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State Board · Class 5 · Mathematics

Lesson 14: Pictographs

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Reading a pictograph and its key

From daily life

A class makes a chart where one small picture of a book means 20 books borrowed from the library. A long row of book pictures instantly tells which day was busiest. That chart is a pictograph.

Simple definition

A pictograph (चित्रालेख) shows data with pictures or symbols. The key (scale, सूची) tells how many items one symbol stands for. Number of items = number of symbols × value of one symbol.

A pictograph of fruit sold, 1 symbol equal to 10 kg: apple 50 kg, banana 30 kg, orange 40 kg.Fruit soldAppleBananaOrangekey: 1 symbol = 10 kg5 × 10 = 50 kg3 × 10 = 30 kg4 × 10 = 40 kg

In the figure : Fruit sold: each symbol is 10 kg, so apple 5 symbols = 50 kg.

Rule 1: Read the key first — Count the symbols and multiply by the key.

  • Easy : Key: 1 symbol = 20 books. 6 symbols = 6 × 20 = 120 books.
  • Medium : Key: 1 symbol = 50 students. 4 symbols = 200 students.
  • Exam-type : Key: 1 symbol = 8 pencils. 7 symbols = 56 pencils.
Three full symbols and one half symbol with 1 symbol equal to 10 cars show 35 cars.Key: 1 symbol = 10 cars= 3 × 10 + 5 = 35= 5half symbol = half of 10

In the figure : 3 full symbols and a half symbol show 35 when 1 symbol = 10.

Rule 2: Half symbol — A half symbol means half the value of the key.

  • Easy : Key 1 symbol = 10. 2 full symbols and a half = 20 + 5 = 25.
  • Medium : Key 1 symbol = 4. A half symbol = 2.
  • Exam-type : Key 1 symbol = 50. 3 symbols and a half = 150 + 25 = 175.
Live figure

Reading a pictograph and its key

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Remember

Always find the key first. Without it the symbols mean nothing.

Common mistake

Counting symbols as the answer, forgetting to multiply by the key.

Shortcut

Memory clue: Key first, count next, multiply last.

Spot the difference

PartWhat it tells
Symbolone unit of data
Keyvalue of 1 symbol
Half symbolhalf of the key

Practice questions

Easy
  1. 1Key: 1 symbol = 20 books. How many books are shown by 6 symbols?
  2. 2Key: 1 symbol = 50 students. What do 4 symbols show?
  3. 3Key: 1 symbol = 8 pencils. What do 7 symbols show?
Medium
  1. 4Key: 1 symbol = 10. What do 2 full symbols and a half show?
  2. 5Key: 1 symbol = 4. What does a half symbol show?
  3. 6Key: 1 symbol = 50. What do 3 and a half symbols show?
Challenging
  1. 7A row has 8 symbols and the key is 1 symbol = 25 kg. How many kg?
  2. 8Ravi sees 5 symbols and says 5 books. The key is 1 symbol = 20 books. Correct him.
Show answers (try them yourself first)
  1. 1120
  2. 2200 students
  3. 356 pencils
  4. 425
  5. 52
  6. 6175
  7. 7200 kg
  8. 85 × 20 = 100 books.

Answering questions from a pictograph

From daily life

The chart says: rice 6 symbols, wheat 4 symbols and dal 3 symbols, where 1 symbol = 5 kg of grain sold. Which sold most? How much more than dal? We answer from the key and the symbols.

Simple definition

To answer questions: (1) read the key, (2) count symbols in each row and multiply, (3) compare rows or add them. Most symbols = biggest. Fewest symbols = smallest.

Rule 1: One row — Value of a row = symbols × key.

  • Easy : Rice: 6 × 5 = 30 kg.
  • Medium : Wheat: 4 × 5 = 20 kg. Dal: 3 × 5 = 15 kg.
  • Exam-type : Rice sold 3 symbols more than dal: 3 × 5 = 15 kg more.

Rule 2: Difference and total — Difference = difference in symbols × key. Total = total symbols × key.

  • Easy : Rice − dal = (6 − 3) × 5 = 15 kg.
  • Medium : Total symbols = 6 + 4 + 3 = 13. Total = 13 × 5 = 65 kg.
  • Exam-type : Cars sold, key 1 symbol = 20: Mon 3, Tue 5, Wed 2 and a half → 60, 100, 50. Total = 210 cars.
Remember

Add the symbols first and multiply once; it is quicker.

Common mistake

Subtracting the symbols and forgetting the key. 3 symbols less is 15 kg, not 3.

Shortcut

Memory clue: Rows tell the story: biggest row, smallest row, then do the sums.

