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3rd Grade · 5th Grade · 3.G.A.1 · 5.G.B.3 · 5.G.B.4

Classifying quadrilaterals in 3rd and 5th grade

Classifying quadrilaterals means sorting four-sided shapes into groups by what they have in common, such as equal sides or square corners. In 3rd grade, your child learns that squares, rectangles and rhombuses all belong to one big group, the quadrilaterals. In 5th grade, your child puts the groups inside each other in a chart and explains why every square is also a rectangle.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties.

What it means, in plain words

3rd grade: shapes that share attributes 3.G.A.1

A quadrilateral is any flat, closed shape with 4 straight sides. Quadrilaterals come in many kinds. Squares, rectangles and rhombuses are quadrilaterals, and so is a lopsided four-sided shape with no special name.

Classifying quadrilaterals in 3rd grade starts with attributes. An attribute is a feature you can check, such as the number of sides, sides of the same length or right angles. A right angle is a square corner, like the corner of a sheet of paper. A rectangle has 4 right angles. A rhombus has 4 sides of the same length. A square has both, so it is a rectangle and a rhombus at the same time.

Lessons on the attributes of quadrilaterals teach one big idea: shapes in different groups can share an attribute, and that shared attribute makes a bigger group. Squares, rectangles and rhombuses all have 4 sides, so they all belong to the quadrilaterals. Your child also draws quadrilaterals that are not squares, rectangles or rhombuses, to see that the big group holds more than the shapes with names.

Your child should be able to:

  • Say that a quadrilateral is any closed shape with 4 straight sides
  • Recognize squares, rectangles and rhombuses as quadrilaterals
  • Name an attribute two shapes share, such as 4 equal sides or 4 right angles
  • Draw a quadrilateral that is not a square, a rectangle or a rhombus

Example

A shape has 4 straight sides and 4 right angles. Two of its sides are 5 cm long and the other two are 3 cm long. Which names fit this shape?

  1. It is a closed shape with 4 straight sides, so it is a quadrilateral.
  2. It has 4 right angles, so it is a rectangle.
  3. Its sides are not all the same length, so it is not a rhombus and not a square.
  4. The shape is a quadrilateral and a rectangle.

5th grade: what is true for a group is true for every shape inside it 5.G.B.3

Classifying quadrilaterals in 5th grade adds a new idea: the groups sit inside each other. Every square is a rectangle, and every rectangle is a parallelogram. A parallelogram is a quadrilateral with 2 pairs of parallel sides. Parallel sides point the same way and never meet, like the two rails of a train track.

This leads to one rule. If every shape in a big group has an attribute, every shape in a smaller group inside it has that attribute too. The rule passes facts down from the big group to the smaller one. It never passes them back up, because the big group holds shapes that the smaller group does not.

Your child should be able to:

  • Explain that a fact about a big group is true for every smaller group inside it
  • Use that rule to say what must be true about a square, a rectangle or a rhombus
  • Explain why a fact about a smaller group does not have to be true for the big group

Example

Every rhombus has 4 sides of the same length. Every square is a rhombus. What must be true about the sides of a square?

  1. The fact is about the big group: every rhombus has 4 equal sides.
  2. Squares are inside that group, because every square is a rhombus.
  3. So the fact passes down, and every square has 4 sides of the same length.
  4. It does not pass back up. A square has 4 right angles, but a rhombus does not have to.

5th grade: the quadrilateral hierarchy 5.G.B.4

A hierarchy of shapes is a chart that shows which groups sit inside which. In the quadrilateral hierarchy, quadrilaterals are at the top. Trapezoids and parallelograms come next. Rectangles and rhombuses sit inside the parallelograms. Squares are at the bottom, inside both the rectangles and the rhombuses.

Schools use two definitions of a trapezoid. Some say a trapezoid has exactly one pair of parallel sides. Others say it has at least one pair, which puts every parallelogram inside the trapezoids too. It helps to check which one your child's class uses.

To classify a shape, your child lists its attributes and then finds its most specific name, the name lowest in the chart that still fits. The names above it are also true, but the most specific name tells you the most about the shape.

