Virginia SOL 7.MG.3.a.i
The Standard
Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid: parallel/perpendicular sides and diagonals
Virginia Standards of Learning for Mathematics · The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students classify quadrilaterals by checking which sides are parallel or perpendicular and how the diagonals relate. They compare categories and recognize that one figure may belong to several groups.
What Mastery Looks Like
- Students correctly identify all categories that fit a quadrilateral, including overlapping categories. They justify each choice with side or diagonal relationships and explain why other categories do not fit.
Common Misconceptions
- Students often treat each shape name as a separate group, so they do not recognize a square as a rectangle, rhombus, and parallelogram. They may confuse diagonals with opposite sides or assume all diagonals are perpendicular. They may also decide from appearance instead of marked properties.
How to Assess It
- Exit ticket: “A quadrilateral has two pairs of parallel sides, four right angles, and diagonals that are not perpendicular. Name every category that must fit and explain why.”
Lesson moves
Ways to Teach It
Give pairs rulers, protractors, and quadrilateral cards to measure sides, angles, and diagonals, then sort each card into every matching group.
Ask students to write: “Why is every square a rectangle and rhombus, but not every rectangle or rhombus a square?”
Play Property Bingo by calling clues such as “perpendicular diagonals” or “two pairs of parallel sides” while students cover matching shapes.
Photograph windows, tiles, signs, and fence patterns, then label each quadrilateral and cite two visible or measured properties.
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