Geometry
Geometry in Grade 3 asks you to classify shapes by their attributes and to partition shapes into equal areas. You need precise vocabulary: sides, angles, parallel, and the names of quadrilaterals.
Core rules
- A quadrilateral has 4 sides and 4 angles.
- A rectangle has 4 right angles. A rhombus has 4 equal sides. A square has 4 right angles and 4 equal sides, so it is both a rectangle and a rhombus (3.G.A.1).
- Shapes stay in the same category when rotated or flipped; orientation does not change attributes.
- Partition a shape into parts with equal areas. The area of each part is a unit fraction of the whole: 1/6 if there are 6 equal parts (3.G.A.2).
- Equal-area parts do not have to be congruent. A rectangle can be cut into 4 equal-area triangles that are not all the same shape.
Worked example
Is a square a rectangle? A rectangle is defined by having 4 sides and 4 right angles. A square has 4 equal sides and 4 right angles, so it meets the definition. Therefore a square is a rectangle. Is every rectangle a square? No. A 6 cm by 3 cm rectangle has right angles but not 4 equal sides, so it is a rectangle that is not a square.
Traps that cost marks
- Saying a square is not a rectangle because it looks different.
- Classifying a rhombus as “not a quadrilateral” because it is tilted.
- Partitioning into equal-shaped pieces but unequal areas, or the reverse.
- Naming a unit fraction from the number of shaded parts instead of the total number of equal parts.
- Assuming a shape with 4 sides is automatically a rectangle.