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Primary Maths · Year 4Chapter 11 · Statistics
Year 4 · Pictograms, Bar Charts and Time Graphs · Lesson 11.2

Year 4: Pictograms

Part of the Year 4 pictograms, bar charts and time graphs chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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11.2

Pictograms

Year 4
Interpret and present discrete data using pictograms, Solve comparison, sum and difference problems using pictograms

A pictogram uses small pictures, called symbols, to show data. Each symbol is one thing that is counted. The picture below shows the pets that children in Class 4 have. Each heart stands for 1 pet.

Pets in Class 4DogsCatsFishRabbitsKey:= 1 pets
A pictogram. The key says 1 heart = 1 pet. Cats has 8 hearts, so 8 children have a cat.

When there is lots of data, we do not want to draw hundreds of pictures. So one symbol can stand for 2, 5 or 10. The key tells us how many each symbol is worth. Always read the key first!

Cakes sold at the school saleMonTueWedThuKey:= 5 cakes
Here 1 symbol = 5 cakes. Tuesday has 7 symbols, so 7 × 5 = 35 cakes.

Sometimes the data does not fit exactly. A half symbol is worth half of what a whole symbol is worth. If the key says 1 symbol = 10 people, then a half symbol is 5 people. To draw a pictogram, divide each number by the key to find how many symbols to draw.

Favourite colourRedBlueGreenKey:= 10 pupilsand= 5 pupils
Key: 1 square = 10 pupils and half a square = 5 pupils. Red has 2 squares and a half: 20 + 5 = 25.

Key ideas

  • The key says how many one symbol stands for. Read it first.
  • To read a row: count the symbols, then multiply by the key. A half symbol is worth half the key.
  • To draw a row: divide the number by the key. Use a half symbol for a remainder that is half the key.
  • Draw all the symbols the same size, in a straight line with equal gaps.
Worked example 11.2.1
The pictogram shows the pets in Class 4. How many children have a cat?
Pets in Class 4DogsCatsFishRabbitsKey:= 1 pets

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. Look at the picto carefully and read off the number for Cats.

  1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
    1 symbol = 1 pets
  2. Count the symbols in the row for Cats. Multiply the number of symbols by what one symbol is worth.
    Cats: 8 symbols
    8 × 1 = 8
  3. Write the answer.
    Cats = 8 pets
    Pets in Class 4DogsCatsFishRabbitsKey:= 1 pets

Check. Count back: 8 ÷ 1 = 8 symbols. ✓

Watch out. Do not forget the key. A symbol is not always worth 1. A half symbol is worth half.

Worked example 11.2.2
The pictogram shows how many stickers Class 4 won each day. How many stickers did they win altogether?
Stickers won by Class 4MonTueWedThuFriKey:= 2 stickers

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. Read each number from the picture, then add them all.

  1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
    1 symbol = 2 stickers
  2. Read every number. We need these numbers for the calculation.
    Mon = 6
    Tue = 10
    Wed = 4
    Thu = 8
    Fri = 12
    Stickers won by Class 4MonTueWedThuFriKey:= 2 stickers
  3. Add the numbers together. Altogether means add everything. Add one number at a time.
    6 + 10 + 4 + 8 + 12
    6 + 10 = 16
    16 + 4 = 20
    20 + 8 = 28
    28 + 12 = 40
  4. Write the answer.
    Total = 40 stickers

Check. Add in the opposite order: 12 + 8 + 4 + 10 + 6 = 40. ✓

Watch out. Do not leave out a row or a bar. Check you have used every one.

Worked example 11.2.3
How many more goals did the team score in Match 3 than in Match 2?
Goals scored by the school teamMatch 1Match 2Match 3Match 4Key:= 5 goals

Key words. The difference between two numbers is how much bigger one is than the other. We find it by subtracting. “How many more” and “how many fewer” questions are difference questions. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. To find “how many more”, read both numbers and then subtract the smaller from the bigger.

