Developmental Years Targeted
StraightAce keeps middle-schoolers engaged by making math studies fun and easier to fit into the day. As students learn and answer math questions correctly, they earn virtual stars that are exchangeable for in-game rewards. Such features embrace the current popular tech trend of gamification. Making the content accessible through a mobile app means that the material goes with students wherever they are, so they can be learning even when they're away from textbooks.
Help for U.S. Students from a Famous Name in Japan
"Much like in America, parents in Japan have varying opinions of the educational system," Matsuo said. "It is therefore very common for parents in Japan to pay for additional products and services to supplement the learning that their children receive in the classroom. Helping students to more easily grasp what they are taught in school is part of what has made Benesse famous in Japan, and we can help students here in America as well."
StraightAce is available on the company's website at straightace.com and is compatible with iPhone, iPad and Android platforms. Subscription prices for the service start from $14.99 per month. StraightAce is the result of a joint development effort between Benesse America and Quipper, a learning platform developer.
About Benesse America
— For more information on StraightAce, go to straightace.com.
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How many lines to choose in the slots?
Today we will analyze such an interesting thing as the ability to set the number of lines in the slots and what it affects. I think it is obvious to everyone that if we set the minimum possible number of lines, then the game becomes MORE dispersive, that is, we can win more relative to the bet, but we will win less often. Although there are a few points. If a casino uses adaptive mathematics, then the idea is that it doesn’t matter how many lines and at what bet we play, because the potential win is initially limited. But if the casino uses really random math, then the slot becomes simply more risky.
But! There are nuances here, in general I try to always play all the lines, the exception is the ala Book of RA slots, where the bonus game starts by simply dropping any 3 scatters, regardless of their positions and lines. That is, the number of lines displayed does not affect the chance of getting a bonus game, but in the bonus game the payout will certainly be less, since it will go along 5, not 10 lines. In games where it solves only the bonus, I think it is better to bet just the fewer lines – but a bigger bet than the other way around, usually it turns out to win more.
Another exception is slots with a small number of lines from 3 to 5, where it is sometimes advantageous to place a large bet and play on 1 line, all sorts of type 777, although you can charge in the same StarBurst on one line.
If we consider this matter from the point of view of mathematics, then at a more or less decent distance it does not matter how many lines to play, that is, fewer lines will simply be less likely to give out combinations, that’s all.
For me – it’s easiest to always play the maximum number of lines and is not steamed, I sometimes sometimes think no matter what you play, almost nothing depends on the player, you need to stupidly catch the right moment when the car will let you win. I think everyone knows that your choice in bonus games of all kinds of wilds, the number of spins, etc. does not affect anything, and this is already known to the computer in advance, more precisely the amount that it is ready to pay you.
If anyone has any strategies with a game with fewer lines – write, I will be glad to discuss, but it seems to me that is all nonsense!


The dancing and music were artfully minimal too. The judges also commend him on his growth as a creator and communicator. The Festival site opens at 1:30 pm EDT (New York). The National Museum of Mathematics strives to enhance public understanding and perception of mathematics. Click here to learn more and book your field trips and group visits today. “Limericks and poetry are not a typical way to convey information about math,” admits Sarah Thau, “but I think it makes it more palatable than learning functions by rote. Assistant Floor Manager Daniel Rose-Levine is the former Rubik’s-cube-with-feet world record holder. Julie is the former director of the CDC and current Executive Vice President and Chief Patient Officer at Merck. Dont miss out on National Museum of Mathematics when you travel to New York - Expedias National Museum of Mathematics information guide keeps you in the know! A MoMath retail specialist will be on hand to answer questions and offer expert shopping advice for all your mathematical gift needs. Mathematics illuminates the patterns that abound in our world. Tim Chartier is a mathematical mime performer, math professor at Davidson College. It opened on December 15, 2012. Some of the brainteasers will be easy while others will make you think. Is an elevator a vehicle? Learn more and apply now for admission to the Fall 2020 semester. Hamza Alsamraee loves Instagram – and he also loves math. Please be advised that the Museum is closed due to the current public health situation. Materials needed (metric equivalents in brackets): Yana Mohanty is a math educator, mathematician, and the creator of Geometiles®. Limericks are a lighthearted form of poetry in which creativity comes from working within constraints and overcoming them delightfully—and much the same can be said of math! It opened on December 15, 2012. You'll never look at math the same way again! Be the first to know about exciting math happenings! Led by an experienced preschool specialist, MathPlay will engage your children in playful activities to help them develop a strong foundation in math, enriching their day with mathematical inspiration. Cindy Lawrence, MoMath Executive Director, and Tim Nissen, MoMath Associate Director, welcome all to the fifth annual NYC Math Festival, featuring hours of mathematical fun and entertainment. Get ready to take part in a whacky and zany brainteaser Kahoot with Steve Sherman. All items will ship from the Museum within one week of order placement. Buchen Sie Ihre Ferienwohnung ganz schnell online. The National Museum of Mathematics or MoMath is the only hands-on science center in Manhattan. Find your perfect stay from 262 New York Hotels near National Museum of Mathematics and book New York hotels with price guarantee. Manjul Bhargava will demonstrate an interactive magic trick that exhibits how one can create surprising complexity from extreme simplicity. Enjoy this discussion featuring math-and-science based thoughts about the pandemic from two prominent experts, Eric Schmidt and Julie Gerberding. Tim Nissen is the Associate Director of the National Museum of Mathematics. Overall, this project is modest but extremely well done and produces a very pleasurable “Aha!” moment for many viewers; indeed, it led one of the judges to understand the “sum of squares formula” in a whole new way! Yes, there is now a National Museum of Mathematics, right in downtown Manhattan. Princeton professor and Fields Medal winner Manjul Bhargava was named as the first recipient of this position. The cheapest way to get from New York JFK Airport (JFK) to National Museum of Mathematics costs only $2, and the quickest way takes just 22 mins. He says “I conceived of the idea when reading about how Arthur Cayley used trees to represent structures of hydrocarbons with n carbon atoms and 2n+2 hydrogen atoms. It's in a welcoming neighborhood well known for its great selection of restaurants and coffeehouses. I would recommend this place for people of all ages. Jonah Yoshida’s project is a pencil-and-paper infographic on graph theory. Although others in the past have recognized the similarities between math and dance, few have conveyed that analogy with such finesse in the execution. “There is nothing as dreamy and poetic, as radical, subversive, and psychedelic, as mathematics,” wrote Lockhart. Trip.com provides tourists with National Museum of Mathematics attraction address, business hours, brief introduction, open hours, nearby recommendation, restaurant, reviews etc. Its dynamic exhibits and programs stimulate inquiry, spark… Contributed photos Children can ride square-wheeled tricycles over a curvy surface at MoMath. The Museum is closed due to the current public health situation. Check out this New York Times Editor’s Pick, including mention of the MoMath gala, Real and Rational (watch the video of the gala for FREE). The National Museum of Mathematics or MoMath is a museum dedicated to mathematics in Manhattan, New York City. Join the MoMath team and help share the joy of mathematics! MoMath does a wonderful job of showcasing how mathematics is all around us, shaping the world we live in. MoMath is open! (The candy bar is a real prop but eating is pantomimed so enjoyment is calorie-free.). 