Moving between diagrams and equations with fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Moving between diagrams and equations with fractions

Mathematics · Mathematical Thinking · ages 8-9
Name ______________________   Date ____________

  1. Ella walks 1 km to the park. Her walk is drawn as a line cut into 5 equal steps, and she has finished 3 steps. What fraction of the walk has she done?

    Ticks: 0, 1/5, 2/5, 3/5, 4/5, 1. Marked values: 3/5. Hop from 0 to 3/5: 3 steps done.01/52/53/54/513 steps done
    • 5/3
    • 3/8
    • 3/5

  2. A fraction bar has 4 equal parts with 3 shaded. This matches three quarter-steps from 0 on a number line marked in quarters. What fraction is shown?

    Ticks: 0, 1/4, 1/2, 3/4, 1. Marked values: 3/4. Hop from 0 to 3/4: 3/4.01/41/23/413/4
    • 3/4
    • 4/3
    • 1/4

  3. Each step on a number line is one fifth. How many steps do you take from 0 to land on 4/5?

    Ticks: 0, 1/5, 2/5, 3/5, 4/5, 1. Marked values: 4/5. 01/52/53/54/51

    Answer: ______________

  4. Write the fraction 3/10 as a decimal.

    Answer: ______________

  5. A song is drawn as a line cut into 10 equal steps. Tom starts listening at the 2nd step and stops at the 7th step. How much of the song did he hear?

    Ticks: 0, 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 1. Marked values: 2/10, 7/10. 01/102/103/104/105/106/107/108/109/101
    • 7/10 of the song
    • 9/10 of the song
    • 5/10 of the song

  6. A fraction bar shows 2 out of 4 parts shaded. Which number line matches it?

    • Start at 0 and take 2 jumps on a line split into 4 equal jumps to make one whole
    • Start at 0 and take 2 jumps on a line split into 3 equal jumps to make one whole
    • Start at 0 and take 4 jumps on a line split into 4 equal jumps to make one whole

  7. A bar model shows 4 equal rows with 23 dots in each row. Which multiplication matches the model?

    • 4 x 23 = 92
    • 4 + 23 = 27
    • 23 - 4 = 19
    • 4 x 32 = 128

  8. 5 friends share 2 pies equally. What fraction of a pie does each friend get?

    • 2/5
    • 5/2
    • 1/5

  9. Leo says 0.3 and 3/10 land on different points on a number line. Is Leo correct?

    Circle one:   True   False

  10. Nadia draws 4 equal bars, each worth 15, and splits every bar into 10 and 5. Which pair of pieces matches her drawing?

    • 4 x 10 = 40 and 4 x 15 = 60
    • 4 x 10 = 40 and 4 x 5 = 20
    • 10 x 5 = 50 and 4 x 4 = 16
LightMySky · lightmysky.comW1-mt_3VmBdlAeOZ-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Moving between diagrams and equations with fractions W1-mt_3VmBdlAeOZ-s1

  1. 3/5 · The whole walk is 5 equal steps and Ella has done 3 of them, so she has walked 3/5 of the way.
  2. 3/4 · The bar and the number line hop both show 3 out of 4 equal parts, which is 3/4.
  3. 4 · The top number of 4/5 counts the steps, so you hop 4 steps of one fifth from 0.
  4. 0.3 · 3/10 means 3 tenths, and 3 tenths written as a decimal is 0.3.
  5. 5/10 of the song · From the dot on step 2 to the dot on step 7 is 5 steps, and each step is one tenth, so Tom heard 5/10 of the song.
  6. Start at 0 and take 2 jumps on a line split into 4 equal jumps to make one whole · The bar has 4 equal parts, so the matching number line must also be split into 4 jumps, landing on the 2nd one.
  7. 4 x 23 = 92 · 4 rows of 23 is the multiplication 4 x 23, and 4 x 23 = 92.
  8. 2/5 · Sharing 2 pies among 5 friends is 2 divided by 5, which is 2/5 of a pie each.
  9. False · 0.3 and 3/10 name the exact same point on a number line, three tenths of the way from 0 to 1.
  10. 4 x 10 = 40 and 4 x 5 = 20 · Each bar splits into 10 and 5, so the four bars give 4 x 10 = 40 and 4 x 5 = 20. Those two pieces add to 60, which is 4 x 15.
Worksheet · LightMySky