Pictograms · applications

Applications: Pictograms

10 question types · Primary 2 · each worked step by step with a figure that follows the steps

PSLE · O-Level · GCSE Higher

01

Each Picture Stands for 1: The Longest Row and the Shortest Row

strategyCount the Pictures in Each Row, Then Subtract

A pictogram shows the pets of some children. Each picture stands for 1 pet. The Cat row has 6 pictures. The Dog row has 9 pictures. The Fish row has 2 pictures. The Bird row has 4 pictures. (a) Which pet is there the most of, and which pet is there the fewest of? (b) How many more pets are in the longest row than in the shortest row?

Cat= 6Dog= 9Fish= 2Bird= 4= 1 pet
Each picture stands for 1 pet, so the number of pictures in a row is the number of pets.
Look at the key. Each picture stands for 1 pet, so count the pictures in each row: Cat 6, Dog 9, Fish 2 and Bird 4.
step 1 of 4

The key says that each picture stands for 1 pet, so the number of pictures in a row is the number of pets. The longest row has the most and the shortest row has the fewest.

  1. Look at the key. Each picture stands for 1 pet, so count the pictures in each row: Cat 6, Dog 9, Fish 2 and Bird 4.
  2. The longest row is the Dog row, with 9 pictures. The shortest row is the Fish row, with 2 pictures.
  3. (a) There are the most dogs, 9, and the fewest fish, 2.
  4. (b) Subtract to find how many more: 9 − 2 = 7. There are 7 more dogs than fish.

answer(a) the most dogs, 9, and the fewest fish, 2; (b) 7 more

techniqueReading Pictograms

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Choosing the Cat row as the longest because it is the first row. The first row is not always the longest one. Count every row before you choose.
  • Adding for part (b) and writing 9 + 2 = 11. "How many more" asks for the difference between the two rows, so subtract: 9 − 2 = 7.
02

Each Picture Stands for 2: A Row of 6 Pictures

strategyRead the Key First, Then Count in 2s, Once for Each Picture

A pictogram shows the favorite toys of some children. Each picture stands for 2 children. The Car row has 6 pictures. The Doll row has 4 pictures. The Ball row has 3 pictures. (a) How many children chose the car? (b) How many children chose the car or the doll altogether?

CarDollBall= 2 children
Look at the key first. Each picture stands for 2 children.
Look at the key first. Each picture stands for 2 children, so count in 2s and say one number for each picture.
step 1 of 5

The key says what one picture is worth. When each picture stands for 2 children, count in 2s along the row and say one number for each picture.

  1. Look at the key first. Each picture stands for 2 children, so count in 2s and say one number for each picture.
  2. The Car row has 6 pictures. Count 2, 4, 6, 8, 10, 12.
  3. (a) 12 children chose the car.
  4. The Doll row has 4 pictures. Count 2, 4, 6, 8. So 8 children chose the doll.
  5. (b) Add the two rows: 12 + 8 = 20 children.

answer(a) 12 children; (b) 20 children

techniqueReading Pictograms · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Writing 6 children for the Car row because the row has 6 pictures. The key says each picture stands for 2 children, so 6 pictures stand for 12 children.
  • Adding the pictures for part (b) and writing 6 + 4 = 10 children. 10 is the number of pictures. Each picture stands for 2 children, so 10 pictures stand for 20 children.
03

Each Picture Stands for 5: The Total of Two Rows

strategyCount Each Row in 5s, Then Add the Two Numbers

A pictogram shows the stickers that three children have. Each picture stands for 5 stickers. Amy's row has 4 pictures. Ben's row has 3 pictures. Cal's row has 2 pictures. (a) How many stickers does Amy have? (b) How many stickers do Amy and Ben have altogether?

AmyBenCal= 5 stickers5, 10, 15, 20
Each picture stands for 5 stickers. Amy's row has 4 pictures: 5, 10, 15, 20.
Each picture stands for 5 stickers. Amy's row has 4 pictures. Count in 5s: 5, 10, 15, 20.
step 1 of 4

Each picture stands for 5 stickers, so count in 5s along a row. To find the total of two rows, find each row first and then add.