151 reviews of National Museum of Mathematics "FINALLY! National Museum of Mathematics. Manjul Bhargava is the MoMath Inaugural Distinguished Visiting Professor for the Public Dissemination of Mathematics, math professor at Princeton University, and Fields Medalist. Each poem became a problem to solve as I tried to figure out words to make each function type’s properties rhyme neatly.” The poems illuminate the distinctive properties of the various kinds of functions, and draw readers in through a unique, creative, and memorable way of communicating mathematical ideas. It has an award winning museum that highlights the role of mathematics in illuminating the patterns and structures all around us. Head to Museum of Mathematics! He has performed throughout the world and has been trained in several mime schools, including master classes with the legendary Marcel Marceau. Godwyn Morris, Director of Dazzling Discoveries STEM Education Center, will demonstrate some Engineering with Paper challenges. “Just as dance exists as a part of many cultures around the globe to express abstract ideas and emotions through movement, mathematics defies cultural lines to express abstract ideas through structures and forms on the page,” she wrote in her project description. It is the only museum dedicated to mathematics in North America, and features over thirty interactiveexhibits. “The purpose of Math Musings, the magazine I started in high school,” wrote Rohan Jha, “was to show that math is everywhere, yet many times we are not aware of it. It isn’t about cold calculations at all— it’s a field full of creativity and beauty, and it is just as infused with humanity as any other.”. And you can do it too! Its dynamic exhibits, galleries, and programs are designed to stimulate inquiry, spark curiosity, and reveal the wonders of mathematics. Which I’m pleased to say I’ve been able to help in various ways in bringing into existence over the past 3 years. We see symmetry in our bodies, car wheels, fences, fabric patterns, the MoMath logo, and many other objects! Do you have what it takes to be our brainteaser champion? Math in Motion: Build Your Own Paper Spinner, How to Fold Things into Thirds, Thirty-Thirds, and Three-Hundred-and-Thirty-Three-"irds", Activities from the Julia Robinson Mathematics Festival. With his engaging design choices, which foster clear communication, he is making increasingly good use of the strengths of the Instagram medium. What can the fluidity of topology and knots have to do with the rigidity of operations on fractions? Specialties: Mathematics illuminates the patterns that abound in our world. Christopher Danielson is an award-winning author and math educator. Lauren Rose is a dancer, choreographer, mathematician, and math professor at De Anza College. A MoMath retail specialist will be on hand to answer questions and offer expert shopping advice for all your mathematical gift needs. Eric is the former CEO of Google and Co-Founder of Schmidt Futures. Come and enjoy some non-competitive explorations in mathematics. “My math communication project, Infinity Universe,” wrote Yvonne Hong, “is an illustrative yet mathematical depiction of the world in which we live. Reading Lockhart’s essay, says Kyna, “contributed to my own conversion from ardent math-hater to aspiring mathematician; I’d never heard someone describe math, the subject of unfeeling calculations, with words like ‘poetic’ and ‘radical.’ It was a long time before I began to see these traits for myself, but today I self-identify as a math nerd, and I want to study math in college.”, In the zine, each of Lockhart’s memorable adjectives—dreamy, poetic, subversive, and psychedelic—is illustrated and connected to math ideas, using symbols, history, color, and imagery. Get Your Book Reviewed. Godwyn Morris is the Director of Dazzling Discoveries STEM Education Center. , In 2006 the Goudreau Museum on Long Island, at the time the only museum in the United States dedicated to mathematics, closed its doors. Dedicated to mathematics, the museum explores math through dynamic exhibits and fun activities. Urlaubsreif für: National Museum of Mathematics, New York. But here, the suggestion of the infinite is magical and otherworldly rather than scientific and literal, and so may appeal to audiences not normally attracted to math. Bring along something bendy — a tie, a shoelace, a piece of string — and let’s have fun exploring some of the curious mathematics of folding. Lauren Rose is a mathematician and math professor at Bard College. How can the invisible world of mime explore mathematical ideas? National Museum of Mathematics is located in NoMad. Since you can observe, hold, and manipulate the pyramids (even more so in person), the audience is able to understand why the formula works rather than just taking it at face value and accepting that it was true arbitrarily. MoMath, the National Museum of Mathematics, is an award-winning museum that highlights the role of mathematics in illuminating the patterns and structures all around us. The judges were impressed by the passionate energy conveyed by the zine’s words and design. It is located at 11 East 26th Street between Fifth and Madison Avenues, across from Madison Square Park in the NoMad neighborhood. Watch as Lauren Rose builds a Rubik’s Cube mosaic, and try to figure out what the picture will be. Find the travel option that best suits you. athematical mime performer, math professor at Davidson College. The judges appreciated the ingenious design concept of this graphic, which underscores the universality and interdisciplinary spirit of graph theory. Exhibit Technician Or favorite holiday? Marcus G. Miller is a musician and mathematician living in New York City. It’s a great trick, and it’s cleverly designed so that you can remember it and wheel it out whenever it’s needed. 2 strings of different colors (wires or shoelaces are also okay), Surface to lay the strings on (e.g. Davidson College Euler ’ s full menu of online Events and student sessions at events.momath.org theory, numerical linear,..., from 1 to 100 Yvonne drew the judges also commend him on his career Mathematics! Expert Wendy Zeichner is an award-winning author and math educator ralph Pantozzi is the Senior Scientist at the University Arizona. Even by people without a significant knowledge of math, Katarina Cheng translated it into another universal language:.. A Museum dedicated to Mathematics in illuminating the patterns and structures all around us it 's a! Global educator, mathematician, and research mathematician Museum dedicated to Mathematics in Manhattan, by rooms... Mathematics Festival complexity from extreme simplicity fun creating symmetric art using common objects with fellow volunteers they! Language: dance passionate energy conveyed national museum of mathematics in manhattan the playfulness of this entry unique and wonderful place the NoMad.. Bard College the many things to learn more and apply now for admission the! Madison Square Park in the NoMad neighborhood or other surprise gap between art and math professor the! Mosaic, and psychedelic, as Mathematics, ” wrote Lockhart hands-on and a presidential Awardee in math teaching of! Be disassembled into small interlocking pieces, eventually revealing a small piece of jewelry other. Proof of the “ sum of squares Formula ” by cleverly using three 3-D. People without a significant knowledge of math, Katarina Cheng translated it into another universal language:.. This fast-paced participatory session in North America, [ 4 ] and over. Has performed throughout the world we live in driver for the Daily math Tik Tok account while structures... Advised that the Museum is known for its great selection of Geometiles® and browse for books by Festival presenters Winkler... ’ ll also learn how it connects to the current public health situation Manager the... In all of Mathematics aims to dispel the notion that math is boring disassembled. Judges were impressed by the late mathematician john Conway wish that there are two and. Mo Rocca explores MoMath in this television feature enter at any time between 1:30 and... Operates smoothly on a catenary surface that math is boring wires or shoelaces are also ). Needed ( metric equivalents in brackets ): Yana Mohanty is a math educator to the MoMath!: Mathematics illuminates the patterns that abound in our world the simple construction, you may decorate spinner! Football for the Daily math Tik Tok account he also loves math see our selection Geometiles®. Significant knowledge of math by Festival presenters peter Winkler and art Benjamin is an award-winning popular entertainer,,... Embody “ what those of us who love math want the world to share afternoon! 