For educators: classroom use & standards alignment
This site is a set of 23 free, individually usable geometry resources — one per shape or coordinate formula — each with an interactive explorer, a worked example with real numbers, learning objectives, and Common Core alignment. Everything is openly accessible: no account, no sign-up, no ads, no tracking beyond aggregate analytics. This page explains who the resources are for and how to teach with them.
Who these resources are for
The collection spans grades 3 through 12, with most resources landing in the grade 6–10 band where area, surface area, volume, and coordinate geometry are taught:
- Students (grades 6–12) — as a reference during homework, as a self-check tool (every explorer shows the full substitution, not just the answer), and as exam revision via the printable sheet builder.
- Teachers — as a projected demonstration tool for whole-class instruction, as an embeddable widget inside an LMS or class site, and as a source of printable formula sheets differentiated per unit.
- Tutors and homeschool educators — as a complete, verified formula reference with worked examples that need no preparation.
- Multilingual classrooms — core resources are available in Spanish.
How to teach with them
Each resource page carries its own Classroom use section with objectives, aligned standards, and a specific suggested activity. Three patterns work across all of them:
- Predict, then check. Project the explorer, set a parameter, and ask students to predict the result before revealing it. Because the diagram, the formula, and the arithmetic update together, a wrong prediction becomes a discussion rather than a correction.
- Expose the substitution. Every explorer shows each stage of the arithmetic. Pause on the step where errors cluster — squaring in the Pythagorean theorem, the ⅓ in cone and pyramid volume, height versus slant height.
- Build the sheet as you teach. The Sheet Builder lets a class add each formula as its unit is reached, so the printed sheet becomes a running record of learning rather than a wall of formulas handed over at once.
Why the mathematics is trustworthy
Every formula on this site is computationally verified before it ships. A test script checks each shape's compute function against independently known values — the 3-4-5 triangle, the unit circle, a sphere of radius 3 where volume and surface area both equal 36π, and 119 other assertions. The printed formula, the worked example, and the live explorer all render from that same verified function, so they cannot disagree with each other. Content last reviewed August 2026.
Accessibility
Every explorer is operable by keyboard alone: sliders are native range inputs paired with number fields, and the draggable coordinate widgets accept arrow-key input after focus. Mathematics is rendered as styled HTML at build time rather than as images, so it reflows, zooms, and is selectable by screen readers. All four page types score 100 for accessibility in Lighthouse. Diagrams use a 1.5px stroke with amber dimension annotations chosen to hold contrast in both light and dark themes.
Reuse and licensing
Diagrams and printable formula sheets are released under CC BY-SA 4.0 — free to retain, reuse, revise, remix, and redistribute with attribution. Page content is CC BY-NC-SA 4.0. The compute engine is MIT licensed. Full terms and ready-to-paste attribution are on the license page.
Interactive explorers can be embedded in any page that accepts HTML with one line of markup — no account, no watermark, no cost.
Standards alignment index
Every resource mapped to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
| Standard | Descriptor | Resources |
|---|---|---|
3.MD.C.7 | Relate area to multiplication and addition. | Square, Rectangle |
3.MD.D.8 | Solve real-world problems involving perimeters of polygons. | Square, Rectangle |
6.G.A.1 | Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing shapes. | Square, Rectangle, Triangle, Trapezoid, Parallelogram, Rhombus |
