Bar charts · applications

Applications: Bar Charts

10 question types · Primary 3 · each worked step by step with a figure that follows the steps

PSLE · O-Level · SAT

01

The Tallest Bar, the Shortest Bar and Their Difference

strategyFollow Each Bar Across to the Scale, Then Subtract

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?

012345678910AliBenCaraDev9Eve
The tallest bar is Dev's. Its top is level with 9 on the scale.
Look for the tallest bar. It is Dev's bar. Follow its top across to the scale: it stops at 9.
step 1 of 4

The tallest bar shows the most and the shortest bar shows the fewest. Follow the top of each of these bars across to the scale to read its number, then subtract.

  1. Look for the tallest bar. It is Dev's bar. Follow its top across to the scale: it stops at 9.
  2. Look for the shortest bar. It is Ben's bar, and it stops at 3.
  3. (a) Dev read the most books, 9. Ben read the fewest books, 3.
  4. (b) Subtract to find the difference: 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

techniqueReading Bar Charts

examsPSLE · O-Level · SAT

Common pitfalls

  • 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.
02

A Scale in 2s and a Bar That Ends Between Two Marks

strategyHalfway Between Two Marks Is 1 More Than the Lower Mark

A bar chart shows the pets that the children in Class 3A keep. The scale goes up in 2s: 0, 2, 4, 6, 8, 10. The Cat bar stops at 2 and the Dog bar stops at 8. The Fish bar stops halfway between 6 and 8. The Bird bar stops halfway between 4 and 6. (a) How many fish are there? (b) How many fish and birds are there altogether?

0246810CatDogFishBird
The scale goes up in 2s. Halfway between two marks is 1 more than the lower mark.
The scale goes up in 2s, so the number halfway between two marks is 1 more than the lower mark.
step 1 of 5

On a scale that goes up in 2s, each space between two marks is worth 2. A bar that stops halfway up a space is 1 more than the mark below it.

  1. The scale goes up in 2s, so the number halfway between two marks is 1 more than the lower mark.
  2. The Fish bar stops halfway between 6 and 8. Halfway is 6 + 1 = 7.
  3. (a) There are 7 fish.
  4. The Bird bar stops halfway between 4 and 6. Halfway is 4 + 1 = 5, so there are 5 birds.
  5. (b) Add the two bars: 7 + 5 = 12 fish and birds altogether.

answer(a) 7 fish; (b) 12 fish and birds

techniqueReading Bar Charts · Skip Counting

examsPSLE · O-Level · SAT

Common pitfalls

  • Reading the Fish bar as 6 because 6 is the nearest number printed on the scale. The bar goes past the 6 mark, so there are more than 6 fish.
  • Reading the Fish bar as 612 because it stops halfway. Each space on this scale is worth 2, not 1, so halfway up a space is 1 more, which is 7.
03

A Scale in 5s and the Total of All the Bars

strategyRead Every Bar, Then Add in Pairs That Are Easy

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?

0510152025303540Apple30Pear15Mango25Plum35
Count up the scale in 5s to read each bar: 30, 15, 25 and 35.
Read each bar against the scale, counting up in 5s: Apple 30, Pear 15, Mango 25 and Plum 35.
step 1 of 4

Count up the scale in 5s to read each bar. 'Altogether' means every bar on the chart, so add all four. Then subtract the total from the number the stall had in the morning.

  1. Read each bar against the scale, counting up in 5s: Apple 30, Pear 15, Mango 25 and Plum 35.
  2. Add the bars in pairs that are easy: 30 + 15 = 45 and 25 + 35 = 60.
  3. (a) 45 + 60 = 105. The stall sold 105 pieces of fruit altogether.
  4. (b) Subtract from the number in the morning: 160 − 105 = 55 pieces were left.

answer(a) 105 pieces; (b) 55 pieces

techniqueReading Bar Charts · Skip Counting

examsPSLE · O-Level · SAT

Common pitfalls

  • 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.
04

How Many More Chose One Than Two Others Together

strategyCombine First, Then Compare

Each child in Primary 3 chose one club, and a bar chart shows the results. The scale goes up in 2s. The Soccer bar stops at 18, the Swim bar at 6, the Run bar at 4 and the Dance bar at 12. (a) How many children chose Swim and Run together? (b) How many more children chose Soccer than Swim and Run together?

02468101214161820Soccer18Swim6Run4Dance
The question names three bars: Soccer 18, Swim 6 and Run 4.
Read the three bars that the question names: Soccer 18, Swim 6 and Run 4.
step 1 of 4

The question compares one bar with two bars joined together. Join the two bars first by adding, then compare by subtracting.

