NY Next Generation Math NY-5.G.4

Math5th GradeClassify two-dimensional figures into categories based on their properties.

The Standard

Classify two-dimensional figures in a hierarchy based on properties.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students organize two-dimensional figures into nested groups using properties such as parallel sides, equal sides, and right angles. They place a figure in every category that fits.
What Mastery Looks Like: The student can build and explain a hierarchy such as square, rectangle, parallelogram, trapezoid, and quadrilateral. The student uses the inclusive definition, so parallelograms and rectangles are also trapezoids.
Common Misconceptions: Students may treat shape categories as separate boxes, placing a square only in the square group. They may use an exclusive trapezoid definition or classify by appearance instead of stated properties.
How to Assess It: Give students a square, a non-square rectangle, a parallelogram, and a quadrilateral with exactly one pair of parallel sides. Ask them to place each in a hierarchy and justify every placement.

Lesson moves

Give groups shape cards and yarn loops to build nested categories based on side and angle properties.
Ask students to explain why every square belongs in the rectangle group but every rectangle does not belong in the square group.
Play a property sorting game where students place each shape card in every category that applies.
Have students classify floor tiles, signs, and package faces, then draw a hierarchy for the shapes they found.

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