Sorting shapes by their sides and angles
In 4th grade, children learn to sort flat shapes by whether they have parallel sides, perpendicular sides, or angles of a certain size; and to recognize right triangles as their own group.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th 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
Sofia draws a triangle with angles of 90°, 50° and 40°. What kind of triangle is it?
- An obtuse triangle
- A right triangle
- An acute triangle
Why this matters
Sorting shapes by their features teaches your child to look for evidence instead of judging by appearance, a way of thinking that reaches well beyond geometry. It is also why a square counts as a rectangle. In 5th grade they build a family tree of shapes, learning that every square is a rectangle and every rectangle is a parallelogram, and in middle school these features help them find areas and angles.
Where kids can get stuck
- Deciding a triangle is not a right triangle because it is turned so the square corner is not at the bottom.
- Leaving a square out of the group with parallel sides or right angles, because it already has its own name.
- Calling two sides parallel because they look close, without checking that they stay the same distance apart.
How you can help
- Cut shapes out of an old cereal box, including triangles, squares, and slanted shapes. Ask your child to sort them into piles, such as "has a right angle" and "no right angle," and explain each choice.
- Look at road signs on a drive. Ask your child which signs have parallel sides and which have right angles, such as a rectangular speed limit sign or a triangular yield sign.
- Draw a triangle with a square corner, then turn the paper upside down. Ask your child whether it is still a right triangle, and have them check the corner with a piece of paper.
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 sort shapes this way?
Sorting by features, such as parallel sides or right angles, teaches your child to look for evidence rather than judging shapes by how they look. Two shapes that look different can share important properties. This careful thinking helps your child understand why a square can also be called a rectangle, and it prepares them for 5th grade, where shapes are organized into families.
Is a square a rectangle?
Yes. A rectangle is a four-sided shape with four right angles. A square has four right angles too, plus four equal sides, so it meets every requirement of a rectangle. This often surprises children because they think of a rectangle as long and thin. Sorting shapes by properties helps them see that a square belongs in the rectangle group, and in other groups too.
What is a right triangle?
A right triangle is a triangle with one right angle, a square corner of 90 degrees. It can be turned any way on the page and is still a right triangle. A triangle can only have one right angle, because the angles inside any triangle add up to 180 degrees. That fact comes later, but your child can check for the square corner with the corner of a sheet of paper.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- Questions matched to your child’s level, a few minutes a day
- Hints when they are stuck, and a celebration when it clicks
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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 4.G.A.2: “Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.G.2)