### Q & A: When the unit price of orange was reduced by $3.00, the number of oranges bought for $180.00 increased by 5. Find the present price per orange?

Here's how to solve this problem. If x represents the unit price, x - 3 will represent the reduced unit price. We will let y represent the number of oranges purchased. We can now create two equations (system of equations):

180/x = y

180/(x - 3) = y + 5

The parts on the left will yield the number of oranges purchased. The first equation will get the original number of oranges purchased (y), and the second equation will get the number after the price reduction (y + 5). Using substitution to solve for x, we take 180/x, which equals y, and plug it into the second equation’s y variable. This gets us the following single variable equation:

180/(x - 3) = 180/x + 5

Next, multiply both sides by (x - 3):

180 = [180(x -3)]/x + 5(x - 3)

180 = (180x - 540)/x + 5x - 15

180 = 180 - 540/x + 5x - 15

Then multiply both sides by x (to remove the last x in a denominator):

180x = 180x - 540 + 5x^2 - 15x

Subtract both sides by 180x, and we have the following quadratic equation:

5x^2 - 15x - 540 = 0

Divide both sides by 5:

x^2 - 3x - 108 = 0

Factor:

(x - 12)(x + 9) = 0

This means that x either equals 12 or -9. Since a negative price can be thrown out, we see that the original price, x, must have been $12. That means the new price (i.e. the reduced price, x - 3) must be **$9 per orange**.

We can verify this by showing that 180/12 = 15 oranges purchased, and 180/9 = 20 oranges purchased, which indeed means 5 more oranges can be bought.

Accordingly, we now see that the **new price per orange is indeed $9.00**.

### EP065: 5 ways to get your kids to listen

Vicki Glembocki recently wrote an article on parents.com that offers some amazing tips and insights on how to get kids to stop ignoring and start obeying. The beauty of the article is that the advice is logical, practical, and easy to implement. Join Huzefa as he discusses the article while sharing his own insights along the way.

To check out the article, go to http://www.parents.com/parenting/better-parenting/advice/5-ways-to-get-kids-to-listen/

To check out the book that is mentioned, the title is "How to Talk So Kids Will Listen & Listen So Kids Will Talk."

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### EP064: This is your brain on math. Any questions?

Researchers at Carnegie Mellon University have conducted a study to determine precisely what happens in your brain when processing and solving math problems. The goal is to apply the information learned to develop more robust and versatile education curriculums to improve student comprehension and mastery. Join Huzefa as he discusses the study and describes the four stages of cognition during math processing.

To check out the New York Times article on the study, go to http://www.nytimes.com/2016/07/29/science/brain-scans-math.html?_r=0

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### EP063: Are "mistakes" actually good? Or are you just saying that?

Huzefa revisits the topic from episode 50, and explains precisely why there is a disconnect between the message promoting mistakes and the seemingly contradictory notion in school that mistakes irrevocably harm your GPA. This episode dives into the real world applications of mistakes when it comes to building a business and thriving at a job. Moreover, it explains how mistakes can be used safely as a learning vehicle during school while still maintaining a healthy GPA.

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### EP062: Tips for international students applying to U.S. universities

Huzefa shares tips from U.S. News ans Unigo on how to maximize odds for getting to into U.S. colleges as an international student. If you are applying to an American school from another country, make sure to tune in to this important show that will tell you precisely what you need to consider when aiming to get into a school in the states.

To check out the article from U.S. News, go to http://www.usnews.com/education/blogs/college-admissions-experts/2011/09/14/what-are-some-tips-for-international-students-applying-to-us-colleges

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### Math Jeopardy: a personal story of unparalleled classroom engagement

It was February of 2016. It had been about two and a half years since my precipitous departure from the world of patent law. Times had been tough along the way, but I had finally found a sincere and authentic groove with respect to one-on-one tutoring. I was now fully comfortable and confident with respect to the tutor-student dynamic, and my understanding of all pertinent math concepts had reached a new level. Math instruction had become second nature. Moreover, my time was nearly fully booked with eager students across the Los Angeles area. In addition to my many private tutoring clients, I had just acquired a new homeschool student that needed math tutelage for an hour every morning from 8:15 to 9:15 am. While the student was less than thrilled to be learning math, it was a fascinating challenge to deliver a full-fledged 2nd grade math curriculum from A to Z. It was extremely tough to charge the sessions with energy and enthusiasm as my new pupil’s obstinacy was uncanny, but it was an impediment that I embraced as a learning opportunity.

