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. A number line is cut into 10 equal steps to make one whole. A point sits 5 steps from 0, at 0.5. Which fraction names the same point?

    0123456789100.5 = 1/2
    • 1/2
    • 1/5
    • 2/5

  2. Which way of reading a number line lands you on 1/2?

    • Start at 0 and take 1 step on a line cut into 2 equal steps
    • Start at 0 and take 1 step on a line cut into 4 equal steps
    • Start at one whole and take 1 more step on a line cut into 2 equal steps

  3. 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?

    0123453 steps done
    • 5/3
    • 3/8
    • 3/5

  4. Four friends share 3 granola bars equally. Which division equation matches this sharing problem?

    • 3 ÷ 4
    • 4 ÷ 3
    • 3 × 4

  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?

    012345678910
    • 7/10 of the song
    • 9/10 of the song
    • 5/10 of the song

  6. Ravi says 2/3 must sit past one whole, because 2 and 3 are both bigger than 1. Is Ravi right?

    Circle one:   True   False

  7. A number line is cut into 10 equal steps to make one whole. A point sits 7 steps from 0. Write this point as a decimal.

    0123456789107 tenths

    Answer: ______________

  8. A number line is cut into 4 equal steps to make one whole. Where does 4/4 land?

    01234
    • Just past the whole
    • Exactly on the whole
    • Halfway to the whole

  9. On a line cut into 10 equal steps, one dot sits at 0.5 and another dot sits 5 steps from 0. Which dot is further from 0?

    012345678910
    • The dot at 0.5
    • The dot 5 steps from 0
    • Neither, they sit on the same point

  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
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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. 1/2 · 0.5 is halfway to one whole, and so is 1/2. They are the same point.
  2. Start at 0 and take 1 step on a line cut into 2 equal steps · The bottom number 2 says one whole is cut into 2 equal steps, and the top number 1 says you take 1 step from 0.
  3. 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.
  4. 3 ÷ 4 · Sharing 3 bars among 4 friends means 3 divided by 4, so each friend gets 3/4 of a bar.
  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. False · The 2 and the 3 are not distances. They say cut one whole into 3 equal steps and take 2 of them, which stops before the whole.
  7. 0.7 · 7 out of 10 equal steps from 0 is 7 tenths, written as 0.7.
  8. Exactly on the whole · 4 steps of one quarter use up every step on the line, so the hop stops exactly on the whole.
  9. Neither, they sit on the same point · 5 steps of one tenth is 5/10, which is halfway to the whole, and 0.5 is halfway to the whole too, so both dots sit on one point.
  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