Assignment 2 Microteaching Lesson Plan

LESSON PLAN PRE-CALCULUS 11

Unit: Quadratics

Lesson: Completing the Square

Big Ideas:

Algebra allows us to generalize relationships through abstract thinking.


The meanings of, and connections between, operations extend to powers, radicals, and polynomials.

Curricular Competencies:

Visualize to explore and illustrate mathematical concepts and relationships


Represent mathematical ideas in concrete, pictorial, and symbolic forms


Solve problems with persistence and a positive disposition

Learning Objectives:

Understand why completing the square is essential in finding the roots of a quadratic equation


Develop a geometric interpretation of what completing the square looks like


Be able to complete the square algebraically


Apply the process of completing the square to solve quadratic equations

Materials needed:


Whiteboards + markers


Paper


Scissors


Pencil/pen





Lesson:

Introduction: (3 mins) - Lisa L leading

Recap: we already learned about quadratic factoring.


Intuition for today’s lesson

Try to find the roots of this: x2+6x-11=0 using factoring. You can't, right?


This leads us to today’s lesson. Many quadratics are not factorable, but still have roots. So how do we find the roots?


Remember perfect squares? We can easily solve for x if we could rewrite this problem into a perfect square, then simply use basic algebra. How can we make a quadratic into a perfect square?

Demo: (5 mins) - Nathaniel leading (others are walking around helping students who are struggling)

Pass out paper and scissors to students. Instruct students how to visualize completing the square with this short arts and craft

Fold the paper along a diagonal to make a square & cut that square out. That square has side lengths x and area x2


The remaining paper is a rectangle with side lengths b and x, resulting in an area of bx. Together with step 1), the total area is x2+bx


Now we want to fold the rectangle in half lengthwise and cut it. Notice how each cut rectangle has length x by b/2, since we cut it. Each cut rectangle has area bx/2. Align one strip below the square and one strip to the right of the square. Notice how we haven’t removed any paper so the area is still x2+bx.


Now how do we make this a square? What do we need to add? The remaining value that we are missing is a square with side lengths b2. So its area is b2/2. This is why when we “complete the square,” we “half n square.” So to make a square, we add the value that is half the coefficient of the x term and then square.

Direct Instruction: (7 mins) - Lisa D leading (Lisa L helping co-teach. Nathaniel walking around & observing if students are understanding the concepts)

Relate what we did in the demo to how we complete the square algebraically with an example or two.

Closure: Exit Slip (5 mins) - everyone walks around helping students

Everyone get into groups of 3 and tries a problem

Assessment (formative):

Introduction & Direct Instruction: Are students paying attention? Are students engaged, asking/answering questions, and participating in discussions? Are students able to follow along with the examples discussed? Are students able to find connections between the visual representation and algebraic representation of completing the square?

Hands-on Practice (group-work): Teacher walks around and guides students in their groups. During the demo, do students understand how to make a square (complete the square) visually with the crafts? Are students able to complete the square of the given examples algebraically?