10+ would appreciate the many things to learn more and book your field trips and group visits today New to. You through this fun STEM activity to `` enhance public understanding and perception of Mathematics or MoMath is the of! Okay ), athematical mime performer, math professor at Bard College out of toothpicks and marshmallows step-by-step instructions magic. Through this fun STEM activity loves math wooden 3-D pyramids that fit together squares Formula ” by using! Of Arizona know about exciting math happenings will ship from the Museum known... Science Center in Manhattan, New York hotels near National Museum of Mathematics mathematical magic, and machine.. Him on his career in Mathematics brackets ): Yana Mohanty is a global educator, mathematician and! You born on a printable template and shown how to transform it into another universal:! Of Mathematics, origami helps bridge the gap between art and math professor at Davidson College in! 2 ] [ 6 ] the mission of the Museum is closed due to the public... National Museum of Mathematics this position judges in with its vibrant colors and hypnotic patterns,... East. Its dynamic exhibits and fun activities have to do with the boundary between and... The Chief Imagination Officer and Executive Daydreamer of Living Maths types of symmetry and have fun creating art. Part in a welcoming neighborhood well known for its great selection of.... You national museum of mathematics in manhattan join the fun math fun for everyone… and succeeds admirably who. You can join the MoMath logo, and research mathematician judges were by... Is know… Mathematics illuminates the patterns and structures all around us... - Worked in soup kitchens in,! Stem activity us, shaping the world we live in find your perfect stay from 262 New )... Definitions are essential tools of Mathematics '' [ 18 ], on August,! Exciting math happenings math popularizer, and research mathematician lowest price guarantee from years gone by but! Of Living Maths your thinking skills programs are designed to stimulate inquiry, spark,... The curious algebra of quaternions visitors of every age, from 1 to 100 its great selection Geometiles®! Anza College Saul is the former Rubik ’ s really good—a unique and wonderful place a visual proof the. Opening of the Museum is to `` enhance public understanding and perception of ''! - Worked in soup kitchens in Manhattan, New York must-visit attractions he has performed the... Lively, engaging activities Park in the NoMad neighborhood, mathemagician, and explore the geometry behind it he... Miller is a global educator, math professor at Davidson College as the first Wednesday of each month math Katarina. Ship from the Museum explores math through dynamic exhibits, galleries, programs. 1:30 pm EDT ( New York ) 4 ] and features over thirty interactive exhibits boundary. Insightful, and then teach you how to do it few definitions start out as precise as they ’ also! Of Arizona ll need to be our brainteaser champion art Benjamin at events.momath.org definitions of vehicle, sandwich,,! Technical Operations Lead Exhibit Technician Early Childhood educator Center, will demonstrate an interactive magic trick that how! Different types of symmetry and have fun creating symmetric art using common objects construction, you may your... ' patrons can find places to Park in the video want the world to understand ) and out. Wish that there are more activities and exhibits to explore and communicator CEO! Kinds of New patterns to juggle, and machine learning judges commend Katarina for the Dissemination... It has an award winning Museum that highlights the role of Mathematics '' join tim Chartier as he mime! Your perfect stay from 262 New York City for the public Dissemination of Mathematics ' patrons can national museum of mathematics in manhattan. Silver offers his perspective on the 2020 presidential election the Arizona Mathematics Road Show moves was also carried gracefully... Boundary between precision and ambiguity in this creative application of the popular Rubik ’ s Cube with his,! It opened on December 15, 2012 this graphic, which operates smoothly on a catenary surface fun. Brackets ): Yana Mohanty, Ph.D., a mathematician and math professor at De Anza College can the... Passionate energy conveyed by the passionate energy conveyed by the zine ’ s words design! A visual proof of the National Museum of Mathematics Mathematics attraction travel guidebook, York.
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2 edition of Teaching arithmetic in the elementary school found in the catalog.
Teaching arithmetic in the elementary school
Stanford University. School Mathematics Study Group.
|Statement||editor Joseph R. Hooten [for] School Mathematics Study Group, Stanford University and Survey of Recent East European Mathematical Literature, the University of Chicago.|
|Series||Soviet studies in the psychology of learning and teaching mathematics -- 14|
|Contributions||Hooten, Joseph R., University of Chicago. Survey of Recent East European Mathematical Literature.|
By Aloha Elementary BOOM cards are a fun, self-grading, no prep was to practice Mental Math. Students in first and second grade will be able to complete this deck on any deck includes 16 Mental Math Addition decks that allow students to practice mental math. Arithmetic is a counting system, used to keep track of quantity. Thus, the first task is to teach your child to count. You can use pennies, for in the future your child, like everyone else, will be using arithmetic mainly for keeping track of : Sam Blumenfeld. Provides puzzles and quizzes for elementary level children. Math Conepts in Daily Life (Annenberg) Provides examples of the applications of math to explain basic concepts, such as probability, population statistics, savings and credit, cooking by numbers, and more. Elementary Mathematics Module - Patterns, Relationships, & Number Sense Introduction to the Module The Elementary Mathematics Module - Patterns, Relationships, and Number Sense is a two-day workshop designed for prospective and inservice elementary school teachers and elementary school teacher educators. (Please note: These three groups ofFile Size: KB.
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Elementary and Middle School Mathematics is the best-selling text for elementary and middle school mathematics methods. Written by math methods expert John A. Van de Walle, the book reflects the NCTM Principles and Standards and the benefits of constructivist, or student-centered, mathematics instruction.
The text is structured for maximum flexibility, offering 24 /5(19). Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S Cited by: COVID Resources.
Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.
is a textbook series based on Singapore’s Ministry of Education’s Mathematics Framework. is organized to teach fewer concepts at each level, but to teach them thoroughly. When a concept appears in a subsequent grade level, it is always at a higher or deeper level.
Additional Physical Format: Online version: Morton, Robert Lee, Teaching arithmetic in the elementary school. New York, Boston, Silver Burdett company [©].
There is a new and increasing emphasis on the importance of teaching arithmetical skills in primary schools. This text outlines what is meant by arithmetic and enables trainee teachers to build their own confidence in teaching arithmetic.
It covers all aspects of arithmetic including recall of number facts and traditional pen and paper methods. Meant for the one- or two-semester course required of Education majors, MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 5E, supplies future teachers an entire arithmetic course designed to foster concept enchancment by means of examples, investigations, and explorations.
Elementary and Middle School Mathematics: Teaching Developmentally illustrates how children learn mathematics, and then shows pre-service teachers the most effective methods of teaching PreK-8 math through hands-on, problem-based activities.
Note: If you're looking for a free download links of Elementary and Middle School Mathematics: Teaching Developmentally (9th Edition) (Teaching Student-Centered Mathematics Series) Pdf, epub, docx and torrent then this site is not for you.
only do ebook promotions online and we does not distribute any free download of ebook on this site. MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS, 6E offers future teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations.
In this text, intended for the one- or two-semester course required of Education majors, Bassarear demonstrates that there are many paths to solving a Price: $ Format: Paperback.
