grid geometry parallels

Pierre van Hiele maintained that geometry should be started off using a square grid

it might be advantageous to describe (and define) parallel lines as having the same gradient/slope/journey/vector on a grid

dwelling on the properties of shapes:

• parallel sides
• right angles (perpendiculars)
• equal sides
• convex/concave
• mirror symmetry and rotational symmetry

should probably precede the naming of shapes and classifying them

a powerpoint is here