Teacher will visit each group:
Expert Group #1:
Students will use graphing strategies to find solutions to polynomial equations.
The opening of this lesson will center around the display and review of some special functions in graph form. Students will click on the link below as the teacher guides them through the activity below:
The students will be randomly assigned one of the sample problems and asked to make a table of values for graphing the assigned equation, then sketch the graph on grid paper.
To build the students' understanding, the following link will help students visualize the procedure for finding the roots of polynomial functions using the graphing calculator.
Activity: Students will use the following guidelines when using any type of computer / calculator in problem-solving:
1. Students must understand the operation of their own calculator. Students will begin by entering expressions in a way that guarantee that their calculator is performing the operation correctly.
2. Students will focus first on analyzing the problem. A strategy will be developed. The student will then use the calculator to help implement the strategy.
3. Students will check their solutions using a calculator. Check for reasonableness.
4. To lesson the chance of errors, students should clear the calculator and check all settings before beginning a new problem.
Expert Group #2:
Students will use the 'complete the square' method.
Teacher will remind students when solving a quadratic equation by completing the square, the leading coefficient must be 1. When the leading coefficient of a quadratic equation is not 1, you must divide each side by the coefficient before completing the square.
Complete the Square:
1. Move the constant to the right side of the equation.
2. Take 1/2 of the middle term and square the results.
3. Add the value in step 2 to each side of the equation.
4. Factor the perfect square trinomial.
5. Take the square of each side.
6. Move the constant to the right side of the equation to reveal the roots of the equation.
Students will use the following link to work through some additional examples.
Expert Group #3:
Students will use the Quadratic Formula to find the roots of a quadratic equation.
-b ± √b2-4ac ⁄ 2a
Students will discover that in the quadratic formula, the radicand b2- 4ac is called the discriminant of the equation. The discriminant tells the nature of the roots of a quadratic equation or the zeros of the related quadratic function.
*b2 - 4ac > 0 implies two distinct roots/zeros
*b2 - 4ac = 0 implies exactly one root/zero (The one real root is actually a double root.)
*b2 -4ac < 0 implies no real roots/zero (two distinct imaginary roots/zeros)
Students will use the following link for additional practice with the quadratic formula.
After each expert group has completed their assigned activities, the students will form new groups of 3 with an expert from each of the previous groups. Strategies and methods will be shared by each expert.
Reteaching / Correcting Common Errors - Error: Students begin to write equations for a problem before the problem is completely understood. Prescription: While a problem is being discussed, students will put their pencils down. No writing is permitted until the conditions and the variables are identified. Given problem situations, individual students will tell the steps of the solution and uncover each step. Students will continue to work in their groups and write steps for each method. This should eliminate mistakes made by taking short cuts or completing too many steps at one time.