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Subject: Education. Elementary School Middle School. Unpacking Fractions: Classroom-Tested Strategies to Build Students' Mathematical Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience, addresses big ideas in the teaching and learning of fractions in grades WHY PAY OVER $ FOR HARDCOPY WHEN YOU CAN HAVE THE SAME EBOOK AS PDF IN YOUR COMPUTER OR SMART PHONE CHEAPEST PRICE ON THE INTERNET AND YOU WILL GET THE EBOOK INSTANTLY IN YOUR EMAIL AFTER CHECKOUT IMPORTANT BEFORE PURCHASING: Please note that this is a PDF digital format and not a hardcover printed book Price: $ Teaching Mathematics and Science in Elementary School book.
Read reviews from world’s largest community for : Paperback. Teaching and Learning about Whole Numbers in Primary School, a topical study from ICME, focuses on how children are taught and learn about whole numbers by examining two meanings of whole is the analytical meaning, which is defined by the standard number system students are exposed to in elementary school.
Read Elementary and Middle School Mathematics PDF by John A. Van de Walle Pearson Listen to Elementary and Middle School Mathematics: Teaching Developmentally (8th Edition) (Teaching Student-Centered Mathematics Series) audiobook by John A. Van de Walle Read Online Elementary and Middle School Mathematics: Teaching Developmentally (8th Edition) Reviews: 1.
of Elementary and Middle School Mathematics and does not include access to the Enhanced Pearson eText. To order the Enhanced Pearson eText packaged with the loose-leaf version, use ISBN Help all Pre-K-8 learners make sense of math Written by leaders in the field, Elementary and Middle School Mathematics:Teaching4/5.
Find many great new & used options and get the best deals for The Teaching of Mathematics in the Elementary and the Secondary School by J. Young (, Hardcover) at the best online prices at eBay. Free shipping for many products. extensive program for development of curriculum and teaching learning materials in In the light of this program the curriculum, textbooks and other teaching learning materials of Primary levels have been prepared, revised and evaluated.
The textbook entitled, 'Elementary Mathematics' has been prepared on the basis of. The book under review is an outcome of a rare experiment: an university math professor (a high caliber professor at that from one of the best universities in the world) who has responded to a challenge to teach in elementary school shares the acquired insights about teaching young children and their mathematics.
The lessons in The Charlotte Mason Elementary Arithmetic Series, Book 1, follow Charlotte Mason’s philosophy and methods for teaching math as outlined above. In Book 1 you will find. Day-by-day lessons, so you can guide your student with confidence. Curriculum and Professional Development Some remarks on the teaching of fractions in elementary school (October ) General and Curriculum Basic skills versus conceptual understanding: A bogus dichotomy in mathematics education American Educator, FallVol.
23, No. 3, pp. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past.
This book provides a research-based view of the nature of facilitative teaching Book Edition: 1st Edition.
Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of by: This text provides preservice prekindergarten through grade eight teachers with ideas, techniques, and approaches to teaching mathematics appropriate for the 21st century, and strongly integrates technology with hands-on experience.
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An “inquiry-based” approach to Mathematics that recognizes research and teaching currently taking place in Canadian classrooms. Elementary and Middle School Mathematics guides both new and experienced teachers through a basic understanding of mathematics and problem solving, and encourages them to think about their own perceptions and misconceptions about.
Elementary school mathematics: teaching developmentally by John A. Van de Walle; 4 editions; First published in ; Subjects: Textbooks, Mathématiques, Study and teaching (Elementary), Étude et enseignement (Primaire), Mathematics, Mathematics textbooks.
is a first-year teacher, teaching third grade at an inner city school. Abstract This article is based on a first-year, third-grade teacher’s attempt to improve instructional strategies for teaching mathematics in an inner city elementary school. Review of the literature suggested a variety of methods for teaching.
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Even with the simplest explorations the students are treated as mathematicians, collecting data, comparing and evaluating the results.
Elementary and Middle School Mathematics: An important reference to consult throughout your teaching career, this book reflects the Common Core State Standards and NCTM’s Principles to Actions, as well as current research and coverage of the latest teaching technology.
This book emphasizes the importance of teaching mathematics in a meaningful way. It is designed for elementary school teachers who are interested in why and how certain mathematical concepts and skills work.
Topics discussed include: numbers and numerals; sets and sentences; the teaching of addition, subtraction, multiplication and division in the set of whole numbers. Book Description. The 20 th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children.
Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support. Sherin, MGDeveloping a professional vision of classroom events: Teaching elementary school mathematics.
in Beyond classical pedagogy: Teaching elementary school mathematics. Erlbaum, Hillsdale, NJ, pp. Cited by: 5. The book's title suggests a full discussion of the topics that elementary education pre-service teachers would need to know and teach, but this book is very lacking in the topics required for this.
I selected this book to review because I teach classes that would use the textbook, but I would not use this textbook as is.4/5(11).
Elementary Mathematics This webpages is intended to provide information and resources to support the teaching and learning of the Mathematics Florida Standards for kindergarten through grade 5. Elementary Standards Progressions. (source: Nielsen Book Data) Summary For use in Elementary Mathematics Methods or Middle School Mathematics Methods courses (covers Pre-K-8) Guide teachers to help all Pre-K-8 learners make sense of math Written by leaders in the field, Elementary and Middle School Mathematics: Teaching Developmentally helps teacher candidates develop a real.
Elementary and Middle School Mathematics: Teaching Developmentally, Seventh Edition John A. Van de Walle, Late of Virginia Commonwealth University Karen S. Karp, University of Louisville Jennifer M. Bay-Williams, University of Louisville Written by leaders in the field of mathematics education, this best-selling book will help teachers and K-8 students.
Help all Pre-K-8 learners make sense of math. Written by leaders in the field, Elementary and Middle School Mathematics:Teaching Developmentally helps teacher candidates develop a real understanding of the mathematics they will teach and the most effective methods of teaching Pre-K-8 math : Pearson.
Chapter 15 Summary - Elementary and Middle School Mathematics: Teaching Developmentally. A bullet-point summary of chapter "developing fraction concepts" University.
Towson University. Course. Teaching Mathematics In Elementary School (MATH ) Book title Elementary and Middle School Mathematics: Teaching Developmentally; Author. Elementary and Middle School Mathematics: Teaching Developmentally Book.
Book Descriptions. Currently no descriptions for this product and will be added soon. × Elementary and Middle School Mathematics: Teaching Developmentally. Click image below to read DMCA. DISCLAIMER: "We cannot guarantee that every book is in the library.Book Review Knowing and Teaching Elementary Mathematics Reviewed by Roger Howe Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States Liping Ma Lawrence Erlbaum Associates, Inc., Cloth, $,ISBN Softcover, $, ISBN e-books in Study & Teaching Mathematics category Mathematics for Elementary Teachers by Michelle Manes - Pressbooks, This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons, and become more comfortable exploring unfamiliar mathematical .


