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  • regular polygons, in rings

    Dan MacKinnon
    20 Jul 2015 | 9:01 pm
    Looking at the Kepler pentagonal tiling, you may notice the nice looking rings of pentagons around the decagons.You can also make up other tilings with these rings of pentagons - to get the one below to work you have to sneak in some dented or overlapping pentagons.But which regular n-gons can form rings like this? You obviously can't do it with a square.And some regular n-gons, like heptagons, nonagons, decagons, and hendecagons (11-gons) don't work either.All the angles of the regular n-gon are (n-2)pi/n - so the angles of the polygon in the center would have to be 4pi/n, but for that…
  • How to Get to the Fourth Dimension

    Scientific American - Math
    31 Jul 2015 | 6:30 am
    A new book offers mathematical puzzles, such as fitting a coin through a hole that seems too small to accommodate it -- Read more on
  • Math Mammoth Grade 7 (pre-algebra)

    Homeschool Math Blog
    25 Jun 2015 | 2:06 pm
    Math Mammoth Grade 7 and 7-B are available now - as downloads! Printed books and a CD version will follow soon. Check for description and samples.
  • Jun 17, Exponents rules

    Math-for-all-grades Blog
    17 Jun 2015 | 12:22 am
    Exponents rules enable arithmetic expression of base and index.
  • Median = Geometric Mean? A Common Core Investigation

    Dave Marain
    18 Jul 2015 | 4:12 pm
    As tweeted on J noticed that for an arithmetic sequence like 3,7,11,15,19 the median equals the arithmetic mean. In this case, the median and "mean" are both 11. She found this was well-known and not too difficult to prove. She wondered if there was an analogous rule for geometric sequences like 2,4,8,16,32. Instead of the arithmetic mean she tried the geometric mean: (2•4•8•16•32)^(1/5) which equals 8, the median. VERIFY THIS WITHOUT A CALCULATOR! Unfortunately her conjecture failed for a geometric sequence with an even number of terms like 2,4,8,16…
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    MATH - Google News

  • New York City Questions English, Math and Science Taught at Yeshivas - New York Times

    31 Jul 2015 | 7:17 pm
    New York TimesNew York City Questions English, Math and Science Taught at YeshivasNew York TimesThe New York City Department of Education plans to investigate whether roughly three dozen private yeshivas are providing an adequate education in secular subjects like English, math and science, in response to a letter from parents, former students
  • Algebra Camp boosts math skills for 300-plus incoming ninth-graders - Your Houston News

    31 Jul 2015 | 5:48 pm
    Your Houston NewsAlgebra Camp boosts math skills for 300-plus incoming ninth-gradersYour Houston News“The Algebra camp helped to excite students about math before they enter ninth grade,” said Yolonda Sneed, Jersey Village camp director. “Students are exposed to a rigorous high school curriculum while having fun without any grade penalties. Students ...
  • Statesville Middle summer camp focused on science, math - Statesville Record & Landmark

    31 Jul 2015 | 5:15 pm
    Statesville Record & LandmarkStatesville Middle summer camp focused on science, mathStatesville Record & Landmark... head-start this summer. For the past three weeks, about two dozen students discovered different ecosystems around creeks, planted and maintained vegetables, used math to create birdhouses and constructed boats with aluminum and swimming noodles.and more »
  • Barbie's Bungee Jump Adventure Illustrates Math Concepts - KFYR-TV

    31 Jul 2015 | 4:30 pm
    KFYR-TVBarbie's Bungee Jump Adventure Illustrates Math ConceptsKFYR-TVThere's often a disconnect when trying to teach students how math and science applies in the real world. Teachers from around the state are in Bismarck to learn new and fun techniques. For most adults, Barbies are just a childhood memory. For North ...and more »
  • Tuscaloosa City Schools holds job fair for math teachers - FOX6 WBRC -

    31 Jul 2015 | 4:02 pm
    Tuscaloosa City Schools holds job fair for math teachersFOX6 WBRC - MyFoxAL.comTuscaloosa City Schools held an invitation-only job fair for highly qualified math teachers on Friday morning. School starts in two weeks and they have five openings that need to be filled. Administrators say there are about 100 openings statewide for and more »
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    Search for "math OR mathematics"

  • Former teacher pleads guilty to child seduction

    31 Jul 2015 | 9:41 pm
    A former New Haven High School math teacher pleaded guilty Friday to one count of child seduction, a Level 5 felony, and one count of dissemination of harmful material, a Level 6 felony. Four other charges were dismissed.
  • Lehrman has seen four decades of ACAC's best

    31 Jul 2015 | 9:40 pm
    For the last four decades, the Allen County Athletic Conference has been led by football coaching giants. Rick Minnich , Bob Yager , Kirk Sorg , Mark Lefebvre , Leland Etzler and then Jared Sauder built an identity of tough, hard-hitting football for the league.
  • Teachers Are Not Stressed, Underpaid

    31 Jul 2015 | 9:39 pm
    I am responding to the July 19, 2015, article written by Marshall Greenstein regarding teacher stress and salaries.
  • Stamford help exchange

    31 Jul 2015 | 9:23 pm
    To submit an item to Help Exchange, email with "Help Exchange" in the subject line. For more information, contact the Volunteer Center of United Way of Western Connecticut at 203-348-7714 unless otherwise noted.
  • Breathtaking photos capture rare blue moon

    31 Jul 2015 | 9:20 pm
    Friday night's blue moon wasn't blue, but its grandeur still prompted many to look up to the night sky in awe. People from all over the world gawked at the lunar rarity.
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    Mathematics News -- ScienceDaily

  • Ants in the lead: How ants cooperate in steering food to their nest

    30 Jul 2015 | 7:45 am
    A physics-based model can explain how ants cooperate in steering food to their nest. To lug a large object, a number of ants surround it -- the back ones lift, those on the leading edge pull. How do they stay on track, instead of simply pulling all around in a sort of tug-of-war? Scientists used video analysis to track the individual movements of ants in a group that was carrying a large food item toward their nest.
  • Majority rule: Why conformity can actually be a good thing

    28 Jul 2015 | 9:57 am
    Like to go your own way? Most of us actually prefer to follow the pack, according to research. That's one of the outcomes from a study that examines how mathematical models predict human behavior.
  • A new litmus test for chaos?

