Completing the Square Activities

Instructor: Sharon Linde
Teach students what 'completing the square' means with this fun and interactive lesson. We'll lay out several activities you can use to teach with simple manipulatives, and that can be used with students who have varying levels of understanding.

High-Level Math

Don't be fooled by students' ages or ability levels. Students of all ages, even high-level and performing students, benefit from doing activities related to mathematics. Whether working on concrete ideas, representational concepts or abstract application, using manipulatives and playing games is a solid way to support your math instruction.

Square One

This activity requires students to work in cooperative groups to learn a concrete level of this skill. Make sure to circulate the room as students work in their groups to support and guide them, pulling those aside who need extra assistance.


  • Construction paper
  • Scissors


  • Start the lesson by asking students what words come to mind when you say the word 'square.'
  • Allow each student to share their ideas, then break them into small groups to answer:
    • What rules do you know about squares?
    • What rules do you know about squaring a number?
  • Give each small groups scissors and construction paper and have them cut out a simple 2 x 2 square.
  • Now have them make two more squares of this size and arrange them in an 'L' shape. Ask:
    • Is this shape a square? Why or why not?
    • What would we need to do to make this a square?
  • Write the quadratic equation - x squared + 4x + 4 - on the board.
  • Now have students cut their paper to create a model of this equation. Use one of the squares as the x squared, then cut one of the squares into four strips and place two next to the first square and two below it. Cut the remaining square into four small pieces to fill in the bottom right portion.
  • Ask groups to discuss and explain the model, then write the following problems on the board for them to do independently:
    • x squared + 2x
    • x squared + 6x
  • As students work, walk around to support and guide. Encourage them to create and use manipulatives to assist in their concrete application.
  • Share answers to finish, discussing how students solved the equations.

Box It Up

In this activity, students will be using a box diagram to help them complete the square. In this representational method, students apply prior learning in a more formulaic manner.


  • Paper
  • Pencil
  • Dice


  • Divide students into partner pairs.
  • Start by drawing a square on the board, then divide it into four sections and write the equation x squared + 20x .
  • Have students copy into their notebooks.
  • Write the following in the boxes:
    • The coefficient for the x square term in the upper left box.
    • The x term divided by 2 in the upper right and lower left. In our example, the number is 10.
  • Finish the square by multiplying 10 X 10 to get 100.
  • The finished product should look like this:

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account