Engaging Free Resources to Enhance Mathematics Learning: http://illuminations.nctm.org/.
Note: Unfortunately this resource is no longer free such publication of this article but it is still worth the low subscription fees!
Illuminations is a treasure trove of wonderful, free lessons and inter-actives for learning mathematics and is a project designed by the NCTM (National Council of Teachers of Mathematics, USA).
The lessons are divided into grade levels from pre-k to 12 using the NCTM’s Principles and Standards:
Number & Operations
Data Analysis & Probability
and the CCSS (Common Core State Standards) from kindergarten to grade 12.
Illuminations offers two main categories to enhance math learning:
Inter-actives that includes: downloadable mobile and web apps, a web sketchpad tool which includes interactive applets.
Here is an example of an inter-active on fractions:
2. Lessons that are based on an inquiry-based approach that also include virtual manipulates and games. Each lesson contains printable teachers’ notes, materials required, students task sheets, assessments and extensions, questions and reflections, and related resources. All lessons are set up as investigations with questions to guide students. I would suggest to complete each investigation either pairs or small groups to promote collaboration and communication.
Some lessons approach traditional topics in a different way such as the activity titled “Pi Line” by Martha Haehl (http://illuminations.nctm.org/Lesson.aspx?id=1860) which helps connect the concepts of a fixed ratio with linear functions by asking students to graph the function C= pi X d.
If you are just starting out on your inquiry-based mathematics learning journey then I highly recommend you take a look at the wonderful resources on illuminations!