    28 Jul 2015 | 8:07 am
    Researchers have come up with a new definition of chaos that applies more broadly than Lyapunov exponents and other previous definitions of chaos. The new definition fits on a few lines, can be easily approximated by numerical methods, and works for a wide variety of chaotic systems.
  • The algorithm of writing

    24 Jul 2015 | 12:19 pm
    Researchers explores the promise and peril of computer-based writing assessment software.
  • Model for robots with bacteria-controlled brains

    16 Jul 2015 | 6:15 am
    A scientist used a mathematical model to demonstrate that bacteria can control the behavior of an inanimate device like a robot.
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    Loren on the Art of MATLAB

  • Incremental Delaunay Construction

    Loren Shure
    15 Jul 2015 | 11:47 am
    I'm happy to welcome back Damian Sheehy as guest blogger. Last time Damian wrote about how Natural Neighbor interpolation addresses FAQs in scattered data interpolation. In this blog he will answer a FAQ on adaptively editing a Delaunay triangulation.ContentsIs delaunayTriangulation More Efficient than delaunay?When is Incremental Delaunay Important?Performance Example of Incremental Delaunay ConstructionYour Need for Geometric Tools?Is delaunayTriangulation More Efficient than delaunay?A technical support question that occasionally crops up asks about the best and most efficient way to…
  • Natural Neighbor – A Superb Interpolation Method

    Loren Shure
    1 Jul 2015 | 11:46 am
    I'm happy to welcome Damian Sheehy as this week's guest blogger. Damian works on the development of geometry-related features at MathWorks. He will provide answers to two frequently asked questions; one on scattered data interpolation that he will cover in this blog and the other on Delaunay triangulation that he will cover in the next. Over to you, Damian...ContentsAn Email from Customer SupportWhy griddata or scatteredInterpolant May Be InconsistentExample of Inconsistent Behavior in Linear InterpolationWhy Natural Neighbor Interpolation is SuperiorYou Tell Me!An Email from Customer…
  • How Do You Modify the Background of an Image?

    Loren Shure
    24 Jun 2015 | 8:36 am
    Today I'd like to introduce guest blogger Brett Shoelson. Some of you may know Brett through his File Exchange submissions, or through his involvement with the Pick of the Week blog, or from occasional guest posts on Steve’s blog on image processing.Contents"The visa problem"The original photoFirst question: how do we isolate the background?Is the effort of automation justified?Improving the maskModifying the backgroundTwo problems remain...Planewise manipulationsFixing the interfaceA final note"The visa problem"Loren recently told me she had a pending international trip that requires a…
  • Getting Started with Kaggle Data Science Competitions

    Loren Shure
    18 Jun 2015 | 11:44 am
    Have you been interested in data science competitions, but not sure where to begin? Today's guest blogger, Toshi Takeuchi, would like to give a quick tutorial on how to get started with Kaggle using MATLAB.ContentsThe Titanic Competition on KaggleData Import and PreviewEstablishing the BaselineBack to Examining the DataExploratory Data Analysis and VisualizationFeature EngineeringYour Secret Weapon - Classification LearnerRandom Forest and Boosted TreesModel EvaluationCreate a Submission FileConclusion - Let's Give It a TryThe Titanic Competition on KaggleMATLAB is no stranger to competition…
  • Advice for Making Prettier Plots

    Loren Shure
    11 Jun 2015 | 6:27 am
    A few years ago, Jiro wrote a popular post for making pretty plots on this blog. We also host a blog specifically about graphics by Mike. And with the R2014b release of MATLAB came an updated graphics system that Dave described last year in a 3 part series: Part 1, Part 2, and Part 3.Even with that, I continue to hear questions about how to accomplish certain tasks, such as using a symbol to indicate degrees. This post contains a collection of a few tips that may help you update your plots to match more closely what you are trying to convey.ContentsPlotting Temperature DataAdd Y Label with…
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    Homeschool Math Blog

  • Math video for kids: Adding three numbers

    8 Jul 2015 | 1:23 pm
    Let your little ones have fun learning how to add three numbers with this new video of mine, which also features Mathy the Mammoth as my mascot. :)The video is intended for first grade.
  • Math Mammoth Grade 7 (pre-algebra)

    25 Jun 2015 | 2:06 pm
    Math Mammoth Grade 7 and 7-B are available now - as downloads! Printed books and a CD version will follow soon. Check for description and samples.
  • Homeschooling - history and state today

    16 Jun 2015 | 3:19 pm
    Here's an interesting infographic about homeschooling - its history and its state today. Click to enlarge. :) Source:
  • Homeschooling With Greater Joy and Peace

    11 Jun 2015 | 12:55 pm
    This is a guest post by Alecia Baptiste.Some days homeschooling our children can be amazing.  We wake up in the morning feeling rested, excited about facing the challenges of the new day and eager to explore with our children.  On those days our children are excited about learning and cooperative.  And don't you love it when your children have those “Aha” moments?  When they finally get that math concept or they make some connection between facts or after months of struggling to read, you see them lying contently in bed reading a book. On those day we think to…
  • Math Mammoth printed versions in color

    4 Jun 2015 | 6:05 am
    Did you know? Math Mammoth grades 1-3 printed books are now available as color versions through Rainbow Resource.Currently you need to access them via their search function: search for "math mammoth color". Hopefully they'll get their own category page soon.
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    Let's Play Math!

