Sorting 2D Shapes by a Single Attribute

Sorting 2D shapes by a single attribute means choosing just one feature of a shape, like the number of sides, the number of corners, or the size, and using that one feature to decide where each shape belongs. Every shape in the group is checked against the same rule, and only that rule, before it is placed into a bin.

This is different from sorting by several features at once. When you sort by a single attribute, a shape only needs to match one thing to belong to a group. For example, if the rule is "shapes with 4 sides," then a small blue square and a large red rectangle both belong together, even though they look different in color and size, because they share the same number of sides.

Before sorting any group of shapes, it helps to know which attributes are usually used. Here are the most common ones:

• Number of sides: Triangles have 3 sides, squares and rectangles have 4, pentagons have 5, and hexagons have 6.
• Number of corners (vertices): This usually matches the number of sides for straight-sided shapes.
• Type of sides: Some shapes have only straight sides, while a circle has one curved side and no corners at all.
• Size: Shapes can be grouped as big or small, even if they have the same number of sides.
• Color: This attribute ignores shape entirely and only looks at what color the shape is.

Picking the right attribute is the first and most important step. Once you know the rule, sorting becomes a simple matter of checking each shape one at a time.

Suppose you have a mixed pile of shapes: a triangle, a square, a rectangle, a pentagon, and a hexagon. The task is to sort them by the attribute "number of sides."

1. Choose the attribute. Here, the attribute is the number of sides each shape has.
2. Look at one shape at a time. Count its sides carefully, going around the whole shape.
3. Place the shape in a matching group. Shapes with the same number of sides go into the same bin.
4. Repeat for every shape until the whole pile has been sorted.
5. Check your work. Go back through each bin and confirm every shape truly matches the count for that group.

The figure below shows this sorting rule in action, separating shapes with 3 sides from shapes with 4 sides.

Another useful single attribute is whether a shape has curved sides or only straight sides. A circle is a special case: it has 1 curved side and 0 corners, so it never belongs in a group with triangles, squares, or other straight-sided shapes.

Try this rule on a group containing a circle, an oval, a triangle, and a hexagon. Sorting by "has a curved side" puts the circle and the oval together, while the triangle and hexagon go into the "all straight sides" group, no matter how big or small each shape is.

Size is an attribute that works completely independently of the number of sides. If the rule is "big or small," a large triangle and a large hexagon can end up in the same "big" group, while a small triangle and a small square end up in the "small" group. This shows why it matters to state the attribute clearly before sorting: the same pile of shapes can be grouped very differently depending on which single attribute is chosen.

Sorting by one attribute at a time builds the habit of looking closely at shapes and describing exactly why they belong together. This skill leads directly into more advanced shape work, such as composing 2D shapes out of smaller pieces, and it also transfers to solid figures when you practice sorting 3D shapes by a single attribute. Once sorting feels comfortable, many students move on to using pattern blocks to create composite shapes to combine what they know about attributes with building new shapes.

• Say the attribute out loud before sorting, such as "I am sorting by number of corners."
• Count sides and corners slowly, tracing around the shape with a finger if needed.
• Sort the same pile of shapes twice, using two different attributes, to see how the groups change.
• After sorting, ask "why does this shape belong here?" for at least one shape in every group.

Related lessons

• Math 1