Your child should be able to:

  • Place quadrilaterals, trapezoids, parallelograms, rectangles, rhombuses and squares in a chart
  • List the attributes of a shape from a picture with marked sides and angles
  • Give the most specific name for a shape and the other names that are also true

Example

A quadrilateral has 2 pairs of parallel sides. Its sides are 4 cm, 7 cm, 4 cm and 7 cm, and none of its angles is a right angle. What is its most specific name?

  1. It has 2 pairs of parallel sides, so it is a parallelogram.
  2. It has no right angles, so it is not a rectangle and not a square.
  3. Its sides are not all the same length, so it is not a rhombus.
  4. Its most specific name is parallelogram. It is also a quadrilateral, and a trapezoid if the class uses the "at least one pair" definition.

Where children usually get stuck

  • Your child says a square is not a rectangle, because a rectangle is long and thin.

    In everyday speech, a rectangle is a shape with two long sides and two short sides. In math, a rectangle only needs 4 straight sides and 4 right angles, and a square has both.

    What helps. Read the math rule for a rectangle out loud together. Then check a square against it, one corner at a time.

  • Your child sees a square turned on its point and calls it a diamond, not a square.

    Squares in books usually sit flat on one side, so the name gets tied to how the shape is turned. Turning a shape does not change its sides or its angles.

    What helps. Cut a square out of paper and turn it slowly on the table. Ask at which moment it stopped being a square.

  • Your child decides that every rhombus is a square, because every square is a rhombus.

    The sentence was read in both directions. Facts and names pass down the chart from the big group to the smaller one, never back up.

    What helps. Try the same sentence with something familiar: every poodle is a dog, but not every dog is a poodle. Then say the shape sentence the same way.

Try four practice questions

Real 3rd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Which object has the shape of a quadrilateral?
    A
    wall clock
    B
    yield sign
    C
    sticky note
    D
    bicycle wheel
    Show the answer and how to solve it

    The sticky note is the quadrilateral. It is a closed shape with exactly 4 straight sides.

    1. 1A quadrilateral is a closed shape with exactly 4 straight sides. To find the quadrilateral, look at each object and count its straight sides.
    2. 2The wall clock has a curved outline. It has 0 straight sides, so it cannot be a quadrilateral.
    3. 3The bicycle wheel also has a curved outline. It has 0 straight sides, so it cannot be a quadrilateral.
    4. 4The yield sign has 3 straight sides. That makes it a triangle, not a quadrilateral.
    5. 5The sticky note has 4 straight sides. That makes it a quadrilateral.

    Common mistake. A common mistake is counting any pointy outline as a quadrilateral — a quadrilateral must have exactly 4 sides, not more or fewer.

    The idea underneath. A quadrilateral is any closed shape with exactly 4 straight sides — including squares, rectangles, AND diamonds (rhombuses), no matter how the shape is turned.

  2. 2On level
    The table names a larger shape category, one subcategory, and facts that are true for every shape in the larger category.
    Larger categorySubcategoryGiven facts about the larger category
    ParallelogramRectanglehas 2 pairs of parallel sides has opposite sides of equal length has opposite angles of equal measure
    Which statements can you prove using only the listed facts about parallelograms? Choose one answer in each row.
    StatementFollows from given factsDoes not follow from given facts
    has 2 pairs of parallel sides
    has opposite sides of equal length
    has no pairs of parallel sides
    has exactly 1 pair of parallel sides
    Show the answer and how to solve it

    Mark Follows from given facts for 'has 2 pairs of parallel sides' and 'has opposite sides of equal length.' Mark Does not follow from given facts for 'has no pairs of parallel sides' and 'has exactly 1 pair of parallel sides.'

    1. 1Rectangle is a subcategory of parallelogram, so every rectangle keeps every fact listed for parallelograms.
    2. 2The statements 'has 2 pairs of parallel sides' and 'has opposite sides of equal length' match the listed parallelogram facts exactly, so those statements must be true for a rectangle.
    3. 3The statement 'has no pairs of parallel sides' directly contradicts the listed fact that parallelograms have 2 pairs of parallel sides, so it does not have to be true.
    4. 4The statement 'has exactly 1 pair of parallel sides' changes the count. The listed parallelogram fact says 2 pairs of parallel sides, not 1. So this statement does not have to be true.

    Common mistake. A common mistake is marking 'has exactly 1 pair of parallel sides' as must be true. The listed fact says 2 pairs, not 1, so the count does not match.

