CCSS.Math.Content.HSA.REI.B.4.b

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

The Quadratic Factors activity allows students to make use of multiple structures to create factors for quadratic functions. The patterns developed by this activity allow students to find the numerical factor portion of the quadratic functions. Both methods used within this activity allow students to see the patterns of addition and multiplication needed to find the numerical factors within quadratics.

Students are likely to struggle with factoring quadratics with a leading coefficient other than one as it requires them to use grouping (split the middle method) to complete the factoring. Beyond this, students will likely fail to differentiate when to use each factoring method.

This activity could be easily modified by using area model to create factors. The activity could also be broken apart so as to only cover quadratics with a leading coefficient of one at first, then later bring in the quadratics with leading coefficients not equal to one.