Sorting four-sided shapes into a family tree
In 5th grade, children learn to sort shapes into a family tree by their sides and angles, showing how quadrilaterals, parallelograms, rectangles, rhombuses, and squares fit inside each other.
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
Omar draws a quadrilateral with four sides of the same length. None of its angles is a right angle. Which name fits Omar's shape?
- A square
- A rectangle
- A rhombus
Why this matters
Sorting shapes by what they are, not how they look, teaches your child to define things carefully and see how ideas nest inside each other. That matters next year, when area formulas for parallelograms and triangles rely on knowing what a shape is, and in high school geometry, where shapes are identified and proved by their sides and angles.
Where kids can get stuck
- Naming shapes by how they are turned, calling a square tipped onto its corner a "diamond" instead of a square.
- Placing each shape in only one group, so a square goes under squares but not under rectangles or rhombuses.
- Mixing up the branches, thinking a rhombus needs right angles or a rectangle needs four equal sides.
How you can help
- Cut a few four-sided shapes out of cereal boxes, including squares, rectangles, rhombuses, and lopsided ones. Ask your child to sort them into groups and explain where each one belongs.
- Go on a shape walk and look for quadrilaterals in windows, signs, and tiles. For each one, ask your child to name every group it belongs to, not only the most specific name.
- Draw a family tree on paper with quadrilaterals at the top and squares at the bottom. Let your child fill in the middle branches and add a drawing of each shape.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child learning to classify shapes in a hierarchy?
A hierarchy shows how shapes relate to each other, which is more useful than memorizing names. When your child sees that a square is a special rectangle and a special rhombus, they understand why it shares properties with both. Sorting by properties, such as parallel sides and right angles, builds careful reasoning used throughout geometry.
Is a trapezoid a parallelogram?
It depends on the definition your child's school uses, because there are two in common use. Some define a trapezoid as having exactly one pair of parallel sides, which makes it separate from parallelograms. Others say at least one pair, which makes every parallelogram a trapezoid. Check your child's class materials or ask the teacher which one they use.
What is the difference between a rhombus and a square?
A rhombus has four equal sides, and its angles can be any size, so it often looks like a tilted, pushed-over square. A square has four equal sides and four right angles. That means every square is a rhombus, but a rhombus is only a square when all its angles are right angles.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited practice, completely free
- 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.4: “Classify two-dimensional figures in a hierarchy based on properties.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.G.4)