There has been a lot of talk lately about creating educational videos for your students, whether you mean to use them in class, on the web, or both. Fewer people really talk about the different options for the format of your video — by which I don’t mean the technical file format, but rather the actual *style* of what will be on the screen. Should you use an on-camera teacher? Animation? Screencasts? You have lots of style choices when you’re making educational videos.

At Knewton we spend a lot of time thinking about how to make videos that are engaging and effective, but can still be produced in a manageable and scalable way. If you want to create some educational videos but don’t know where to start, here are some elements to consider:

Slideshows can be exported to a series of images and then narrated by a teacher — an easy, versatile option. All you need is a mic and presentation software. Even better, although you’ll need additional software (for example, Camtasia), is a “screencast” or a digital screen capture: a video of exactly what’s going on on your computer screen. With some programs, you can circle, underline, annotate, doodle on your slides — anything to illustrate what you’re saying and keep your students watching. As a benefit, teachers who are uncomfortable being on camera don’t need to be. No worrying about hair or wardrobe either! The downside is that since you can’t see the teacher in the video, the overall experience can be less engaging for the student, especially if the video is more than a few minutes long.

*Tip:* At Knewton, we particularly like using simple screencasts with voiceover to demonstrate brief solutions to single problems. As a plus for subjects like math, you can actually write out your solution and allow the students to easily follow along.

*A screencast video with voiceover showing the teacher’s handwriting. We used a tablet computer, Powerpoint slides, and a stylus to create this video.*

**2. Teachers**

Having an on-screen teacher is a great way to increase the human factor of a course that is largely online, and it can often increase a student’s engagement. On the other hand, being forced to watch a boring or awkward speaker may actually decrease a student’s interest, so teachers must be telegenic as well as knowledgeable.

You’ll also need to think about how much of the person to show. Is your teacher sitting down behind a desk? Standing at a podium? Can you only see the face and shoulders? Consider both the physical limitations of your space — how much can you light, and how much can you back up your camera? — and the natural motions of your teacher. A teacher standing up could seem awkward, or she may move and gesture more naturally than she would while sitting. A teacher behind a desk may feel more comfortable himself, but the video may be more boring for the students.

*Tip:* For Knewton’s longer videos (ex. mini-lectures in our Math Readiness courses), we often film one of our super-charismatic teachers using a green screen so that we can put their images in front of a screencast.

*We filmed our teacher Jen in front of a green screen, then superimposed the screencast from the tablet she’s writing on behind her.*

*Tip:* In the case of our On-Demand GMAT courses, which are much longer videos, we chose to use a two-teacher set-up, and have them sitting. This allowed us to have room for the large slides, and allowed the teachers to banter and play off each other while teaching. It’s a bit unconventional, but our students really responded to the natural, conversational feeling of the lessons.

*In these videos, shown here in our custom video viewer application, two teachers sit side by side while walking through slides in a longer lecture.*

**3. Camera angle and number of cameras**

Putting your teacher onscreen means that you have to come up with a way to deal with errors. Some will be small, but the longer the video, the more mistakes you’re bound to have! A single continuous take lessens the need for editing but might be tough to get perfect all in one go. On the other hand, if you use multiple camera angles or cut between a teacher and a full-screen slideshow or screencast, you’ll need more video resources (cameras, people to film, and people who know how to edit) but you’ll put less pressure on your teachers to be perfect all in one take.

If you already have a classroom setup available, you can film your teacher in front of a whiteboard, or writing on an overhead projector. This is a nice, cost-effective way to have both a teacher and visual aids in your video. These set-ups are great if you want to replicate the traditional classroom, but don’t allow as much innovation over the classic lecture model. Even with an engaging teacher, your students will likely feel as though they’re in class, but with less accountability since it’s on a computer. Technically, these videos are also much harder to light appropriately — your teacher may be in the dark, or your projector or board might be washed-out and too bright. If you do use a whiteboard, avoid common mistakes: make sure your teacher’s writing is well-lit, large and clear!

*An example of a whiteboard video. The text is hard to read and the colors look washed out, but it’s easy to make many videos in a short amount of time.*

Some concepts — like surface area, or centripetal forces — might be best addressed by animation or interactive tutorials. Adding animation and interactivity to your course is a great idea, especially for kinesthetic learners. But you’ll need more software, and maybe even additional staff who know how to use it.

Choosing a format isn’t necessarily obvious or simple, but we hope we’ve given you some ideas to think about! Try out some sample videos in a couple of formats, to see which one feels easiest and most natural to you and the subject you’re teaching. Once you’ve chosen a format for your video, gotten your software and hardware ready, and prepared your lesson, you’re ready to start filming.

Good luck!

