3.G.A.1 – Understand that shapes in different categories may share attributes: Learners analyze the circular sticker as a geometric shape divided by horizontal, vertical, and diagonal guidelines - partitioning the circle into two equal regions and comparing how each splitting strategy (top/bottom, left/right, opposite corners) creates symmetrical halves that serve as mirror-image designs when the thaumatrope spins.

4.G.A.3 – Recognize a line of symmetry for a two-dimensional figure: Example: Learners identify the line of symmetry each splitting strategy draws across the circular sticker - a horizontal fold line for top/bottom, a vertical fold line for left/right, a diagonal fold line for opposite corners - checking that folding the sticker along their chosen guideline lines up the two halves before they commit to drawing.

7.G.A.1 – Solve problems involving scale drawings of geometric figures: Example: Learners reproduce their sticker design at a different scale in the Sticky Note Supersized extension, transferring the same image pair from the small circular sticker onto a larger sticky note while keeping the proportions of their drawing the same, then troubleshooting the new alignment challenges a bigger scale creates.

7.G.B.4 – Know the formulas for the area and circumference of a circle and use them to solve problems: Learners measure the radius of the circular sticker and use πr² to find its area, then work out how much area each half-image occupies under the three splitting strategies - halves for the top/bottom and left/right splits, diagonal quadrant pairs for the spiciest technique - and use 2πr to compare how far a point on the rim travels in a single rotation.

3-PS2-1 – Investigate the effects of balanced and unbalanced forces on motion: Learners observe how the centered versus off-center placement of the paper tube on the motor connector affects rotational motion, discovering that a misaligned tube causes the entire base to vibrate and wobble across the table, directly demonstrating how unbalanced forces disrupt steady rotation.

3-5-ETS1-3 – Plan and carry out fair tests to identify failure points: Learners iterate through multiple sticker design attempts using the three spice-scale splitting techniques, testing each design by spinning and observing whether the illusion blends correctly, identifying which approach worked and why - and using sticky notes or cut practice sheet drawings when stickers run out to extend their testing.

MS-LS1-8 – Gather and synthesize information that sensory receptors respond to stimuli by sending messages to the brain: Learners investigate how the visual system’s sensory receptors transmit signals to the brain faster than the brain can resolve two distinct images when the thaumatrope spins, modeling the phi phenomenon as the brain’s integration of rapidly alternating visual stimuli into a single perceived image - directly connecting the retina’s response to spinning stimuli to the neural processing that produces the optical illusion.

MS-ETS1-2 – Evaluate competing design solutions using criteria and constraints: Learners compare the three sticker splitting strategies on the spice scale, evaluating each against the criteria of image clarity and the constraint of the circular sticker boundary, using evidence from spinning results to determine which technique (top/bottom, left/right, or opposite corners) best meets the goal of producing a convincing blended illusion.