Geometry (Grade 3)
Geometry in Grade 3 asks students to reason about quadrilaterals and their attributes, and to partition shapes into parts with equal areas. On the NYS test, students identify shapes by their properties, explain why a shape belongs to more than one category, and name the area of each equal part as a unit fraction.
Quadrilaterals and their attributes
- A quadrilateral has 4 sides and 4 angles.
- A parallelogram has two pairs of parallel sides.
- A rectangle has 4 right angles; a rhombus has 4 equal sides; a square has 4 right angles and 4 equal sides.
- Categories overlap. A square is also a rectangle, a rhombus, and a parallelogram. All squares are rectangles, but not all rectangles are squares.
- A trapezoid is a quadrilateral in the quadrilateral family; use the definition your class uses, since definitions of this shape vary.
Equal parts and unit fractions
- Partition a shape into b parts with equal areas. Each part has area 1/b of the whole.
- Equal area does not require parts to look the same shape.
Worked example
Partition a rectangle into 6 equal parts and shade 2. The whole is divided into 6 equal areas, so each part is 1/6 of the rectangle. Two shaded parts are 2/6 of the whole, which is equivalent to 1/3 because 2/6 and 1/3 cover the same amount of area. The six parts must have equal area, even if they are not all congruent.
Traps
Saying all rectangles are squares, which reverses the relationship. Assuming any shape with 4 equal sides must be a square, when it could be a rhombus. Calling parts equal when their areas differ. Naming the number of parts instead of the fraction each part represents.