Yesterday, we designed an Algebra II lesson using 3D modeling to derive the factored formula for difference of cubes. As we began to finish up, Sheila (@mrssheilaorr), the math teacher sitting beside me made a passing reference to being frustrated trying to prove the sum of cubes formula. Me, being a geometry teacher by trade decided to give it a try perhaps hoping to offer a fresh perspective. I mean, I was curious. It looked like this:

On the surface, it didn’t seem unapproachable. I quickly became frustrated as well. Most frustrating was the mutual feeling that we were so stinkin’ close to cracking the missing piece. Finally, Luann, a math teaching veteran sat down beside us, commented on her consistently getting stuck in the same spot we were stuck and then, as the three of us talked about it, the final piece fell in and it all made sense (it’s…

Let’s be honest. One of the most dangerous things about trying new games every now and then on the iPhone or other iOS devices is that you risk finding something cheap and addictive that can seriously take away from your free time. And the fact that in most cases these games can be played using just one hand makes them even more fun.

InteractiveMathematics There is something for those who are learning everything from integers to higher (gulp) calculus here. There is also the option to download a variety of graph paper from the site as well. In addition to the examples, answers and explanations of a wide variety of math levels, there are also some games thrown in, just in case you didn’t get enough math fun in for the day. I love that this site, and all of the other free math sites exist, I just wish all of this free help had been around in my day…(sighs)

WolframMathWorld While this site is primarily geared toward higher math, it’s an invaluable resource to have “at the ready” for when your student (or you) venture into this level of mathematics. A worthy site to keep on hand!

Calculus is the mathematical study of change. The way that we examine what happens at one point, and how things change when we examine the same concept somewhere else. Today we’re going to get a basic understanding of what Calculus is, what we can use it for and why it’s so scary.

According to Dr. Derek Martinez, a Math professor at UNM, Calculus classes have two purposes. The explicit purpose is to teach students how to do the math. The implicit purpose is to make engineering and medical students mentally stronger and intellectually prepared for future careers.

Many a student has made it through Algebra and Trigonometry classes only to be cut down to size by the dreaded Calc 1 or worse, Calc 2. When you meet a surprisingly smart Psych major, or a meticulously picky Foreign Languages major, that probably means they decided at some point that integrals are…

Purplemath  This site has everything from preliminary topics such as fractions and absolute value to the beginnings of trig. Each unit of study is broken up into groups/categories to help you zoom in on exactly what you need. A problem is shown, then the step-by-step explanation is given out beside it, with diagrams/drawings to go along with it where necessary. This site would be helpful for many, especially those going through any stage of learning algebra.

PatrickJMT  Here you will find numerous math videos ranging from basic arithmetic to trigonometry, all provided for free. The videos are very clearly listed by categories, then more specific subcategories beneath. The site is very straightforward and easy to navigate, which is great when you are frustrated already and trying to find very specific help for a very specific math problem.

VisualFractions  While this site is devoted to, you guessed it, fractions, it…

STEM subjects are at the forefront of the media’s focus on education. What are they? It’s simple; Science, Technology, Engineering, and Mathematics. Why are they so important? Well, they’re the future of our world. These fields are making rapid advancements and needing more brain power to do so. (Which they’d have if not for the sexism that exists within these fields perpetuating the idea that women are not adept in such studies.) Besides that though, there is a need to generate interest in STEM subjects that has been greatly diminished by the social norm of finding them ‘uncool.’

There is, of course, great reward in entering these fields. Especially engineering, with some starting salaries higher than the median salary of my future career (clinical psychology). As shown by the chart I’ve attached, there is a much higher percentage of people earning more than those at an…

In staying with the same vein as last week, we wanted to share a few new math resources appropriate for middle and high school level.

1.  Symbaloo – This is a bookmarking website that has real potential.  We really like how visual it is! You can create a symbaloo for your students or parents of students of tutorial sites, virtual manipulative sites, and textbook sites.  Or, you can create a symbaloo for your own organization of sites you frequent regularly.  They can be organized on the board by color, icon, and location.  It takes very little time to create.   The math half of us started one called CCSS Math – Parvankin.  It is full of math sites that are often referenced.  And, not to be outdone, the Literacy half of us started one called CCSS Literacy – Elliot including Literacy Resources featured last week here, as well…

Myth #1: All children with dyscalculia have the same difficulties with math.

Fact:Dyscalculia actually refers to a wide range of math issues, so your child’s trouble spots may be different from another child’s. For example, some kids with dyscalculia have a hard time with basic number concepts. Others have difficulty with the kind of visual-spatial thinking that’s needed for geometry. What most kids with dyscalculia have in common, though, is challenges remembering basic math facts and completing math problems.

