Understand math, one step at a time
New questionMy practice

Visual math · For students

Beyond the answer,
understand why each step works.

Why draw that auxiliary line? What changes when the point moves? See the reasoning alongside the diagram, and ask about the step you do not understand.

Explore follow-up questions
Enter my problemBrowse public examples

Explore examples without logging in · Log in to submit your own question

Start with this questionRectangle and moving point
Rectangle ABCD with moving points E and FAB = 4 and AD = 8. E moves on a circle with centre A and radius 2. BE and BF are equal and perpendicular. G is the midpoint of BC; F moves on the circle with centre G and radius 2.ABCDEFG48

The point keeps moving. How do we find the shortest distance?

Follow the rotation from E to F, then see why F moves on a circle.

View “Rotation and distance” in full

Ask a follow-up about the current step

Stay with the step that needs explaining.

Open Ask a follow-up in your own lesson. The current step and diagram are included automatically, so you can focus on what is unclear.

Return to the original solution and connect the extra explanation to the reasoning you have already seen.

Generate my explanation and ask follow-ups

Log in to ask follow-ups on your own lessons. You can read and play public examples without an account.

The learning process

See it. Pause. Explain it yourself.

Use the animation to examine the reasoning, then check your understanding without the hints.

  1. Read the givens and the goal

    Identify what is known and what the question asks. Match each number and symbol to its meaning in the diagram.

  2. Pause where the reasoning changes

    Watch a transformation, compare two frames or ask a follow-up in your own lesson. Check why the next step is justified.

  3. Rebuild the argument

    Hide the answer and describe the steps in your own words. Try a related problem to check that you understand the method.

Public examples

Eight ways to start exploring

Choose a topic you are studying. Each public example includes the original question, a written solution and an animation.

Primary · Word problems

Planning a school trip

Understand why we subtract before dividing equally.

Question · Worked solution · Animation
Geometry · Arcs

Petal perimeter

Combine equal arcs into complete circumferences.

Question · Worked solution · Animation
Geometry · Proportion

Cube proportions

Compare length, area and volume ratios.

Question · Worked solution · Animation
Geometry · Moving points

Rotation and distance

Use a rotation to find a moving point's locus.

Question · Worked solution · Animation
Algebra · Geometry

Exploring a parabola

Connect symmetry, intercepts and a quadratic equation.

Question · Worked solution · Animation
Trigonometry

Sine transformations

Separate amplitude, period and phase.

Question · Worked solution · Animation
Sets

Set inclusion

Check interval inclusion and the empty-set case.

Question · Worked solution · Animation
Sets · Parameters

Complements and parameters

Rewrite the complement condition before considering cases.

Question · Worked solution · Animation

Tips

Use animation to support reasoning

A diagram is not a proof

Moving a point can suggest a pattern, but one position does not prove every case. Check the theorem's assumptions, boundary cases and when equality holds.

Check your own question

Type a problem or upload a clear image. Review the recognized text, numbers and symbols before generating an explanation, and check the result against the original question.

Before you begin

You might also like

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.

How is a follow-up different from a new problem?

A follow-up includes the current step and diagram of your own lesson. It helps you explore a particular point without restating the whole question. Public examples can be read and played anonymously; generating and discussing your own lesson requires login.

Does every question work equally well as an animation?

Examples cover geometric changes, function graphs, sets and quantities. Results and available interactions vary by problem. Carefully check written reasoning for calculations and complicated conditions.

Take another look at that difficult step.

Try a public example, then bring your own question. Leave room to think, pause and understand.

Enter my problemTry an example