Partitioning shapes Knowledge-Based Download PDF

Questions

1. 1.

   A rectangle is divided into four parts that are not equal in size. Which statement explains why none of these parts can be called a fourth of the rectangle?

   • A) A part is only a fourth when the whole shape is partitioned into four equal shares.
   • B) A part can only be a fourth if it has the exact same shape as the other three parts.
   • C) A part can only be a fourth if the dividing lines are parallel to the sides of the rectangle.
   • D) A part is only a fourth when the whole shape is partitioned into two pairs of identical halves.
2. 2.

   A circle is partitioned into 3 equal shares. Which statement correctly describes these shares?

   • A) Each share is a half of the circle, and two halves make the whole circle.
   • B) Each share is a third of the circle, and three thirds make the whole circle.
   • C) Each share is a fourth of the circle, and three fourths make the whole circle.
   • D) Each share is a third of the circle, and two thirds make the whole circle.
3. 3.

   Two identical sheets of paper are each partitioned into two equal shares. One sheet is divided down the middle into two rectangles, while the other sheet is divided diagonally into two triangles. Which statement correctly compares these shares?

   • A) A rectangular share and a triangular share have equal areas, showing that equal shares do not have to have the same shape.
   • B) The rectangular share has a larger area than the triangular share because it retains four right angles.
   • C) The triangular share has a larger area than the rectangular share because the diagonal dividing line is longer.
   • D) The shares cannot be compared because halves of identical wholes must always have the same shape.
4. 4.

   Two identical squares are partitioned into equal shares: the first square into halves and the second square into fourths. Which statement correctly compares one share of the first square to one share of the second square?

   • A) One share of the first square is larger than one share of the second square.
   • B) One share of the first square is smaller than one share of the second square.
   • C) One share of the first square is equal in size to one share of the second square.
   • D) One share of the first square is one-fourth the size of one share of the second square.
5. 5.

   A rectangle is partitioned into 4 equal shares. Which statement correctly describes each share of the rectangle?

   • A) Each share is a fourth of the rectangle, and all shares have the same area.
   • B) Each share is a third of the rectangle, and all shares have different areas.
   • C) Each share is a half of the rectangle, and two shares make up the whole.
   • D) Each share is an eighth of the rectangle, and all shares have different sizes.