Fun Math — figures that move.
No submit buttons. No timers. Just figures you can drag, slice, and shade until the formula makes sense at a glance.
Visual intuition for circle area, composite figures, and proportional reasoning — built for Grades 4–7.
Where Does πr² Come From?
Slice, rearrange, discover
Cut a circle into 32 wedges and stagger them into a near-perfect parallelogram. The area formula reveals itself — no memorization required.
Drag the Radius, Feel r²
See area grow quadratically
Watch the gold r×r square in the corner. Each time the radius grows by one unit, a whole new ring of squares appears — that is r² getting bigger.
Unroll a Circle into a Rectangle
From 4 slices to 32
Add slices and watch the curved edge straighten. By 32 wedges the circle becomes a rectangle of base πr and height r.
Four Quarter-Circles in a Square
Compose the leftover region
A 6×6 square with quarter-circles bitten out of every corner. The leftover white piece in the middle is exactly 36 − 9π.
Square Minus Inscribed Circle
Compute the four corner gaps
Carve the largest possible circle from an 8×8 pizza. The four leftover corners add up to roughly 13.73 — and the ratio is always π/4.
Stadium-Shape Area
Decompose an athletic track
A rectangle plus two half-circles equals one full circle plus a rectangle. Once you see the structure, the formula is obvious.
Why visual math beats memorization
Most students memorize πr² without ever seeing where it comes from. Fun Math reverses that — every formula here is something you can drag, slice, or shade until the geometry clicks.
Built for intuition
Each demo strips a geometry concept down to a single moving picture. No grading, no timer, no submit button — just the part of the problem your eyes can solve before your pencil does.
Aligned with CCSS
Demos map directly to Common Core standards on circle area and composite figures (CCSS 7.G.B.4, 6.G.A.1, 4.MD.A.3) and reinforce proportional reasoning across Grades 4–7.
For curious learners
Designed for middle-schoolers, homeschool parents, and tutors who want the "aha" moment behind formulas like area = πr², circumference = 2πr, and the area of a stadium-shaped track.
Pairs with practice
Once a concept clicks, take it into a graded mission. The same manipulatives appear in our Socratic curriculum at /grade-6/circlearea with hint-by-hint guidance.
What you'll explore
Every demo is a self-contained playground covering one geometry idea — animated, draggable, and ready in seconds.
- ✦ Derive the circle area formula by rearranging slices into a parallelogram.
- ✦ Watch r² grow as you drag the radius slider from 1 to 5.
- ✦ See a circle morph into a rectangle as the slice count climbs.
- ✦ Solve composite figures with quarter-circles and inscribed circles.
- ✦ Compute the area of a running track using shape decomposition.
- ✦ Build the foundation for integral calculus — without the calculus.
Frequently asked
- Is Fun Math free to use?
- Yes. Every demo loads instantly in your browser — no signup, no paywall, no ads.
- Which grades is it for?
- Geometry demos target Grades 4–7, but the visual approach helps anyone — including high-schoolers reviewing fundamentals or adults relearning circle math.
- Do I need an account to track progress?
- No. Fun Math has no scoring or progress tracking — that lives in the graded curriculum at /grade-3 and beyond.
- How is this different from a textbook diagram?
- Textbook figures are frozen. These move — you control the radius, the slice count, and the shading, so the formula isn't a fact you memorize but a pattern you discover.
Want to take these visualizations into a graded mission? Head to /grade-6/circlearea/ to unlock 8 Socratic exercises — same visuals, three-step C-P-A pacing.