Gradient Glide

The rise-and-run triangle is drawn under the line the whole time, so the gradient is a shape before it is a number: across, then up, and the line is the hypotenuse of what you just did. Ends settle onto whole coordinates when a student lets go, which is what makes it read 3/2 rather than 1.47 — turn that off in the studio for a class working with decimals. A vertical line says its gradient is undefined rather than showing a very large number, and a line lying along an axis says it crosses everywhere; both are the cases worth stopping on. Practice generates its own questions and marks them with a tolerance, so a shaky drag is never marked wrong. The plane's own controls sit on its top-right corner: carry the line on past its ends, put the triangle away, snap to whole coordinates, zoom, and go back to the origin. The pens are in the tray at the bottom right — D, E and C from the keyboard. Practice runs as a streak with a par clock and sweets to spend on a skip; every one of those numbers is yours to set in the studio. The measurements panel can be dragged anywhere on screen and stays where you put it. Battleground is the whole-class form: put this screen at the front, students join by code, and one equation goes up for everybody at once — every line in the room lands on the big plane in its own colour, so a class watches thirty attempts converge and can see a near miss for what it is, parallel but too high or through the right point at the wrong angle.