Teaching CCSS.Math.Content.HSA-CED.A.2

Instructions for You

Objective: They say nothing teaches like teaching, and they're totally right (whoever they are). Turning a word problem into an equation is fine and well, but there's just something about making up your own examples that really makes a concept stick, like your hair after you fall asleep chewing gum. So let's kick it into reverse and do things backwards for once.

In this activity, students will dismantle and reverse-engineer a two-variable equation and invent their very own word problem to represent it. Then they'll present their problem to their classmates, who'll try to put Humpty back together again by figuring out what the equation was. Throw in a hearty round of graphing at the end, and your students will be experts at this standard before you can say "Common Core."

Activity Length: 2 class periods (or more if you have a giant class size)
Activity Type: Individual
Materials Needed: Tons of Post-It sticky notes in 4 or 5 different colors, scratch paper

Preparation: Write down each of the following equations on the back (sticky side) of a Post-It note, using a variety of colors (at least 4). Each equation should have its own Post-It so you can stick it up on your whiteboard or desk with the actual equation hidden on the underside (no chuckling, please).

Linear:
y = 2x + 3
y = 3x + 2
y = 4x + 1
y = 0.5x
y = 0.5x + 2
y = 3x + 2
y = 13x + 200
y = 8x + 50
y = 22x + 70
y = 33x + 22

Quadratic:
y = x² + 2
y = 2x²
y = x² + 3
y = 0.5x²

Exponential:
y = 10(2)^x
y = 100(0.5)^x
y = 5(3)^x
y = 3^x
y = 10(1.2)^x
y = 300(1.5)^x
y = 500(0.5)^x

If you haven't covered quadratics or exponentials in class yet, go ahead and skip those ones. And if you've got more students than this, feel free to make up a few more variations.

Once you've got a Post-It for each equation, stick them up either on your whiteboard, on an empty desk, or wherever else is convenient. Make sure the equations themselves aren't visible and that there's a good mix of colors. And don't color-code them by equation type—use a wide and random variety of shades. The more, the merrier!

Step 1: Have each of your students come up and randomly choose one Post-It. Make sure they keep 'em secret!

Step 2: Once everyone's got a Post-It and is back in their seats, have the class come up with a few different categories/contexts for their equations, out loud. Write these all down on your white- or blackboard, but only take as many suggestions as you have colors of Post-Its.

Some easy ones are Animals, Money, and Superheroes, but you can go as goofy as you want with this (Zombies, Star Trek, etc.). Keep them usable though—your students will need to create a word problem based broadly in whatever category they get assigned, so stuff like Quantum Physics or Kubrick Films probably won't work.

Now choose one Post-It color for each category (decide on this yourself this time, without input from students), and write the color next to its respective category on the board. You can even color-code 'em with your whiteboard markers if you're feeling real fancy. Tell your students that the color of their Post-It represents the category they'll need to use in their equation.

Step 3: Now comes the big part: each student should create a word problem that can be modeled by the equation on their Post-It, and they have to use whatever category matches their note's color (e.g. if they got y = 0.5x and their category is Animals, they could come up with something like "there are half as many lions as giraffes"). This is the real meat of the activity, so take as long as you need on this. Take a few laps around the room to help out anyone who's struggling.

Step 4: Presentation time! After the chorus of groans has subsided, have your students present their word problem to the class via dramatic reading (spooky voices encouraged, especially if they've got a Ghost category). Make sure they know not to tell everyone what their actual equation is, and keep it hidden on the back of their Post-It. (Depending on your class size, you might need to spread the presentations out over two days.)

After each brief presentation, have the rest of the class take out some scratch paper and figure out what equation the word problem represents, on their own. Then have each of them sketch a quick graph of it, with each axis labeled with its respective units (like "lions" and "giraffes," or whatever it was). The kid who just presented should take this time to graph their own equation.

Step 5: Ta-da! In a dramatic reveal, have your presenter reveal their equation to the class, and have the class check their answers. You can take the reins and do a brief little class discussion here if it was a particularly tricky equation to figure out. Then move on to the next presenter.

Step 6: When the whole group has presented, have everyone write down their own word problem, equation, and graph on a fresh sheet of paper and hand it in to you. They'll need to label their axes and units, too. Victory dances are optional, but encouraged.

Instructions for Your Students

Look, we get it. Sitting at your desk and turning word problem after word problem into equations, while necessary, is kind of like the World Golf Championship of math—not quite the most exciting use of your time. So we're gonna let you drive the golf-cart around yourself for a bit.

This activity is all about starting with an equation and inventing your very own story problem to go with it. Just like golf as a sport would be way better with jetpacks or swords (or both!), you'll be spicing up an equation with vampires, or werewolves, or something else—all to show the relationship between two variables in a decidedly less-dull light. We're talking less golf-clapping, more raucous screaming applause with electric guitars in the background. Make things as bizarre or interesting as you want!

Step 1: Head up to the Wall of Post-Its when your teacher tells you to, and randomly choose one sticky note. It will have an equation on the back of it. Don't show anybody! Keep it secret, keep it safe.

Step 2: When everyone's nabbed a Post-It, your teacher will take some suggestions on categories for the word problems you're about to create. Make sure you come up with some truly rad ones—we don't want this to be boring, right? It can be almost anything: Vampires, Dragons, Money, Sci-Fi, you name it.

Now your teacher will assign a different Post-It color to each category. If you have a pink Post-It and the pink category is Dogs, you'll need to come up with a word problem about Chihuahuas or Great Danes or whatever. Hopefully it's a good one.

Step 3: Grab a sheet of scratch paper and figure out a good word problem that can be represented by your equation and category. You'll want something that relates the dependent variable (y) to some other unknown quantity (x).

For example, if you got y = 10x and Vampires for your category, you might come up with something like, "There are ten times more water-vampires than bat-vampires in Transylvania today." Take your time! It ain't a race, slick. If you do finish before everyone else, draw a sweet picture of your problem (water-vampires have fish tails, duh).

Step 4: Now you're gonna present your word problem to the rest of the class, using your best dramatic voice. Don't reveal what your equation is yet, though—just tell everyone what your situation is. Paint 'em a word-picture, you know? After your presentation, everyone else will try to figure out what your equation is and graph it (on their own, at their desks). You can head back to your seat, and take the time to sketch a graph of your own equation (with axes and units labeled, of course).

If you're not the one presenting, grab some scratch paper and use what you know about related quantities to turn the presenter's word problem into a sweet, sweet equation in two variables. Then graph that bad boy.

Step 5: After everybody's written down their equation and graph answers, the presenter should give a mighty roar and tell the class what their equation really was. Actually, better scratch the roaring. That can wait for P.E.

Step 6: When everyone's done presenting, snag a fresh piece of paper and jot down your equation from your Post-It, the word problem you invented, and your graph. Oh, and turn it in. Dunzo!