Myth #2: Dyscalculia is another name for math anxiety.

Fact: Dyscalculia and math anxiety are not the same thing. It’s understandable that people confuse the two, though. It’s common for kids who struggle with math—like kids with dyscalculia—to become anxious about doing math homework or going to math class. Learn more about key differences between dyscalculia and math anxiety.

Myth #3: Dyscalculia is basically dyslexia for math.

Fact: Although dyscalculia…

MM4B Quadratic Functions. This video re-visits Quadratic Functions, presents a summary of the features of Quadratic Functions, shows the various ways of solving quadratic equations, talks about the use of the discriminant and then show how completing the square can be used to describe the transformation steps from the basic function of a quadratic to a new variant in turning point form. The video was made for students studying Mathematical Methods (CAS) in Year 12, a course fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia

All currency coins or notes are issued in these 4 denominations: {1, 2, 5, 10} but not {3, 4, 6, 7, 8, 9}.

Reason: These 4 numbers {1, 2, 5, 10} just need at most  2 operations (+ or -) to generate any number from 1 to 10.

(1 = 1)
(2 = 2)
3 = 1 + 2
4 = 2 +2
(5 = 5)
6 = 1 + 5
7 = 2 + 5
8 = 10 – 2 = 1 + 2 + 5
9 = 10 – 1 = 2 + 2 + 5
(10 = 10)

As I’ve already described, I’m worried about the oncoming MOOC revolution and its effect on math research. To say it plainly, I think there will be major cuts in professional math jobs starting very soon, and I’ve even started to discourage young people from their plans to become math professors.

I’d like to start up a conversation – with the public, but starting in the mathematical community – about mathematics research funding and why it’s important.

I’d like to argue for math research as a public good which deserves to be publicly funded. But although I’m sure that we need to make that case, the more I think about it the less sure I am how to make that case. I’d like your help.

So remember, we’re making the case that continuing math research is a good idea for our society, and we should put up some money towards it…

SM3C Inverse Circular Functions. Inverse Circular Functions of Cosecant, Secant and Cotangent are introduced and then transformations of the their graphs are explored and implied domains and ranges are calculated. The video was produced for students undertaking Specialist Mathematics in Year 12 in the State of Victoria, Australia.

Hello reader,

I am an applicant to Oxford/Cambridge, and sometime after I was informed about whether I was accepted/rejected, I decided to write up on the application process for new applicants who may not know too much about Oxford and Cambridge. I have recently done some research, whipped up some numbers which I hope can help you in your application. Most people start off thinking about applying to Oxford and Cambridge (and other famous universities) without anything except their ambition to start with, and I hope this guide can provide you with useful information for your university applications.

This is written mostly from a Singaporean student’s perspective, although some information is applicable to applicants from other countries as well.

Overview of Oxford and Cambridge

Oxford and Cambridge are the oldest and 2nd oldest universities in the English speaking world respectively, and 2^nd and 3^rd oldest in the world…

Original lithograph (M. C. Escher, 1961)

This is the first entry of the “Infinity Series”, which will introduce you to the peculiar world of infinity. Today, we will be talking about something with finite area but with infinite perimeter. That sounds odd and impossible but I’ll show you how it can be done.

Draw a circle and an equilateral triangle inside it, with the three vertices of the triangle touching the circle.

Since we know that the circle has a finite area, the triangle inside must have finite area as well. At this point, we still have finite perimeter on the triangle as well.

Now, divide each edge of the triangle into thirds; draw an equilateral triangle using the middle piece of the divided edges as the base, as follows:

With careful observation, you can see that the perimeter has increased. Specifically, the perimeter increased by a third: instead of one…

There are countless situations in mathematics where it helps to expand a function as a power series. Therefore, Taylor’s theorem, which gives us circumstances under which this can be done, is an important result of the course. It is also the one result that I was dreading lecturing, at least with the Lagrange form of the remainder, because in the past I have always found that the proof is one that I have not been able to understand properly. I don’t mean by that that I couldn’t follow the arguments I read. What I mean is that I couldn’t reproduce the proof without committing a couple of things to memory, which I would then forget again once I had presented them. Briefly, an argument that appears in a lot of textbooks uses a result called the Cauchy mean value theorem, and applies it to a cleverly chosen function. Whereas I…

Most Important SAT Book

The Official SAT Study Guide a.k.a. Blue Book, 2nd edition
The Official SAT Study Guide: Second Edition™ features 10 official SAT® practice tests created by the test maker.

