Unit 6 · Topic 02 · Basic Geometry
Kabir held up a piece of paper and called it a shape. Anaya held up a dice and called it a shape too.
Ms. Rao said only one of them could ever lie perfectly flat on a table.
The difference between those two kinds of 'shape' turned out to matter a lot.
"Draw a square on paper," said Ms. Rao. Kabir drew one. "Now hand me a real cube — a dice will do." Anaya passed one over.
"Kabir's square exists entirely on a flat surface — length and width, nothing else. That's a 2D (two-dimensional) shape. Anaya's dice has length, width, AND height — it takes up real space. That's a 3D (three-dimensional) shape."
"So 2D shapes are flat and 3D shapes are solid?" asked Kabir.
"Exactly. 2D shapes — squares, triangles, circles, rectangles — are bounded by lines or curves and have an area, but no volume, because they have no thickness. 3D shapes — cubes, spheres, cylinders, cones — are bounded by flat or curved SURFACES and have both a surface area and a volume, because they genuinely take up space."
Ms. Rao then pulled apart a cardboard cube along its edges, flattening it into six connected squares. "This flattened-out pattern is called a net. Fold it back up along the lines, and it becomes the 3D cube again."
Anaya tried folding a different net — a cross-shape of six squares — and it also folded into a perfect cube. "There's more than one net for the same solid?"
"Several different nets, yes, as long as the folds recreate the same six faces meeting the same way," said Ms. Rao.
She then introduced vocabulary for 3D shapes: "A FACE is a flat surface, like one square of the cube. An EDGE is where two faces meet in a straight line. A VERTEX is a corner point where edges meet."
Kabir counted on the cube: 6 faces, 12 edges, 8 vertices.
"Every solid shape can be described this way," said Ms. Rao. "A cylinder, though, has curved surfaces, so counting straight edges and flat vertices doesn't quite work the same way — a useful reminder that not every 3D shape is made only of flat faces.
A 2D (two-dimensional) shape is flat, with length and width only — squares, triangles, circles, rectangles. It has an area but no volume.
A 3D (three-dimensional) shape is solid, with length, width AND height — cubes, spheres, cylinders, cones. It has both surface area and volume, because it occupies real space.
A net is a flattened-out 2D pattern that folds up into a 3D solid. The same solid can often be represented by more than one valid net.
3D shapes are described using face (a flat surface), edge (where two faces meet in a line), and vertex (a corner point where edges meet). A cube has 6 faces, 12 edges, 8 vertices.
Find 3 real 3D objects at home and count each one's faces, edges and vertices.
Draw a net for a rectangular box (cuboid) and try folding it into shape.
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