Be Thankful: ACT


The calendar has turned over to December, but that doesn’t mean that you should forget the lessons of the Thanksgiving holiday that just passed. While spending time with my family, I was able to pause and reflect on all the things that I’m thankful for. That’s an exercise that always leaves me feeling fortunate because I take the focus off of my little struggles and appreciate the big picture. In that spirit I’ve done some thinking about the tests that I teach in order to give you that same perspective. So, without further ado, here are five things to be thankful for about your test.


  1. The ACT is different- It used to be that your region of the country determined whether you would take the ACT or the SAT, but these days more and more students take both tests. While the two are similar in most respects, be thankful for the fact that the ACT is different, so if you struggled with the SAT, you may find the ACT suits your needs better.


  1. The science section isn’t too sciency- Many people are thrown by the fact that the ACT has a science section (while the SAT does not). Don’t worry! Just because it says science doesn’t mean you need to dredge up all those long-forgotten notes from your biology class! The science portion of the ACT is really more like reading comprehension because it asks you to analyze the set-up of experiments and their results rather than more substantive questions.


  1.  College is the reward for a good ACT score- And college is really, really fun. Sometimes you just need a reminder of the pot of gold at the end of the rainbow.


  1. No wrong answer penalty- Guess away! The ACT doesn’t penalize you for missing questions, so you might as well give each one your best shot.


  1. The ACT rewards quick workers- If you like to move slowly and methodically, maybe you aren’t thankful for this one, but for the rest of you, just keep moving! The ACT puts you under some time pressure, but if you like to work quickly, you’re going to get an advantage from that, and if you’re able to answer more questions you’re going to see your score go up!


Be thankful and happy studying!

 Concentrated Liquids


If you’re looking for a technical, precise explanation on handling concentrated liquid problems, look elsewhere. For the rest of you, this may be helpful.

When I say concentrated liquid problems, I mean problems that take the following form:

5 gallons of a mixture of cranberry juice and water is 15 percent juice. How much water will have to be added in order to create a mixture that is 10 percent juice?

You see these problems in various forms, sometimes asking you to evaporate out some water, or sometimes to add some water. Sometimes you’re given the total volume of the desired mixture and asked to determine the concentration. Other times you’re given the desired concentration and asked to figure out the total volume in some form. However, despite the specific form that you’re given, I have some very eloquent advice that’s going to make tackling these problems much simpler: Find out how much stuff you’ve got.

Yup, that’s right “stuff”. Almost all of the problems of this type that I’ve encountered involve a mixture of water and something else. That something else is the “stuff” we’re interested in. Water will simply be a filler that will take up all of the space not occupied by “stuff”. Let’s take a look at the problem I mentioned earlier to illustrate this concept.

Here we have 5 gallons of mixture and we know that it’s 15% cranberry juice. That’s our stuff. We need to find out how much cranberry juice we have. The simple calculation is:

Once we know how much stuff we have, we just need to set that 0.75 gallons equal to 10 percent of x to find out the volume of the new mixture. This one is relatively straightforward, so we know that the total volume will equal 7.5 gallons. Since we started with 5 gallons, and all we’re adding is water to get to 7.5 gallons, we need to add 2.5 gallons of water and there’s your correct answer.

Regardless of the question type or form, when you see one of these concentrated liquids problems make sure you find out how much “stuff” you have! The rest will be water and you’ll be well on your way to a correct answer!

 Summer Balance



My sister is an elementary school teacher, and around this time of year she starts to get worried about brain rot. After a year full of new experiences, challenges, and knowledge many of her students are off to a summer where they will only be challenged by getting to level 10 of their new video game.


However, brain rot isn’t a phenomenon limited only to children. For those of you still in school, the summer may still be a respite or an opportunity to take a mindless job to save some cash. But maybe summer should also be your opportunity to prepare for the next step in your life.


Taking on a challenge like a college entrance exam or a test to get you into graduate school is a great way to spend the summer. It’s not a great way to spend the entire summer obviously, but it’s a great way to add balance into the long summer days. There’s still plenty of time for cook-outs and beach days, sleeping in and golf trips. Just put your nose in a book every once in a while to balance everything out.


My favorite fortune cookie of all time says “Balance is essential for walking and life.” It’s not really a fortune, but it’s no less true. Trying to take relaxation to its peak for an entire summer and then trying to jump back to full mental function is the fall is a plan that’s bound to fail. At the same time, studying to the point of obsession tends to lead only to burnout.


During the most study-intensive summer of my life when I was preparing to take the bar exam, I took a summer job umpiring softball games a few times a week. If nothing else game me a reason to put down the books and be outside for a couple hours, which recharged me and allowed me to get back to the studying.


Does your summer have balance? Or is “Do Nothing” at the top of your summer to do list. If you seek that balance in your summer, you’ll be able to appreciate the times of relaxation even more and you may even put those dreams for the next part of your life one step closer.

 Math Payoffs


“When am I every going to use this?”


It’s a familiar refrain from math students everywhere, so I’ll take this opportunity to show you exactly where you can use your math training. It’s a great example of how preparing for your test can also help you in the real world.


My wife was recently at the store to take advantage of two promotions. First, she had a 20% off coupon. Second, the store was offering a $10 gift card for all $50 purchases (with certain products excluded). Due to cashier error, the $10 gift card didn’t come up automatically when she checked out. That’s where the math comes in.


She needed to be able to calculate the total amount of her purchases before tax, subtract out the purchases of items that weren’t eligible and then subtract 20% of that total to make sure that it all came out to over $50.


Both the manager and the cashier would have preferred to rely on the machine. Their position was that if the magic box doesn’t spit out a code for a gift card, the customer probably shouldn’t get one. A customer who was less confident in her math would have relented and walked out without the $10, but my wife was perfectly comfortable walking through each step of the process to make sure she got what she deserved.


It’s only $10, and maybe that doesn’t seem like adequate payoff for the tedium of math classes and test prep, but that’s one example. Every time you decide whether to buy your flight, hotel and rental car separately or bundle them, that’s a math payoff. When you decide whether to buy the giant package of toilet paper at Costco, that’s a math payoff. And when you decide whether to invest money toward retirement or pay off student loans given the interest rates, that’s a math payoff.


Sitting there poring over numbers and remembering how to calculate percent discounts and the like may not be your idea of a good time, but it pays off in the end.