  • Math(s) Teachers at Play #88 via mathematicsandcoding

    Denise Gaskins
    30 Jul 2015 | 11:20 am
    From elementary to high school, manipulatives to Minecraft, there’s plenty of fun to be had at this month’s math education blog carnival: Math(s) Teachers at Play 88 Enjoy! So, here is issue 88 of the Math(s) Teachers at Play blog carnival. This acts as a round up of some cool blog posts that have been published since issue 87 over at cavmaths. As usual people have submitted entries, which I will supplement with some posts that I have really enjoyed reading in the last few weeks. Click here to read the blog carnival post at mathematicsandcoding. [Feature photo (top) by Pratham…
  • Noticing Fractions in a Sidewalk

    Denise Gaskins
    28 Jul 2015 | 5:04 am
    My daughters didn’t want to admit to knowing me, when I stopped to take a picture of the sidewalk along a back street during our trip to Jeju. But aren’t those some wonderful fractions? What do you see? What do you wonder? Here is one of the relationships I noticed in the outer ring: And this one’s a little trickier: Can you find it in the picture? Each square of the sidewalk is made from four smaller tiles, about 25 cm square, cut from lava rock. Some of the sidewalk tiles are cut from mostly-smooth rock, some bubbly, and some half-n-half. I wonder how far we could go…
  • Murphy Strikes My Paperbacks :(

    Denise Gaskins
    23 Jul 2015 | 5:55 pm
    The colors are supposed to go all the way off the edge. They worked just fine in the pre-publication proof…Murphy’s Law struck today, and the paperback books that looked so good in the proof copies turned out to have a cover glitch, at least in the ones I ordered from Amazon. I’m working with CreateSpace to make sure it gets straightened out—but that means the books may show up as “unavailable” for awhile. As with any print-on-demand glitch, if you got a badly printed book you can ask Customer Support to replace it. It could be worse. The interior of the…
  • 30% Discount for Email Newsletter Subscribers

    Denise Gaskins
    21 Jul 2015 | 12:41 am
    [Feature photo (above) by Glen Wright via Flickr (CC BY 2.0).] Wouldn’t it be wonderful if math was something your children WANTED to do? With the Math You Can Play series, your kids can practice their math skills by playing games with basic items you already have around the house, such as playing cards and dice. Paperback editions of the first two Math You Can Play books will be out any day now. If you’re subscribed to my Tabletop Academy Press Updates email newsletter, I’ll be sending you a 30% discount code by Thursday, or as soon as both books pass through the last few…
  • Education Bloggers: Share Your Post!

    Denise Gaskins
    20 Jul 2015 | 4:48 am
    photo by Omar Omar via flickr If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s Math Teachers at Play (MTaP) math education blog carnival. Click here to submit your blog post. Don’t procrastinate: The deadline for entries is this Friday, July 24. The carnival will be posted next week at mathematicsandcoding. If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing… Need an Idea-Starter?
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    Computational Complexity

  • Explain this Scenario in Jeapardy and some more thoughts

    28 Jul 2015 | 8:44 pm
    In the last post I had the following scenario: Larry, Moe, and Curly are on Jeopardy. Going into Final Jeopardy: Larry has $50,000, Moe has $10,000, Curly has $10,000 Larry bets $29,999, Moe bets $10,000, Curly bets $10,000 These bets are ALL RATIONAL and ALL MATTER independent of what the category is. For example, these bets make sense whether the category is THE THREE STOOGES or CIRCUIT LOWER BOUNDS. Explain why this is. EXPLANATION: You were probably thinking of ordinary Jeopardy where the winner gets whatever he gets, and the losers take-home is based ONLY on their rank (2000 for second…
  • Explain this Scenario on Jeopardy

    27 Jul 2015 | 3:22 pm
    Ponder the following: Larry, Moe, and Curly are on Jeopardy. Going into Final Jeopardy: Larry has $50,000, Moe has $10,000, Curly has $10,000 Larry bets $29,999, Moe bets $10,000, Curly bets $10,000 These bets are ALL RATIONAL and ALL MATTER independent of what the category is. For example, these bets make sense whether the category is THE THREE STOOGES or CIRCUIT LOWER BOUNDS. Explain why this is. I'll answer in my next post or in the comments of this one depending on... not sure what it depends on.
  • New Proof of the Isolation Lemma

    23 Jul 2015 | 6:07 am
    The isolation lemma of Mulmuley, Vazirani and Vazirani says that if we take random weights for elements in a set system, with high probability there will be a unique set of minimum weight. Mulmuley et al. use the isolation lemma to randomly reduce matching to computing the determinant. The isolation lemma also gives an alternative proof to Valiant-Vazirani that show how to randomly reduce NP-complete problems to ones with a unique solution. Noam Ta-Shma, an Israeli high school student (and son of Amnon), recently posted a new proof of the isolation lemma. The MVV proof is not particularly…
  • Hartley Rogers, Author of the first Textbook on Recursion Theory, passes away

    21 Jul 2015 | 10:53 am
    Hartley Rogers Jr passed away on July 17, 2015 (last week Friday as I write this).He was 89 and passed peacefully. For our community Rogers is probably best known for his textbook on Recursion Theory which I discuss below. He did many other things, for which I refer you to his Wikipedia page here. His book was: The theory of recursive functions and effective computability. It was first published in 1967 but a paperback version came out in 1987. It was probably the first textbook in recursion theory. It was fairly broad. Here are the chapter headings and some comments. Recursive functions…
  • Microsoft Faculty Summit

    16 Jul 2015 | 5:40 am
    Last week I participated in my first Microsoft Faculty Summit, an annual soiree where Microsoft brings about a hundred faculty to Redmond to see the latest in Microsoft Research. I love these kinds of meetings because I enjoy getting the chance to talk to computer scientists across the broad spectrum of research. Unlike other field, CS hasn't had a true annual meeting since the 80's so it takes events like this to bring subareas together. "Unlike other fields" is an expression we say far too often in computer science. This was the first summit since the closing of the Silicon Valley lab and…
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    Mathematics and Computation

  • Intermediate truth values

    Andrej Bauer
    30 Jul 2015 | 1:16 am
    I have not written a blog post in a while, so I decided to write up a short observation about truth values in intuitionistic logic which sometimes seems a bit puzzling. Let $\Omega$ be the set of truth values (in Coq this would be the setoid whose underlying type is $\mathsf{Prop}$ and equality is equivalence $\leftrightarrow$, while in HoTT it is the h-propostions). Call a truth value $p : \Omega$ intermediate if it is neither true nor false, i.e., $p \neq \bot$ and $p \neq \top$. Such a “third” truth value $p$ is proscribed by excluded middle. The puzzle is to explain how the…
  • The troublesome reflection rule (TYPES 2015 slides)