  1. Read the three bars that the question names: Soccer 18, Swim 6 and Run 4.
  2. (a) Combine Swim and Run first: 6 + 4 = 10 children.
  3. Now compare Soccer with the two clubs together: 18 − 10.
  4. (b) 18 − 10 = 8. Soccer has 8 more children than Swim and Run together.

answer(a) 10 children; (b) 8 children

techniqueReading Bar Charts · Two-Step Word Problems

examsPSLE · O-Level · SAT

Common pitfalls

  • Working from left to right as 18 − 6 + 4 = 16. Swim and Run must be added first, because the question compares Soccer with the two of them together.
  • Using the Dance bar because it is on the chart. The question names only Soccer, Swim and Run, so the Dance bar is not needed.
05

A Bar Chart with Bars That Go Across

strategyRead Down to the Bottom Scale, Then Pick the Bars Past a Number

A bar chart shows the books a library lent on five days. The bars go across the page, and the scale along the bottom goes up in 5s. Monday's bar stops at 20, Tuesday's at 35, Wednesday's at 15, Thursday's at 40 and Friday's at 45. (a) On how many days did the library lend more than 25 books? (b) How many books did it lend on those days altogether?

05101520253035404550Mon20Tue35Wed15Thu40Fri45
The bars go across, so go down from the end of each bar to the scale along the bottom.
The bars go across, so read each bar by going down from its end to the scale at the bottom: 20, 35, 15, 40 and 45.
step 1 of 4

When the bars go across, the numbers are along the bottom. Go down from the end of a bar to read it. A bar shows more than 25 when it goes past the 25 mark.

  1. The bars go across, so read each bar by going down from its end to the scale at the bottom: 20, 35, 15, 40 and 45.
  2. Find 25 on the scale and look for the bars that go past it: Tuesday (35), Thursday (40) and Friday (45).
  3. (a) The library lent more than 25 books on 3 days.
  4. (b) Add those three bars: 35 + 40 + 45 = 120 books.

answer(a) 3 days; (b) 120 books

techniqueReading Bar Charts · Skip Counting

examsPSLE · O-Level · SAT

Common pitfalls

  • Looking for the numbers at the side, where the days are written. On this chart the scale is along the bottom, so go down from the end of the bar.
  • Counting Monday because 20 is close to 25. 'More than 25' means the bar must go past the 25 mark, and Monday's bar stops before it.
06

A Chart with One Bar Missing and the Total Given

strategyAdd the Bars You Have, Then Subtract from the Total

Four children have 30 stickers altogether. A bar chart shows Amy's bar at 9, Raj's bar at 6 and Lin's bar at 8. Sam's bar has not been drawn yet. (a) How many stickers do Amy, Raj and Lin have altogether? (b) How tall must Sam's bar be?

012345678910Amy9Raj6Lin8Sam?
Three bars are drawn: Amy 9, Raj 6 and Lin 8. Sam's bar is missing.
Read the three bars that are drawn: Amy 9, Raj 6 and Lin 8.
step 1 of 4

All four bars add up to the total. Add the three bars that are drawn, and what is left of the total is the missing bar.

  1. Read the three bars that are drawn: Amy 9, Raj 6 and Lin 8.
  2. (a) Add them: 9 + 6 + 8 = 23 stickers.
  3. The four bars must add up to 30, so Sam's bar is what is left: 30 − 23.
  4. (b) 30 − 23 = 7. Draw Sam's bar up to 7. Check: 9 + 6 + 8 + 7 = 30.

answer(a) 23 stickers; (b) 7

techniqueReading Bar Charts · Two-Step Word Problems

examsPSLE · O-Level · SAT

Common pitfalls

  • Drawing Sam's bar up to 30. 30 is the total for all four children, not the number of stickers Sam has.
  • Guessing a height that looks right beside the other bars. The height comes from the total, so work it out before you draw.
07

Two Charts with Different Scales

strategyRead the Scale Before You Compare the Heights

Two classes collected cans in Week 1 and Week 2, and each class drew its own bar chart. Class 3A's scale goes up in 2s, and its bars stop at 8 and 12. Class 3B's scale goes up in 10s, and its bars stop at 20 and 30. On the page, Class 3A's Week 2 bar is taller than Class 3B's Week 2 bar. (a) How many more cans did Class 3B collect than Class 3A in Week 2? (b) How many cans did the two classes collect altogether in the two weeks?

Class 3A, scale in 2s024681012Week 1Week 2Class 3B, scale in tens0102030405060Week 1Week 2
One space is 2 cans on the first chart and 10 cans on the second, so the heights cannot be compared by eye.
Read the scale of each chart first. One space is 2 cans on Class 3A's chart and 10 cans on Class 3B's chart, so the heights cannot be compared by eye.
step 1 of 5

A bar's height means nothing until you know the scale. Read each bar against the numbers on its own chart, and compare the numbers, not the heights.