  1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
    1 symbol = 5 goals
  2. Read the numbers we need from the picture. We need these numbers for the calculation.
    Match 3 = 25
    Match 2 = 10
    Goals scored by the school teamMatch 1Match 2Match 3Match 4Key:= 5 goals
  3. Find the difference. To find how many more (or fewer), subtract the smaller number from the bigger number.
    25 − 10 = 15
  4. Write the answer.
    15 more

Check. Add back: 10 + 15 = 25. ✓

Watch out. Subtract: do not add. The question asks for the difference.

Worked example 11.2.4
The key says 1 symbol = 10 cars. How many cars were in the car park on Monday?
Cars in the school car parkMonTueWedThuFriKey:= 10 carsand= 5 cars

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. Look at the picto carefully and read off the number for Mon.

  1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
    1 symbol = 10 cars
    Half a symbol = 10 ÷ 2 = 5 cars
  2. Count the symbols in the row for Mon. Multiply the number of symbols by what one symbol is worth.
    Mon: 4 whole symbols and 1 half symbol
    4 × 10 = 40
    Half symbol = 5
    40 + 5 = 45
  3. Write the answer.
    Mon = 45 cars
    Cars in the school car parkMonTueWedThuFriKey:= 10 carsand= 5 cars

Check. Count back: 45 ÷ 10 = 4 and a half symbols. ✓

Watch out. Do not forget the key. A symbol is not always worth 1. A half symbol is worth half.

Worked example 11.2.5
Priya borrowed 20 maths books. The pictogram shows 4 symbols in the Maths row, but the key is hidden. How much is one symbol worth?
Books borrowedMathsReadingKey:= ?

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. The key is how much one symbol is worth. Divide the number by the number of symbols.

  1. Count the symbols in the row. We need to know how many symbols make the number.
    Books: 4 symbols
  2. Divide the number by the symbols. If 4 symbols are worth 20, one symbol is worth 20 ÷ 4.
    20 ÷ 4 = 5
  3. Write the answer.
    1 symbol = 5

Check. 4 × 5 = 20. ✓

Watch out. Divide: do not add or subtract.

Worked example 11.2.6
The table shows how many pupils walked to school. Draw the symbols for Tuesday and Thursday on the pictogram. The key is 1 symbol = 10 pupils.
DayMonTueWedThuFri
Pupils4025301535
Pupils who walked to schoolMonTueWedThuFriKey:= 10 pupilsand= 5 pupils

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. Divide each number by the key to find how many symbols to draw.

  1. Read the key. The key tells us what one symbol is worth. Here a symbol is not worth 1.
    1 symbol = 10 pupils
    Half a symbol = 10 ÷ 2 = 5 pupils
  2. Work out how many symbols each row needs. Divide each number by the key. A half symbol is used for half a key.
    Tue: 25 ÷ 10 = 2 remainder 5, so 2 symbols and a half symbol
    Thu: 15 ÷ 10 = 1 remainder 5, so 1 symbol and a half symbol
  3. Draw the symbols. Draw them neatly in a line, with the same size and the same gaps.
    Pupils who walked to schoolMonTueWedThuFriKey:= 10 pupilsand= 5 pupils

Check. Count the symbols you drew. They should be worth 25, 15. ✓

Watch out. Use a half symbol if the number is half way between two whole symbols.

Worked example 11.2.7
Mia recorded the books she read: Mon 8, Tue 12, Wed 6, Thu 10. Draw a pictogram. Use 1 symbol = 2 books.

Key words. A pictogram uses small pictures (symbols) to show data. The key tells you how many each symbol stands for. A half symbol stands for half of that number.

Method. Choose a key, divide every number by the key to find the symbols for each row, then draw the pictogram with its key.

  1. Choose a key. The key should divide into every number. The biggest number is 12. With a key of 2 we need only 6 symbols for the longest row.
    1 symbol = 2 books
  2. Work out the symbols for each row. Divide every number by the key.
    Mon: 8 ÷ 2 = 4
    Tue: 12 ÷ 2 = 6
    Wed: 6 ÷ 2 = 3
    Thu: 10 ÷ 2 = 5
  3. Draw the pictogram and the key. Draw the symbols for each row. Do not forget to write the key.
    Books readMonTueWedThuKey:= 2 books

Check. Count the symbols in one row and multiply by 2 to check. ✓

Watch out. Always draw the key. Without it nobody knows what a symbol is worth.