  1. Each picture stands for 5 stickers. Amy's row has 4 pictures. Count in 5s: 5, 10, 15, 20.
  2. (a) Amy has 20 stickers.
  3. Ben's row has 3 pictures. Count in 5s: 5, 10, 15. Ben has 15 stickers.
  4. (b) Add the two rows: 20 + 15 = 35 stickers. Check: the two rows have 4 + 3 = 7 pictures, and 7 fives are 35.

answer(a) 20 stickers; (b) 35 stickers

techniqueReading Pictograms · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Adding all three rows for part (b). The question asks about Amy and Ben only, so Cal's row is not part of the total.
  • Writing 4 + 3 = 7 stickers. 7 is the number of pictures in the two rows. Each picture stands for 5 stickers, so the two rows stand for 35 stickers.
04

Each Picture Stands for 10 and a Half Picture Stands for 5

strategyCount the Full Pictures in 10s, Then Add 5 for the Half Picture

A pictogram shows the cans that three classes collected. Each full picture stands for 10 cans. Class 2A has 3 full pictures and 1 half picture. Class 2B has 2 full pictures. Class 2C has 4 full pictures and 1 half picture. (a) How many cans did Class 2A collect? (b) How many cans did Class 2A and Class 2B collect altogether?

2A2B2C= 10 cans= 5
A full picture stands for 10 cans. A half picture stands for half of 10, which is 5 cans.
Each full picture stands for 10 cans. A half picture stands for half of 10, which is 5 cans.
step 1 of 5

A half picture stands for half of what a full picture stands for. Half of 10 is 5. Count the full pictures in 10s first, and then add 5 for the half picture.

  1. Each full picture stands for 10 cans. A half picture stands for half of 10, which is 5 cans.
  2. Class 2A has 3 full pictures. Count in 10s: 10, 20, 30. The half picture adds 5: 30 + 5 = 35.
  3. (a) Class 2A collected 35 cans.
  4. Class 2B has 2 full pictures. Count in 10s: 10, 20. Class 2B collected 20 cans.
  5. (b) Add the two rows: 35 + 20 = 55 cans altogether.

answer(a) 35 cans; (b) 55 cans

techniqueReading Pictograms · Halves, Quarters, Thirds · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Counting the half picture as a full picture and writing 40 cans for Class 2A. The half picture is only half of 10, so it adds 5, not 10.
  • Leaving out the half picture and writing 30 cans for Class 2A. The half picture is part of the row. It stands for 5 more cans, so the row is 35.
05

How Many More: Compare the Pictures First, Then Use the Key

strategyFind the Extra Pictures, Then Count What They Stand For

A pictogram shows the sports that some children chose. Each picture stands for 2 children. The Swim row has 7 pictures. The Run row has 4 pictures. The Dance row has 5 pictures. (a) How many more pictures are in the Swim row than in the Run row? (b) How many more children chose swimming than running?

SwimRunDance= 2 children
The Swim row has 7 pictures and the Run row has 4 pictures.
Look at the Swim row and the Run row. The Swim row has 7 pictures and the Run row has 4 pictures.
step 1 of 4

The pictures in a pictogram are lined up, so two rows can be compared picture by picture. The pictures that have no partner in the shorter row are the extra pictures. The key says how many children the extra pictures stand for.

  1. Look at the Swim row and the Run row. The Swim row has 7 pictures and the Run row has 4 pictures.
  2. (a) 7 − 4 = 3. The Swim row has 3 more pictures than the Run row.
  3. Each picture stands for 2 children, so the 3 extra pictures stand for 2 + 2 + 2 = 6 children.
  4. (b) 6 more children chose swimming. Check: the Swim row is 14 children and the Run row is 8 children, and 14 − 8 = 6.

answer(a) 3 more pictures; (b) 6 more children

techniqueReading Pictograms · Equal Groups

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Writing 3 more children for part (b). 3 is the number of extra pictures. Each picture stands for 2 children, so 3 extra pictures stand for 6 children.
  • Comparing the Swim row with the Dance row because the Dance row is next to it. The question names the Run row, so compare 7 pictures with 4 pictures.
06

Drawing a Row That Is Missing

strategyCount in 2s Up to the Number, and Draw One Picture for Each Count

A pictogram shows the favorite colors of some children. Each picture stands for 2 children. The Blue row has 5 pictures and the Green row has 3 pictures. The Red row is not drawn yet. 12 children chose red. (a) How many pictures must be drawn in the Red row? (b) How many pictures will the whole pictogram have then?

