Bars and a scale
A class voted for their favorite color, and a bar chart shows the votes. Each color has its own bar, with its name written underneath. The numbers up the side are the scale. They start at 0 at the bottom and go up by one at each line.
The blue bar reaches the line marked 6, so 6 children voted for blue.
Follow the top across
To read a bar, find its top and follow it straight across to the scale. The top of the blue bar is level with 6, so 6 children voted for blue. In the same way, red has 3 votes and green has 4.
Only the height of a bar tells you how many. The tallest bar shows the most votes, wherever it stands on the chart, and the shortest bar shows the fewest.
How many more, and how many altogether
Two bars can be compared. Blue reaches 6 and green reaches 4, so blue has 6 − 4 = 2 more votes than green. "How many more" is a difference, so subtract.
Bars can be added too. Blue and green together have 6 + 4 = 10 votes. Each child voted once, so all three bars together count the whole class: 3 + 6 + 4 = 13 children.
A scale in twos
A scale does not always go up in ones. On this chart the numbers up the side are 0, 2, 4, 6, 8 and 10, so each line is worth 2. Read the scale before you read any bar.
The blue bar reaches the fifth line, and five twos are 10, so blue has 10 votes. Red reaches the line marked 4, and green reaches the line marked 6.
Each line is worth 2. The blue bar reaches the fifth line, which is marked 10.
Read the numbers, not the lines
The usual mistake is to count the lines as ones and read the blue bar as 5. The fifth line on this chart is marked 10, so blue has 10 votes. Always read the number the bar reaches.
A scale can go up in fives or tens as well. On a scale in fives, the lines are 5, 10, 15, 20 and so on, and a bar that reaches the third line stands for 15.
On a scale in fives, the red bar reaches the third line, which is marked 15.
Worked example: The Tallest Bar, the Shortest Bar and Their Difference
Question A bar chart shows the books five children read in June. Ali's bar stops at 8, Ben's bar at 3, Cara's bar at 7, Dev's bar at 9 and Eve's bar at 5. (a) Who read the most books, and who read the fewest? (b) How many more books did the child with the most read than the child with the fewest?
1.Look for the tallest bar. It is Dev's bar. Follow its top across to the scale: it stops at 9.
The tallest bar is Dev's. Its top is level with 9 on the scale. 2.Look for the shortest bar. It is Ben's bar, and it stops at 3.
The shortest bar is Ben's. Its top is level with 3. 3.(a) Dev read the most books, 9. Ben read the fewest books, 3.
(a) Dev read the most books, 9. Ben read the fewest, 3. 4.(b) Subtract to find the difference: 9 − 3 = 6. Dev read 6 more books than Ben.
(b) 9 − 3 = 6. Dev read 6 more books than Ben.
Answer: (a) Dev read the most (9 books) and Ben read the fewest (3 books); (b) 6 books
Common mistakes
- Choosing the first bar or the last bar on the chart instead of the tallest bar. The order of the bars does not matter. The height of a bar tells you how many.
- Adding 9 + 3 = 12 for part (b). 'How many more' asks for the difference between two bars, so subtract.
Worked example: A Scale in 5s and the Total of All the Bars
Question A bar chart shows the fruit a stall sold on Saturday. The scale goes up in 5s. The Apple bar stops at 30, the Pear bar at 15, the Mango bar at 25 and the Plum bar at 35. (a) How many pieces of fruit did the stall sell altogether? (b) The stall had 160 pieces of fruit in the morning. How many pieces were left?
1.Read each bar against the scale, counting up in 5s: Apple 30, Pear 15, Mango 25 and Plum 35.
Count up the scale in 5s to read each bar: 30, 15, 25 and 35. 2.Add the bars in pairs that are easy: 30 + 15 = 45 and 25 + 35 = 60.
Add the bars in pairs: 30 + 15 = 45 and 25 + 35 = 60. 3.(a) 45 + 60 = 105. The stall sold 105 pieces of fruit altogether.
(a) 45 + 60 = 105 pieces of fruit were sold. 4.(b) Subtract from the number in the morning: 160 − 105 = 55 pieces were left.
(b) 160 − 105 = 55 pieces were left.
Answer: (a) 105 pieces; (b) 55 pieces
Common mistakes
- Counting the marks instead of reading the numbers, for example saying the Pear bar shows 3 because it reaches the third mark. Each mark on this scale is worth 5, so the third mark is 15.
- Leaving one bar out of the total. 'Altogether' means all four bars, so tick each bar as you add it.