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Teaching CCSS.Math.Content.HSA-SSE.B.3

Equal opportunity expressions.

  • Activities: 3
  • Quiz Questions: 0

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Expressions, like people, are multifaceted. You can't know someone's life story just by glancing at them, and A-SSE.3 lets students know that expressions are the same way. A quadratic may tell you all about its zeros when factored, gush about its maximum or minimum value when you complete the square, and show off its dance moves after a romantic dinner for two.

Check out Shmoop's Teaching guides for all the smooth how-tos for helping expressions loosen up and express themselves in all new, but equivalent, ways.

What's Inside Shmoop's Math Teaching Guides

Shmoop is a labor of love from folks who love to teach. Our teaching guides will help you supplement in-classroom learning with fun, engaging, and relatable learning materials that bring math to life.

Inside each guide, you'll find handouts, activity ideas, and more—all written by experts and designed to save you time. Here are the deets on what you get with your teaching guide:

  • 3-5 in-class activities specifically designed with the Common Core in mind.
  • 4 handouts (with separate answer keys!) that'll get your students thinking deeply about the concepts and calculations.
  • Additional resources that'll help make any math topic hip, hot, and happening.
  • A note from Shmoop's teachers to you, telling you what to expect from teaching the standard and how you can overcome the hurdles.

Want more help teaching Teaching CCSS.Math.Content.HSA-SSE.B.3?

Check out all the different parts of our corresponding learning guide.



Instructions for You

Objective: The objective of this activity is for the students to learn the nuts and bolts of completing the square for a quadratic equation, and how it can tell us more about the equation. We could get the same information by Facebook stalking, but this a little less…well, creepy.

Activity Length: 1 class period
Activity Type: Groups of 3-4
Materials Needed: One coin, one die, a timer, and a whiteboard.

Step 1: To start, let's build a random quadratic function for your students to work with. Start with the equation y = x2 ± bx ± c, and use coin flips to determine the signs and die rolls to decide the values of a and b. Trust us on this one. It'll really give it the whole our-fate-is-out-of-our-hands je ne sais quoi.

So for instance, if you flip a heads first and tails second and roll a 4 and then a 6, you'll wind up with the equation y = x2 + 4x – 6.

Step 2: Start a timer for 1 or 2 minutes. In teams, have students use the completing the square method to convert the equation into vertex form and answer the following questions before the timer goes off.

  1. What is the vertex form of the equation?
  2. What is the vertex?
  3. Is this a minimum or a maximum?

You can have students answer the questions aloud and award points or have them turn in their work individually. Dealer's choice.

Step 3: Repeat steps 1-2 a once or twice—or however long it takes until students get comfortable with these types of equations. Make sure they know what they're doing, because from this point on, it's all variations on a theme.

Step 4: Repeat steps 1-2, only with equations of the form y = ax2 ± bx ± c. That means three die rolls this time—one for each of a, b, and c.

Step 5: Repeat Steps 1-2, only with equations of the form y = ±ax2 ± bx ± c. That means three coin flips and three die rolls—one for ±a, ±b, and ±c.

Instructions for Your Students

Student intro: A lot of things that might seem simple hide depths of complexity. Your iPad—a tiny tablet of glass and metal—can store all sorts of information and media. A simple leaf from a tree can absorb light and produce energy. And, as we know from feature films and cartoons, a fancy sports car is sometimes a robot from space who's friends with other space robots.

Quadratic equations also hide their share of complexity. In this activity, you'll transform simple quadratic equations in standard form to ones that reveal all sorts of information about the graphs they produce. They won't harness the rays of the sun or turn into a truck, but finding information about vertices is pretty good, right?

Step 1: Split up into teams. Your teacher will create a random quadratic equation for you to work with using coin flips and die rolls. (See? They truly are random!)

Step 2: Your mission, which you kind of have to accept, is to rewrite the equation in vertex form, find the vertex, and determine whether the vertex is a maximum or minimum value within the time limit given by your teacher. Ready…set…go!

Step 3: You'll repeat this for several rounds, with the equations getting tougher and tougher. The team with the highest number of points wins the game—or, at the very least, gets a better grade. And hey, you can't complain about that.