    Andrej Bauer
    19 May 2015 | 8:10 am
    Here are the slides of my TYPES 2015 talk “The troublesome reflection rule” with fairly detailed presenter notes. The meeting is  taking place in Tallinn, Estonia – a very cool country in many senses (it’s not quite spring yet even though we’re in the second half of May, and it’s the country that gave us Skype). Download slides: The troublesome reflection rule (TYPES 2015) [PDF].
  • Another PhD position in Ljubljana

    Andrej Bauer
    3 Apr 2015 | 4:12 am
    It is my pleasure to announce a second PhD position in Ljubljana! A position is available for a PhD student at the University of Ljubljana in the general research area of modelling and reasoning about computational effects. The precise topic is somewhat flexible, and will be decided in discussion with the student. The PhD will be supervised by Alex Simpson who is Professor of Computer Science at the Faculty of Mathematics and Physics. The position will be funded by the Effmath project (see project description). Full tuition & stipend will be provided. The candidate should have a…
  • A HoTT PhD position in Ljubljana

    Andrej Bauer
    22 Nov 2014 | 4:16 am
    I am looking for a PhD student in mathematics. Full tuition & stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is somewhat flexible and varies from constructive models of homotopy type theory to development of a programming language for a proof assistant based on dependent type theory, see the short summary of the Effmath project for a more detailed description. The candidate should have as many of the following desiderata as possible, and at the very least a master’s degree (or an equivalent one): a…
  • TEDx “Zeroes”

    Andrej Bauer
    16 Oct 2014 | 12:01 am
    I spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics. Taking John Baez’s The Bauty of Roots as an inspiration, I drew a very large image (20000 by 17500 pixels) of all roots of all polynomials of degree at most 26 whose coefficients are $-1$ or $1$. That’s 268.435.452 polynomials and 6.979.321.752 roots. It is two degrees more than Sam Derbyshire’s image,  so consider the race to be on! Who can give me 30 degrees? The code…
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    IMA Journal of Applied Mathematics - current issue

  • Travelling wave solutions in periodic monostable equations on a two-dimensional spatial lattice

    Cheng, C.-P., Li, W.-T., Lin, G.
    15 Jul 2015 | 8:48 am
    This paper is concerned with travelling wave solutions of periodic monostable differential equations on a two-dimensional lattice. The existence, stability and uniqueness of supercritical travelling wave solutions are obtained by comparison principle.
  • Linear complementarity representation of piecewise linear functions

    Sakurai, T., Murofushi, T.
    15 Jul 2015 | 8:48 am
    We investigate a representation of piecewise linear function containing a complementarity condition, and call it a linear complementarity representation. This representation is also known as ‘Bokh1’ or ‘state-variable representation’ in literature. We discuss two spacial types of representation, called P-representation and ULT-representation, and give an elementary proof to show that either one of these two types of representation completely characterizes any piecewise linear function. We can also demonstrate that a P-representation can be transformed into a…
  • Low-frequency on-site identification of a highly conductive body buried in Earth from a model ellipsoid

    Perrusson, G., Vafeas, P., Chatjigeorgiou, I. K., Lesselier, D.
    15 Jul 2015 | 8:48 am
    Identification of a highly conductive orebody buried in Earth using an equivalent, perfectly conducting, triaxial model ellipsoid is investigated. The real data available (three-component magnetic fields collected along a borehole due to a single-frequency current loop at the Earth surface) are simulated via a low frequency, closed-form power series expansion of the electromagnetic fields scattered off an equivalent ellipsoid within a homogeneous, conductive medium, the source itself being idealized as a vertical magnetic dipole nearby. The approach provides formulations amenable to fast yet…
  • Spatial dynamics of a time-delayed reaction and diffusion malaria model

    Xu, Z., Zhang, Y.
    15 Jul 2015 | 8:48 am
    This paper is concerned with the spatial dynamics of a time-delayed reaction and diffusion malaria model. We first analyse the well-posedness of the initial-boundary value problem of the model. Then, we study the global stability of the disease-free or endemic steady state for the system by structuring two Lyapunov functionals. Moreover, by applying Schauder fixed-point theorem, we establish the existence of travelling wave solutions connecting the two steady states: the disease-free steady state and the endemic steady state if the basic reproduction ratio $\mathcal {R}_0 > 1$, and show the…
  • European option pricing with transaction costs and stochastic volatility: an asymptotic analysis

    Caflisch, R. E., Gambino, G., Sammartino, M., Sgarra, C.
    15 Jul 2015 | 8:48 am
    In this paper, the valuation problem of a European call option in the presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion is shown to be the classical Black and Scholes solution, the correction terms appear at O(1/2) and O(). The optimal hedging strategy is then explicitly obtained for Scott's model.
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    WordPress Tag: Mathematics

  • An open letter to Dr. Palmer, the killer of Cecil the Lion

    Dan Ma
    31 Jul 2015 | 9:15 pm
    Dear Dr. Walter J. Palmer: Because of your “adventure” in Zimbabwe, you are now the most famous dentist in the world. You recently have admitted to killing Cecil, a 13-year-old lion that is the best known lion in Zimbabwe. Cecil was lured from a wild life sanctuary with bait, shot with an arrow by you, tracked for 40 hours, and finally shot dead with a rifle and then beheaded and skinned. No doubt, this would be another trophy to add to your huge collection (you are known to be an experienced hunter with 43 kills of exotic animals under your belt). However, Cecil was wearing a GPS…
  • the reveries of a solitary wa*ker: wa*k 4 (universal matters)

    stewart henderson
    31 Jul 2015 | 5:28 pm
    could someone be spreading BS over the internet? The universe is more turbulent than we imagined. It’s a quantum computer. It’s nothing but information. Where’s all the lithium? Is it really spinning, and are we anywhere near the axis? What was in the beginning? Pure energy? What does that mean? Energy without particles? The energy coalesced into particles, so I’ve read. Sounds a bit miraculous to me. The fundamental particles being quarks and electrons. Leptons? But quarks aren’t leptons, they’re fermions but leptons are also fermions but these are but names. Quarks came together…
  • About Completeness

    Dialid Santiago
    31 Jul 2015 | 3:23 pm
    About this Quote These words were said by David Hilbert during his lecture “Mathematical Probl
  • Arts Review: The Amazing World of MC Escher.