Right around the time that I began my stint with the homeschool student, a local private elementary institution brimming with bright and enthusiastic students asked if I would be interested in taking over the fourth grade math class. I was quite intrigued to say the least. Since the beginning of my career in education, it had never been my goal to become a classroom teacher. But after mulling over the opportunity for a few days, I realized that the position would come with some major upsides for me. Firstly, this would be my inaugural classroom experience, and although I had logged loads of hours teaching math one-on-one, explaining mathematical principles to a class would be a brand new journey replete with lessons and wisdom along the way. Secondly, it was a terrific opportunity to learn from the many seasoned teachers at the school. The only issue was that the class was being held from 9:00 am to 10:15 am, a temporal conflict with my current schedule. I anticipated that this would be an unsolvable problem; lucky for me, however, my homeschooling client was easy going about rescheduling. Just like that, my fate as a substitute fourth grade math teacher had been sealed.

I couldn’t believe how eager the children were to learn and get ahead. I had several students plowing far beyond the pace of the class on Aleks, the school’s primary online math platform, because they simply found the process intrinsically rewarding. As a result of the incredible energy and motivation the children possessed, teaching the class felt like a breeze. Despite the students’ passion and zeal for math, I was constantly trying to figure out ways to inject a bit of added excitement into the lessons to maintain a high level of engagement. For example, we would occasionally play math oriented games to reinforce arithmetic fluency like “Around the World,” a frenzied one-on-one showdown to see who could answer mental multiplication problems the fastest. When the math curriculum was weaved into games, it seemed that the class was especially alive.

That’s when I decided to take gamification to the next level. I sought to fuse my favorite TV game show with a review session for an upcoming math test. Growing up, my family would religiously watch the Jeopardy game show while eating dinner. We would play alongside the contestants, racing each other to nail each question. My mom’s expertise would shine through anytime the topics required medical knowledge; my dad was especially adept at answering math and engineering based questions. My sister and I seemed to come out on top whenever answers required a bit of pop culture knowledge. Regardless of who racked up more imaginary points, it was a great mental workout and just plain fun.

Now, when we talk about using Jeopardy as a vehicle for learning in the classroom, I am obviously not the clever inventor of that concept. I played Jeopardy games in class during my middle school and high school years as well. Hordes of teachers across the country use this game routinely to mix up the classroom dynamic and allow kids to learn while engaging in some friendly competition. It was now my turn to implement this timeless and incredibly fun trivia game.

One Saturday afternoon, after recording a number of videos for a soon-to-be-released standardized test prep course on Udemy (an online learning platform), I finally decided to make good on my internal promise to put together a math Jeopardy game. But I didn’t want to just write a bunch of questions; instead, I wanted to replicate the feel of the actual game show. I intended to use PowerPoint, the classroom smartboard, and a school podium to engender an authentic experience for the kids.

My first thought was to create a PowerPoint template myself that resembled the actual Jeopardy game. But, as I just stated, I knew I wasn’t the first teacher to use Jeopardy. Accordingly, as any good efficiency hacker might do, I trawled the web for premade Jeopardy PowerPoint templates. Lo and behold, I came across a treasure trove of well-designed and interactive layouts. The cream of the crop, in my opinion, was unearthed at http://www.edtechnetwork.com/powerpoint.html. The presentation template was clean, simple, adjustable, and fully functional. Oh, and I forgot the best part… it was free!

I spent the weekend modifying the slides for my purposes and created a total of 25 different questions based on topics we had covered in class. The questions were spread across the following five categories: (1) mental math, (2) decimals and fractions, (3) conversion, (4) area and volume, and (5) data analysis.

In addition, I made one Final Jeopardy question that would be answered at the end of the game. Once everything had been completed, I went to sleep and braced myself for the reaction of my students. Fourth graders are pure of heart in the sense that their thoughts will not be masked to spare my feelings; if they liked the game, they would say so. If not, well, that would be made quite clear as well.

The next day, I showed up to class a bit early so that I could make sure all of the audiovisual technology was working smoothly. Once I was certain that we would experience no technical snafus, I broke the news: the class would be participating in a team-based math Jeopardy game...

To my relief, the kids were ecstatic! I was pumped as well, but I had to make sure that the enthusiasm didn’t devolve into frenetic chaos. I quickly divided the class into two teams and disseminated the rules of the game. Yes, this was a derivative form of Jeopardy, but my version of the game had some substantial tweaks that merited a quick explanation. Here are the rules as I presented them to the class:

- The class will be divided into two teams
- One member from each team will step up to the podium at a time
- Turns will alternate from one team to the next regardless of answers or score
- The team member who is at the podium will have one chance during his team’s turn to select and answer a question; if he is correct, his team will be awarded the points related to the question; if he is incorrect, the other student who is at the podium from the opposing team will have a chance to steal
- If a student is able to steal a question, he still gets to take his next turn
- Students must answer each question individually without help from other team members; the two exceptions to this are for Daily Doubles and Final Jeopardy
- Daily Doubles, when selected, allow teams to make a wager up to the amount of points they currently have; there is no penalty for an incorrect answer; teams may collaborate to come up with an answer; if a team answers incorrectly, the opposing team may collaborate and steal
- For Mental Math questions, students may not use whiteboards or paper to make calculations
- Final Jeopardy questions will require a wager up to the amount of the points the teams currently have; if a team answers incorrectly, the points wagered will be subtracted from the current score; teams may collaborate to come up with an answer
- Absolutely no talking is permitted while students are attempting to answer a question

