Completing the Square: Choose Your Own Expression
Skill:
Solve quadratic equations by completing the square.
Completing the Square: Choose Your Own Expression
Choose your own expression and observe the process of completing the square with algebra tiles as a visual model.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Open-ended question 1
Describe the process of completing the square.
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Open-ended question 2
Explain how the phrase “complete the square” can be used to describe multiple aspects of this process.
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Open-ended question 3
If we would like to add 1s to complete the square, we need to also add the same number of negative 1s. Explain why this is the case.
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Open-ended question 4
Notice how the slider to change the coefficient for the term only allows even integers. What would happen to the figure if the slider allowed for term like ? What would happen to the algebraic expressions?
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Open-ended question 5
Complete the square for and using the algebra tiles. What do you notice about the result? What do you notice about the coefficients of the original expressions?
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