Primary · Number sense
Count once, even when the arrangement changes
Follow one object at a time and discover why moving objects does not change how many there are.
Explore animation← Back to the academyWatch an idea.
The animated math studio
Watch an idea.
Make it make sense.
See numbers become groups, a circle become a wave, and a slope become a derivative. Take control of the mathematics, one clear experiment at a time.
Choose your grade1,400 grade investigations + 24 featured animations · Free · Starts paused
Start with a connection
Explore the unit circle
A question. A worked solution. A moving example.
Explore 10,000 guided practice chapters.
Find a new mathematical scenario from Grade 1 to graduate study. Try the question, compare your reasoning, and control its animated example. Search by grade or topic and take one chapter at a time.
Open the practice library10,000 distinct practice scenarios using reusable math models. Filmed teaching videos are a separate collection.
01
Predict
Read the question before pressing Play. Name the quantity you think will change and explain your guess.
02
Investigate
Play once, pause on a useful frame, then change a value. Use the timeline or Step for as much thinking time as you need.
03
Explain
Connect the picture to its equation. Try the challenge and compare your explanation, then follow a full lesson.
A hundred ways to investigate each level
Find your grade. Follow your curiosity.
Each collection has 10 topic units and 100 guided animations. Related investigations revisit a visual model with a new situation, starting values, and a question to solve. Grade labels are study guides; school sequences vary.
Grade 1
100 animations · 10 topic units
Grade 2
100 animations · 10 topic units
Grade 3
100 animations · 10 topic units
Grade 4
100 animations · 10 topic units
Grade 5
100 animations · 10 topic units
Grade 6
100 animations · 10 topic units
Grade 7
100 animations · 10 topic units
Grade 8
100 animations · 10 topic units
Grade 9
100 animations · 10 topic units
Grade 10
100 animations · 10 topic units
Grade 11
100 animations · 10 topic units
Grade 12
100 animations · 10 topic units
Undergraduate
100 animations · 10 topic units
Graduate
100 animations · 10 topic units
A growing collection of moving ideas
Choose your next “now I see it.”
Start with counting and equal parts, build toward functions and calculus, or explore selected university models. Level labels suggest background knowledge; the explanations state the assumptions behind each model.
1,424 animations · Showing 1–20
Primary · Place value
Trade ten ones for one ten
Move ten individual units into a new bundle without changing the value of the collection.
Explore animationPrimary · Fractions
Make smaller pieces, keep the same fraction
Subdivide every quarter equally and watch the numerator and denominator change together.
Explore animationMiddle school · Signed numbers
Add a signed change on a number line
Start at one number, move left or right, and separate your position from the change in position.
Explore animationPrimary · Multiplication
Build multiplication one equal row at a time
Create equal groups in a rectangular array and connect repeated addition with a product.
Explore animationMiddle school · Linear equations
Solve while keeping both sides equal
Remove the same constant from both sides, then divide equal groups to reveal x.
Explore animationHigh school · Geometry
Grow squares on a right triangle
Compare the areas on two perpendicular legs with the area on the hypotenuse.
Explore animationMiddle school · Circle geometry
Rearrange a circle to understand its area
Move equal sectors into an alternating strip and see why its limiting dimensions are πr and r.
Explore animationHigh school · Trigonometry
The unit circle in motion
Rotate a radius and watch its horizontal and vertical projections become cosine and sine.
Explore animationHigh school · Trigonometry
Build a traveling sine wave
Separate amplitude, spatial frequency, and phase by watching a wave travel to the right.
Explore animationHigh school · Differentiation
From a secant to a tangent
Bring two points together and compare an average rate with the exact derivative.
Explore animationUniversity · Integration
Build an integral with rectangles
Refine a right-endpoint sum and measure its error against an exact integral.
Explore animationHigh school · Functions
Move and reshape a parabola
Control opening, horizontal shift, and vertical shift while a point traces the graph.
Explore animationHigh school · Sequences and series
Add a shrinking geometric series
Watch finite partial sums fill a bar while a strictly positive remainder stays visible in the numbers.
Explore animationUniversity · Optimization
Take gradient descent steps
Choose a learning rate and see why convergence can be steady or oscillating.
Explore animationUniversity · Differential equations
Follow exponential growth and decay
Connect an amount to its rate of change through the simplest proportional differential equation.
Explore animationHigh school · Vectors
Add vectors head to tail
Slide a displacement without turning it, then connect the starting point to the final destination.
Explore animationUniversity · Linear algebra
Watch a matrix reshape the plane
Stretch and shear a unit square, and compare its area with the determinant.
Explore animationUniversity · Linear algebra
Find directions a matrix preserves
Separate a vector into two perpendicular eigen-directions and watch each scale independently.
Explore animationHigh school · Probability
Count successes with a binomial model
Explore the exact probability of each success count instead of relying on a random sample.
Explore animationKeep experimenting
The original five hands-on labs.
Use these still-frame controls to compare fractions, area, circular motion, averages, and tangent slopes. The original experiments are still here whenever you want a quick comparison.
Explore with your eyes. Explain in your words.
Same whole. Different pieces.
Change a value. Notice a pattern.
Fraction
3 / 8
Percentage
37.5%
Try 1/2, 2/4, and 4/8. What stays the same?
Explore number foundations →