SAT Strategy Book

SAT Prep Black Book: The Most Effective SAT Strategies Ever Published
The Black Book works best when used with the authentic SAT questions in the “Blue Book,” which is the College Board’s Official SAT Study Guide. The Black Book shows you how to beat the SAT, while the Blue Book gives you real SAT questions to practice with. Please buy College Board Blue Book to understand the strategies with questions from Blue Book.

SAT Math

Introductory SAT Math Book:
The New Math SAT Game Plan: The Strategic Way to Score Higher
A new edition, The New Math SAT Game Plan features updated strategy guides, more Algebra-II topics and all of those subversive tactics that have…

SAT Blogs/Websites

PWN the SAT

Excellent blog for SAT Math Tips and Tricks.

The Critical Reader
Another Excellent blog for SAT Grammar and Reading Tips and Tricks.

SparkNotes Free SAT Online Book
Excellent Free SAT Online Book covering SAT Math, Critical Reading and Writing Section.

Silverturtle’s Guide to SAT and Admissions Success
Excellent strategy guide from a student covering SAT and College Admission. It also included an excellent SAT Grammar section study guide.

Websites

College Board SAT Biology E/M Practice Tests and Information Website

How to Study for the SAT Biology E/M Subject Test

Study Guides

Cracking the SAT Biology E/M Subject Test, 2013-2014 Edition
This book practice tests are more closer to real test.

Barron’s SAT Subject Test Biology E/M, 4th Edition
Barron Book has more details than Cracking the SAT Biology E/M Subject Test but questions are harder than real test.

Sparknotes Free Online SAT Biology E/M Subject Test Guide
Good introductory SAT Biology study guide

So there’s a whole lot of posts, including one from this very blog, which give intuitive explanations of why a negative times a negative is a positive.

I haven’t seen nearly as much material for a negative divided by a negative. One can certainly appeal to the inverse — since $latex 1 \times -1 = -1$, $latex \frac{-1}{-1} = 1$. Google searching leads to answers like that, but I’ve found nothing like the multiplication picture above.

Can anyone explain directly, at an intuitive level, why a negative divided by a negative is a positive? Or is the only way to do it to refer to multiplication?

University of Idaho is offering a book club on What’s Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject by Jo Boaler.

The book club is free and includes a copy of the book! There is an option to participate for 1 credit offered through the University of Idaho for $60. Check out the flyer below and contact irmc@uidaho.edu to register.

American Mathematics Contest 10
The AMC 10 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with algebra and geometry concepts.

American Mathematics Contest 12
The AMC 12 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts.

United States of America Mathematical Olympiad
The United States of America Mathematical Olympiad (USAMO) and the United States of America Junior Mathematical Olympiad (USAJMO) are six question, two day, 9 hour essay/proof examinations. All problems can be solved with pre-calculus methods. Approximately 270 of the top scoring AMC 12 participants (based on a weighted average of AMC 12 and AIME score) are invited to take the USAMO. Approximately 230 of the top scoring AMC 10 participants (based on a weighted average of AMC 10 and AIME…

My college algebra course boasts one of the driest textbooks on the planet. It’s one of those versions that has exercises from 1 to 99 for each section…brutal.   Can you relate?
The topics for college algebra are very standard and cover little more than what students should have encountered recently in their algebra 2 course. I therefore decided that this class would lend itself quite nicely testing out the theory that a high-level, rich question questioning can be facilitated from a traditional, drill-and-kill style textbook.

Previously, I recall that Operations on Functions was a particularly awful topic for both me and my students.  The textbook presents this concept in exactly the way you might think:

f(x) = [expression involving x]  and g(x) = [similar expression involving x]

Find f(x) + g(x), f(x) – g(x), f(g(x), f(x) *g(x), f(x)/g(x)…f(snoozefest)…you get the point.  It’s boring, they’ve done it before, and there’s…

I found this discussion on reddit “How to avoid careless mathematical errors?“:

Hi //math.

I am a high school student who happens to be VERY good at math, but who consistently fails to get As on tests due to careless errors. Most of the time, they come from forgetting a 0 after a decimal place, multiplying instead of dividing, putting a decimal point in the wrong place, or just factoring wrong. I actually had to drop a Precalc Honors class because I got Ds on tests from the sheer number of stupid mistakes I made, despite understanding the material very well.

I assume that this occurs because I work quickly, but if I work slowly, I run out of time on the test. Additionally, my handwriting is horrible, but there’s really nothing I can do about that. And even when I check my answers after finishing, I still…

這是一個測試網誌。