]]>**The dilemma:** For quite some time now, there have been a bunch of extra Knewton Frisbees lying around the office — more Frisbees than any company (even one with its own recreational Ultimate Frisbee team) could ever use.

**The solution:** A flash-Frisbee distribution in Union Square! After all, if there’s anything people love more than a Frisbee, it’s a free Frisbee.

**The result:** A little bit of fun and levity was added to the lives of our fellow New Yorkers on a Friday afternoon (and the gospel of Knewton was spread!).

Check out the video we filmed for more:

*(Music by Sláinte)*

After you practice long enough for the GMAT, you may find yourself answering certain common types of problems on autopilot. But always read carefully –sometimes a problem looks like one you’ve seen a million times before, and yet it’s actually about something else altogether.

Let’s try out this sample problem:

Eunice sold several cakes. If each cake sold for either exactly 17 or exactly 19 dollars, how many 19-dollar cakes did Eunice sell?

- Eunice sold a total of 8 cakes.
- Eunice made 140 dollars in total revenue from her cakes.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

(D) EACH statement ALONE is sufficient to answer the question asked.

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Try it out for yourself, then read on for a full explanation!

If you chose option C for this problem, you wouldn’t be alone. You’ve probably had it drilled into your head (especially if you’re a Knewton student) that if you have two variables and only one equation, you can’t solve for both variables. In this problem, you’ve got two unknown quantities (the number of 17-dollar cakes and the number of 19-dollar cakes that Eunice sold), and you automatically expect to need two separate equations to find those numbers.

But sometimes, particularly in tricky word problems like this one, the GMAT actually gives you **more** information than you realize. A problem like this, that seems to be testing the simple concept of an insufficient system of equations, for example, is actually be testing you on your ability to understand number properties.

The difference in this problem is that the word “several” in the question stem refers to *integers.* Eunice could have sold three cakes, or three hundred, but even so, there’s a big difference between, for example, “Eunice sold several cakes” and “Eunice used a certain amount of flour to make her cake.” She can only sell her cakes in whole numbers.

So there’s an infinite set of numbers that *can’t* be the answer to this question: 3.5, Ï€, âˆš7. (Of course, there’s still pretty much an infinite set that could; even if it’s* *unlikely that Eunice sold, say, a million cakes all by herself, we can’t rule the possibility out.) Still, you’ve eliminated a whole lot of answers before you even get to the statements. As you’ll see, this thought process is key to arriving at the correct answer.

Now, let’s evaluate the statements.

Statement 1 says that Eunice sold a total of 8 cakes. Â But this tells you nothing about what each cake cost. Half of them could have cost 17 dollars, or maybe all but one. So statement 1 is definitely insufficient, even though there are only a few possible answers (1, 2, 3, 4, up to 8).

Statement 2 says that Eunice made 140 dollars total. If this were a regular algebra problem, and not a word problem, you might write something like this: 17*x* + 19*y* = 140, where *x* and *y* were the numbers of 17- and 19-dollar cakes. And in that case, you would be able to graph all the solutions to this equation on a line, which means that there would be infinite solutions.

But you know that *x* and *y* are integers, and that they’re positive (otherwise Eunice would be buying cakes from her own customers, which isn’t a great business model!). So instead of using straight algebra, use this information to figure out how many cakes Eunice sold.

First, 17 goes into 140 about 8 times. If Eunice sold 8 cakes for 17 dollars each, she’d make 8 * 17 = 136. But if she sells any more than that, say 9, her least possible revenue is 17 * 9 = 153. So she couldn’t have sold more than 8 cakes, because she would have made at least 153 dollars. Meanwhile, 19 goes into 140 about 7 times. If Eunice sells only 7 cakes, she makes, at most, 7 * 19 = 133. So she couldn’t have sold 7 or fewer cakes.

You’ve narrowed it down: Eunice must have sold 8 cakes. Now you can figure out how many of each type she sold using a simple system of equations:* x* + *y* = 8 and 17*x* + 19*y* = 140.

In fact, you could stop here. 2 equations with 2 variables is clearly sufficient information, so answer choice B is correct. But here’s a quick explanation of how to solve the system (just remember not to worry about solving on test day — instead, move on as soon as possible after establishing sufficiency!).

*x *+ *y* = 8 becomes *x* = 8 — *y* (remember you’re looking for y, so substitute *x*). Next, plug that into the other equation: 17(8 – *y*) + 19*y* = 140, or 136 + 2*y* = 140. Then you have *y* = 2, so Eunice sold 2 19-dollar cakes.

“Wait,” you might be thinking. “What if I happened to find this same combination intuitively? I wouldn’t have had to go through all these steps.” Â That’s the difference between problem solving, where guess-and-check often works fine, and Data Sufficiency, where you have to know for sure that there’s only one possible answer. So you would still have to make sure that it was impossible for any integer number of cakes to have been sold other than 8.

