Visual math · For teachers
Make the change visible.
Let students explain the reason.
Bring dynamic geometry, graphs and set relationships into a discussion. Ask before a change, pause at a useful position, and return to the givens and proof.
Explore follow-up questionsExplore examples without logging in · Log in to submit your own question
Did this transformation change amplitude or period?
Compare with the baseline sine graph and discuss amplitude, period and phase separately.
View “Sine transformations” in fullAsk a follow-up about the current step
Explore likely questions while preparing.
Generate your own lesson and ask follow-ups about the reasoning at a particular step. Use the responses as material to review, not as automatic validation of a proof.
Check the conditions and reasoning before class, and choose where to pause or ask students to predict the next change.
Generate my explanation and ask follow-upsLog in to ask follow-ups on your own lessons. You can read and play public examples without an account.
The learning process
Observe, discuss and justify
An animation can make a change easier to see. The mathematical argument still needs to be stated and checked.
Choose a clear observation goal
Decide which quantity, invariant or transformation students should notice. Preview the entire lesson before using it in class.
Pause before revealing the next step
Ask students to predict what changes and what stays fixed. Compare frames or adjust an available parameter to examine their predictions.
Return to a written argument
Ask which definition or theorem supports the observation. Check boundary cases and equality conditions, then let students write the proof or calculation.
Public examples
Examples for a focused classroom discussion
Open the written solution and preview the animation before class.
Rotation and distance
Which distances and angles does a rotation preserve?
Question · Worked solution · AnimationSine transformations
How does each parameter change the graph?
Question · Worked solution · AnimationComplements and parameters
Why is the complement condition equivalent to inclusion?
Question · Worked solution · AnimationCube proportions
Why are length, area and volume ratios different powers?
Question · Worked solution · AnimationTips
Prepare the mathematics as well as the demonstration
Check the generated lesson
Verify the question, diagrams, calculations and proof. A playable animation is not evidence that every mathematical claim is correct.
Plan for the actual classroom
Test the display size, audio and network in advance. Written solutions remain useful when an animation is unavailable, and narration can be turned off for discussion.
Keep students reasoning
Ask students to explain an invariant or predict a result before revealing it. Use independent follow-up work to assess understanding.
Before you begin
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Do I need to log in?
You can read and play the eight public examples without an account. Log in to submit your own problem, recognize an image or ask a follow-up on your own lesson.
Can I read the solution without playing the animation?
Yes. Public examples include a question, diagram and written steps in the initial page. JavaScript is needed only for animation and interactive exploration.
Can I use every lesson interactively?
Only lessons with supported adjustable elements offer interactive controls. Others can still be played, paused or compared frame by frame.
Does an animation establish a proof?
No. A visual pattern can motivate a conjecture, but a proof must justify all relevant cases from the assumptions. Review both generated and written explanations before teaching with them.
Let the diagram start a mathematical conversation.
Choose one change to observe, one question to ask and one reason for students to explain.