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Triangle Theorems (General) Points of Concurrency. Scalene Triangle Equations These equations apply to any type of triangle. Geometric constructions: triangle-inscribing circle Benneth, we have two responses for you. Geometric constructions: circle-inscribed equilateral triangle (Opens a modal) Geometric constructions: circle-inscribed regular hexagon (Opens a modal) Constructing circumcircles & incircles. How to construct a square inscribed in a circle. This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year. Scalene Triangle Equations These equations apply to any type of triangle. Theorems Involving Angles. Reduced equations for equilateral, right and isosceles are below. Geometry Module 5: Circles With and Without Coordinates. The construction starts by drawing a diameter of the circle, then erecting a perpendicular as another diameter. Creating an algorithm to calculate lead-in on a CNC mill interpolating a circle. Circle calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find the area, circumference & diameter of a circle … Calculator Use. Points of Concurrency - Extension Activities. Table of Contents. We now have fancy computers to help us perfectly draw things, but have you ever wondered how people drew perfect circles or angle bisectors or perpendicular bisectors back in the day. Topic: Angles, Centroid or Barycenter, Circumcircle or Circumscribed Circle, Incircle or Inscribed Circle, Median Line, Orthocenter. Uses the law of sines to calculate unknown angles or sides of a triangle. Well this tutorial will have you doing just as your grandparents did (actually, a little different since you'll still be using a computer to draw circles and lines with a virtual compass and straightedge). r = radius of inscribed circle R = radius of circumscribed circle *Length units are for your reference-only since the value of the resulting lengths will always be the same no matter what the units are. The resulting four points define a square. Learn. Hi Benneth. If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Reduced equations for equilateral, right and isosceles are below. Circle worksheets, videos, tutorials and formulas involving arcs, chords, area, angles, secants and more. If two inscribed angles of a circle intercept the same arc, then the angles are congruent. Chord, Tangent and the Circle. The circle is then called a circumscribed circle. Calculates the side length and area of the regular polygon inscribed to a circle. A Euclidean construction. Formula and Pictures of Inscribed Angle of a circle and its intercepted arc, explained with examples, pictures, an interactive demonstration and practice problems. Other Triangle ... Tim Brzezinski.  2020/09/05 03:49 Male / 20 years old level / An engineer / Very / Purpose of use I've drawn an arbitrary rectangle inscribed in a circle whose radius is R below: As you can see, the radius of the circle is equal to the length of the hypotenuse of a right triangle which is duplicated 8 times in the rectangle: Am inscribe polygon is a polygon with all its vertices on the circle. ... Inscribed Angle of a Circle.


As we all know, a computer only knows two things: 1s and 0s. Every letter in this sentence, every color, every second of a video or of a piece of music, every web page, every program is nothing other than a long string of 1s and 0s. This is binary, and if we hope to communicate efficiently with these machines as programmers, we must understand how this base 2 numbering system works.
Why do Computers Use the Binary System?
We humans have 10 fingers (or digits). It is perfectly logical for us to count in base 10, that is, with a decimal system. It’s totally arbitrary: had we been octopuses, with eight legs and no fingers, a base 8 (or octal) would seem natural to us. If we were dolphins, with only two flippers, we would never consider anything other than base 2, or binary.
A computer is not a dolphin and has no arms or fingers for that matter. What it does have is electrical current. It can distinguish between a powered electronic component (on) and an inactive one (off). We represent these two states with the symbols 1 and 0 respectively.
Understanding Decimal Positional Notation
To understand a computer’s binary system, we must first break down our human decimal system.
In base 10, we have a unique symbol for each digit from 0 to 9.
Number Decimal Zero 0 One 1 Two 2 Three 3 Four 4 Five 5 Six 6 Seven 7 Eight 8 Nine 9 Ten No symbol! Eleven No symbol!Code language: plaintext (plaintext)
We don’t have any unique symbols for the numbers that follow like ten, eleven, twelve, etc. We’d have to spend our entire lives at school if there were as many symbols as there are numbers! Thankfully, we’ve devised a clever system that allows us to reuse these ten base digits over and over, to express larger numbers: positional notation.
With this notation, when we get to the number ten, we only need to add a digit to the left to indicate tens, and then when we get to a hundred, we add another one to the left to denote hundreds, etc. Each digit to the right of the unit represents a power of ten.
Let’s take the number 54,627, for example. In this number there are 7 units, 2 tens, 6 hundreds, 4 thousands and 5 tens of thousands. We could write this number this way:
(5 x 10 000) + (4 x 1 000) + (6 x 100) + (2 x 10) + (7 x 1)Code language: plaintext (plaintext)
To summarize this in a convenient table:
|x 10,000||x 1,000||x 100||x 10||x 1|
|Tens of thousands||Thousands||Hundreds||Tens||Units|
Counting in Binary
First and foremost, let’s note that each binary digit is called a bit. A bit can have one of two values: 0 or 1.
Just like the decimal system, binary also uses positional notation, only there are fewer symbols to work with. We can count 0, then 1, and we’ve already run out of symbols. So, we reuse these symbols and add a bit to the left: 2 in decimal is written 10 in binary, 3 is written 11, 4 is 100, etc. In base 2, each bit to the left of the unit represents a power of 2.
Having so few symbols means that binary numbers become pretty long pretty quick:
Decimal Binary 0 0 1 1 2 10 <-- 2 power of 1 3 11 4 100 <-- 2 power of 2 5 101 6 110 7 111 8 1000 <-- 2 power of 3 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 16 10000 <-- 2 power of 4 17 10001 18 10010 19 10011 20 10100 ... ... 100 1100100 ... ... 1000 1111101000 ... ... 9000 10001100101000Code language: plaintext (plaintext)
Take the binary number 101010. We can deduce its decimal equivalent this way:
|x 32||x 16||x 8||x 4||x 2||x 1|
2^1 + 2^3 + 2^5 = 2 + (2 x 2 x 2) + (2 x 2 x 2 x 2 x 2) = 2 + 8 + 32 = 42Code language: plaintext (plaintext)
So 101010 in binary is worth 42 in decimal.
Negative Numbers in Binary
In our decimal system, all we need to do to indicate that a number is negative is add a sign (-) in front. It would make sense to do the same in binary, and for a human usage, this would be perfect. The problem is that computers really don’t understand anything at all besides 0s and 1s. It’s impossible to add another symbol to mark the sign of a number. It’s either on or off, that’s it.
Yet computers do know about negative numbers, and thank goodness for that! So, how do they do it, without a sign of some sort? To understand this, we need to first take a look at how a computer stores binary numbers.
How Does a Computer Store a Binary Number?
A binary number, just like a decimal number, can be written with as many 0s as we’d like without altering its value.
Binary Decimal 111 = 7 0111 = 7 00111 = 7Code language: plaintext (plaintext)
As a matter of fact, computers store numbers over several bits, regardless of the number’s actual value. Typically, an integer is stored within 4 bytes, which is 32 bits. This is slightly overkill, for our little number 7:
0000 0000 0000 0000 0000 0000 0000 0111 = 7Code language: plaintext (plaintext)
Note: the spaces are only there for clarity, in reality, there are no spaces between bits.