The takeaway? Counting words, like “several,” and any discrete objects that appear in a word problem are your tip-off that you’re dealing with integers. It may seem strange since a majority of GMAT problems have integer solutions regardless, but knowing that the solution is an integer is a key piece of information to solve many problems!

]]>So you’re *really *prepared for the LSAT. You’ve taken every practice test in every book. You can identify patterns in logic games in your sleep. You should feel confident, but you’re sitting here on test day, frozen with fear. You can’t even remember what the last sentence of the reading comprehension passage was by the time you get to the first question.

Does this scenario haunt you? Being nervous on test day is normal, but being *too* nervous is one of the major reasons why someone who did all the right things to prepare might still fall down on test day. The LSAT is a big culprit because you’re not supposed to find it easy to finish, even if you’re a top test-taker.

In college, I was a typical stressed-out student. When you’re stressed, you sweat more, your heart palpitates, and you may breathe faster or become jittery. Plus, changes occur in your brain that make your thoughts chaotic and disorganized —not something you want during a test. But then a very wise coworker persuaded me to accompany her to a Bikram yoga class: 90 minutes of intense yoga in a steamy 105-degree room.

I spent the first few minutes trying to hide my giggles as everyone around me, their arms contorted into a “W” shape, took loud, slow, wheezing breaths together. But by the end of class, I was a (very warm) convert, already feeling calmer and even happier after all that hard work. I never managed to touch my forehead to my shins, but what I did learn from years of going to yoga classes is that physical and mental relaxation are much more connected than I’d ever thought.

Whether or not you’re interested in sweating through a whole yoga class, you can still mine this connection as you prepare for a high-pressure standardized test. Focus on these three B’s—breath, bed, and breakfast—and you’ll be on your way. (The Birkenstocks are optional.)

**BREATH**

Bikram yoga starts out with an exercise in which you clasp your hands under your chin, breathe in slowly while lifting your elbows towards the ceiling, and then breathe out slowly while stretching your elbows forward. Sound uncomfortable? It is.

Whenever you find yourself in a panic, you can use this simple breathing technique. Psychologists swear by it, and all you need is oxygen.

Sit up with your back loose but straight, rest your hands on your knees and your feet on the ground a few inches apart, and start counting through slow, even breaths. Air should come in through your nose and out through your mouth. Once you’ve gotten to thirty breaths, the symptoms of anxiety will probably have lessened.

We’d recommend taking those thirty slow breaths whenever studying stresses you out. But if you’re in the middle of the actual test, you probably don’t have time for thirty. It’s okay — just five breaths can accomplish a similar effect.

*Pro tip:* Let your thoughts come and go while you count your breaths, without trying to control them. Sternly telling yourself not to think about anything usually has the opposite effect!

**BED**

Make sure you don’t ignore visits from the Sandman while you’re prepping for the LSAT. Not only does sleep actually help your memory — probably more than the extra hours of cramming would — but, that’s right, it will also help you cope with stress.

Caffeine at night will mess up your sleep, there’s no question. (So will alcohol, so don’t fall prey to the temptation of drinking to “relax.”) In fact, caffeine in the morning should be kept to a minimum too. Recent studies actually suggest that caffeine might be mostly a placebo: it doesn’t improve alertness, and instead just staves off the drowsy symptoms of withdrawal.

*Pro tip:* You’ve heard this one before, but don’t study near your bed. You can’t forget you have the LSAT coming up when your head is resting on the same pillow that you use to prop up your study materials.

**BREAKFAST**

So you didn’t finish that last question before time was called? Instead of dwelling on the past, move on and concentrate on the next section. One benefit of breakfast is that it keeps your mood on an even keel throughout the day. You’ll be able to respond to setbacks better.

Nutrition experts give all kinds of conflicting advice over what kinds of food are actually better for your brain. The two clearest things are that a nutritious breakfast will help your mental performance, and that highly fatty foods will harm it. Still, enjoy whatever you decide to eat, knowing that you’re helping yourself out by eating *something.*

*Pro tip:* At Knewton, we love bagels with cream cheese in the morning. Make that a whole wheat bagel (and maybe swap the cream cheese for peanut butter or scrambled eggs), and you’ve got yourself some great brain food. Yum!

Considering taking an SAT II test in math? You have two different options: Mathematics Level 1 and Mathematics Level 2. They’re both 50 questions and 60 minutes long, but they have some important differences.

While the SAT I is a “Reasoning Test,” the SAT II is a “Subject Test.” The Subject Tests are intended to test your knowledge of mathematics from courses you’ve taken in school. The Level 2 test involves more advanced topics than the Level 1 test, which overlaps more with SAT I subject matter.

