Amplify-ready polypad submission

Build the Equation. Grow the Artwork.

Every tile, root, and petal is generated by the same factors.
Virtual tile manipulative
x + 4
x + 3
x2
xxxx
xxx
111111111111
x-tiles7
unit tiles12
shape typerectangle
Generated geometric artwork
Geometric artwork generated from the factor rectangle12unit petals7 x-ribs | roots -3, -4
Drag the roots

Move either blue root on the graph. The tile rectangle and artwork rebuild from the new factor pair.

Quadratic graph with draggable roots-3-4
Student insight
area modelx2 + 3x + 4x + 12
combine like termsx^2 + 7x + 12 = 0
factor form(x + 3)(x + 4) = 0
solutionsx = -3, -4
Why this is submission-worthy
  • Students manipulate factors, tiles, roots, graph, and artwork as one system.
  • The unit count becomes visual art, so factoring has a creative payoff.
  • The same model supports exploration, explanation, and quick assessment.
  • It is generic: changing two factors creates an entire family of quadratics.
Classroom prompt
Create a bloom with exactly 12 unit petals. Explain how its rectangle, graph, and roots prove your equation.