  1. Read the scale of each chart first. One space is 2 cans on Class 3A's chart and 10 cans on Class 3B's chart, so the heights cannot be compared by eye.
  2. Read the Week 2 bars against their own scales: Class 3A collected 12 cans and Class 3B collected 30 cans.
  3. (a) 30 − 12 = 18. Class 3B collected 18 more cans, although its bar looks shorter.
  4. Read the Week 1 bars as well: Class 3A collected 8 cans and Class 3B collected 20 cans.
  5. (b) Add all four bars: 8 + 12 + 20 + 30 = 70 cans.

answer(a) 18 cans; (b) 70 cans

techniqueReading Bar Charts · Skip Counting

examsPSLE · O-Level · SAT

Common pitfalls

  • Saying Class 3A collected more in Week 2 because its bar is taller. The two charts have different scales, so a taller bar can stand for a smaller number.
  • Reading Class 3B's bars with Class 3A's scale, as 4 and 6. Each chart must be read against its own numbers, and Class 3B's scale goes up in 10s.
08

Three Statements About a Chart, One of Them False

strategyTest Each Statement Against the Numbers

A bar chart shows the drinks a canteen sold at recess. The scale goes up in 2s. The Milk bar stops at 12, the Juice bar at 20, the Tea bar at 8 and the Water bar at 16. Statement A says, 'Juice sold the most.' Statement B says, 'Water sold 4 more than Milk.' Statement C says, 'Tea and Milk together sold more than Juice.' (a) How many drinks did Tea and Milk sell together? (b) Which statement is false?

02468101214161820MilkJuice20TeaWaterA is true
Statement A: the tallest bar is Juice, at 20. It is true.
Statement A: the tallest bar is Juice, at 20. Statement A is true.
step 1 of 4

Take the statements one at a time. For each one, read the bars it names, do the working, and see whether the numbers agree with the words.

  1. Statement A: the tallest bar is Juice, at 20. Statement A is true.
  2. Statement B: Water is 16 and Milk is 12, and 16 − 12 = 4. Statement B is true.
  3. (a) Statement C: Tea and Milk together sold 8 + 12 = 20 drinks.
  4. (b) Juice also sold 20. 20 is equal to 20, not more than 20, so Statement C is false.

answer(a) 20 drinks; (b) Statement C is false

techniqueReading Bar Charts

examsPSLE · O-Level · SAT

Common pitfalls

  • Judging Statement C by eye and calling it true because two bars together look like a lot. Add the two bars and compare the numbers: 20 and 20 are equal.
  • Stopping at the first true statement and choosing it. The question asks for the false statement, so every statement has to be tested.
09

From a Tally Table to the Heights of the Bars

strategyCount the Bundles in Fives, Then Draw the Bar to That Number

Mei counted the kites at a park in a tally table. Red has 2 bundles of five and no single marks. Blue has 2 bundles of five and 4 single marks. Green has 1 bundle of five and 1 single mark. She draws a bar chart from the table. (a) How tall must the Blue bar be? (b) How many more blue kites than green kites are there?

Red= 10BlueGreen0246810121416Red10BlueGreen
Each bundle is 5. Red is 5 + 5 = 10, so the Red bar goes up to 10.
Each bundle is 5. Red is 5 + 5 = 10, so the Red bar goes up to 10.
step 1 of 4

In a tally table, four upright marks with one mark across them make a bundle of 5. Count the bundles in fives, add the single marks, and draw each bar up to that number.

  1. Each bundle is 5. Red is 5 + 5 = 10, so the Red bar goes up to 10.
  2. (a) Blue is 5 + 5 + 4 = 14, so the Blue bar must go up to 14.
  3. Green is 5 + 1 = 6, so the Green bar goes up to 6.
  4. (b) Compare the Blue bar and the Green bar: 14 − 6 = 8 more blue kites.

answer(a) 14; (b) 8 kites

techniqueReading Bar Charts · Reading Tables

examsPSLE · O-Level · SAT

Common pitfalls

  • Counting a bundle as 4 because it has four upright marks. The mark across the four is the fifth one, so a bundle is 5.
  • Counting each bundle as 1, which makes Blue 2 + 4 = 6, the same as Green. Count the bundles in fives: 5, 10, and then the 4 single marks.
10

Each Child Voted Once: Those Who Did Not Choose the Favorite

strategyThe Bars Add Up to the Number of Children

Every child in a class voted once for a favorite fruit, and a bar chart shows the votes. The scale goes up in 2s. The Apple bar stops at 8, the Banana bar at 14, the Grape bar at 4 and the Orange bar at 6. (a) How many children are in the class? (b) The fruit with the most votes is the favorite of the class. How many children did not choose it?

0246810121416Apple8Banana14Grape4Orange68 + 14 + 4 + 6
Each child voted once, so the four bars add up to the number of children.
Each child voted once, so the bars add up to the number of children: 8 + 14 + 4 + 6.
step 1 of 4

Each child voted once, so every child is counted in exactly one bar. The bars add up to the number of children, and taking away the tallest bar leaves the children who chose something else.

  1. Each child voted once, so the bars add up to the number of children: 8 + 14 + 4 + 6.
  2. (a) 8 + 14 + 4 + 6 = 32. There are 32 children in the class.
  3. The tallest bar is Banana, at 14, so banana is the favorite fruit of the class.
  4. (b) Take the banana votes away from the class: 32 − 14 = 18 children did not choose banana. Check: 8 + 4 + 6 = 18.

answer(a) 32 children; (b) 18 children

techniqueReading Bar Charts · Two-Step Word Problems

examsPSLE · O-Level · SAT

Common pitfalls

  • Answering 14 for part (b). 14 is the number of children who chose banana, and the question asks for the children who did not.
  • Counting the bars and saying there are 4 children. Four is the number of fruits. The children are counted by the heights of the bars.
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