Success criteria
- I classify shapes using properties, not appearance or orientation.
- I understand that one shape can belong to several nested groups.
- I justify “always, sometimes, or never” with a property or counterexample.
Learn and explain
A hierarchy is inclusive: a specific shape keeps every broader name whose rules it satisfies. But the hierarchy branches; it is not one chain.
| Broader family | Branches or overlap |
|---|---|
| Quadrilateral | Trapezium (US: trapezoid), using the inclusive rule below |
| Trapezium | Parallelogram |
| Parallelogram | Rectangle branch; rhombus branch |
| Rectangle and rhombus | Square—the overlap, so every square belongs to both branches |
This lesson uses trapezium (US: trapezoid) for a quadrilateral with at least one pair of parallel sides. Some materials instead require exactly one pair, so always state which rule is being used. With the inclusive rule, the helper confirms that a square belongs to the rectangle and rhombus groups: both branches.
A square does not stop being a rectangle when it also satisfies the rhombus rule. It is the intersection of those two sibling branches.
Create property cards for: number of sides, parallel side pairs, right angles, and equal sides. Sort paper quadrilaterals, then explain why turning a shape does not change its family.
Independent practice
Which statement is always true?
A square meets every rectangle rule and has an additional equal-side property.
A shape has four sides, two pairs of parallel sides, and four right angles, but not four equal sides. Which most specific name is guaranteed?
Its memberships include quadrilateral, trapezium (US: trapezoid), parallelogram, rectangle; rectangle is the most specific guaranteed name here.
Unfamiliar transfer — fix the museum labels
A museum sign says, “Squares are not rectangles because rectangles have two long sides.” Write a two-sentence correction. Include the defining properties and a counterexample to the sign’s rule.
Delayed check
One week later, draw the branching hierarchy from memory. Show rectangle and rhombus as sibling branches below parallelogram, then link square to both. Label trapezium “US: trapezoid,” state whether your rule is inclusive or exclusive, and add one “always” statement and one “sometimes” statement.
Evidence path
Save the corrected sign and hierarchy to jeremy/portfolio/math/unit-5/lesson-15-shape-hierarchy/.
Next step
- Repair: sort physical shape cards using one property at a time.
- Continue: if the hierarchy can be explained without prompts, use properties in a coordinate design.
- Stretch: compare the inclusive and exclusive definitions of trapezium (US: trapezoid) and redraw only the relationships that change.