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Teaching CCSS.Math.Content.HSA-REI.A.1

Logic. Reason. Equations. Shmoop.

  • Activities: 4
  • Quiz Questions: 0

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Unless you've time traveled from the 24th-and-a-half century, your students aren't robots. You can't feed them punched cards full of equations and expect to get any solutions back; a lot of tears, angry parental phone calls, and assault charges seem more likely. Don't worry, though. It's better this way. We'd much rather have students understand what they're doing—and why they're doing it—when solving equations.

Shmoop's A-REI.1 Teaching Guide is here to help you navigate the student-teacher interface. With our help, you'll be one step ahead in helping your students understand the solution-finding process—and one step ahead in stopping that whole robot uprising thing that happened in the 23rd-and-a-half century.

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-REI.A.1?

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



Instructions for You

Objective: In this activity, students will apply their knowledge about how to create successive equalities—but instead of solving equations, they'll be starting from simple equations and building algebraic monstrosities. It'll require the same skills and knowledge, but now they'll be using these tools to try to stump their classmates.

Students won't be making Frankenstein's monster, but their creations should be pretty electrifying.

Activity Length: 1 class period
Activity Type: Individual
Materials Needed: Document camera / projector or board for showing problems, paper

Step 1: Introduce the idea of algebraic monstrosities to the class. Explain that, although successive equalities can be used to solve equations, making them simpler, this process can also be used to make equations more complicated. This can be shown with an example, like this blooming of x = -2:

Step 2: Get the students to write some algebraic monstrosities of their own. As in the example, have them start with a relatively simple equation, and then go wild, making it as complicated as they can. At each step, though, they need to justify why the step works. Have them make five monstrosities.

Step 3: Now that they have their monsters, ask them to take a new sheet of paper, and write out these monsters as challenges. At the top of the page, have them write out all the initial equations in a row, then at the bottom of the page, have them write out all the corresponding monsters.

Step 4: Have each student trade their challenge paper with another student. Each student should now have a page with a bunch of initial equations and a bunch of monsters, and their challenge is to grow each initial equation into its corresponding monster. If any equations prove too difficult, put them up on the board, and see if the entire class can solve them.

Instructions for Your Students

Student intro: Complicated equations can often seem like real monsters. Big, ugly, and difficult to control. That said, these monster equations tend to have pretty humble beginnings, and in this activity, you'll develop some mathematical monsters of your own.

Not only that, but you'll trade monsters with your classmates, to see if they're up to the challenge of recreating the things you've made. It'll involve a lot of cunning and creativity, and unlike the creation of Dr. Frankenstein, your monsters are unlikely to terrorize any nearby villages. Just your classmates.

Step 1: You know that successive equalities can be used to solve equations, making them simpler, but this process can also be used to make equations more complicated. If this seems a bit fuzzy, take a look at this example monstrosity, made from a humble x = -2:

Step 2: Now you can create some algebraic monstrosities of your own. You'll start with a relatively simple equation, and then go wild, making it as complicated as you can. At each step, though, you'll need to justify why that step works. After all, where's the fun in making monsters if it doesn't come with a whole lot of explanatory precision? You should be able to come up with five monsters.

Step 3: Now that your monsters have been made, take a new sheet of paper and write out these monsters as challenges. At the top of the page, write out all the initial equations in a row, then at the bottom of the page, write out all the corresponding monsters.

Step 4: Now, find another student, and trade your challenge sheets. You should now have a page with a bunch of initial equations and a bunch of monsters, and your challenge is to grow each initial equation into its corresponding monster. If any of the equations prove too difficult, pass on it for now. If it ends up being too tough to solve, maybe your teacher will put it up on the board, and you can see if the entire class can tame this wild monster.