Partitioning shapes Knowledge-Based Practice

Questions

1. 1.

   A circle is partitioned into three equal shares. Which statement correctly describes one of these shares and the whole circle?

   • A) One share is a half, and the whole circle is two halves.
   • B) One share is a fourth, and the whole circle is four fourths.
   • C) One share is a third, and the whole circle is two thirds.
   • D) One share is a third, and the whole circle is three thirds.
2. 2.

   A rectangle is divided into three pieces of different sizes. Why can these pieces not be described as thirds of the rectangle?

   • A) Rectangles can only be partitioned into two or four equal shares.
   • B) Thirds can only be created by partitioning circles rather than rectangles.
   • C) The pieces must have different geometric shapes to be called thirds.
   • D) Thirds must be three equal shares that each represent the exact same amount of the whole.
3. 3.

   A square piece of paper is partitioned into two equal shares in two different ways: once with a vertical cut to create two rectangles, and once with a diagonal cut to create two triangles. Which statement correctly compares the area of one rectangular share to the area of one triangular share?

   • A) The rectangular share has a larger area because the vertical cut preserves right angles.
   • B) Both shares have the same area because each share is one half of the same square.
   • C) The triangular share has a larger area because the diagonal cut is longer than the vertical cut.
   • D) The two shares cannot have the same area because shapes with different numbers of sides always have different areas.
4. 4.

   Two identical rectangular sheets of paper are partitioned into equal shares: the first sheet is partitioned into two equal shares, and the second sheet is partitioned into four equal shares. Which statement correctly compares the size of a share from the first sheet to a share from the second sheet?

   • A) Each share of the first sheet is smaller than each share of the second sheet because four is greater than two.
   • B) The shares from both sheets are identical in size because both wholes have the exact same starting area.
   • C) Each share of the second sheet is twice as large as each share of the first sheet.
   • D) Each share of the first sheet is larger than each share of the second sheet because partitioning a whole into fewer equal shares creates larger pieces.
5. 5.

   A rectangle is partitioned into 4 equal shares. What is each individual share called, and how many of these shares are needed to make the whole rectangle?

   • A) Each share is a third, and 3 shares make the whole rectangle.
   • B) Each share is a fourth, and 4 shares make the whole rectangle.
   • C) Each share is a half, and 2 shares make the whole rectangle.
   • D) Each share is a fourth, and 2 shares make the whole rectangle.

Answers and step-by-step solutions appear after you finish the test.