Grade 4 Bar Charts

What this problem type covers

Thirteen problem types across five levels: the spread between the largest and smallest bar, converting a table into gridlines, working out the scale from a single stated value, turning quantities into money with a price list, recovering a torn-off bar from the total, rounding up a ride count, splitting a total time across four bars, comparing two series under an equal-total condition, converting marks into points, reading how two quantities move together across a pair of charts, scoring arrows across two rings, recovering a hidden die face from the sum of the throws, and saying which of two arrangements of the same data shows what.

Example problems

One example from each difficulty band, with worked solutions.

Ці задачі створюються автоматично. Відповіді визначаються під час складання задачі й перевіряються тестами, але помилки можливі — повідомте нам, якщо знайдете.

1. 1 · ★1
   The table is to be drawn as a bar chart. If Autumn is drawn 11 gridlines tall, how many gridlines tall is Winter?
   

   • Spring 26
   • Summer 22
   • Autumn 22
   • Winter 24
   • ①12
   • ②24
   • ③14
   • ④13
   • ⑤11
   Show solution

   ①12

   1. The given item is 11 gridlines, so work out what one gridline is worth.
   2. One gridline is 2.
   3. The item asked about is 24.
   4. 24 ÷ 2 = 12, so it is 12 gridlines tall.
2. 2 · ★2
   The chart has no numbers on its scale. If Cat is 18, how many were surveyed in total?
   
   • ①50
   • ②34
   • ③26
   • ④52
   • ⑤54
   Show solution

   ④52

   1. With no numbers on the scale, the given value fixes what one gridline is worth.
   2. That bar is 9 gridlines and stands for 18, so one gridline is 2.
   3. Count the gridlines of each other bar and convert.
   4. Adding them all gives 52.
3. 3 · ★3
   The chart shows how many of each item a shop sold in a day. With the prices below, what do Zoo and Gallery come to together?
   

   • Zoo: 1,100 each
   • Gallery: 400 each
   • Science: 1,100 each
   • Park: 300 each

   
   
   • ①11,000
   • ②16,000
   • ③27,000
   • ④28,000
   • ⑤55,000
   Show solution

   ③27,000

   1. Read the two quantities off the chart.
   2. Zoo: 10 × 1,100 = 11,000
   3. Gallery: 40 × 400 = 16,000
   4. Together they come to 27,000.
4. 4 · ★4
   The chart shows the men and women in each village. Villages A and C have the same number of people. Adding the men-women difference for village B and village C gives how many?
   
   
   • ①1,500
   • ②3,500
   • ③1,000
   • ④2,000
   • ⑤500
   Show solution

   ①1,500

   1. Add the men and women in village A to get its population.
   2. Village C has the same population, so its women number 2,000.
   3. Find the men-women difference in village B and in village C.
   4. Adding the two differences gives 1,500.
5. 5 · ★5
   Each student shot 10 arrows. The chart shows how many hit the ring worth 8 points; the rest all hit the ring worth 3. What is the difference between the highest and lowest score?
   
   • ①70
   • ②6
   • ③30
   • ④48
   • ⑤38
   Show solution

   ③30

   1. Read the high-scoring hits for each student; the rest scored the lower value.
   2. The highest total is 70.
   3. The lowest is 40.
   4. The difference is 30.

Where people usually go wrong

• Treating one gridline as one. The scale has to be read before any bar can be.
• Adding gridline counts instead of the values they stand for.
• Rounding a ride count down. The leftover group still has to ride.
• Answering the difference in marks when the question asked for points.
• Forgetting the arrows that hit the lower ring; every arrow scores something.
• Reading a torn bar as zero instead of working it out from the total.
• Saying two arrangements of the same data show the same things. Side by side compares the parts; end to end compares the total.