    The idea underneath. In a shape hierarchy, every member of the subcategory keeps the listed properties of the larger category.

  3. 3On level
    Each statement below describes a quadrilateral by its properties. For each one, select the most specific quadrilateral name that the listed properties guarantee.
    1. Has two pairs of parallel sides and all 4 sides equal.
    A
    Square
    B
    Rectangle
    C
    Rhombus
    D
    Parallelogram
    E
    Trapezoid
    2. Has two pairs of parallel sides and 4 right angles.
    A
    Square
    B
    Rectangle
    C
    Rhombus
    D
    Parallelogram
    E
    Trapezoid
    3. Has exactly one pair of parallel sides.
    A
    Square
    B
    Rectangle
    C
    Rhombus
    D
    Parallelogram
    E
    Trapezoid
    Show the answer and how to solve it

    Statement 1 is Rhombus because two pairs of parallel sides plus all 4 sides equal guarantees a rhombus but not a square. Statement 2 is Rectangle because two pairs of parallel sides plus 4 right angles guarantees a rectangle but not a square. Statement 3 is Trapezoid because exactly one pair of parallel sides rules out every other category.

    1. 1For each statement, choose the most specific quadrilateral name the listed properties force to be true. The key distinctions are: two pairs of parallel sides plus right angles gives rectangle; two pairs plus all sides equal gives rhombus; both together give square; exactly one pair of parallel sides gives trapezoid.
    2. 2Statement 1 says two pairs of parallel sides and all 4 sides equal. Those properties force a rhombus. The figure is not forced to be a square because 4 right angles is not stated. The correct answer is Rhombus.
    3. 3Statement 2 says two pairs of parallel sides and 4 right angles. Those properties force a rectangle. The figure is not forced to be a square because all 4 sides equal is not stated. The correct answer is Rectangle.
    4. 4Statement 3 says exactly one pair of parallel sides. The word exactly rules out parallelogram, rectangle, rhombus, and square, since all of those have two pairs of parallel sides. The correct answer is Trapezoid.

    Common mistake. A common mistake is choosing square for statement 1 or 2 because the figure could be a square. Square is only guaranteed when both all 4 sides equal and 4 right angles are stated. For statement 3, do not pick parallelogram, since the word exactly rules out two pairs of parallel sides.

    The idea underneath. Quadrilateral categories are nested, so pick the narrowest category that the listed properties force to be true. Add right angles or all sides equal to two pairs of parallel sides to move from parallelogram down to rectangle or rhombus, and require both to move to square.

  4. 4Stretch
    Select all the statements that are true.
    A
    A rectangle is a quadrilateral.
    B
    A rhombus is a quadrilateral.
    C
    A pentagon is a quadrilateral.
    D
    A circle is a quadrilateral.
    E
    A square is a quadrilateral.
    F
    A triangle is a quadrilateral.
    Show the answer and how to solve it

    The true statements are: 'A rectangle is a quadrilateral.', 'A rhombus is a quadrilateral.', and 'A square is a quadrilateral.' Each of these shapes has exactly 4 straight sides, which is what makes a shape a quadrilateral.

    1. 1A quadrilateral is a closed shape with exactly 4 straight sides. To find the true statements, count the straight sides for each shape named.
    2. 2Check each shape's number of straight sides. A rectangle has 4 straight sides — true. A circle has no straight sides (it is curved) — false. A rhombus has 4 straight sides — true. A triangle has 3 straight sides — false. A square has 4 straight sides — true. A pentagon has 5 straight sides — false.
    3. 3The shapes with exactly 4 straight sides are rectangle, rhombus, and square. So the true statements are: 'A rectangle is a quadrilateral.', 'A rhombus is a quadrilateral.', and 'A square is a quadrilateral.'

    Common mistake. A common mistake is selecting the triangle or pentagon statement because both are polygons — but a quadrilateral specifically needs 4 sides, and a triangle has only 3 while a pentagon has 5. Another common mistake is selecting the circle statement because a circle is a familiar shape, but a circle has no straight sides at all.

    The idea underneath. Rectangle, rhombus, and square are all special kinds of quadrilaterals. They each have 4 straight sides plus extra features (rectangles and squares have square corners; rhombuses and squares have all sides the same length), so they all belong to the larger quadrilateral family.