Every student is different, so you should focus on which test will best help you to achieve your academic goals. Here are four factors to keep in mind while you’re making your decision, roughly in order of importance:

**Previous Coursework **

The simplest way to decide which test to take is to look at the classes you’ve already taken. The College Board tailors the Level 1 test towards students who’ve taken three years of college-preparatory math, which usually means two years of algebra and one of geometry. The Level 2 test is for students who have taken more than three years—generally, those who have taken a pre-calc or trigonometry course, or who have moved on to the really fun stuff like calculus.

Some of the topics that are on the Level 2 test that do not appear on the Level 1 test are series, vectors, more advanced functions, polar coordinates, and trigonometric functions and equations. Meanwhile, the Level 1 test covers plane Euclidean geometry, which does not appear on the Level 2 test.

**Prospective Colleges **

Research the admissions policies of schools you’re interested in. If you must, go ahead and be that person in your information session who asks questions about seemingly everything! Requirements and recommendations can vary widely from school to school. Obviously, you’ll have to take Level 2 in order to apply to a school that requires it. And if you know that your dream school prefers Level 2, try to plan ahead so you will be prepared to take it.

**Intended Major **

Many schools recommend or require that you take the Level 2 test if you are applying to their engineering or other science programs. Even at schools that don’t have an explicit preference, taking the Level 2 test (and doing well on it) will particularly help your application if you state an intent to major in a math-related field. If you’re focused on other subjects, taking Level 2 is less critical.

**Comfort Level **

What if you could take either test, but you think you would do much better on Level 1, and you’re planning to major in, say, art history or East Asian languages anyway? If you’ve completed enough coursework for the Level 2 test but received B— or lower grades in the more advanced classes, you should at least consider taking Level 1 instead. Just keep in mind that your most recent math coursework is probably freshest in your mind, and that taking a Level 2 test, if your score is only slightly lower, may still look more impressive on your application.

The SAT lets you use your calculator for any problem, so why would you consider opting out at all? Because a huge part of the test is timing. The faster your mental math is, the faster your test-taking can be.

Below you’ll find a list of six tips for quick calculation. Some are facts you should simply memorize, if you haven’t yet. Our other tricks can help you rack up speed.

Top three memorization tasks:

1. The times tables through 12. Pay special attention to perfect squares and their roots, because they show up everywhere from right triangles to algebra.

2. Cubes of integers up through 5, powers of 3 up through 3^{4}, and powers of 2 up through 2^{10} (that’s 1,024). The test-makers love these higher powers, so you’ll have to cozy up to them too!

3. Common fraction-decimal-percent conversions. For example, 25% = .25 = 1/4.

Three speedy math tips:

1. Those times tables can still apply if the numbers end with a zero or zeroes. If you know what 8 × 9 is, you know what 80 × 9 is—just add a zero to the end of the product.

2. Numbers close to a “round” number are easier to add, subtract, and even multiply in your head. For example, 37 × 101 is definitely something you can punch into your calculator, but you might also realize, “Hey! That’s just 37 more than 3700!” That’s because 101 is one more than 100—and 37 × (100 + 1) is the same as (37 × 100) + (37 × 1).

3. Sometimes multiplication can be broken into two simple chunks. Multiplying a number by 4 is the same as doubling the number twice. Multiplying by 5 is the same as multiplying by 10 and then dividing by 2. Multiplying a number by 20 is the same as doubling the number and then multiplying it by 10 (adding a zero). Try applying similar logic with division if you feel comfortable.

But when it comes to decision time—brain or machine?—remember, “can” does not equal “should.”

The very best tip we can give you is not to take risks with either your accuracy or your time. Don’t try to skip the calculator if you think there’s any chance of getting something wrong on your own. As long as you type carefully and mind your order of operations, your calculator won’t let you down.

Likewise, if your typing is faster than your mental math, go electronic. No one’s grading you on whether you use your calculator, so choose the most efficient approach.

In other words, all of our suggestions above should be used only if you’re 100% solid on them—and 110% speedy!

And even if you’re a superstar mental mathlete, the SAT is no time to prove it to yourself. You absolutely should use your calculator for tougher arithmetic, such as long division, arithmetic with exponents or decimals, and even addition of two-digit numbers.

Finally, here’s our inevitable PSA on calculator use: Make sure well before your test date to locate an eligible scientific or (preferably) graphing calculator that you’re familiar with. Before the test, check that your calculator is working, and bring spare batteries (or even a spare calculator). If your calculator malfunctions or runs out of juice, you’re on your own—test centers don’t provide extra equipment, and students can’t share. Sure, the math section is designed so that calculators aren’t strictly necessary, but why find out for yourself?

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