How an Average 2, 000 Calories a Day Diet Inspired a Math Lesson

All of the seventh grade math teachers have been in a room lamenting about the content in our curriculum. One topic of conversation was equations. How, do you make fantastic, hands-on lessons with equations? There is no shortage of such lessons if your topics are geometry or statistics, but equations, rational numbers, inequalities? Everything is so contrived.

Ok, so perhaps I might have contributed to the complaining, I won’t confirm or deny. Regardless, I was motivated to find or create something better. Within the context of rational numbers, I had used Dan Meyer’s age activity, I had even made my own for a few, but equations and expressions? I was stumped. I tweeted out to Dan Meyer and Andrew Stadel and the world asking, no begging, for ideas. Granted, I only recently began tweeting about math and have a total of 3 followers, but that is not the point.

The angels in the twitter universe answered my math prayers and Andrew Stadel recommended Robert Kaplinsky’s lesson idea for inequalities. Since I had already spent time creating an inequality lesson based on Mr. Stadel’s sweet snacks activity, I didn’t think I wanted to throw out all of my work before even trying it. As I analyzed the 2, 000 calorie lesson, I noticed an option to use it for equations. Eureka, I thought. Now I have a great lesson for inequalities and equations!

For those who have never seen the 2, 000 calorie clip, I implore that you view it. The funny coincidence is that I had stumbled upon it during my summer searching for all things math, saved the link to a folder, and promptly forgot about it. Thankfully, Andrew Stadel reminded me of its existence.

Robert Kaplinsky offered up a video that showcases the amount of food it takes to reach the daily recommended 2, 000 calorie consumption. Some of the foods featured include McDonald’s menu items, carrots, eggs, bacon, bagels, pizza, and even M&M’s. It is fascinating for someone of any age to watch.

For a brief introduction, I reminded students that the daily recommendation for an average person is a 2, 000 calorie diet. We quickly discussed if the average American consumed more or less and one of my students shared that he once read that the average American consumed 3200 calories a day. I don’t know if he was right, but it captivated the rest of the students as they started to discuss what this overeating would lead to for the average person.

Before I showed my students Mr. Kaplinsky’s amazing video, I created a slide on a Google Spreadsheet listing all of the foods that would appear in the video. I asked them to consider the quantity of each food needed to yield 2,000 calories, and in that regard, to write a number that was deemed too high and too low for each. The stipulation was that the too high and too low guesses couldn’t be extreme; they couldn’t guess that 3 million M&M’s were too high, for example.  As Dan Meyer has pointed out, having students do this instead of asking them to just guess the exact number removes the pressure of having to be “right.”  In addition, it forces students to think beyond one number and analyze the situation in a big picture sort of way.

What this estimation process also inspires students to do is become invested in the lesson. They paid close attention because once they generated all of their guesses; they want to know their degree of accuracy. I believe curiosity is one of the greatest motivators in the math classroom.

As students were mulling over their guesses, I was asked, “Dr. Polak, aren’t avocados super fattening?” Before I even tried to respond another student interjected, “Yes, but it is the good kind of fat.” The comments and questions ran the gamut from, “I love Chipotle to what is a Cobb salad?” Basically, the students were IN.

After enough time had been provided, I played Robert Kaplinsky’s video. The reactions were priceless. Many were high fiving each other if their guesses had been close and others were giggling at just how far off they had been. A very brief discussion about nutrition emerged and then students were diving into algebraic equations. The directions were simple. The students were instructed to create an equation that would help them solve the questions about to be asked on upcoming slides. They were also directed to perform substitution to check their solutions.

The first slide, displayed a clipped image from the video of bagels. Students were asked to write an equation and determine how many calories there were per bagel. Students came up with 2000/x=7 and 7x=2000.

The next question asked was how many slices of bacon were equal to one donut. This question presented a challenge for them and many struggled. Students got out of their seats and went to consult other students across the room with their interpretations. Energy rose, anxiety increased, and anticipation mounted. At the end, there were three equations shared that all worked, but the voted-on favorite was (2000/50)x=(2000/6.6).

The scenarios increased in complexity and students were grappling, laughing, complaining, and collaborating to solve. A few wanted me to just give them equations to solve; others felt it was just too difficult, while many were eager for the next question at the next level. Without exception, they all wanted to know whether or not they were right. Naturally, I asked them to use substitution and their math sense to make that determination…Although I eventually confirmed with solutions presented on the slide.

When asked for their takeaways from the day, students’ comments included, “I never realized how quickly calories add up and the types of combinations that might make us overweight.” Perhaps that comment is not exactly related to solving algebraic equations, but it was a good point. Another added, “I learned that I prefer to solve an equation, not create one myself.” (Laughter ensued) Still, someone else said, “I understand equations better now. They are not just questions from a book, but there is meaning behind them.” Someone else added, “It shows the math serves a purpose.”