BlueGreenRed?= 2 children2, 4, 6, 8, 10, 12
Each picture stands for 2 children. Count in 2s until you reach 12: 2, 4, 6, 8, 10, 12.
Each picture stands for 2 children. Count in 2s until you reach 12: 2, 4, 6, 8, 10, 12.
step 1 of 4

Drawing a row is reading a row the other way round. Each picture stands for 2 children, so count in 2s until you reach the number of children. Each count is one picture to draw.

  1. Each picture stands for 2 children. Count in 2s until you reach 12: 2, 4, 6, 8, 10, 12.
  2. That is 6 counts, so 12 children need 6 pictures.
  3. (a) Draw 6 pictures in the Red row. Check: 6 twos are 12.
  4. (b) Count the pictures in all three rows: 5 + 3 + 6 = 14 pictures.

answer(a) 6 pictures; (b) 14 pictures

techniqueReading Pictograms · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Drawing 12 pictures because 12 children chose red. Each picture stands for 2 children, so 12 pictures would stand for 24 children.
  • Writing 5 + 3 + 12 = 20 pictures for part (b). 12 is the number of children who chose red. The Red row has 6 pictures, so the pictogram has 5 + 3 + 6 = 14 pictures.
07

The Same Numbers Drawn Again with a New Key

strategyFind the Number from the First Key, Then Count It Out with the New Key

A pictogram shows the books that Ann and Raj read. Each picture stands for 2 books. Ann's row has 4 pictures and Raj's row has 6 pictures. The teacher draws the pictogram again. In the new pictogram each picture stands for 4 books. (a) How many books did Raj read? (b) How many pictures are in Raj's row in the new pictogram?

First pictogramAnnRaj= 2 books2, 4, 6, 8, 10, 12
In the first pictogram each picture stands for 2 books. Raj's row has 6 pictures: 2, 4, 6, 8, 10, 12.
In the first pictogram each picture stands for 2 books. Raj's row has 6 pictures. Count in 2s: 2, 4, 6, 8, 10, 12.
step 1 of 4

A new key changes the number of pictures. It does not change the number of books. Read the number of books from the first pictogram, and then count that number out in 4s for the new one.

  1. In the first pictogram each picture stands for 2 books. Raj's row has 6 pictures. Count in 2s: 2, 4, 6, 8, 10, 12.
  2. (a) Raj read 12 books.
  3. In the new pictogram each picture stands for 4 books. Count in 4s until you reach 12: 4, 8, 12. That is 3 counts.
  4. (b) Raj's row has 3 pictures in the new pictogram. The row is shorter because each picture now stands for more books. Raj still read 12 books.

answer(a) 12 books; (b) 3 pictures

techniqueReading Pictograms · Equal Groups

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Saying that Raj read fewer books in the new pictogram because his row is shorter. The key changed, not the number of books: 3 pictures of 4 books are still 12 books.
  • Keeping 6 pictures in Raj's row in the new pictogram. With the new key, 6 pictures would stand for 24 books, and Raj read only 12.
08

The Whole Pictogram: How Many Children Were Asked

strategyEvery Child Is in the Pictogram Once, So Count All the Pictures

Some children were asked to choose one drink each. A pictogram shows what they chose. Each picture stands for 5 children. The Milk row has 3 pictures. The Juice row has 4 pictures. The Water row has 2 pictures. (a) How many pictures are in the pictogram altogether? (b) How many children were asked?

MilkJuiceWater= 5 children3 + 4 + 2
Each child chose one drink, so every child is in the pictogram once. Count the pictures in all the rows.
Each child chose one drink, so every child is in the pictogram once. Count the pictures in all the rows: 3 + 4 + 2 = 9.
step 1 of 4

Each child chose one drink, so each child is counted in one row and in no other row. All the rows together are all the children who were asked.

