Incorporating inquiry into a math lesson has many benefits (as outlined here), but creating a quality inquiry-based lesson can be a challenge. Below are 4 questions that can spark planning and lesson ideas for discovery lessons.

**Is this a hands-on concept?**

When a concept can be taught with physical objects or models, use those to guide your lesson planning. Many geometry topics fit in this category. Plan for students to explore and think about models. An inquiry-based lesson can begin with students playing with physical objects, then answering questions, and then proving a concept. Many formulas can be discovered by students when given the opportunity and guidance.

Examples of Hands-On Inquiry-Based Learning:

- Volume of Rectangular Prisms
- Area of Parallelograms, Triangles, and Circles
- Circumference
- Angle Relationships
- Pythagorean Theorem
- Transformations on the Coordinate Plane

**Is there a pattern?**

We’ve been trained to find patterns since we were young. If a standard is based on extending a pattern in math (and many are), we can let students figure out the pattern and discover the rule. To build a lesson, let students examine patterns, prompt them with questions, and lead them to figuring out how the pattern continues.

Examples of Pattern Inquiry-Based Learning:

- Integer Exponents
- Operating in Scientific Notation
- Quadratic Functions in Vertex Form
- Absolute Value Functions
- Central and Inscribed Angles
- Trigonometry Ratios

**Does this concept build on a previous topic?**

Some concepts seem brand new to students, but many lessons we teach are building on previous learning. Even when students are familiar with a topic, inquiry learning can still be applicable. If students already know the basics, we can push them into deeper understanding with questioning. Begin with what they know how to do and guide them to go further.

Examples of Inquiry-Based Learning Building on Previous Learning:

- Reflecting over an Axis on the Coordinate Plane
- Slope Intercept Form
- Graphing Systems of Equations
- Finding Midpoints

**Is there a real world application?**

Most math concepts can be applied to real world situations, but we often wait until after students understand the concept to do so. Sometimes, the real world connection can help students discover and understand the concept. We can use real world questions to get students thinking and problem solving. Through this process, they can figure out solutions and discover new learning.

Examples of Inquiry-Based Learning through Real World Application:

*I hope these ideas help with your inquiry-based lesson planning. Thanks for reading!*

*-Rachael*