This grade 3 quadrilaterals lesson explains quadrilaterals and partitioning shapes in one printable page, with definitions, a method and a worked example.
A quadrilateral is a closed shape with 4 straight sides and 4 corners. Rectangles, squares, rhombuses, kites and trapezoids are quadrilaterals. They are sorted by attributes such as equal sides and right angles. A shape can also be partitioned into parts with equal areas, and each part is a unit fraction of the whole.
Grade 3 Quadrilaterals Lesson: key facts
- A quadrilateral has exactly 4 sides and 4 vertices.
- A rectangle has 4 right angles; a rhombus has 4 equal sides.
- A square has 4 equal sides and 4 right angles, so it is both a rectangle and a rhombus.
- Cutting a shape into 4 equal-area parts makes each part \(\frac{1}{4}\) of the whole.
- Equal parts can have different shapes if their areas are equal.
What is a quadrilateral?
Look around the classroom. Windows, book covers and floor tiles all have four straight sides. Math has a name for any closed shape like that.
A quadrilateral is a closed shape with exactly 4 straight sides and 4 vertices (corners).
A triangle has 3 sides and a pentagon has 5, so neither one is a quadrilateral. The six shapes above all have 4 sides, even though they look very different.
How do you sort quadrilaterals by their attributes?
An attribute is something you can measure or count, such as the length of a side or the size of a corner. A corner that makes a perfect square corner is a right angle.
| Shape | Key attribute |
|---|---|
| Rectangle | 4 right angles |
| Rhombus | 4 sides of equal length |
| Square | 4 equal sides and 4 right angles |
A square has both attributes, so a square is also a rectangle and also a rhombus. A kite or a trapezoid is a quadrilateral that is none of these three.
How do you decide what to call a shape?
- Count the sides. If there are not 4, it is not a quadrilateral.
- Check the sides. Are all 4 the same length?
- Check the corners. Are all 4 right angles?
- Use the answers to pick the name.
Example: A shape has 4 sides, each 6 inches long, and 4 right angles. Step 2 says the sides are equal. Step 3 says the corners are right angles. So the shape is a square, and it is also a rectangle and a rhombus.
What does it mean to partition a shape into equal parts?
To partition a shape means to cut it into parts that fill it with no gaps and no overlaps. The parts have equal areas when they cover the same amount of space.
If a shape is cut into 4 parts with equal areas, each part is \(\frac{1}{4}\) of the whole shape. With 3 equal parts, each is \(\frac{1}{3}\). With 8 equal parts, each is \(\frac{1}{8}\).
Equal area does not mean equal shape. A square can be cut into two halves in many ways, and each half still covers the same space.
Quadrilaterals and Partitioning Shapes: frequently asked questions
What is a quadrilateral in third grade math?
A quadrilateral is a closed shape with 4 straight sides and 4 vertices. Squares, rectangles, rhombuses, kites and trapezoids are all quadrilaterals.
Is a square a rectangle?
Yes. A rectangle is a quadrilateral with 4 right angles, and a square has 4 right angles. A square also has 4 equal sides, which makes it a special rectangle.
What is the difference between a rhombus and a square?
Both have 4 equal sides. A square must also have 4 right angles. A rhombus can lean over, so its corners are not right angles.
Can a quadrilateral be none of the named kinds?
Yes. A kite, a trapezoid or a four-sided shape with uneven sides is a quadrilateral that is not a rhombus, a rectangle or a square.
How do you name the area of one equal part?
Count the equal parts in the whole. If a shape is cut into 6 equal-area parts, each part is \(\frac{1}{6}\) of the shape’s area.
How to use this grade 3 quadrilaterals lesson
Use this grade 3 quadrilaterals lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 3 math page.