How much do the groups depend on your choices?
Author a small feature table and compare cluster assignments under alternative scales and starting centres.
Assign each point to its closest centre under weighted squared distance, then recalculate means and repeat.
Cut these cards apart. Use the original example first, then let a partner supply a changed case. Keep sealed/final cards with the teacher until the learner commits a rule.
x: 1
y: 2
My prediction and reason:
x: 2
y: 2
My prediction and reason:
x: 3
y: 4
My prediction and reason:
x: 7
y: 6
My prediction and reason:
x: 8
y: 8
My prediction and reason:
x: 9
y: 7
My prediction and reason:
Two clusters and a Euclidean geometry are assumptions; no category truth is supplied.