The Galileo website is an awesome starting place for teaching with inquiry. They have articles and resources to learn about inquiry-based education as well as plenty of research.
Start on the home page, then check out the full set of classroom lessons and examples. They have plans for specific high school, middle school, and primary school math investigations.
You can also download the Focus on Inquiry eBook, read more about what inquiry means, learn how to construct essential questions, and much more.
NCTM offers a set of math resources on the Illuminations site. One of my favorite features here is the enormous library of virtual manipulatives. You can allow your students to drag around the virtual algebra tiles, discover triangle congruence theorems, and shade equivalent fractions (and that's all just pulled from the first page of manipulatives!) This set is perfect for classrooms with computers or ipads.
There are also some fantastic lessons. They're sorted by grade level. Check out some lessons for grades 6-8 or 9-12. There are lessons for younger kids too.
The brain teasers are also fun and would be great warm-ups. There are plenty available.
I use GeoGebra to make exploration easy in Geometry class. Students can sketch a figure into the software (parallel lines intersected by a transversal, centers of triangles, tangent lines, etc.). GeoGebra allows them to easily display angle measures, drag points around, and notice properties by observing what measures change and what measures stay the same. There are endless possibilities with this, especially if you are trying to incorporate a little discovery-based learning.
Download the free software for your classroom or check out the teacher pages that are packed with worksheets, samples, and ideas for lessons that use GeoGebra.
Desmos is the new way to do all your graphing and plotting. It's ideal for Algebra investigations. Use this site to allow students to transform functions and create fun or artistic graphs.
Try the graphing calculator or browse the teaching resources and activities that are available. You can also check out videos that show some of the many uses of the desmos calculator.
5. Inquiry Maths
As an inquiry fan, I have loved the Inquiry Maths site for a long time. The question prompts are perfect ways to get students thinking critically about math concepts.
Take a look at the question prompts in each category on the left sidebar. There are tons of great Number Prompts, Algebra Prompts, Geometry Prompts, and Statistics Prompts.
I also recommend checking out their assessment framework and tips for writing your own prompt.
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