Why a square is also a rectangle
In 5th grade, children learn that every feature of a shape category belongs to all the shapes inside it, so a square has every feature of a rectangle, because it is one.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Ines sorts tiles. She knows every rhombus has four sides of the same length. Which tile must also have four sides of the same length?
- A parallelogram tile
- A square tile
- A rectangle tile
Why this matters
This is one of the first places your child reasons like a mathematician: if something is true of every rectangle, it is true of every square. That kind of thinking, from a general rule to a specific case, is what geometry proofs in high school are built on. It also clears up a belief many adults still hold, that a square is not a rectangle.
Where kids can get stuck
- Insisting a square is not a rectangle because rectangles have "two long sides and two short sides."
- Reversing the reasoning, so they say all rectangles have four equal sides because squares do.
- Forgetting that a rectangle is a parallelogram, so its parallel, equal opposite sides come as a surprise.
How you can help
- Find rectangles around the house, such as a door, a book, and a square coaster. Ask your child to check whether each has four right angles using the corner of a sheet of paper.
- Use a family comparison: all dogs are animals, so anything true of all animals is true of dogs. Then ask your child to try the same reasoning with rectangles and squares.
- Ask your child to convince you that a square is a rectangle. Listen for features like four sides and four right angles, and ask whether the square has every one of them.
If it’s helpful, you can sign up for free, adaptive practice in Bobby's Math Club.
Questions parents ask
Why is my child learning that a square is a rectangle?
In math, a rectangle is defined as a four-sided shape with four right angles. A square has four sides and four right angles, so it fits the definition. It also has the extra feature of four equal sides. Teachers emphasize this because it teaches your child to judge shapes by their features, not by how they usually look.
Is a rectangle a square?
Not always. A rectangle needs four right angles, and a square needs four right angles and four equal sides. Some rectangles have equal sides, and those are squares. Most rectangles, like a typical door, do not. So every square is a rectangle, but only some rectangles are squares. This one-way relationship is the heart of this skill.
How does this reasoning help my child later?
This is an early example of logical thinking: if something is true for a whole group, it is true for each member. That reasoning is used throughout math, especially in geometry and algebra. Next, your child will use it to sort shapes into a family tree, and in high school it underpins writing geometric proofs.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited free practice
- Practice that starts where your child is and grows with them
- You see their progress and what to work on next
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
Ready to watch your child’s confidence grow?
Your 5th grade child can start today with free, unlimited practice that grows with them.
Join the clubNote for teachers: This skill is covered by Common Core math standard 5.G.B.3: “Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.G.3)