Methods, apparatus, systems and articles of manufacture are disclosed to facilitate secure screen input. An example disclosed system includes a user interface (UI) manager to generate a UI comprising a quantity of ordinal entry points, each one of the quantity of ordinal entry points comprising a repeating selectable pattern, an ordinal sequence generator to generate an initial randomized combination of the quantity of ordinal entry points, the randomized combination stored in a trusted execution environment, and an offset calculator to calculate a password entry value by comparing an offset value and direction value retrieved from the UI with the initial randomized combination of the quantity of ordinal entry points.