Socratic inquiry
Geometry · Cone- 1Predict
- 2Explore
- 3Explain
Horizontal slice
As the slice rises toward the tip, does the circle get larger, smaller, or stay the same?
Make a prediction. Then find the evidence yourself.
Free math practice.See why it works.
Inquiry-based learning. Socratic questions. With Inquiry AI, children predict, explore a 3D model, and explain what they discover. Guiding questions help them work out why, one step at a time.
- Free to use
- No sign-up
- Works in your browser
Continue the full cross-section inquiry
Math practice for every elementary grade
Find a topic, explore the visual explanation, and work through a guided mission.
Grade 1
Addition & number sense
360 guided missions
Grade 2
Place value & measurement
420 guided missions
Grade 3
Multiplication & fractions
450 guided missions
Grade 4
Fractions, decimals & shapes
390 guided missions
Grade 5
Fraction operations & volume
360 guided missions
Grade 6
Ratios, equations & statistics
368 guided missions
Our full lesson collection covers Grades 1–6. Kindergarten and secondary pages focus on tools and developing pathways.
A topic in mind? Start here.
Explore a visual model, practice a skill, or read a step-by-step guide.
Multiplication
Build times tables with arrays and equal groups.
Fractions
Compare, combine, and explore fractions with visual models.
Division
Make sense of each step in long division.
Ratios
Use models to compare quantities and find equivalent ratios.
Equations
Use balance models to understand and solve equations.
Geometry
Explore shapes, angles, and volume with interactive models.
Socratic questions that make room for thinking.
Inquiry turns a question into an experiment. Socratic prompts help learners explain what happened. A new transfer question then checks whether they can use the idea independently.
Predict, then explore
Start with your own idea, then move or rotate the model to see whether the evidence supports it.
Reason with questions
What changed? What stayed the same? Why? Socratic questions connect what children observe to the mathematics.
Try a new question
Use the idea once without hints, then review a summary of this learning session.
A little support for the adults, too.
Bring a useful model into homework time or your next lesson.
For parents
Find a starting point when homework gets difficult, with grade-by-grade guidance and questions to ask together.
Get help with math at home → View a sample learning reportFor teachers
Use visual manipulatives for demonstrations, choose Common Core practice, and follow up with printable worksheets.
Find classroom resources → Printable math worksheetsBefore you start
Need a hand? Contact us →What is Inquiry AI?
Inquiry AI is a free math learning site combining inquiry-based learning with Socratic questions. Learners predict, explore visual models, and explain their reasoning. Its full lesson collection covers Grades 1–6, alongside a growing K–12 tool catalog and guided labs.
Is the math practice free, and do I need an account?
Public practice, interactive tools, study handbooks, and printable worksheets are free to open. No account or email is required to get started.
How does this fit with Common Core?
Grade and topic pages connect elementary practice to Common Core standards. Use the grade hubs or Common Core review page to find the relevant skill and its visual explanation.
Does Inquiry AI generate answers or save a long-term learning profile?
The guided questions and hints are pre-written, with no live AI answer generation during practice. Guided labs finish with a summary of that session. Cross-session learning profiles are not available; the parent report is a sample.