Pile up paper cut-outs of triangles, squares, circles, hexagons, ovals. Sort them — by sides, by colour, by symmetry, by size. Different rules, different piles.
108.0°
72.0°
540°
5
One pile, many rules
The same pile of cut-outs sorts differently depending on the question you ask: 'how many sides?' makes one set of piles, 'does it have a right angle?' makes a totally different set. The shapes don't change — the rule does.
Lay out your piles and let a friend guess your sorting rule. If they can work it out, the rule is clean. If they can't, it's probably two rules tangled together — split it.
You sort shapes into 'has at least one line of symmetry' vs 'has none'. Which pile does a scalene triangle go in?
Sorting rules to try
- Number of sides — 3, 4, 5, 6, more, none
- Has straight sides vs has curves
- Has right angles vs doesn't
- Has symmetry vs doesn't
Get a friend to guess your sorting rule from the piles alone. If they can, your rule is clean. If they can't, refine it.