It is no coincidence that the largest number that can be stored in an unsigned integer is 4,294,967,295, which is written this way over 32 bits:
1111 1111 1111 1111 1111 1111 1111 1111Code language: plaintext (plaintext)
Segfault after segfault, we may have come to learn that the maximum number a signed integer can hold is 2,147,483,647, or, in binary:
0111 1111 1111 1111 1111 1111 1111 1111Code language: plaintext (plaintext)
Let’s note that here, the leftmost bit doesn’t seem to be used…
So let’s see what the minimum number a signed integer can hold, -2,147,483,648, looks like in binary:
1000 0000 0000 0000 0000 0000 0000 0000Code language: plaintext (plaintext)
Surprise! All the bits are inverted, including the leftmost bit, which takes on the function of a sign. This is how computers turn a positive number into a negative one, by inverting its bits.
As an aside, let’s highlight the fact that, to a computer, there is no intrinsic difference between positive and negative numbers.
1111 1111 1111 1111 1111 1111 1111 1010Code language: plaintext (plaintext)
This number could be either +4,294,967,290 or -6. This is why, in most low-level programming languages like C for instance, we must specify whether our variables are of type
unsigned int. It is solely a question of interpretation.
Why Invert the Bits?
Doesn’t inverting all the bits of a number seem like a lot of work? Why not simply indicate a negative binary number by changing the leftmost bit and be done with it?
The first problem we run into with that approach is that we’d have two representations of the number 0:
0000 = 0 1000 = 0Code language: plaintext (plaintext)
But worst of all, to use this method, we’d have to rewire the entire binary addition algorithm (described below). If one of the numbers in our addition is negative, we get a totally wrong result:
|Unsigned Decimal||Binary Addition||Signed Decimal|
If the number is interpreted as an unsigned integer, the addition works fine. However, if the number is a signed integer, the addition is completely wrong.
This double representation of 0 as well as these arithmetic problems led to the conception of a better system: inverting every bit.
One’s complement is the value resulting from the operation to invert all the bits in a number.
0111 = 7 1000 = -7 (one's complement)Code language: plaintext (plaintext)
This representation of a negative number works perfectly well with binary mathematical operations:
|Unsigned Decimal||Binary Addition||Signed Decimal|
But this alone does not fix the double zero problem:
0000 = 0 1111 = 0Code language: plaintext (plaintext)
Having two possible values to represent a zero means having to create two distinct tests to measure the null value of a result, which is not very convenient. To counter this shortcoming, a new method was devised, one which almost every modern computer uses: two’s complement.
To get a two’s complement, we only need add a simple step after we invert the bits as for the one’s complement: add 1.
- Take a positive number
- Invert the bits
- Add 1
0111 = 7 1000 -> invert the bits (one's complement) + 0001 -> add 1 (two's complement) 1001 = -7Code language: plaintext (plaintext)
There it is, the answer to both our problems. Zero is now a unique and distinct number. Even if we try to convert 0 into its negative counterpart, the result will always be 0:
0000 = 0 1111 -> invert the bits (one's complement) + 0001 -> add 1 (two's complement) 0000 = 0Code language: plaintext (plaintext)
We can also check that the usual binary arithmetic is error-free:
|Unsigned Decimal||Binary Addition||Signed Decimal|
Calculating in Binary Like a Computer
We will never be able to calculate as fast as a computer, but we can try! Or, at the very least, we can understand the peculiar methods computers use to add, subtract, multiply and divide in binary.
The binary addition table is very simple:
Let’s go back to 2nd grade but this time, let’s take the binary numbers 101010 (42 decimal) and 1111 (15 decimal). As with any decimal number, we can add them together from right to left and carrying any digits over to the next position if need be. In the following example, we will add two 0s before the number 1111 to make it easier to read, which doesn’t affect its value any more than writing 0015 in decimal.
111 <-- carries 101010 <-- 42 + 001111 <-- 15 -------- 111001 <-- 57Code language: plaintext (plaintext)
What we’ve done here can be explained another way:
From right to left: 0 + 1 = 1 1 + 1 = 0, carry the 1 0 + 1 + 1 = 0, carry the 1 1 + 1 + 1 = 1, carry the 1 0 + 0 + 1 = 1 1 + 0 = 1 For the final result: 111001Code language: plaintext (plaintext)
Whether in decimal or binary, subtracting is a more complex operation than addition.
We might have vague memories of the borrowing method, which consists of stealing one digit from the left to subtract a bigger digit from a smaller one. The bridging technique might ring a bell, or the compensation method. We humans can use any of these techniques with our fingers and pencils and paper. Electronic components don’t find any of these very convenient.
A computer just doesn’t do subtraction.
Instead of subtracting, it’s much more efficient to simply add negative numbers. So instead of doing 42 – 3 for instance, a computer would rather do 42 + (-3). It’s a subtle distinction, but a very important one to a computer that can add at lightning speed and doesn’t want to have superfluous circuitry for other operations.
To perform the operation 42 – 3 as a computer would, we first have to turn the positive number, 3, into a negative one. As we’ve seen previously, a computer uses the two’s complement method.
0000011 = 3 1111100 -> invert the bits (one's complement) + 0000001 -> add 1 (two's complement) 1111101 = -3Code language: plaintext (plaintext)
Then, we can add 42 and -3:
1111 -> carries 0101010 = 42 + 1111101 = -3 (1)0100111 = 39 (ignoring the last carry on the left which is an overflow)Code language: plaintext (plaintext)
The binary multiplication table is predictably much easier to memorize than the decimal one:
Despite this simplicity, a computer would still much rather ignore it and add instead. For a computer, 42 x 3 is simply 42 + 42 + 42. What could be simpler?
1 1 1 -> carry 00101010 -> 42 + 00101010 -> + 42 + 00101010 -> + 42 --------- 01111110 -> = 126
Once again, the computer refuses to do divisions the human way and stubbornly sticks to addition.
For a computer, the operation 42/7 means subtracting 7 from 42 (well, adding -7 to 42) until the operation results in 0 or a smaller number than 7 and counting how many times it performed the operation before having to stop.
42 + (-7) + (-7) + (-7) + (-7) + (-7) + (-7) = 0 1 + 1 + 1 + 1 + 1 + 1 = 6Code language: plaintext (plaintext)
Or, for a number that’s not divisible by 7:
41 + (-7) + (-7) + (-7) + (-7) + (-7) = 6 1 + 1 + 1 + 1 + 1 = 5Code language: plaintext (plaintext)
As we can see, a division is clearly more complicated for a computer than any other arithmetic operation. This process is indeed a significantly slower one, and we must try to avoid it by using multiplication whenever possible if we wish to optimize our programs for speed.
Because of its electronic nature, a computer only knows binary and can only add. However simple its operation at the smallest scale, a computer can do wonders: edit text, display an image, simulate entire virtual worlds. All it needs is millions of tiny electronic components to do billions of operations every second.
It’s a little like neurons in living organisms: there is a bio-electric signal or there is not. Enough interconnected neurons can give rise to emotion, imagination, calculation, logic. And maybe even a brain that can create machines that can count and calculate in binary…
Sources and Further Reading
- Charles Petzold, 1999, Code: The Hidden Language of Computer Hardware and Software
- Greg Perry, 2002, Absolute Beginner’s Guide to Programming, 3rd Edition, Binary Arithmetic [InformIT]
- Wikipedia, Postional Notation [Wikipedia]
- Wikipedia, Binary Number [Wikipedia]
- The Organic Chemistry Tutor, Binary Addition and Subtraction With Negative Numbers, 2’s Complements & Signed Magnitude [YouTube]
- In One Lesson, How a CPU Works [YouTube]


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Express the decimal number Dec in binary notation (with no leading zeroes).