    31 Jul 2015 | 1:23 pm
    My lack of patience with M.C. Escher is a thread which I can trace all the way back to a definite be
  • Maths, maths, maths!

    31 Jul 2015 | 12:16 pm
    Today I have wrestled with weighted linear regression, multiplying and inversing matrices and trying to convert an extremely complex excel spreadsheet full of formulae I had never seen before in my life into a PHP function! So that was fun! Still I am not as bad as this guy.
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  • Balanced Learning is not Blended or Flipped

    Dave Marain
    30 Jul 2015 | 4:53 pm
    Haven't been up to one my passionate rants in a long time so buckle up...Technology has enabled educators to reimagine the  traditional classroom, how students learn and how we facilitate this process, aka teach. Incredible new opportunities to empower students to take more control over their own learning in a "space-time continuum" sort of way. Not to mention providing powerful tools to analyze data to individualize and maximize learning. Are there any buzzwords I omitted!BUT...We have strayed from NCTM'S central message from over 25 years ago: ***BALANCING*** PROCEDURAL LEARNING and…
  • Modeling - What Algebra Looks Like on the New SAT/PSAT and the Common Core

    Dave Marain
    28 Jul 2015 | 6:20 pm
    On bear population, P(t), after t yrs,  is modeled by P(t)=M-k(t-20)², 0≤t≤20. Initial population:356 Max pop'n:500 Estimated population after 10 yrs? Answer: 464COREFLECTIONSIs this the "new" algebra? Students given a function with PARAMETERS which "models" real world data? Questions like this have appeared on SATs for a few years now and, based on the sample new SAT/PSATs released by the College Board, they will become even more common. Students will be asked to analyze the function and use it in application. The Common Core also emphasizes algebra models -…
  • 37 not 42 the Answer to The Meaning of Life? A Common Core Investigation

    Dave Marain
    25 Jul 2015 | 3:31 am
    From Middle School Common Core InvestigationIs 37 an "interesting" #?37x4=148; 4-1="3",8-1="7" 37x13=481 37x22=81437x5=185; 8-5="3",8-1="7" 37x14=518 37x23=851How far can you extend the pattern?And is 37 patriotic (apologies to AK&HI)??37x48=1776And my favorite ...1/37=0.027027... 1/27=0.037037...Is it all because 37x3=111?First we engage, then illuminate...VISIT ME DAILY ON TWITTER AT
  • Parabolas, NEW PSAT/SAT and the Common Core

    Dave Marain
    20 Jul 2015 | 10:11 am
    As posted on SHOW: The line with slope 1 intersecting y=-(x-h)²+k at its vertex also intersects at (h-1,k-1). COREFLECTIONS How would you modify this to make a grid-in or multiple choice question? A question similar to this appears on the published practice NEW PSAT. It is one of the last 3-4 questions on the grid-in with calculator section and was rated "medium" difficulty. I would rate it as more difficult! I recently tweeted the link for this practice test but easy to find on the College Board website. Do the parameters h,k discourage use of graphing…
  • Median = Geometric Mean? A Common Core Investigation

    Dave Marain
    18 Jul 2015 | 4:12 pm
    As tweeted on J noticed that for an arithmetic sequence like 3,7,11,15,19 the median equals the arithmetic mean. In this case, the median and "mean" are both 11. She found this was well-known and not too difficult to prove. She wondered if there was an analogous rule for geometric sequences like 2,4,8,16,32. Instead of the arithmetic mean she tried the geometric mean: (2•4•8•16•32)^(1/5) which equals 8, the median. VERIFY THIS WITHOUT A CALCULATOR! Unfortunately her conjecture failed for a geometric sequence with an even number of terms like 2,4,8,16…
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    Math Bootcamps

  • Reading scatterplots

    9 Jul 2015 | 1:55 pm
    Scatterplots are used to understand the relationship or association between two variables. Questions like “When the temperature increases, do gas prices also increase?” or “How are changes in the price of gas related to the number of miles people drive each month?” can be answered by studying the pattern in a scatterplot. Basic Structure Given a scatterplot, the variable on the horizontal axis is the predictor (or independent variable) and the variable on the vertical axis is the response (or dependent variable). Using this terminology, a scatterplot is used to…
  • Making two way tables

    20 Jun 2015 | 10:35 am
    Two way tables, also known as contingency tables, show frequencies (counts) as they relate to two variables. As usual, we will use an example to see how they work! Example Suppose that a company is doing market research on a new product and have selected a random sample of potential customers to help choose the most effective TV commercial. Out of the 180 people in the sample 65 viewed the first version, 30 viewed the second version, and the remainder viewed the third. Of those who viewed the first version, 25 indicated that they were likely to buy the product while the rest said they were…
  • Scatterplots on the TI83 or TI84 graphing calculator

    19 Jun 2015 | 4:04 pm
    Scatterplots are used to visualize the relationship or association between two variables. For example, can you say in general that studying more will result in higher grades? We could investigate this by collecting data on how long students studied and perhaps their grade on a final exam and then creating a scatterplot. The overall pattern would help us determine what kind of association time spent studying has with final exam grades. On the TI83 or 84 series of graphing calculators, getting a scatterplot is pretty easy. Let’s use an example data set to walk through the process. Example…
  • How to read a boxplot

    14 Jun 2015 | 11:33 am
    Boxplots are a way of summarizing data through visualizing the five number summary which consists of the minimum value, first quartile, median, third quartile, and maximum value of a data set. If a data set has no outliers, a boxplot will be made up of the following values. But, if there ARE outliers (those are values that fall far from the main pattern of the dataset), then a boxplot will instead be made up of the following values. As you can see above, outliers (if there are any) will be shown by stars or points off the main plot. If there are no outliers, you simply won’t see those…
  • Common shapes of distributions

    13 Jun 2015 | 5:18 pm
    When making or reading a histogram, there are certain common patterns that show up often enough to be given special names. Sometimes you will see this pattern called simply the shape of the histogram or as the shape of the distribution (referring to the data set). While the same shape/pattern can be seen in many plots such as a boxplot or stemplot, it is often easiest to see with a histogram. In the examples below, we will look at each of these shapes and some of their important properties. Bell shaped / symmetric Histograms that are bell shaped/symmetric appear to have one clear center that…
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    Institute for Mathematics and Computer Science

  • IMACS Expands to New Locations in Delray Beach and Pembroke Pines!