Spot the difference

QuestionHow to find
Mostrow with most symbols
Difference(symbols difference) × key
Total(all symbols) × key

Practice questions

Easy
  1. 1Key 1 symbol = 5 kg. Rice has 6 symbols. How many kg?
  2. 2Which grain sold the most: rice (6), wheat (4) or dal (3)?
  3. 3Which sold the least?
Medium
  1. 4How many kg of wheat were sold?
  2. 5How much more rice than dal was sold?
  3. 6Find the total grain sold.
Challenging
  1. 7Key 1 symbol = 20 cars. Mon 3, Tue 5, Wed 2 and a half. Find the total cars.
  2. 8Sita says rice is 3 kg more than dal because the difference is 3 symbols. Correct her.
Show answers (try them yourself first)
  1. 130 kg
  2. 2Rice
  3. 3Dal
  4. 44 × 5 = 20 kg
  5. 515 kg
  6. 613 × 5 = 65 kg
  7. 710.5 symbols × 20 = 210 cars
  8. 83 symbols × 5 = 15 kg more.

Choosing a scale and drawing a pictograph

From daily life

A shopkeeper wants to show sales of 15, 30, 45 and 60 mangoes. Drawing one picture for each mango would be too long. He chooses 1 picture = 15 mangoes, which gives 1, 2, 3 and 4 pictures.

Simple definition

To draw a pictograph: choose a scale that divides all the numbers neatly, then divide each number by the scale to get the symbols. A bigger scale gives fewer symbols; a smaller scale gives more.

The same data of 20 shown with scales 1, 4 and 10: a bigger scale needs fewer symbols.Dogs = 20 children1 = 11 = 41 = 1020 ÷ 10 = 2 symbols20 ÷ 4 = 5

In the figure : The same number 20 with scales 1, 4 and 10: bigger scale, fewer symbols.

Rule 1: Choose the scale — The scale should divide every number, or leave only halves.

  • Easy : For 15, 30, 45, 60 use scale 15: 1, 2, 3, 4 symbols.
  • Medium : For 12, 24, 36 use scale 12: 1, 2, 3 symbols.
  • Exam-type : 42 cannot be shown exactly with scale 10 (4.2 symbols). Use scale 6: 42 ÷ 6 = 7 symbols.

Rule 2: Symbols from numbers — Symbols = number ÷ scale.

  • Easy : 30 ÷ 5 = 6 symbols.
  • Medium : 75 ÷ 25 = 3 symbols.
  • Exam-type : 90 ÷ 20 = 4 and a half symbols (90 = 4 × 20 + 10).
Live figure

Choosing a scale and drawing a pictograph

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Remember

A half symbol shows only half the scale, so 42 with scale 10 is not possible.

Common mistake

Using a scale that gives too many symbols, like 1 symbol = 1 for 500. Choose 1 symbol = 100.

Shortcut

Memory clue: Big scale – few pictures; small scale – many pictures.

Spot the difference

ScaleSymbols for 60
1 symbol = 512
1 symbol = 106
1 symbol = 203

Practice questions

Easy
  1. 1Draw how many symbols for 30 with scale 5?
  2. 2How many symbols for 75 with scale 25?
  3. 3How many symbols for 60 with scale 10?
Medium
  1. 4Choose a good scale for 15, 30, 45 and 60.
  2. 5How many symbols for 90 with scale 20?
  3. 6Why is scale 10 not good for 42? Suggest a better scale.
Challenging
  1. 7A shop sold 500 pens. Which is better: 1 symbol = 1 pen or 1 symbol = 100 pens? Why?
  2. 8Data: 25, 50, 75. Give a scale and the symbols for each.
Show answers (try them yourself first)
  1. 130 ÷ 5 = 6
  2. 23
  3. 36
  4. 415 (or 5). Symbols: 1, 2, 3, 4.
  5. 54 and a half
  6. 642 ÷ 10 = 4.2, not a whole or half symbol. Use scale 6 or 7: 42 ÷ 6 = 7.
  7. 71 symbol = 100 pens: only 5 symbols instead of 500.
  8. 8Scale 25: 1, 2, 3 symbols.

Tally marks and tables

From daily life

You ask your friends their favourite fruit and make a mark for each answer – a vertical line for every vote. After four lines you cross them with a fifth. You are using tally marks.

Simple definition

Tally marks (ताळचिन्हे) count as we survey. Four lines and a fifth across them make a group of 5. Then make a table, add to find the total and draw the pictograph.

Tally marks in groups of five: red 8, blue 12 and green 5.Red8Blue12Green5

In the figure : Tally marks in groups of five show red 8, blue 12 and green 5.

Rule 1: Reading tally marks — Count the groups of 5, then add the single lines.