6.G.A.2 | Find volumes of right rectangular prisms; apply V = lwh and V = Bh. | Cube, Rectangular Prism |
6.G.A.3 | Draw polygons in the coordinate plane; use coordinates to find side lengths. | Rectangle, Midpoint formula |
6.G.A.4 | Represent 3-D figures using nets and use the nets to find surface area. | Cube, Rectangular Prism, Triangular Prism |
7.G.B.4 | Know and use the formulas for the area and circumference of a circle. | Circle, Arc Length, Sector Area |
7.G.B.6 | Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects. | Triangle, Trapezoid, Parallelogram, Rhombus, Cube, Rectangular Prism, Triangular Prism, Pyramid |
8.EE.B.6 | Use similar triangles to explain why slope is the same between any two points on a line. | Slope formula |
8.G.A.5 | Use informal arguments to establish facts about angle sums and exterior angles of polygons. | Regular Polygon |
8.G.B.7 | Apply the Pythagorean theorem to find unknown side lengths in right triangles. | Right Triangle, Chord Length, Cone, Pyramid, Distance formula |
8.G.B.8 | Apply the Pythagorean theorem to find the distance between two points in a coordinate system. | Distance formula |
8.G.C.9 | Know and use the formulas for the volumes of cones, cylinders, and spheres. | Cylinder, Cone, Sphere, Hemisphere |
HSG.C.A.2 | Identify and describe relationships among inscribed angles, radii, and chords. | Chord Length |
HSG.C.B.5 | Derive the arc-length and sector-area relationships using similarity. | Arc Length, Sector Area |
HSG.CO.C.11 | Prove theorems about parallelograms. | Parallelogram, Rhombus |
HSG.GMD.A.1 | Give an informal argument for circumference, area, and volume formulas. | Circle, Regular Polygon, Cylinder, Cone, Pyramid |
HSG.GMD.A.3 | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. | Cylinder, Cone, Sphere, Hemisphere, Pyramid |
HSG.GPE.B.5 | Prove the slope criteria for parallel and perpendicular lines. | Slope formula |
HSG.GPE.B.6 | Find the point on a directed line segment that partitions it in a given ratio. | Midpoint formula |
HSG.GPE.B.7 | Use coordinates to compute perimeters and areas of polygons via the distance formula. | Distance formula |
HSG.MG.A.1 | Use geometric shapes, their measures, and their properties to describe objects. | Triangle, Right Triangle, Regular Polygon |
HSG.SRT.C.8 | Use trigonometric ratios and the Pythagorean theorem to solve right triangles. | Right Triangle |
All resources by grade band
| Resource | Grade band | Aligned standards |
|---|---|---|
| Square | Grades 3–8 | 3.MD.C.7, 3.MD.D.8, 6.G.A.1 |
| Rectangle | Grades 3–8 | 3.MD.C.7, 3.MD.D.8, 6.G.A.1, 6.G.A.3 |
| Triangle | Grades 6–10 | 6.G.A.1, 7.G.B.6, HSG.MG.A.1 |
| Right Triangle | Grades 8–11 | 8.G.B.7, HSG.SRT.C.8, HSG.MG.A.1 |
| Circle | Grades 7–10 | 7.G.B.4, HSG.GMD.A.1 |
| Arc Length | Grades 9–12 | HSG.C.B.5, 7.G.B.4 |
| Sector Area | Grades 9–12 | HSG.C.B.5, 7.G.B.4 |
| Chord Length | Grades 9–12 | HSG.C.A.2, 8.G.B.7 |
| Trapezoid | Grades 6–10 | 6.G.A.1, 7.G.B.6 |
| Parallelogram | Grades 6–10 | 6.G.A.1, 7.G.B.6, HSG.CO.C.11 |
| Rhombus | Grades 6–10 | 6.G.A.1, 7.G.B.6, HSG.CO.C.11 |
| Regular Polygon | Grades 8–12 | 8.G.A.5, HSG.MG.A.1, HSG.GMD.A.1 |
| Cube | Grades 6–9 | 6.G.A.2, 6.G.A.4, 7.G.B.6 |
| Rectangular Prism | Grades 6–9 | 6.G.A.2, 6.G.A.4, 7.G.B.6 |
| Triangular Prism | Grades 7–10 | 6.G.A.4, 7.G.B.6 |
| Cylinder | Grades 8–12 | 8.G.C.9, HSG.GMD.A.1, HSG.GMD.A.3 |
| Cone | Grades 8–12 | 8.G.C.9, HSG.GMD.A.1, HSG.GMD.A.3, 8.G.B.7 |
| Sphere | Grades 8–12 | 8.G.C.9, HSG.GMD.A.3 |
| Hemisphere | Grades 8–12 | 8.G.C.9, HSG.GMD.A.3 |
| Pyramid | Grades 7–12 | 7.G.B.6, HSG.GMD.A.1, HSG.GMD.A.3, 8.G.B.7 |
| Distance formula | Grades 8–12 | 8.G.B.8, HSG.GPE.B.7, 8.G.B.7 |
| Midpoint formula | Grades 6–12 | HSG.GPE.B.6, 6.G.A.3 |
| Slope formula | Grades 8–12 | 8.EE.B.6, HSG.GPE.B.5 |
Questions, or want a resource we don't have?
If you teach geometry and something here would work better differently, tell us — we build to requests from teachers.