5th Grade Classifying Two-Dimensional Figures Lesson: Notes and Examples (Free PDF)

5th grade classifying shapes lesson – Maths PDF

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This 5th grade classifying shapes lesson covers classifying two-dimensional figures (Common Core 5.G.B.3, 5.G.B.4), with a free PDF to print.

Key takeaway: This lesson helps fifth grade students classify two-dimensional figures by their sides and angles, and see how categories fit inside each other.

Topic: Classifying Two-Dimensional Figures (5th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 5.G.B.3, 5.G.B.4
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

Two-dimensional figures are sorted into categories by their properties. Every square is a rectangle, a rhombus, a parallelogram and a quadrilateral, because it has all of their properties. Triangles are named by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Tree and Venn diagrams show these groups.

This lesson helps fifth grade students classify two-dimensional figures by their sides and angles, and see how categories fit inside each other. It shows that a figure can belong to several groups, so a square is also a rectangle, a rhombus, and a parallelogram.

Students learn the properties of quadrilaterals and triangles, how to read marks for equal sides and right angles, and how to sort shapes in a Venn diagram and a tree diagram. They also learn to use the most specific name. Also, plan about 25 minutes. Then, sketch each shape and mark its properties as you read.

Grade 5 · Common Core State Standards: 5.G.B.3, 5.G.B.4

Key facts in this 5th grade classifying shapes lesson

Key facts

A quadrilateral has 4 sides; a parallelogram has two pairs of parallel sides.
Next, a rectangle has 4 right angles; a rhombus has 4 equal sides; a square has both.
Every square is a rectangle and a rhombus, but not every rectangle is a square.
Triangles by sides: equilateral, isosceles, scalene.
Triangles by angles: acute, right, obtuse.

What is a quadrilateral?

A quadrilateral is a closed shape with 4 straight sides and 4 angles. Special quadrilaterals have extra properties. A parallelogram has two pairs of parallel sides. A rectangle is a parallelogram with 4 right angles. A rhombus is a parallelogram with 4 equal sides. A square has 4 equal sides and 4 right angles. In this book, a trapezoid has at least one pair of parallel sides.

Tick marks show equal sides, small squares show right angles and arrows show parallel sides.

How are the quadrilaterals related?

A shape that belongs to a group has every property of that group. Read the tree from the bottom up. A square is a rectangle and a rhombus, so it is also a parallelogram and a quadrilateral. The reverse is not true. A rectangle that is 6 cm by 3 cm is not a square, because its sides are not all equal. When you name a shape, the most specific name tells the most about it.

A tree diagram of the quadrilateral family.

How does a Venn diagram show the groups?

Each circle holds shapes with one property. The overlap holds shapes with both properties. Squares have 4 equal sides and 4 right angles, so they go in the overlap. A rhombus with slanted sides has only equal sides, so it goes in the left circle alone. Also, a long rectangle has only right angles, so it goes in the right circle alone. A shape with neither property would go outside both circles.

Rhombus (left only), square (both) and rectangle (right only).

How do you classify triangles?

Name a triangle by its sides and by its angles. By sides: equilateral (3 equal sides), isosceles (at least 2 equal sides) or scalene (no equal sides). By angles: acute (all angles less than 90°), right (one 90° angle) or obtuse (one angle greater than 90°). A triangle always has two names, one for its sides and one for its angles. For example, a triangle with sides 3, 4 and 5 and a right angle is a scalene right triangle.

Triangles classified by their sides.

Triangles classified by their angles.

Steps

Count the sides and check which are equal or parallel.
Look for right angles.
Choose the most specific name.
Check that the shape has every property of its name.

5th grade classifying shapes lesson: questions and answers

Is every square a rectangle?

Yes. A rectangle has 4 right angles and opposite sides equal. A square has 4 right angles and all sides equal, so it has every property of a rectangle.

Is every rectangle a square?

No. A rectangle that is 6 cm by 3 cm has right angles, but its sides are not all equal. Only rectangles with 4 equal sides are squares.

What is the difference between a rhombus and a square?

A rhombus has 4 equal sides. A square has 4 equal sides and 4 right angles. So every square is a rhombus, but a rhombus with no right angles is not a square.

What is a trapezoid?

In this book, a trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases.

Can a triangle be both right and isosceles?

Yes. A triangle with a 90° angle and two equal sides is a right isosceles triangle. Sides and angles are two separate ways of naming the same triangle.

Common mistakes with this 5th grade classifying shapes lesson

Students use the name of a bigger group when a more exact name fits. Instead, if a quadrilateral has four equal sides and four right angles, call it a square.
Students decide a shape is not a rhombus because it looks tilted. Also, a rhombus is defined by four equal sides, not by how it is turned.
Students think a triangle must be one type only. A triangle can be both right and isosceles, because angle names and side names are separate.

How to study this chapter

Make a chart with the shapes down the side and the properties across the top. Then, checking each box shows how groups overlap.
Use the marks on a figure as evidence. Finally, tick marks show equal sides, and arrows show parallel sides.
Parents can ask the child to name five objects at home and give the most specific shape name for each.

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