All in all, the students were animated and lively. The lesson was fun, but I was unsure whether or not I had truly met the objective of helping them with understanding two-step algebraic equations. To find out, I followed up on two separate days with (what I called) calorie math warm ups.  One of those questions was directly offered to me from Robert Kaplinsky himself after I tweeted him a request for a better tie-in to two step equations. That question was, “What is the maximum number of carrots or eggs (I let them choose) you could eat if you had already eaten 720 calories and wanted to eat exactly 1800 calories? Their responses that afternoon let me know the objective was met. Very quickly, the majority of students demonstrated how to interpret real information, come up with an equation to represent a situation, solve the problem, and interpret the information. Don’t get me wrong, there were a few who still needed scaffolding, but by the end of the review, it was clear that the lesson itself had been time well spent.

Robert Kaplinsky, Andrew Stadel, Dan Meyer and so many other mathematicians have changed the teaching game. These wonderful professionals selflessly share their resources with the world to use. The looming question for me after any lesson is always, did I do enough? If I didn’t, what can I improve for the next time? Sometimes, after lessons like these, I cannot think of any improvements, even if I know I can somehow do better. Granted, I already made small changes in my slides to make a clearer presentation, but overall, there wasn’t much I could think to revise. Although there is always room for improvement, as of this teaching moment, I am reveling in gratitude for the opportunity provided to me by Mr. Kaplinsky.

 

bread calorie mathcopy-of-what-does-2000-calories-look-like

 

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In Defense or Offense of Teaching Procedural Math? An Open Letter to Everyone.

Dear Mathematicians, Parents, Students, Educators, and All Interested Parties,

Is it a sign of weakness for a teacher to admit perpetual confusion on the best way(s) to administer instruction? Although I have been teaching for about 15 years, only a few of them have been spent teaching math at the middle school level. Since making the glorious move to middle school, the distinct advantage of pouring all of my extra time and energy into one subject has both reinvigorated my purpose and sent me down a path of wonder.

In my quest to prevent any student from truly thinking he or she does not have the math brain, the amount of articles consumed by me is, to say the least, staggering. Can I remember who wrote most of them? Not usually. I peruse for content. Only after multiple exposures from the same author do I start to take notice. This is why a few names have made their ways to the corners of my cerebrum  where the long term storage of my memory lives (Thank you Sousa). I usually refer to the information annoyingly as, “I read an article that stated…” Yes, I have turned into one of those people.

My favorite pastime is to research lesson structure ideas as this is my professional focus. Some of the names that continually pop up in my consumption within that topic are Jo Boaler, Dan Meyer, Andrew Stadel, and Yeap ban Har. Each of these math gurus share a common thread, which is that mathematics is a subject that spans beyond mere procedure. Although I could not agree more that math is not strictly procedural, each time I read an article I find myself asking, is there still a place, and furthermore, a need to teach procedure(s) in a math class?

If it is true that the best teachers steal from the best, in some small way, that categorizes me as the best. I have “stolen” lessons from my teaching counterparts, Dan Meyer, and Andrew Stadel.  The stolen lessons have been glorious experiences.  However, I do not believe any of the stolen lessons would have been successful if students had not possessed the background knowledge on procedures as well. Now I wonder, did I enhance their conceptual learning or detract from it with that viewpoint?

Our district was blessed by the personal teachings of Yeap ban Har. I spent a good month after that momentous training opportunity trying to design my lessons just like him. This was not easy to do with only one real half-day of training, but I really gave it my all. Some lessons went astonishingly well, others, not so much.

What I do know is my goal is to do better every single day. This is where I feel as if I am on the giant hamster wheel of math instruction.

In my mind, if students do not learn the concepts behind the math, the procedures for any and all algorithms will be meaningless. They will learn a series of steps, study them for a quiz or test, regurgitate them, and then quickly dump the total experience from their memory. Obviously, this reality is not true for all students. Those students who are excellent at rote memorization might remember the steps, but will they have any idea why they are performing them? If they don’t, can that be considered effective math teaching or learning? On the other side of this paradigm, sits many students who demonstrate conceptual learning but struggle with the rote procedures. For example, several students in my class this year forgot how to subtract opposite signed numbers using an algorithm, but when I placed a number line or integer tiles in front of them, they knew how to solve the problem immediately and could explain their thinking. Is their learning inferior because they cannot demonstrate their understanding in an algorithm?

The articles I have been reading lately push my questioning even further. I believe Jo Boaler flat out posited whether or not it is necessary for students to memorize their times tables. Is this type of thinking correct for educators, and more importantly, for students beyond the classroom?

Here is where I flat out ask the community for feedback.  Is there an appropriate balance needed in our classroom between concepts and procedures? Are procedures completely out of date or still necessary? Do we need to argue the opposite ends of the spectrum, or consider that the ideas are not opposing but supporting of one another? I ask you, in a growth mindset sort of way, to reflect carefully. Perhaps someone out there can inspire me to jump off of the hamster wheel, if only for a moment.

Sincerely,

A math teacher looking for answers.