While performance on number-line estimation tasks strongly predicts mathematical achievement, the underlying reasons for this connection are heavily debated. The current research represents an adversarial collaboration, whereby researchers on opposite sides of the number-line estimation debate present a new model, nlFit, that predicts number-line estimates by building from ordinality toward linearity. It incorporates the ability to differentiate number labels (number sensitivity), knowledge of the ordinal relation between those number labels (ordinality), and knowledge of the magnitude of the difference between numbers (linearity). To test the nlFit model, we reanalyzed published data from two labs on either side of the number-line estimation debate. The nlFit model accurately predicted (a) targets estimated across various numerical ranges, (b) participants who estimate numbers on bounded and unbounded number lines, (c) to-be-estimated numbers that are sampled equally across the numerical range versus smaller numbers that are oversampled, and (d) estimates made after participants received feedback about the location of a subjective reference point on the number line (e.g., 500 is the midpoint of the 0–1,000 range). The model fits the responses of children of various ages and adults. We are calling to action members of the math cognition community to test the boundaries of the nlFit model.