Watch out

Do not read a symbol as 1 when the key says it is worth more. Always read the key first. A half symbol is half of the key, not half of 1.

Exercise 11B  Pictograms

Non-calculator
1
FThe key says 1 face = 1 child. Read the pictogram.
Favourite clubsFootballSwimmingDancingJudoKey:= 1 children
(a)How many children chose football?
(b)How many children chose dancing?
(c)How many children chose judo?
(d)How many children chose football or judo?
2
FThe key says 1 star = 2 kg of fruit and half a star = 1 kg.
Fruit sold at the marketApplesPearsPlumsCherriesKey:= 2 kgand= 1 kg
(a)How many kilograms of apples were sold?
(b)How many kilograms of pears were sold?
(c)How many kilograms of plums were sold?
(d)How many kilograms of cherries were sold?
3
FEach book symbol stands for 5 books.
Books read this termClass 3Class 4Class 5Class 6Key:= 5 books
(a)How many books did Class 4 read?
(b)Which class read the fewest books?
(c)How many more books did Class 6 read than Class 5?
(d)How many books did the four classes read altogether?
4
FThe key says 1 triangle = 10 people and half a triangle = 5 people.
How people travel to the town centreBusCarWalkCycleTrainKey:= 10 peopleand= 5 people
(a)How many people travel by car?
(b)How many people travel by cycle?
(c)Which way of travelling is the most popular?
(d)How many more people go by car than by bus?
5
FPut the days in order, from the most cars to the fewest cars.
Cars in the school car parkMonTueWedThuFriKey:= 10 carsand= 5 cars
6
FHow many symbols are needed to show each number? One symbol = the key given. Write the number of symbols.
(a)12 when 1 symbol = 2
(b)15 when 1 symbol = 5
(c)40 when 1 symbol = 10
(d)45 when 1 symbol = 10
7
FThe table shows the sandwiches sold each day. Part of the pictogram is drawn. Work out the symbols needed for Wednesday and Friday. Key: 1 circle = 5 sandwiches.
DayMonTueWedThuFri
Sandwiches2030152535
Sandwiches soldMonTueWedThuFriKey:= 5 sandwiches
(a)How many symbols for Wednesday (15 sandwiches)?
(b)How many symbols for Friday (35 sandwiches)?
8
PSThe key is hidden in each pictogram. Work out how much one symbol is worth.
PointsBlue teamRed teamKey:= ?
TeaMonTueKey:= ?
TravelWalkBusCarKey:= ?
(a)The Blue team row has 4 stars. The Blue team scored 12 points.
(b)The Tuesday row has 6 hearts. 24 cups of tea were drunk on Tuesday.
(c)The Bus row has 5 triangles. 50 pupils came by bus.
9
FDraw a pictogram for the data in the table. Use 1 heart = 2 pets. Write how many hearts are needed in each row.
PetCatsDogsBirdsFish
Number812610
10
FDraw a pictogram for the plants sold. Use 1 star = 5 plants.
PlantRoseTulipDaisyLily
Sold35204015
11
RZainab draws a pictogram of the stickers some children have. Her key says 1 symbol = 4 stickers. Leo draws the same data with the key 1 symbol = 2 stickers. How many symbols does each child need in Leo’s pictogram?
(a)Amira has 12 stickers
(b)Noah has 8 stickers
(c)Priya has 20 stickers
12
RTom looks at the pictogram. He says, “Tuesday has 8 stars, because I counted 8 symbols.” Is he right? Explain.
Gold stars earnedMonTueWedKey:= 2 stars
13
PSThe pictogram shows the cakes sold at the school sale. On Saturday the school sold 30 more cakes than on Wednesday. How many cakes were sold on Saturday?
Cakes soldMonTueWedThuFriKey:= 5 cakes
14
RA pictogram uses 1 symbol = 10 pupils. Red has 2 whole symbols and a half. Blue has 3 whole symbols. Green has the rest of 85 pupils altogether. How many symbols, and half symbols, does Green have?

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