Choose your own expression and observe the process of completing the square with algebra tiles as a visual model.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
Describe the process of completing the square.[br]
Explain how the phrase “complete the square” can be used to describe multiple aspects of this process.[br]
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.[br]
Notice how the slider to change the coefficient for the [math]x[/math] term only allows even integers. What would happen to the figure if the slider allowed for term like [math]5x[/math]? What would happen to the algebraic expressions?
Complete the square for [math]x^2-6x+9[/math] and [math]x^2+4x+4[/math] using the algebra tiles. What do you notice about the result? What do you notice about the coefficients of the original expressions?