Lesson 11 — Solid Shapes: Faces, Sides, and Corners

Summary

Learners meet solid, three-dimensional shapes — cubes, spheres, cylinders, cones, and boxes — and learn to find their faces (flat parts), sides (edges), and corners (vertices) by feeling real objects and tracing their faces. They connect solid shapes to the flat shapes they already know.

Objectives

• Compose and take apart two- and three-dimensional shapes and describe their sides, corners, and faces. (D05.S3.01.01)

Connection

A ball you can roll is a sphere; a box of tea is a box-shaped solid; a cooking pot is a cylinder; the roof of a hut or tent can be a cone. Solid shapes are the shapes that fill space — they have a flat part you can trace (a face), an edge you can run your finger along (a side), and a pointy or square meeting place (a corner). Builders, potters, and basket makers in every land work with solid shapes every day.

Materials

• Solid shapes or everyday objects (a block, a ball, a can, a cone, a box)
• Paper or slate and a drawing tool

Preparation

• Gather solid shapes or everyday objects for each learner or pair.
• Have flat shapes from the last lesson ready to compare.
• Plan to model feeling and counting faces, sides, and corners on one solid.

Facilitator note

This lesson is written to the learner (“you”). It extends the last lesson’s flat shapes into solids, and the new skill is finding and counting faces, sides (edges), and corners (vertices). Teach with a worked example (philosophy §13): feel a cube, count its six square faces, twelve edges, and eight corners. Connect each solid to a flat shape — the cube’s face is a square, the cylinder’s face is a circle. Use everyday objects (boxes, balls, cans, clay) so the lesson is universally available. For learners who are blind or low-vision, this lesson is naturally rich — the hands are the tool; pass each solid and let the learner feel faces, edges, and corners, and use a “feely bag.” For learners who are Deaf or hard of hearing, name shapes in sign and count features with the hands. A learner who does not speak traces or points to each feature. Solid shapes are felt, not just seen — every body can study them.

Procedure

1. Gather — recall flat shapes (5 min). Yesterday you built flat shapes with sides and corners. Today we meet shapes you can hold — solid shapes that fill space, like a ball or a box.
2. Worked example — feel a cube (10 min). Watch and help: take a block (a cube). Run your finger over its flat part — that is a face; a cube has six faces, each one a square. Feel where two faces meet — that is a side (edge). Feel where sides meet — that is a corner. Count them: six faces, twelve sides, eight corners.
3. Feel each solid (12 min). Hold each shape: a ball (sphere — no flat faces, no corners; it rolls), a can (cylinder — two circle faces and one curved side), a cone (one circle face, one point), a box (rectangular prism — six rectangle faces). Count each one’s faces, sides, and corners.
4. Trace a face (8 min). Set a solid on paper and trace one of its faces. What flat shape did you draw? A cube’s face traces a square; a cylinder’s face traces a circle. The flat face is the bridge between solid and flat shapes.
5. Find solids around you (5 min). Look around the room or outdoors. Point to one sphere, one cube or box, one cylinder, and one cone. Name its faces, sides, and corners.
6. Close (3 min). Solid shapes fill the world — and every solid can be described by its faces, sides, and corners. Now you can see and feel that structure.

Differentiation

• Support: Study just two solids (a cube and a ball); count one feature at a time, hand-over-hand if needed.
• Support (blind/low-vision): Use a feely bag to identify each solid by touch and count its features with the fingers.
• Extension: Count and record the faces, sides, and corners of every solid in a simple table, and find a solid with a feature no other has.

Assessment

• Formative (observation): Can the learner identify a solid shape and describe its faces, sides, and corners by feel or sight?

Home connection

At home, go on a “solid shape hunt” with a grown-up: find a ball, a box, a can, and a cone, and count the faces, sides, and corners of each together.

Resources

• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and Middle School Mathematics (10th ed.). Pearson. (Three-dimensional shape attributes — faces, edges, and vertices.)