L4 · Sorting polygons by geometric properties; describing the sorting rule

Learning goal

“I can sort polygons into groups using a geometric property, and I can describe the sorting rule so clearly that someone else could sort the same way. Given a finished sort, I can figure out and state the rule that was used.”

Property — a fact about a shape that can be checked: its number of sides, whether sides are parallel, whether angles are right angles.

Sorting rule — the one property test that decides which group a shape joins: 'has parallel sides' is a sorting rule.

Group — the set of shapes that pass the rule's test (and the set that does not).

Belong — a shape belongs in a group when it passes that group's test - not because it looks like the others.

Worked example

Four shape cards, described in words: A - a triangle with all sides equal. B - a square. C - a pentagon with all sides and all angles equal. D - a rectangle with sides 6 cm, 4 cm, 6 cm, 4 cm. The rule: 'all sides equal.' Test each card against the rule, one at a time: A - all sides equal, in. B - all sides equal, in. C - all sides equal, in. D - sides are 6, 4, 6, 4: NOT all equal, out. Group 'all sides equal' = {A, B, C}; D sits outside. Say it plainly: sorting is just the property test from L1-L3, run on every card. The rule never changes mid-sort.

Check yourself — explain it

Why was card D left out, even though it has SOME equal sides?

Paired problem — example still visible

New rule: 'has a right angle.' Cards: a right triangle (one book-corner angle), a square, a regular pentagon (no right angles), an equilateral triangle (no right angles). Which cards are in? -> The right triangle and the square

Faded completion — last step is yours

"Rule: 'has parallel sides.' A square is in. A triangle is ___." -> out (a triangle has no parallel sides)

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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