2-8: Choosing the Best Method

By Oscar Castanos

​📅 Integrated Math II
Objective 2-8: 🎯 I can choose and defend an efficient method for solving a quadratic equation.
Sub-Objective: I can evaluate a quadratic and justify whether factoring, square roots, completing the square, graphing, or the quadratic formula is most efficient.

Warm-Up:
1️⃣ Review – Solve using any method: x² − 5x + 6 = 0.
2️⃣ Lead-In – Which method would you choose for: 3x² = 75? Why?

​Today’s Plan:
1. Warm-Up:

2. Notes: When Each Method Works Best

3. Mild → Medium Strategy Practice

4. Think-Pair-Share: Defend Your Strategy

5. CYU

​Warm Up:
1️⃣ Review – Solve using any method: x² − 5x + 6 = 0.





2️⃣ Lead-In – Which method would you choose for:
3x² = 75? Why?

​Concept Overview

Big Idea: Different quadratic equations are easier to solve using different methods. Your job is to choose the most efficient method — and defend your reasoning.

​ Decide & Defend: What is the most efficient method to solve:

​Mild

1. x² − 9 = 0

2. x² - 8x − 9 = 0

3. 3x² + 11x − 9 = 0

For each equation, choose the most efficient method:
a. 4x² = 20

b. x² + 6x + 9 = 0

c. x² - 2x - 7 = 0


Tink-Pair-Share: “How do we know when factoring is faster than the quadratic formula?”

​​Mild (Student Try)

Medium (Teacher Model)

​Example – Defend Your Method Solve

1. x² + 12x = −36

2. x² + 12 = 48

3. 7x² + 13x + 2 = 0

​ Choose the best method AND defend your choice:

a. 5x² + 30x + 45 = 0

b. x² − 2x − 11 = 0

c. 6x² − 7x + 10 = 0

Medium (Student Try)

​TPS Prompt: “When is the quadratic formula NOT the best option?”

A student used the quadratic formula to solve x² − 16 = 0.

1. What is the flaw in the strategy?

2. What method would have been most efficient instead?

3. Does the student's incorrect method still work? Why or why not?

​​Error Analysis:

​Mild:
Choose a method for x² + 4x = −4 and explain why.

Medium:
Solve 3x² + 5x − 2 = 0 using the method YOU choose.

Spicy:
Compare two strategies for solving x² + 14x + 24 = 0. Which is more efficient and why?

CYU: