This is a challenging activity to promote students thought, creativity and discovery. It is suitable for ADVANCED students. It contains complex problems, much more engaging than the ordinary one. The product can be used for groups of 2 , 3 or 4 members or as Individual Practice (4 different versions included).
Students will practice solving quadratic equations with rational and irrational coefficients having only irrational solutions. Some of the equations are in standard form and the other have one term on the right side of the equation. Each quadratic equation must be solved by a specified method - completing the square or the quadratic formula.
There are problems included, where students need to
• rationalize denominators containing radicals
• find the square of a sum or a difference between rational and irrational numbers
• find the common root between two equations
*Hints are provided to help students check their ”pretty” answers.
*If this resource is used for group work, there is a group response sheet specially provided. There partners are instructed to calculate the sum or/and product of all their answers to corresponding problems. They record their findings, surprised to discover that their collective answers are so “pretty” numbers too.
I hope you and your students enjoy this activity.
A recording worksheet is included for students to show work. All answer keys are included as well.