Lesson Title: Introduction to Completing the Square Course: Algebra I (grade 9)
Date: ______Teacher(s): ______Start/end times: ______
Lesson Objective(s): What mathematical skills and understanding will be developed?Students will be able to square binomials, factor perfect square trinomials and complete the square. Students will also be able to explain their answers pictorially using algebra tiles and symbolically. The focus of this lesson is to build a conceptual understanding of perfect square trinomials.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific questions, problems, tasks, investigations, or activities will students be working on during the lesson?
Working in pairs students will identify trinomials as perfect squares or not. They will be required to justify their answers pictorially and symbolically.
1. Drill: a. Use algebra tiles to model, express the produce symbolically.
b. Use algebra tiles to factor, express your answer symbolically.
While students complete the drill circulate making sure they remember how to multiply and factor using algebra tiles, and that they understand the difference between pictorial and symbolic representations.
2. Whole class discussion.
Ø “When we first learned about factors and multiplication we often used an array or area model to represent these products. What area models could be used to represent the factors of 12?” Answers should include 2x6, 3x4, and 12x1 models; students should explain why their models are correct.
Ø “Using an array or area model explain why 4,16, and 25 are considered perfect squares”
3. In pairs have students complete In Search of the Perfect Square? Worksheet. While students are working circulate and observe-check each students answer to #1 to ensure that they have the correct concept about representing perfect squares pictorially and symbolically. Ask students to explain their work and justify their answers..
Evidence of Success: What exactly do I expect students to be able to do at the end of the lesson, and how will I know? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have accomplished your objective.
I expect all students to be able to demonstrate why is a perfect square trinomial both pictorially (using algebra tiles) and symbolically. Using algebra tiles (or a sketch) I would expect all students to be able to explain why 25 should to be added to to make it a perfect square trinomial.
Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson?
“What does the Toyota symbol, circles, sound speakers, solving quadratic equations, and building hover crafts have in common?” The answers will vary / Lesson Closure Notes: Exactly what summary activity, questions, and discussion will close the lesson and provide a foreshadowing of tomorrow?
To check for understanding ask “Why is?”
Relate completing the square back to the lesson launch discussion.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Prerequisite skills: To complete this lesson, student must know how to multiply and factor polynomials. They must be able to express their work using algebra tiles as well as symbolically. They will be applying these concepts to completing the square.
Students may be confused by the linear coefficient i.e. think is a perfect square trinomial.
Reinforce that symbolically means with traditional algebraic statements and pictorially in this case means with a sketch of algebra tiles.
Resources: What materials or resources are essential for students to successfully complete the lesson tasks or activities?
Algebra tiles
Tile mat / Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson?
Homework: a brief review of solving quadratic equations by factoring (in the text book). This will lead into the lesson tomorrow which will be on solving quadratic equations by completing the square. Challenge problem: find b so that can be expressed as a perfect square.
Post Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
I will determine the success of the lesson by listening and observing the students as they work on the In Search of the Perfect Square complete
HCPSS Secondary Mathematics Office; adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.