  • Easy : 2 groups and 3 lines = 10 + 3 = 13.
  • Medium : 1 group and 2 lines = 7; 4 groups = 20.
  • Exam-type : 9 votes are drawn as 1 group and 4 lines.

Rule 2: From tally to table and pictograph — Count each tally, write the number, add for the total, then choose a scale.

  • Easy : Mango 9, banana 6, orange 5 → total 9 + 6 + 5 = 20 children.
  • Medium : Most liked: mango (9). Least liked: orange (5). Difference = 4.
  • Exam-type : Scale 1 symbol = 2 children: mango 4 and a half, banana 3, orange 2 and a half symbols.
Live figure

Tally marks and tables

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Remember

A table with the total is a good check: the numbers should add up to the number of people surveyed.

Common mistake

Drawing the fifth line beside the group instead of across it.

Shortcut

Memory clue: Four lines up, fifth line across = 5.

Spot the difference

FruitVotes
Mango9
Banana6
Orange5

Practice questions

Easy
  1. 1How many is 2 groups and 3 lines?
  2. 2How many is 1 group and 2 lines?
  3. 3How many is 4 groups?
Medium
  1. 4Show 9 votes in tally marks.
  2. 5Mango 9, banana 6, orange 5: find the total.
  3. 6In the same data, which fruit is most liked and which is least liked?
Challenging
  1. 7Use scale 1 symbol = 2 children. How many symbols for mango, banana and orange?
  2. 8Rita says 4 lines and a line beside them is 5. What should she do?
Show answers (try them yourself first)
  1. 113
  2. 27
  3. 320
  4. 41 group of 5 and 4 lines
  5. 520
  6. 6Mango (9) most, orange (5) least.
  7. 74 and a half, 3, 2 and a half
  8. 8Draw the fifth line across the four to make a group.

Comparing and interpreting data

From daily life

A shopkeeper compares notebooks sold in four days. Looking at the pictograph, he sees at a glance which day was best and how much sales went up or down.

Simple definition

A pictograph helps us compare, find totals, averages and changes. Average = total ÷ number of items. Change = (symbols difference) × key.

A pictograph of ice-creams sold on four days with totals 18, 30, 24 and 36.Ice-creams sold (1 symbol = 6)Mon18Tue30Wed24Thu36Total 18 symbols × 6 = 108

In the figure : Ice-creams sold on four days: 18, 30, 24 and 36, total 108.

Rule 1: Compare and total — Find each value, compare, then add.

  • Easy : Notebooks: Mon 40, Tue 60, Wed 30, Thu 50. Best day: Tuesday (60).
  • Medium : Total = 40 + 60 + 30 + 50 = 180.
  • Exam-type : Tue − Wed = 60 − 30 = 30 more notebooks.

Rule 2: Average and change — Average = total ÷ number of days. Change = later − earlier.

  • Easy : Average = 180 ÷ 4 = 45 notebooks a day.
  • Medium : Cycles in 4 months: 20, 40, 30, 30 → total 120, average 30.
  • Exam-type : Wheat: 5 symbols in 2018, 8 symbols in 2022, 1 symbol = 30 tonnes. Increase = 3 × 30 = 90 tonnes.
Remember

Always write the unit with the answer: books, kg, tonnes.

Common mistake

Dividing by the number of symbols instead of the number of days for the average.

Shortcut

Memory clue: Compare – add – share (average).

Spot the difference

QuestionMethod
Which is more?compare symbols
Totaladd all
Averagetotal ÷ number of days

Practice questions

Easy
  1. 1Notebooks: Mon 40, Tue 60, Wed 30, Thu 50. Which day is best?
  2. 2Find the total notebooks sold.
  3. 3How many more notebooks on Tuesday than Wednesday?
Medium
  1. 4Find the average notebooks sold per day.
  2. 5Cycles in 4 months: 20, 40, 30, 30. Find the total and the average.
  3. 6Wheat was 5 symbols in 2018 and 8 symbols in 2022. Key: 1 symbol = 30 tonnes. Find the increase.
Challenging
  1. 7Mon 40 and Thu 50: how many more on Thursday and in symbols with key 1 symbol = 10?
  2. 8Anil finds the average of 40, 60, 30, 50 by dividing 180 by 18 symbols. What is the right method?
Show answers (try them yourself first)
  1. 1Tuesday
  2. 2180
  3. 330
  4. 4180 ÷ 4 = 45
  5. 5Total 120, average 30.
  6. 63 × 30 = 90 tonnes
  7. 710 more = 1 symbol.
  8. 8Divide the total by the number of days: 180 ÷ 4 = 45.