    IMACS Staff Writer
    24 Jul 2015 | 6:30 am
    When it comes to providing their children with the lifelong benefits of genuine learning, South Florida parents know where to go — IMACS! For over 20 years, the Institute for Mathematics and Computer Science has been giving students an outlet for reaching their highest potential in math, computer science and logical reasoning. IMACS teaches its unique classes after-school at its own centers as well as at many of the top private schools in the tri-county area, including Pine Crest, American Heritage and University School. To meet the growing demand for its classes, IMACS is expanding to…
  • IMACS Wishes You aHappy Independence Day!

    IMACS Staff Writer
    2 Jul 2015 | 6:06 am
    The IMACS Blog is taking a short summer hiatus and will return next month. Have a safe and happy 4th of July! Looking for an incredibly fun summer experience that exercises the mind? Check out IMACS’ Hi-Tech Summer Camp! Like IMACS on Facebook for the latest information about our local classes and online courses.
  • Slowing Down to Get Ahead in Math

    IMACS Staff Writer
    3 Jun 2015 | 10:00 pm
    "The classrooms that produce high achieving students are those in which students work on deep, rich mathematics through tasks that they can take to any level they want. No one is told what level they can reach and no one is held back by narrow questions that limit students’ mathematical development and creativity." —Jo Boaler, Professor of Mathematics Education, Stanford The above quote comes from a recent article by Stanford professor Jo Boaler. Professor Boaler, through her Youcubed organization, advocates for valuing depth and creative problem-solving over…
  • Motivation and the Gifted Child

    IMACS Staff Writer
    6 May 2015 | 10:00 pm
    "My kid could finish his math homework in no time if he would just do it, but instead he drags it out for an hour, and that’s with me having to nudge him through it." Sound familiar? Parents and teachers often assume that a gifted child will automatically be a high achiever given the child’s high abilities, so it comes as a surprise when he or she underachieves. There can be a variety of reasons for underachievement, but a common cause is lack of motivation. Whereas bright students often enjoy working toward external recognition for their accomplishments, gifted learners…
  • 11-Year-Old Davidson Young Scholar Scores Perfect 800 on SAT Math Test

    IMACS Staff Writer
    8 Apr 2015 | 10:00 pm
    IMACS student Shiva Oswal and his parents pose in front of the magnificent Atlantis Hotel on a family trip to Dubai. When fewer than 1% of 2014 college-bound high school seniors attain a perfect 800 on the math section of the SAT, you know that you’ve met someone special when he’s achieved that amazing feat before even cracking the teen years. That someone is Shiva Oswal, a precocious 11-year-old from Northern California who recently earned that lofty score as part of a program through Johns Hopkins’ Center for Talented Youth (CTY) called the Julian C.
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  • regular polygons, in rings

    Dan MacKinnon
    20 Jul 2015 | 9:01 pm
    Looking at the Kepler pentagonal tiling, you may notice the nice looking rings of pentagons around the decagons.You can also make up other tilings with these rings of pentagons - to get the one below to work you have to sneak in some dented or overlapping pentagons.But which regular n-gons can form rings like this? You obviously can't do it with a square.And some regular n-gons, like heptagons, nonagons, decagons, and hendecagons (11-gons) don't work either.All the angles of the regular n-gon are (n-2)pi/n - so the angles of the polygon in the center would have to be 4pi/n, but for that…
  • regular polygons, intersecting regularly

    Dan MacKinnon
    3 Jul 2015 | 11:54 am
    Looking through the chapter on the number 5 in the really engaging book Single Digits: In Praise of Small Numbers, by Marc Chamberland, I came across an image and description of Kepler's pentagonal tiling, which looks like this:Kepler Pentagonal TilingThis tiling is made of pentagons, pentagrams, decagons, and fused decagons. Both the decagons and the fused decagons can be made from combinations of regular pentagons and dented pentagons (by dented, I mean in the way described here), so this tiling could also be made with pentagons, dented pentagons, and pentagrams.Decagons and fused…
  • regular polygons, dented and sliced

    Dan MacKinnon
    12 Jun 2015 | 8:13 pm
    A while ago, l noticed that sliced up octagons made nice tiles.In particular, octagons that are split in a particular way into a dented octagon and a rhombus are pretty neat. These rhombuses are formed from so that they share with the octagon two adjacent sides of the octagon. The dented octagon is formed by slicing off the rhombus. Four of those dented octagons can be put around a vertex to form a pinwheel pattern, and four of the rhombs can be added to that pinwheel to make a bigger octagon.You can do this sort of rhombic slicing with any regular polygon with more than 4 sides (you could…
  • octo rhomb

    Dan MacKinnon
    30 May 2015 | 1:28 pm
    Regular octagons cannot be used to tile by themselves - if you try, you will find there are square gaps that need to be filled.If you slice a rhombus off your octagon, you'll end up with two tiles - a rhombus and a dented octagon.Each of these shapes can be used to tile by themselves, or tile together. The rhomb-by-itself tiling is easy to visualize (imagine a squashed grid), here is the dented-octagon tiling:Now, here's something else: you can take four of these rhombically challenged octagons to make a bigger octagon:You get a nice tree shape if you remove two rhombs from the original…
  • octagonal iteration with GSP

    Dan MacKinnon
    14 Apr 2015 | 6:51 pm
    Here is a little GSP iteration that I came across that I thought was worth sharing.Start with a line segment - this provides the only "free" points in the sketch - everything else is constructed on top of this, starting with a square based on AB.Next, construct the center of the square, and a circle centered on that square's center and diameter equal to the diagonal of the square.Next, construct points on the circle midway between the points provided by the corners of the squares.We'll iterate by mapping the original line segment onto pairs of these points (in GSP you can select the free…
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    Maths Tips From Maths Insider

  • Does Your Daughter Lack Math Confidence? She’s Not the Only One.