  1. Each child chose one drink, so every child is in the pictogram once. Count the pictures in all the rows: 3 + 4 + 2 = 9.
  2. (a) There are 9 pictures altogether.
  3. Each picture stands for 5 children. Count in 5s, once for each of the 9 pictures: 5, 10, 15, 20, 25, 30, 35, 40, 45.
  4. (b) 45 children were asked. Check: the rows are 15, 20 and 10 children, and 15 + 20 + 10 = 45.

answer(a) 9 pictures; (b) 45 children

techniqueReading Pictograms · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Writing 9 children for part (b). 9 is the number of pictures. Each picture stands for 5 children, so 9 pictures stand for 45 children.
  • Giving the longest row, 20 children, as the number of children asked. The Juice row is only the children who chose juice. The children who chose milk and water were asked too.
09

An Odd Number That Needs a Half Picture

strategyCount in 2s and Stop Before You Pass the Number; the 1 Left Is a Half Picture

A pictogram shows the favorite fruit of some children. Each full picture stands for 2 children, and a half picture stands for 1 child. 7 children chose mango. (a) How many full pictures and how many half pictures must be drawn in the Mango row? (b) The Kiwi row has 4 full pictures and 1 half picture. How many children chose kiwi?

MangoKiwi= 2 children= 12, 4, 6
Count in 2s and stop before you pass 7: 2, 4, 6. That is 3 full pictures.
Count in 2s and stop before you pass 7: 2, 4, 6. That is 3 full pictures. One more full picture would make 8, which is too many.
step 1 of 4

Full pictures of 2 can only make even numbers. An odd number has 1 child left after the full pictures, and that child is drawn as a half picture.

  1. Count in 2s and stop before you pass 7: 2, 4, 6. That is 3 full pictures. One more full picture would make 8, which is too many.
  2. 7 − 6 = 1 child is left. A half picture stands for 1 child, so draw 1 half picture.
  3. (a) The Mango row has 3 full pictures and 1 half picture. Check: 6 + 1 = 7.
  4. (b) The Kiwi row has 4 full pictures. Count in 2s: 2, 4, 6, 8. The half picture adds 1: 8 + 1 = 9 children chose kiwi.

answer(a) 3 full pictures and 1 half picture; (b) 9 children

techniqueReading Pictograms · Halves, Quarters, Thirds

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Drawing 4 full pictures for 7 children because 7 is close to 8. 4 full pictures stand for 8 children, and that is 1 child too many.
  • Counting the half picture in the Kiwi row as 2 children and writing 10. A half picture stands for half of 2, which is 1 child, so the row is 8 + 1 = 9.
10

Two Pictograms Read Together: Monday and Tuesday

strategyFind the Same Row in Both Pictograms, Then Add or Subtract

A fruit shop draws one pictogram for Monday and one for Tuesday. In both pictograms each picture stands for 5 pieces of fruit. On Monday the Apple row has 5 pictures and the Pear row has 2 pictures. On Tuesday the Apple row has 3 pictures and the Pear row has 6 pictures. (a) How many apples did the shop sell on the two days altogether? (b) How many more pears did the shop sell on Tuesday than on Monday?

MondayApplePearTuesdayApplePear= 5 pieces of fruit
Both pictograms use the same key. Each picture stands for 5 pieces of fruit. Find the Apple row in each one.
Both pictograms use the same key: each picture stands for 5 pieces of fruit. Find the Apple row in each pictogram.
step 1 of 5

Two pictograms about the same fruit can be read together. Find the row with the same name in each pictogram, read both rows with the key, and then add them or compare them.

  1. Both pictograms use the same key: each picture stands for 5 pieces of fruit. Find the Apple row in each pictogram.
  2. On Monday the Apple row has 5 pictures, which is 25 apples. On Tuesday the Apple row has 3 pictures, which is 15 apples.
  3. (a) 25 + 15 = 40 apples were sold on the two days.
  4. The Pear row has 2 pictures on Monday, which is 10 pears. It has 6 pictures on Tuesday, which is 30 pears.
  5. (b) 30 − 10 = 20. The shop sold 20 more pears on Tuesday.

answer(a) 40 apples; (b) 20 more pears

techniqueReading Pictograms · Skip Counting

examsPSLE · O-Level · GCSE Higher

Common pitfalls

  • Adding the Apple row and the Pear row of Monday for part (a). That is the fruit sold on Monday. The question asks about apples on both days, so add the two Apple rows.
  • Writing 6 − 2 = 4 more pears for part (b). 4 is the number of extra pictures. Each picture stands for 5 pears, so 4 extra pictures stand for 20 pears.
Mr. Chalk Read the guide