1. Planning Math Lessons using Guided Inquiry- Why? What? When? How?

2. Why is Guided Inquiry a great way to teach math concepts?
can increase rigor in math classrooms
can help develop students’ conceptual math knowledge
when implemented correctly, can be highly engaging for students
can help students make sense of and remember math concepts

3. What is Guided Inquiry? How is Guided Inquiry different than Direct Instruction?
Guided Inquiry (5E) – A teaching method where the teacher presents a specific situation, set of data, phenomenon, etc. to students to explore through guiding questions to direct their thinking so they can generate a strong, aligned conclusion based on their exploration and apply this conclusion to new situations.
Direct Instruction (5-Step) – A teaching method where the teacher directly presents new information and/or explicitly models skills for students who then replicate the teacher’s thinking and/or actions in an increasingly independent way.
Less constructivist
More constructivist
Pure lecture
Direct Instruction (Traditional 5-Step Lesson)
Guided Inquiry (5E)
Open Inquiry
Explicit Instruction with Constructivist-Influenced Activities

4. When should I use Guided Inquiry?
Some objectives are more appropriate to use with guided inquiry than others. Here are some guidelines when deciding if an objective is appropriate to be taught with guided inquiry:
PATTERNS: Are there patterns students can find? Can these patterns be generalized more broadly?
INDEPENDENT DERIVATION: Does arriving at this concept or deriving the formula add value to student understanding of the concept—is the thinking something students would be able to independently recreate if they forget the specifics or the formula later on?
ESSENTIAL CONCEPT: Is the conceptual understanding developed here essential to success in this course? Is this something students must internalize for long after they leave your class?
PREREQUISITES: Have students sufficiently mastered the prerequisite skills and knowledge necessary to discover the key points of this objective?

5. How do I successfully plan and implement a guided inquiry lesson?
One lesson-planning template that could be used when planning a guided-inquiry lesson is the “5E” lesson plan:
Engage (Similar to a Hook- Gets students excited about lesson & activates prior knowledge)
Explore (Students discover)
Explain (Students formalize & articulate what they discovered)
Elaborate (Students practice & apply what they learned)
Evaluate (Students’ learning is assessed)

6. Example Outline-5-E Lesson Plan
Objective: SWBAT discover the Pythagorean Theorem
SWBAT find a missing side in a right triangle
*Note- this lesson plan would take one more than one class period to complete*
Engage- Students will review finding the area of tilted squares, will review parts of a right triangle (leg & hypotenuse) & teacher will discuss some of the real-world applications of the pythagorean theorem to get kids excited about discovering it
Explore- Students will work on an investigation to discover that the area of the squares on each leg of a right triangle is equal to the area of the square on the hypotenuse. Link to activity:
Explain – Students will discuss their findings with their partner & then the class will discuss. Teacher will formalize students’ findings with the Pythagorean Theorem formula and will work through how to find a missing side of a right triangle.
Elaborate- Class will conduct white board practice to find the missing side of right triangles using Pythagorean Theorem.
Evaluate –Students will complete an exit slip requiring them to explain and prove the Pythagorean Theorem in addition to applying the pythagorean theorem to find the missing side in a right triangle.

7. Other Examples
Here are some other examples of objectives where Guided Inquiry could work well:
8th Grade students discover the laws of exponents
7th Grade students learn rules of integers by looking at number patterns
Algebra students group & identify the characteristics of different types of function families (table, graph & equation)