    Caroline Mukisa
    31 Jul 2015 | 5:09 am
    A recent study by the OECD (Organisation for Economic Cooperation and Development) has highlighted the problem of girls’ lack of math confidence. From the report: Girls “lack self-confidence” in their ability to solve mathematics and science problems and achieve worse results than they otherwise would, despite outperforming boys overall Girls do worse at math and sciences than boys, even though they do better in other subjects. This gender gap occurs in the majority of countries who took part in the PISA (Programme for International Student Assessment) tests, but the gap in the…
  • How Can I Help You Help Your Child With Math?

    Caroline Mukisa
    23 Jul 2015 | 2:13 am
    It’s been over 2 years since I blogged here on Maths Insider! So the first thing I’ll say is I’m sorry! I’ve still been connecting with Maths Insider readers through my Maths Insider Facebook page but have neglected those of you who have been coming over here for advice on helping your child with math. So what has Maths Insider been up to for the past 2 years? 1) Working with Tabtor Math For the past 2 years,I’ve been Tabtor’s instructor for International students looking after families everywhere from the UK to Europe to Asia and lots and lots of…
  • How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips

    Caroline Mukisa
    4 Apr 2014 | 8:14 am
    I saw this cool comic strip below, by the funny folks at Saturday Morning Breakfast Cereal (SMBC), a few weeks ago on Facebook , and spent a good few minutes cry-laughing (is that a thing?) Even my daughter in the midst of wrangling with quadratic equations in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving.   As part of my role as Instructor for International Students at Tabtor Math, I was given 5 math worksheets at Grade 5 and 6…
  • Check out These Challenging Online Math Tools for Gifted Kids

    Caroline Mukisa
    3 Dec 2013 | 1:28 am
    This is a guest post by Joseph Rodriguez While many educators agree that it is essential to improve the quality of math education in our public schools, a debate persists about how it should be done. Do we work with the students who are struggling, so that they can do better? Or do we push the students who are excelling, so they can move on to even greater things? Budgets are tight and many schools are pushed to decide one path or the other. Fortunately, many online resources can challenge gifted math students with new coursework and an outlet for their ingenuity. Here’s what you…
  • Holiday Math and More

    Caroline Mukisa
    28 Nov 2013 | 1:12 am
    If you’ve read my Tabtor vs Kumon blog post a few months back, you’ll know that I’ve been working with Tabtor Math, the personalized iPad based math program. I’m Tabtor’s instructor for many of their international students, and I’m also recording instructional videos which accompany each of the Tabtor worksheets as well as writing articles for their blog. As a result, It’s been a bit quiet here at Maths Insider but after the holiday I’ll hopefully be back here with a vengeance. I’ve still got plenty of ideas to share with you on Maths…
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  • Talking About Guns at School

    29 Jul 2015 | 12:09 pm
    I have a concealed handgun license. I own a couple of pistols and enjoy shooting them. I like to shoot trap and skeet. And I’m married to a lifetime member of the NRA. You could say I like guns. Being a teacher and liking guns is a bit of a challenge, though. When students talk about guns, I have to be careful. I don’t want to lie (it’s tough earning trust as a math teacher these days). But I don’t want to encourage inappropriate conversations. I talk about talking about guns. That’s not a typo. I talk about talking about guns with my students. If you try to…
  • Zentangle – Meditation, Art, Math!

    20 Jul 2015 | 4:13 am
    My cousin-in-law recently introduced me to this cool “doodling” method called Zentangle. I’ve been doing it quite a bit – especially since it’s far more socially acceptable to draw than check twitter during meetings. ahem… Zen… WHAT? Zentangle. Zen TANGLE. So it’s Zen-ish (meditative, calm, relaxing), using tangles (like doodles, but more intricate and structured). Each tangle is a design using circles, line segments, curves and/or shading. You repeat the tangle into a pattern, adding variety in size, shape or orientation to make some really…
  • Your Students Are Individuals

    17 Jul 2015 | 1:58 am
    I was so sad to when I made the decision to resign. For the last year I’ve been teaching students with diagnosed neurological differences. They’ve been remarkable from so many perspectives. But when I told one of the administrators how much I’ll miss them, the response was a cool, “There are always more students.” Interchangeable Students This flippant comment didn’t sit well with me. Of course there are always more students. But saying this implies that this year’s students are merely “numbers.” Numbers that can be interchanged with next year’s students. Just…
  • Texas Instruments Little Professor

    15 Jul 2015 | 11:05 am
    This morning I featured the Little Professor “electronic calculator” by Texas Instruments on episode 23 of #KnickKnackYack in the #MathShack. It was so cool and so much fun, I wanted to share it here. If you’re old enough, you might remember having one of these. Or coveting it because your friend had it. And if you’re geeky enough, you might remember actually playing it. You can find the vintage Little Professors here or buy a fancy new Solar Little Professor from TI here. And you can share this on Twitter, Facebook and even Pinterest! I do #KnickKnackYack in the…
  • Smurfy Student Traits You See in Yourself

    3 Jul 2015 | 9:00 am
    This past year I’ve had the incredible joy of teaching a group of students with diagnosed neurological differences. I like to think they learned from what I had to offer them. However, I learned so much more from them. Specifically about myself. Girl, Intensified One of the coolest things about this student population is that their differences make some of their characteristics much more intense. If a student was inclined to frustration, and got frustrated, he would get really really frustrated! Often these intense characteristics were so dramatic that it would drown out other…
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    Math-for-all-grades Blog

  • Jul 8, Interior Angles

    8 Jul 2015 | 3:03 am
    Angles formed between the sides of any polygon are called interior angles
  • Jun 17, Exponents rules

    17 Jun 2015 | 12:22 am
    Exponents rules enable arithmetic expression of base and index.
  • May 26, Distributive-property

    26 May 2015 | 3:18 am
    distributive property distributes an arithmetic operation over others such as addition, multiplication..
  • May 12, 10th-grade-math

    12 May 2015 | 12:11 am
    10th grade math consisting of algebra, arithmetic, geometry, coordinate geometry, statistics.
  • Feb 9, algebra 1 help

    8 Feb 2015 | 10:04 pm
    algebra 1 help includes data analysis tools, functions, equations, inequalities, exponents, polynomials, quadratic equations
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    MIND Research Institute Blog

  • Off the Number Line: We Struck Gold!