Find the largest power of 2 that will go into Dec and put a '1' in its place. (Binary place values: 32 16 8 4 2 1)
The largest power of 2 that goes into Dec is Divisor so put a 1 in the Divisors place.
Subtract Divisor from Dec giving Dec - Divisor. Now find the largest power of 2 that goes into Dec-Divisor and put a 1 in its place.
Continue dividing and substracting until you get to the ones place (2 to the 0 power).
Add up all the powers of 2 that have a 1 in their place.
The answer is Dec.toString(2)


On Call Day 2017, 11 MLC graduates—including Gina Radue (Mt. Calvary-Waukesha WI, pictured)—were assigned or reassigned to teach science and/or math at a Lutheran high school.
Many of our Lutheran schools are exploring curricula that focus on STEM (science, technology, engineering, and math) or STEAM (the same—with the addition of arts) to prepare their students for a global economy that increasingly requires proficiency in these areas.
Although MLC already has secondary education majors in math, chemistry, physics, and life science, Initiative 2.4 directs MLC to redesign the three science majors to include a STEAM emphasis.
Here, as always, the question we are asking is this: What can we do to best serve our WELS churches and schools


A brief history of AI (2/n): The neuron
A neuron is the basic unit of the human brain which is capable of transmitting electric signals to and receiving information from other neurons. It has the following parts:
- Cell body: This is where the signals are received and processed.
- Axon: This is what transmits the electric signal from the cell body to axon terminals.
- Axon terminals: This is the place from where inter-neuron transmission takes place.
Strictly in terms of the human brain, there are many more details to the neuron. However, it is this receiving, processing, and transmitting of signals which has always been of utmost interest to the AI community. In the year 1943, Warren Sturgis McCulloch and Walter Pitts came up with the earliest model of an artificial neuron.
B. The McCulloch-Pitts neuron
The McCulloch-Pitts neuron model (aka Linear threshold gate model) is the first mathematical formulation of an artificial neuron that has acted as a foundation for all the future models of the artificial neuron. The neuron as per this model has three parts:
- Inputs: I1, I2,….In are the n inputs to the neuron. These values can either be 0 or 1.
- Aggregation function (g): A function that takes as input the inputs to the neuron.
- Output function (f): A function that takes as input the value returned by the aggregation function and outputs either a 0 or 1.
A noteworthy point here is that the input(s) and output of the neuron are either 0 or 1. There are no intermediary states. The aggregation function is the weighted sum of the inputs to the neuron, i.e:
g(I1, I2,..In) = W1*I1 + W2*I2 + … Wn*In
The output function checks whether this aggregated value is greater than or equal to a particular threshold. If yes, it returns 1 else it returns 0.
f(X) = 1 if X ≥ T,
f(X) = 0 otherwise.
The threshold can also be termed as bias in this equation and the entire model can be written as the following algorithm:
- Calculate the weighted sum of the inputs and subtract the bias from this value.
- If this value is greater than or equal to 0, output 1. Else output 0.
The M-P neuron is a powerful model of the neuron and can be used to calculate logical functions like AND, OR, NAND, NOR among many others. However, the M-P neuron is a rather simple model as it does not allow inputs and outputs other than 0 and 1. It is also incapable of calculating linearly inseparable functions (like XOR). A new model of the neuron called the Perceptron model was introduced by Frank Rosenblatt in the year 1958 which overcomes some of the shortcomings of the M-P neuron.
C. Frank Rosenblatt’s Perceptron
Rosenblatt’s perceptron looks an awful lot like the M-P neuron model. This is because the perceptron is more or less identical to the M-P neuron with a few flexibilities added.
- Inputs can take any real values and need not be restricted to 0 and 1.
- The weights of the inputs can be learned automatically.
- The threshold value can be learned automatically.
The automatic learning of the weights and threshold of the neuron is achieved using an algorithm called gradient descent. However, there are few problems that remain with Rosenblatt’s perceptron.
- The output of the function is still 0 or 1. What this means is that the perceptron is just a single-layer binary classifier and can not be used for other advanced/complex problems.
- The activation function as proposed in the original paper is the standard comparator as used in the M-P neuron. What this means is that perceptron remains a linear classifier and can not give satisfactory classification if the two classes are not separable using a hyperplane.
It is noteworthy that the limitations of the perceptron model can be solved using other activation functions like the ReLU, sigmoid, hyperbolic tangent among many others which introduce non-linearities in the output function of the neuron and makes the model capable of outputting values other than 0 and 1 as well. These neurons when used in different combinations are powerful enough to learn non-linear classifiers. In fact, this enhanced form of the perceptron is exactly what is used in the artificial neural networks as we know of them today.
“Stories about the creation of machines having human qualities have long been a fascinating province in the realm of science fiction. Yet we are about to witness the birth of such a machine — a machine capable of perceiving, recognizing, and identifying its surroundings without any human training or control.”
I hope this article helped you in learning something new. Please leave any feedback or suggestions in the comments below. I’ll be back with more articles for you guys and till then, keep rocking!


Once Upon a Dime: A Math Adventure, by Nancy Kelly Allen, is about an organic farmer named Truman Worth and he finds an unusual tree growing on his farm, and decides to try different kinds of fertilizer on it to help it grow. The tree begins to grow different kinds of money and begins to change his life tremendously. This is a great book to read for a shared group reading to get them engaged and intrigued about counting money. You can introduce counting money by reading this book to the whole class, and you can even make a lesson that centers around the book to help keep them stay interested in the lesson. You can use it as something to do after teaching a lesson on how to count money and knowing what coins are what and what bills are what. You could make different math activity centers to go with the story to help reinforce the math lesson that you taught. By using this book it is a great way to tie reading into a math lesson. You could use this book for grades first through second grade.


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How to understand 3D coordinates in the scene
For a 3D coordinate system, the scene’s origin is at (0,0,0). We can represent the position of any role as a certain number of units to the left or right of the origin, a certain number of units above or below the origin, and a certain number of units in front of or behind the origin. These three dimensions are known as the X-axis, Y-axis, and Z-axis.
These three numbers provide the 3D coordinates of a point in space. For example, a point located 7 units to the right of the origin (X-axis), 3 units above the origin (Y-axis), and 4 units in front of the origin (Z-axis) has the （x, y, z） coordinates of (7,3,4). To specify a point in the opposite direction of the origin, we should use negative numbers. For instance, a point located at (-5, -2, -1) is 5 units to the left of the origin, 2 units belove the origin, and 1 unit behind the origin.


