CCSS.Math.Content.5.G.B.4

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

The standard

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

Common Core State Standards for Mathematics · Geometry

What this standard means

Students need to sort shapes by their properties, then understand that some groups fit inside larger groups. For example, every square is a rectangle because it has four right angles, and every rectangle is a parallelogram because it has two pairs of parallel sides.

Mastery looks like using properties, not appearance, to name and place shapes in a hierarchy. Students can explain why a square belongs in several groups. Common sticking points are thinking a shape has only one name, relying on tilted or “regular-looking” examples, and mixing up attributes like equal sides, parallel sides, and right angles.

Ways to teach it

Give students shape cards and have them build a hierarchy chart with labels like quadrilateral, parallelogram, rectangle, rhombus, and square.
Ask students to write: Is every rectangle a square, is every square a rectangle, and how do you know?
Show one shape and ask students to list every category it belongs to, then justify each choice with a property.
Have students find classroom objects that look like quadrilaterals and explain which geometry categories fit and which do not.

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Related standards

CCSS.Math.Content.4.G.A
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
CCSS.Math.Content.5.G.B
Classify two-dimensional figures into categories based on their properties.
CCSS.Math.Content.5.G.B.3
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
CCSS.Math.Content.4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. ...