Testinar Grade 3 math

Partitioning Shapes into Equal Areas

Students will partition shapes into equal areas and express each part as a unit fraction.

CH06-12 Geometry and Measurement
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A rectangle is divided into \(4\) equal parts. What fraction of the rectangle is each part?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q001
    1. \(\frac{1}{2}\)
    2. \(\frac{1}{3}\)
    3. \(\frac{1}{4}\)
    4. \(\frac{4}{4}\)

  2. Here is a circle divided into \(2\) equal parts. Each part of the circle is what fraction of the whole circle?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q002
    1. \(\frac{1}{4}\)
    2. \(\frac{1}{2}\)
    3. \(\frac{2}{2}\)
    4. \(\frac{1}{3}\)

  3. A rectangle is split into \(6\) equal strips. What fraction of the rectangle is \(3\) strips?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q003
    1. \(\frac{1}{6}\)
    2. \(\frac{1}{3}\)
    3. \(\frac{3}{6}\)
    4. \(\frac{4}{6}\)

  4. A square is divided into \(8\) equal parts by drawing 1 vertical line and 3 horizontal lines through the middle. What fraction of the square is one part?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q004
    1. \(\frac{1}{4}\)
    2. \(\frac{1}{8}\)
    3. \(\frac{2}{8}\)
    4. \(\frac{1}{2}\)

  5. Here is a rectangle divided into \(3\) equal columns. The shaded part is what fraction of the rectangle?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q005
    1. \(\frac{1}{3}\)
    2. \(\frac{3}{3}\)
    3. \(\frac{2}{3}\)
    4. \(\frac{1}{2}\)

  6. A circle is divided into \(4\) equal parts. If two parts are shaded, what fraction of the circle is shaded?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q006
    1. \(\frac{1}{3}\)
    2. \(\frac{3}{4}\)
    3. \(\frac{2}{4}\)
    4. \(\frac{1}{4}\)

  7. A rectangle is divided equally. One part is \(\frac{1}{6}\) of the whole. How many equal parts is the rectangle divided into?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q007
    1. 4 parts
    2. 8 parts
    3. 3 parts
    4. 6 parts

  8. A circle is divided into \(6\) equal parts. Three parts are shaded. Which fraction shows the shaded part?

    Partitioning Shapes into Equal Areas visual for G3-C06-T12-Q009
    1. \(\frac{1}{6}\)
    2. \(\frac{3}{6}\)
    3. \(\frac{3}{3}\)
    4. \(\frac{2}{6}\)
Teacher and parent reference

Answer key and explanations

  1. C. \(\frac{1}{4}\)

    When a shape is divided into \(4\) equal parts, each part is \(\frac{1}{4}\) of the whole.

  2. B. \(\frac{1}{2}\)

    When a circle is divided into 2 equal parts, each part is \(\frac{1}{2}\) of the whole circle.

  3. C. \(\frac{3}{6}\)

    Three out of six equal strips make \(\frac{3}{6}\).

  4. B. \(\frac{1}{8}\)

    When divided into 8 equal parts, each part is \(\frac{1}{8}\) of the whole square.

  5. A. \(\frac{1}{3}\)

    One shaded column out of three equal columns is \(\frac{1}{3}\) of the rectangle.

  6. C. \(\frac{2}{4}\)

    Two shaded parts out of four equal parts is \(\frac{2}{4}\), which equals \(\frac{1}{2}\).

  7. D. 6 parts

    If one part is \(\frac{1}{6}\), then the rectangle must be divided into 6 equal parts.

  8. B. \(\frac{3}{6}\)

    Three shaded parts out of six equal parts is \(\frac{3}{6}\).

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