Here is a simple GeoGebra applet that can be used in a few different ways. Have a play, or read on for some classroom suggestions!
When you click “New Shape”, the applet generates a new quadrilateral at random.
This could be used for practising finding the midpoint of line segments – students can work out the four midpoints and then tick “show midpoints” to reveal the answers.
All the quadrilaterals are drawn with vertices on integer coordinates, so midpoints will either be whole numbers or end in .5 – challenge students to work out the conditions when the midpoints have integer coordinates.
Joining the midpoints gives a new quadrilateral. Invite students to try a few examples. What do they notice about the new quadrilateral each time? Can they prove their conjecture? This relates to the Triangle Midpoint theorem.
Here is a link to the activity on the GeoGebra website. If you use it in your teaching, I would love to hear about it – get in touch here or on Twitter.