Ignoring the rules meant a swift consequence: being taken out of the game. Since no one wanted that to happen, the students ended up behaving very nicely. We jumped right into gameplay, and the level of engagement was astounding. I saw students focusing, trying, and working harder than ever. Moreover, it seemed as though everyone was having a blast! The students knew that the winning team would get a trip to a local cafe during the following week, so they were quite eager to secure the win. When a victorious team finally emerged, the students showed great sportsmanship. The winners were gracious, showing respect to their diligent competitors. In sum, it was a massive success.

Word spread throughout the school that my math class had gotten to play math Jeopardy. Fourth graders from other math sections were constantly asking if they could partake as well. I spoke with the other teachers, and before I knew it, we had another Jeopardy bout on the calendar. But this time, I wanted to make it more memorable. So, using my video production knowledge, I decided to record the whole event using two cameras and a couple of remote microphones. The outcome was fantastic! I ended up spending two weeks editing down the entire hour long game into 15 minutes of action packed excitement. I then distributed the video to all of the parents so that they could see exactly what we were doing in class. Thereafter, I got some really enthusiastic emails from parents saying how fun it was to watch their kids in action. I wish I could show the video to all of you, but unfortunately I don’t have permission to share the footage outside of the school community.

After the second Jeopardy game, I got even more requests to play yet again. Not wanting to disappoint the youngsters, I decided to get the game going one last time for the entire fourth grade class. Like the previous two times, it started with great success. Everyone was getting involved and I couldn’t have been more pleased. But then something unfortunate happened. As the game progressed, the kids got a bit overzealous. As much as I enjoyed watching the students get so enmeshed with a math related activity, I was sad to see the intensity turn negative. There were even accusations (which were untrue) about students surreptitiously using calculators to find answers. One of my students ended up in tears because the environment became slightly hostile after the final results were announced. At that point, we immediately stopped everything to have a 15 minute conversation with the kids about competition and sportsmanship. We emphasized that the most important part about playing a team-based game was to maintain composure. Winning and losing is more or less immaterial; it’s the process of playing and competing that is ultimately the most valuable.

The major takeaway from this experience is that I need to set the tone more clearly at the onset of the game the next time around. I will make sure to deliver a detailed speech at the beginning of the class period about the importance of good sportsmanship throughout the game. Folks that fail to abide by this general principle will face immediate ejection.

All in all, it was an incredible experience. I plan to make use of this activity again next year for my 6th grade class. Moreover, I encourage any teachers out there to try this activity for yourself. It’s not terribly difficult to modify the template, and the game will no doubt be fun as well as educational. If you do plan to give it a go, please drop me a line and let me know how it turns out!

### EP061: Quadratic functions: real world applications

On the heels of filming a fun music video about the quadratic formula, Huzefa devotes an entire episode to discussing the real world uses of quadratic equations. Join Huzefa as a he shares from an article that describes the following applications to the following fields: (1) ballistics, (2) economics, and (3) textiles.

To check out the article, go to http://www.montereyinstitute.org/courses/Algebra1/COURSE_TEXT_RESOURCE/U10_L2_T1_text_container.html

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### EP060: Math for love

Huzefa is joined by Dan Finkel, a mathematician with a plethora of teaching experience. Dan is also the founder of Math for Love, an education organization that advises dozens of schools on math curriculums in ths Seattle area. Join Dan and Huzefa as they discuss how math education should be modified to foster creativity and interest, and also how games can be used to bolster math fluency.

Math for Love: mathforlove.com

Prime Climb: primeclimbgame.com

Tiny Polka Dot: tinypolkadot.com

TEDx Talk: https://www.youtube.com/watch?v=ytVneQUA5-c

Hampshire College Summer Studies in Mathematics: http://www.hcssim.org/

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### EP059: Why "making" is the key to learning

Huzefa shares and discusses and article from Edutopia about why the process of creation is so important to learning. Following on the heels of yesterday's episode about makerspaces, Huzefa answers the question of why making and creation stimulates the mind in such an effective way compared to standard modalities of education.

To check out the article, go to http://www.edutopia.org/blog/making-is-essential-to-learning-youki-terada

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### EP058: Makerspaces: an interactive approach to learning

Huzefa explores the revolutionary and popular approach to learning called Makerspaces, a centralized location for students to collaborate, design, and create based on their unique visions. Huzefa not only defines and discusses these cauldrons of learning, but he also offers 5 ways to make sure that they are well suited to foster creativity and ingenuity for all types of learners.

To check out the article on how to optimize makerspaces, go to http://www.edutopia.org/blog/makerspaces-equal-access-to-learning-laura-fleming-billy-krakower

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