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Common Core Math5th GradeGeometry

5.G.4: Classify Shapes in a Hierarchy

Also written as 5.G.B.4 and CCSS.MATH.CONTENT.5.G.B.4 · Cluster: Classify two-dimensional figures into categories based on their properties.

Make a 5.G.4 WorksheetAll 26 5th Grade Math Standards

The Official Wording

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

Common Core State Standards, Grade 5, Geometry · Read it at the source · Checked October 14, 2026

What 5.G.4 Means in Plain English

Fifth graders arrange shapes from the widest group to the narrowest. Quadrilaterals sit at the top, parallelograms below them, then rectangles and rhombuses side by side, and squares at the bottom, joined to both branches because a square has four right angles and four equal sides.

It completes the sorting begun in 3.G.1 and 4.G.2, and it rests on 5.G.3: each level keeps every property of the level above. In 7th grade students draw shapes from given conditions and decide whether those conditions allow one shape or many (7.G.2).

5.G.4 I Can Statements

  • I can place a shape at every level of the hierarchy it fits.
  • I can explain what a shape needs to move down a level.
  • I can draw a tree diagram that shows how quadrilaterals are related.

5.G.4 Worked Example

The quadrilateral tree built one rule at a time, then a mystery shape walked down it to its narrowest name.

Problem

Build a hierarchy for quadrilaterals, parallelograms, rectangles, rhombuses and squares. Then place a mystery shape on it: four sides of 3 cm, with angles of 70°, 110°, 70° and 110°.

Building the quadrilateral tree
  1. Start with the widest group, the one with the fewest rules.Top: quadrilaterals, 4 straight sides
  2. Add one rule to get the next level down.Parallelograms: add two pairs of parallel sides
  3. From parallelograms, two different rules split the tree into two branches.Rectangles: add 4 right angles. Rhombuses: add 4 equal sides
  4. A shape that meets both rules sits under both branches.Squares: 4 right angles and 4 equal sides
  5. Walk the mystery shape down. Four equal sides make it a rhombus, which is a parallelogram, and its 70° angle keeps it off the rectangle branch.Quadrilateral, parallelogram, rhombus. Not a rectangle or a square
AnswerQuadrilaterals at the top, then parallelograms, then rectangles and rhombuses side by side, with squares under both. The mystery shape is a quadrilateral, a parallelogram and a rhombus, and its narrowest name is rhombus.

Check it: Read its path back as sentences: it has four sides, two pairs of parallel sides and four equal sides. All true. “It has four right angles” is false, so the walk stops at rhombus.

Common Mistakes with 5.G.4

The square on one branch only

The square drawn under rectangles only, so the tree says a square is not a rhombus

Try this: Check the square against every rule on the tree. It passes the rectangle rule and the rhombus rule, so draw lines to both.

The wider group placed lower

Rectangles drawn above parallelograms because rectangles are the more familiar shape

Try this: Count the rules each group needs. The group with fewer rules holds more shapes, so it goes higher on the tree.

Two definitions of trapezoid

One student places parallelograms under trapezoids, another puts trapezoids on a separate branch, and the class argues about who is wrong

Try this: Agree on the definition first. With “at least one pair of parallel sides,” every parallelogram is a trapezoid, and with “exactly one,” none is.

Where 5.G.4 Fits

Comes Before3.G.1Recognize rhombuses, rectangles and squares as quadrilaterals, and draw ones that are none of these.4.G.2Classify shapes by parallel or perpendicular sides and by right angles.
Alongside5.G.3Know that each subcategory keeps every property of its category.
Comes Next6.G.1Find the area of triangles, special quadrilaterals and other polygons.7.G.2Draw shapes from given measurements and decide when they make one triangle, many or none.

Practice 5.G.4

Math Worksheet GeneratorFree ToolGeometry practice at the 5th grade level with an answer key: name every group a shape belongs to, from quadrilateral down to its narrowest name.Grade 5ShapesAnswer key
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Graph Paper GeneratorFree ToolGrid paper for drawing the tree with a sample shape at every level. Corners on grid points let students check right angles and equal sides by counting.Large squaresFull pagePrint
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Quick Check

  1. List every group a square belongs to in the quadrilateral hierarchy.
  2. Which rule takes a parallelogram down to a rhombus?
  3. A shape has four right angles, two sides of 4 cm and two sides of 7 cm. What is its narrowest name?

5.G.4: Other Names

5.G.45.G.B.4CCSS.MATH.CONTENT.5.G.B.4

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.