Lesson 12 — Sorting Shapes by Their Attributes

Summary

Learners sort shapes into categories by their attributes — number of sides, number of angles, straight or curved edges — and name the rule of each category. They discover that a category is a shared attribute, and that one shape can be described by more than one attribute at once.

Objectives

• Sort shapes into categories by their attributes and recognize that shapes in a category share common properties. (D05.S3.03.02)

Connection

A cook sorts beans by color before cooking; a seed-keeper sorts seeds by size; a caretaker sorts tools by their job. Sorting is how people bring order to a big mixed pile — and shapes are no different. Every shape has attributes: how many sides, how many corners, whether its edges are straight or curved. When you sort by an attribute, you make a category with a rule. Builders, weavers, and tile-makers in every culture have sorted shapes this way to fit them together.

Materials

• A set of shape cards or cut-out shapes (triangles, quadrilaterals, pentagons, hexagons, and shapes with curved edges)
• Three sorting rings, strings, or drawn circles
• Paper or slate and a drawing tool

Preparation

• Give each pair a shape set and three sorting rings.
• Clear space to sort on tables or the floor.
• Plan a worked example (sorting by number of sides).

Facilitator note

This lesson is written to the learner (“you”). It opens the shape attributes strand — the new skill is classifying shapes by an attribute and naming the rule. Teach with a worked example (philosophy §13): sort a mixed set into “three sides,” “four sides,” and “five or more sides,” and state each rule aloud before learners sort their own. The key move is seeing that a category is a shared attribute — the same shape can be sorted by sides, by angles, or by straight-vs-curved, and belong in different piles depending on the rule (Van de Walle et al., 2019). No one’s speed at sorting measures their smartness; two children can sort by different rules and both be right. Sorting is a universal human act — every culture sorts its plants, stones, and tools. Count in the home language. For learners who are Deaf or hard of hearing, sign each attribute and point to the sides; for learners who are blind or low-vision, use cut-out shapes the hands can feel and sort by touch. Learners with limited movement direct a partner to place each shape. Mastery arrives at its own pace.

Procedure

1. Gather — a mixed pile (5 min). Look at the pile of shapes. How could you bring order to it? What is the same about some shapes? That sameness is an attribute.
2. Worked example — sort by sides (10 min). Watch and help: make three rings. Put every shape with three sides in one ring, every shape with four sides in the next, and the rest in the third. Say each rule: “this ring is three-sided shapes.”
3. Sort another way (10 min). Now sort the same shapes by a different attribute: straight edges or curved edges? How many corners? A square can be “four sides” in one sort and “all straight edges” in another. The rule decides the pile.
4. Guided practice — your own rule (12 min). Sort your set by a rule you choose. Write the rule. Then sort the same set by a second rule and write that one too.
5. Mystery sort (5 min). With a partner, sort by a secret rule and let them guess it. Then swap.
6. Close (3 min). Remember: shapes live in categories by shared attributes. Name the rule, and the pile makes sense.

Differentiation

• Support: Sort by one attribute (number of sides) today; add a second attribute another day.
• Support (blind/low-vision): Sort cut-out shapes by touch, feeling the sides and corners.
• Extension: Sort by two attributes at once (for example, “four sides AND all sides equal”) and describe the smaller category that results.

Assessment

• Formative (observation): Can the learner sort shapes by an attribute and name the rule of each category?
• Artifact (portfolio): The learner’s drawn sort with its rule, kept as a record of classification.

Home connection

At home, sort a pile of leaves, buttons, or kitchen tools by one attribute, name your rule, and have a grown-up guess it.

Resources

• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and Middle School Mathematics: Teaching Developmentally (10th ed.). Pearson. (Classifying shapes by attributes and seeing categories as shared properties.)