Goal/materials: select gradient, midpoint or distance from a question; Cards 10–12, grid. Begin with a three-item prerequisite pulse before new model.
- Notice, 3: Point to axes; ask “Which question wants steepness, halfway, straight separation?” Keys: gradient, midpoint, distance. Record any category confusion.
- Model, 5: Card 11 (-6,-4)→(2,2). “For steepness Δy/Δx=6/8=3/4. For straight separation √(8²+6²)=10. Same points, different question and unit.”
- Together, 8: Card 10 (-5,3)→(-1,-3): m=-6/4=-3/2 and M(-3,0). Card 12 (-4,-6)→(4,0): M(0,-3), d=10. Ask why midpoint cannot answer distance.
- Try, 6: Fresh stage layout (-4,0)→(2,8): find midpoint and distance. Keys: (-1,4), √(6²+8²)=10. Mark mathematical prompts separately from graph access.
- Check, 3: “From (0,0) to (4,2), which number is the gradient and which point is the midpoint?” Keys: 1/2; (2,1). If measures conflated, attach units/point notation to the requested output.