    Matthew Peterson and James Huang
    30 Jul 2015 | 9:00 am
    Interviewer: Oh, I get it… They are mining for numbers. Cartoonist: Yes, but look at the awesome number they found! That's the golden ratio: 1.61803398875... Interviewer: I've heard of the golden ratio before, but I never knew it was approximately 1.618. Why is it called “golden”? Cartoonist: It’s "golden" because it has so many beautiful mathematical properties. This irrational number is often written as phi (φ) after the Greek artist Phidias who used this aesthetic ratio in his sculptures that were often literally made of gold. Interviewer: Now I know what to make my math-crazed…
  • Let's Turn Learning Inside Out: Learning from Failure

    28 Jul 2015 | 9:00 am
    This post was originally published on Huffington Post ImpactX. Janine Ingram is the Vice President of Philanthropic Partnerships at MIND Research Institute. Like most parents this summer, I went to see "Inside Out." Unlike most, I went alone. It was on my oldest son's birthday and I wanted to honor our birthday tradition of going to a family movie, despite the fact my newly minted 21-year-old was 860 miles away playing basketball with his Idaho State University teammates. I started crying as I took my seat, realizing our tradition had run its course since both boys are now ginormous men…
  • Off the Number Line: Rational Vs. Irrational Numbers Cartoon

    Matthew Peterson and James Huang
    23 Jul 2015 | 10:18 am
      Interviewer: What are we looking at here? Cartoonist: At the top we have a group of famous irrational numbers, φ, π, e and √2. Hiding behind a wall at the bottom we have two fractions. The 1/5 fraction is saying to the 3/4 fraction: "Oh-no... we're outnumbered!" Interviewer: And... why is this funny? Cartoonist: At the surface level, we have numbers saying they are "outnumbered." This is already funny. Hahahaha... Okay, now that we've composed ourselves, let's explore the depth of the joke here. Back in the time of Pythagoras, people refused to believe that these crazy irrational…
  • The Role of Parents and Teachers in Game-based Learning

    MIND Staff
    21 Jul 2015 | 9:00 am
    Interview with Greg Toppo and Matthew Peterson Part 3 In our final installment of the series, reporter and author Greg Toppo continues the discussion with ST Math creator Matthew Peterson about game-based learning. In his new book, The Game Believes in You, Toppo interviews Peterson and other leaders in the educational game field for an in-depth look at the potential of game-based learning to be, yes, a game-changer in education. Peterson and Toppo recently discussed some of their biggest personal revelations about games, and what they see as the role of teachers and parents in educational…
  • DIRECTV Celebrates Fun, Learning and ST Math in Denver

    Guest Blogger
    14 Jul 2015 | 9:00 am
    DIRECTV and FOX visited Denver’s University Prep Elementary School (U Prep) during the last week of their 2014-2015 school year to host a live-action version of the hit TV show “Are You Smarter Than a 5th Grader.” Stephen Demedis, a member of DIRECTV's Coporate Communications team based at DIRECTV's Denver, Colo. Office, was in attendance and wrote the below blog, which was orginally posted on the DIRECTV GOES TO SCHOOL website. I am smarter than a fifth grader. And I’ve been certain of this since the mid-90s. But as I stood in the back of the gymnasium at…
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    Teach Math for Free

  • 5 Interesting Facts & PowerPoint Presentation about Pythagoras theorem

    29 Jul 2015 | 10:52 am
    I have put together some very interesting facts about Pythagoras for kids. In order to help our readers who are teachers, I have also prepared a powerpoint presentation on the theorem. My last post dealt with the trapezoid as a part of the geometry curriculum. Pythagoras of Samos, as he is known, was a Greek mathematician and an ancient philosopher.   When did Pythagoras live?Although there is limited verified literature available on the life of Pythagoras, he is believed to have lived between 580BC – 500BC hailing from the Greek Island of Samos. An article on the BBC webportal…
  • What is the formula of the Area of a Trapezoid: Geometry Curriculum

    26 Jul 2015 | 2:29 am
    Hi there, Today, as a part of the geometry curriculum, I am going to address one critical question that readers have been frequently asking – “what is the formula of the area of a trapezoid”. In my previous posts I had written about circles and Triangles. Well, before I dwell directly into Area, I will define a few basics: Trapezium or Trapezoid : Are they the same?Yes, Trapezium and Trapezoid refers to the same geometric figure. The former is defined in the UK while the latter is so called in the United States. Define trapezoidA trapezoid is a four sided geometric figure having one…
  • Print Flashcards Online - Interactive Math Activities

    21 Jul 2015 | 4:17 am
    Print Flash Cards OnlineAfter my post on Effective common core strategies for math teachers, I have been constantly receiving requests to suggest if there are resources/ websites that could be used to print flash cards online. Today, I wish to address this query with this post. The importance of making a class interactive is a concept every mathematics teacher strives for. There are various visual learning strategies that are available that could be adopted to achieve this purpose. One such method is the flash cards. When concepts such as addition, subtraction,…
  • Effective common core strategies for math teachers - Instructional Strategies for teachers

    12 Jul 2015 | 10:19 pm
    I have often wondered how teachers deliver a good lecture. What might be the secret behind conducting a good, informative, effective math class. Preparing for a math class is a critical process that a math tutor goes through every day before her class. Today’s post tries to highlight some of those preparative steps:1. An effective Math class requires a teacher to prepare a definite lesson plan – Reaching out to students effectively is the topmost priority for a math tutor; this requires the tutor to prepare a sound lesson plan. A lesson planner acts as a blue print/ road map…
  • Learn Problem Verification - Help for Math Problems Verification

    26 Jun 2015 | 2:09 am
    Hey there, I have always been looking for methods to cross verify problems (be it addition, subtraction, multiplication or division) while writing any competitive exam. I have also had my juniors approach me for some help with math problem verification.  During exams, we are short of time and always want to ensure that answers are right. The importance of result verification is often under emphasized. You might be an ace mathematic question solver but verification is a critical process in itself.The concept of Vedic Mathematics has defined a few rules to assist in cross…
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