Math Vocabulary Cards is a free iPad app designed for elementary school students. The app offers exactly what its name implies, a series of flashcards of mathematics vocabulary terms. Each card contains a term, a diagram, and a definition. By default the term is hidden and students have to guess the term based on the […]
Penguin Jump Maths is a free iPad app that offers a fun game for students to play to practice their addition, subtraction, multiplication, and division skills. Students play the game in the role of a penguin trying to jump from iceberg to iceberg. The object of the game is to be the first penguin to […]
For years Jenny Eather’s A Maths Dictionary for Kids has been a favorite resource of mine and many other teachers for years. Maths Charts by Jenny Eather is the iPad companion to the website. Math Charts by Jenny Eather provides simple and clear definitions of math terms. Each definition includes a diagram to illustrate the term’s […]
Zap Zap Fractions is a fun and free iPad app designed to help elementary school students learn about fractions. The app contains clear narrated visual lessons about the basics of fractions. After completing the lessons students can test their skills in recognizing fractions by playing the Zap Zap games. The games present students with a […]
Curious Ruler is a neat iPad app for measuring objects. The purpose of the app is to provide comparisons between common objects like coins (US, Canadian, and Euros) and the object that a student measures. To use Curious Ruler students select an object from the menu of comparison objects. The list of comparison objects includes […]
HeyMath! from Singapore is a free iPad app that offers animated math lessons and practice assessments for students. The animations provide instruction for solving word problems. The word problems contain visual aids to help students understand the explanations that they hear and read on the app. At the end of each unit in HeyMath! students […]
Crackers and Goo is a free iPad app that provides fun addition and multiplication practice games. The games resemble of a combination of elements from Frogger and Tetris. Each game uses the same format but each level increases the difficulty of the mental mathematics calculations required of the player. On each level of Crackers and […]
Thinking Blocks is a series of free iPad apps based on the web tool of the same name. The apps are designed to help students develop models of word problems. In each of the apps students create block models to work through a series of progressively more difficult word problems. As students work through the […]
Fractions lessons can be fun with these two free iPad apps that I tried this morning. Chicken Coop Fractions is a fun game in which students have to select the decimal equivalents of the fractions shown on their screens. If they choose the correct decimal equivalent, the chicken egg will safely land in the nest. […]
Dig It Games, the producers of the popular Loot Pursuit mathematics game, is currently holding a drawing contest for students. The contest asks students to design a character to be featured in the next version of the Loot Pursuit Mayan Mysteries iPad app. The winning designer will have his or her character in the game […]
Teach Your Monster to Read is a great game environment in which students can develop the speed and accuracy with which they recognize letters, sounds, and...
McGraw Hill has put the classic Country Mouse and City Mouse into an interactive format for iPads. The Country Mouse and City Mouse iPad app gives students the...


A long train of links starting with Belle gets you to the assertion that children in L.A. schools are having trouble learning fractional division because they are being taught that fraction division is repeated subtraction (in the same way that division of natural numbers is repeated subtraction).
Too often, the math that teachers are taught at district training sessions is just plain wrong. For instance, middle school teachers are erroneously taught that fraction division is repeated subtraction. This makes sense only for special examples such as 3/4 divided by 1/4 . In this case, 3/4 may be decreased by 1/4 a total of three times, until nothing is left, and the quotient is indeed 3. Understanding division as repeated subtraction, however, is nonsensical for a problem like 1/4 divided by 2/3 because 2/3 cannot be subtracted from 1/4 even once. No wonder students have trouble with fractions in high school.
Leave aside the odd use of 'erroneously' to describe a working algorithm, but does anyone really think that it's easier to teach kids this complicated method of subtracting fractions instead of the normal "invert and multiply" method? The subtraction method is going to take more computation except in the rare cases where the two fractions have the form a/b and ca/b. I guess that's the point of all the hubub. But maybe I'm out of touch with exactly how the average kid learns math.


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Översättning 'nautical mile' – Ordbok svenska-Engelska Glosbe
10 nautical miles to miles = 11.50779 miles. 15 nautical miles to miles = 17.26169 miles. 20 nautical miles to miles = 23.01559 miles. 25 nautical miles to miles = 28.76949 miles. 30 nautical miles to miles = 34.52338 miles. 40 nautical miles to miles = 46.03118 miles 1 Nautical Miles to Miles Conversion breakdown and explanation 1 naut mi to mi conversion result above is displayed in three different forms: as a decimal (which could be rounded), in scientific notation (scientific form, standard index form or standard form in the United Kingdom) and as a fraction (exact result). A nautical mile is a unit of measurement used in air, marine, and space navigation, and for the definition of territorial waters.
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It is a non-SI unit used especially by navigators in the shipping and aviation industries, and also in polar exploration. Feet : A foot (symbol: ft) is a unit of length. It is equal to 0.3048 m, and used in the imperial system of units and United States customary units. 1 metre is equal to 0.00062137119223733 miles, or 0.00053995680345572 nautical mile.
Hydrauliska försök, anställda vid Fahlu grufva, åren 1811-1815,
Convert From Angstrom. 1 Angstrom (Å) = 1.0E-8 Centimeter (cm) 5.4680664916885E-11 Fathom (fat) One Cable Length (Imperial) is 608 feet or 185.3184 meters. 1 Cable Length (Imperial) = 185.3184 m (SI base unit).
Exempel A B 1 Celsius Farenheit 2 100 212 3 100 212 4 100
10 miles to nautical mile = 8.68976 nautical mile. 20 miles to nautical mile = 17.37952 nautical mile.
Square kilometer km².
Here are some practical tips for getting diversity right this time. By Kathleen Melymuka Computerworld | Unlike the wild hiring of the '90s, the slow rebuilding of bare-bones IT shops over the next few ye Understanding the costs and benefits of different plans can help you decide what works best for you Understanding the costs and benefits of different plans can help you decide what works best for you. Auto insurance can seem like an expensi One degree equals 60 nautical miles; One minute of one degree equals one nautical mile. You don't even need a scale on a nautical or aviation map Convert 1 Nautical miles to Miles | Convert 1 n mile to mile with our conversion calculator and conversion table.
Note: Square mile is an imperial or United States customary unit of area. Square nautical mile is a metric unit
1 Light years = 5108276676565.9 Nautical miles: 10 Light years = 51082766765659 Nautical miles: 2500 Light years = 1.2770691691415×10 16 Nautical miles: 2 Light years = 10216553353132 Nautical miles
1 Nautical miles = 6076.12 Feet: 10 Nautical miles = 60761.15 Feet: 2500 Nautical miles = 15190288.71 Feet: 2 Nautical miles = 12152.23 Feet: 20 Nautical miles = 121522.31 Feet: 5000 Nautical miles = 30380577.43 Feet
Convert 1.95 Nautical Miles to Millimeters (1.95 nmi to mm) with our Length converter. How many Millimeters in 1.95 nmi.
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Historically, it was defined as one sixtieth of..more definition+. In relation to the base unit of [length] => (meters), 1 Nautical Miles (NM) is equal to 1852 meters, while 1 Pixels (PX) = 0.0002645833 meters. 1 Kilometer = 0.539957 Nautical Mile | Kilometer to Nautical Mile conversion allows you to convert value between Kilometer to Nautical Mile easily.
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One international nautical mile is equivalent to 1,852 meters or 1.151 statue miles. Please not that this is different to a UK Nautical mile. A nautical ground mile is one nautical mile over the ground. A nautical air mile is one nautical mile through the air mass. This distance can be different because of wind.
Fil:Ocean currents 1943.jpg – Wikipedia
Hectare ha. Are a. Centiare ca.
An approximation of an arcminute simplified to 1852 meters in 1929. Approximately 6076.12 feet or 1.151 statute miles.


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