Grade 4 Line Graphs

What this problem type covers

Eighteen problem types across five levels: the spread between the highest point and the lowest, the steepest stretch of a rising line, a total turned into money, which of two lines rose more, the day the takings rose most, estimating a day that was not measured, redrawing with a different gridline size, the year two lines are furthest apart, the gap between two estimates, two graphs whose gridlines are worth different amounts, two missing months recovered from a total and a difference, a scale worked out from a total when the axis carries no numbers, the times two lines sit within a stated gap, a journey continued at walking pace, a tank whose filling rate changes partway, a missing day given as a multiple of the next day, a missing score recovered from two totals, and a remainder turned into money.

Example problems

One example from each difficulty band, with worked solutions.

These problems are generated automatically. The answers are derived as each problem is built and are checked by tests, but mistakes are still possible — please tell us if you find one.

1. 1 · ★1
   A line graph of a factory's drink output. What is the difference between the highest month and the lowest?
   
   • ①10
   • ②14
   • ③34
   • ④20
   • ⑤48
   Show solution

   ④20

   1. Five gridlines divided by five makes one gridline worth 2.
   2. The highest is 34 and the lowest is 14.
   3. So the difference is 34 − 14 = 20.
2. 2 · ★2
   A line graph of the audience at a theatre. A ticket costs 7,000 won. On the day the takings rose most against the day before, by how much did they rise?
   
   • ①19,600,000 won
   • ②7,000,000 won
   • ③1,000 won
   • ④3,500,000 won
   • ⑤8,400,000 won
   Show solution

   ②7,000,000 won

   1. The takings rose on the days where the line slopes up to the right.
   2. The biggest rise is at Wed, where the audience grew by 1,000.
   3. So the takings rose by 7,000 × 1,000 = 7,000,000 won.
3. 3 · ★3
   A plant's height, measured every two days. About how much taller was it on day 15 than on day 10?
   
   • ①13
   • ②2
   • ③6
   • ④4
   • ⑤5
   Show solution

   ⑤5

   1. A day that was not measured is taken as halfway between its neighbours.
   2. The neighbours are 12 cm and 14 cm, so halfway is (12 + 14) ÷ 2 = 13 cm.
   3. The first day was 8 cm, so it grew 13 − 8 = 5 cm.
4. 4 · ★4
   Line graphs of the baseballs made by factory A and factory B. Which factory has the bigger gap between its highest month and its lowest?
   
   • ①The two are the same
   • ②It cannot be told
   • ③Neither factory
   • ④Factory A
   • ⑤Factory B
   Show solution

   ⑤Factory B

   1. One gridline is worth a different amount on each of the two graphs.
   2. Reading each with its own scale gives gaps of 80 and 360.
   3. So the bigger gap belongs to Factory B.
5. 5 · ★5
   A line graph of time against distance for a 2,000 m journey. Jungmin cycled at first, then walked from minute 10 onwards, arriving after 30 minutes. If he had walked the whole way, how many minutes later would he have arrived? (Both speeds are steady.)
   
   • ①30 minutes
   • ②50 minutes
   • ③25 minutes
   • ④10 minutes
   • ⑤20 minutes
   Show solution

   ⑤20 minutes

   1. From the graph the cycled part is 1,200 m.
   2. The remaining 800 m took 20 minutes, so walking covers 40 m a minute.
   3. Walking the whole way would take 50 minutes.
   4. So he would arrive 50 − 30 = 20 minutes later.

Where people usually go wrong

• Reading a gridline as one unit when five of them are worth the stated amount.
• Forgetting the wave break and treating the axis as if it started at zero.
• Answering with the value at a point rather than the rise into it.
• Comparing two graphs by how tall the lines look when their gridlines differ.
• Giving the gap between two lines when the question asks what they add to.
• Using the whole journey to work out a pace that only applies to part of it.
• Forgetting the first stretch when a rate changes partway through.
• Reading a value off an axis that carries no numbers.