Splitting shapes into equal parts (age 7+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Cutting shapes into equal shares

Mathematics · Fractions · ages 7-8
Name ______________________   Date ____________

  1. Lena wants to share a rectangular sandwich equally with 3 friends, so everyone gets one fourth. Which way of cutting shows the sandwich cut into fourths?

    • Cut down the middle and across the middle
    • One cut down the middle, making 2 pieces
    • Four cuts that make pieces of different sizes
    • Three cuts that make 5 tiny pieces

  2. Look at the circle. It is cut into 3 equal parts. What is each part called?

    • a half
    • a third
    • a fourth

  3. If a circle is cut into 3 pieces that are not the same size, each piece is still called a third.

    Circle one:   True   False

  4. A rectangle is cut into 4 equal strips. What is each strip called?

    • a third
    • a fourth
    • a fifth

  5. Two pieces from the same whole can look different and still be equal in size.

    Circle one:   True   False

  6. Jamal cut one rectangle into fourths by cutting across the middle and down the middle. His sister cut another rectangle a different way, but her 4 pieces are still the same size. Did she also make fourths?

    • Yes. Four equal shares are fourths, even if the cuts look different
    • No. Fourths must always be cut the same way
    • No. Only rectangles cut in a cross can show fourths

  7. Leo wants to split a rectangle into 4 equal shares. Which way works?

    • Cut it into 4 strips of the same size
    • Cut it into 3 big pieces and 1 small piece
    • Cut it into 4 pieces of different sizes

  8. Zoe cuts a rectangle into 4 equal squares. Amir cuts the same size rectangle into 4 equal strips. Whose pieces are bigger?

    • Zoe's, because squares look bigger
    • Amir's, because strips look longer
    • Neither, they are the same size

  9. Two friends each cut an identical rectangle into thirds. One uses 3 tall strips, the other uses 3 wide strips. Do both rectangles show equal thirds?

    • Yes, both show equal thirds
    • No, only the tall strips are real thirds
    • No, only the wide strips are real thirds

  10. Nina says, 'I cut my rectangle into 4 pieces, so they must be fourths.' What is wrong with her thinking?

    • Nothing, 4 pieces always means fourths
    • Her 4 pieces might not be the same size
    • Fourths only work on circles, not rectangles
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Answer key

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Cutting shapes into equal shares W1-mt_Xp-rj46S2w-s1

  1. Cut down the middle and across the middle · Fourths means 4 equal parts. Only the choice with 4 same-size pieces shows fourths.
  2. a third · Three equal parts means each one is a third.
  3. False · Thirds must be equal in size. Unequal pieces are not thirds, even if there are three of them.
  4. a fourth · Four equal parts means each one is a fourth.
  5. True · Equal means the same size, not the same shape. A tall skinny piece can match a short wide piece in size.
  6. Yes. Four equal shares are fourths, even if the cuts look different · Fourths means 4 equal shares. The cut pattern can change as long as the 4 pieces are the same size.
  7. Cut it into 4 strips of the same size · Fourths means 4 parts, and every part must be the same size.
  8. Neither, they are the same size · Both wholes were cut into 4 equal shares, so each share is the same size even though the shapes look different.
  9. Yes, both show equal thirds · As long as each of the 3 parts is the same size, it does not matter what shape the parts are. Both are thirds.
  10. Her 4 pieces might not be the same size · Cutting into 4 pieces is not enough. All 4 pieces must be the same size to be called fourths.
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