Maths · Suggested Grade 3
Pictographs with a Key: Class 3 Examples & Practice
One book picture can stand for four books. Count the pictures first, then use the key—or a neat-looking graph can give you the wrong answer.
Original explanations and practice by BananaLearn · Published 1 November 2026
On a small screen, swipe across the illustration to read every label.
What a pictograph tells you
A pictograph uses repeated pictures to show quantities in categories. A title says what is being counted, category labels identify the groups, and a key says what one whole picture represents. Our fictional library chart records books borrowed on three days. Every whole book symbol stands for 4 borrowed books.
Start with groups of equal size. Three whole symbols mean three groups of four: 3 × 4 = 12. The symbol is a counting unit chosen by the graph-maker; it does not need to represent one real object. Without a key, you cannot know the actual quantity from the number of pictures alone.
Worked chart: translate every row
Monday shows three whole symbols, Tuesday two whole symbols and a half, and Wednesday four whole symbols. With 4 books per whole symbol, Monday represents 12 books. Tuesday represents 2 × 4 + 2 = 10. Wednesday represents 16. The illustration uses a clearly divided half-symbol; its value is half of the key, not automatically one.
Read each category separately before adding. The three-day total is 12 + 10 + 16 = 38 books. These are borrowing counts: the chart does not tell us whether 38 different children borrowed them or whether a child borrowed more than once. Keep the conclusion as narrow as the title and data allow.
Compare quantities and differences
Wednesday has one more whole symbol than Monday, so the difference is 4 books. Monday has half a symbol more than Tuesday, so the difference is 2 books. You may compare symbol differences first and convert with the key, or convert both values and subtract. Both methods should agree.
The question How many more? asks for subtraction. The question How many altogether? asks for a sum. A common error is answering 1 when asked how many more books Wednesday has than Monday. One is the difference in symbols; the requested unit is books.
Half-symbols and suitable keys
A half-symbol stands for half the full key. If one full symbol means 6 trees, half means 3 trees. If one symbol means 10 votes, half means 5 votes. The picture’s visible size must be explained by the key; a small decorative icon is not automatically half a symbol.
When drawing a graph, choose a key that represents the actual counts clearly. Counts of 12, 10 and 16 work with a key of 4 and half-symbols. A count of 11 would require a quarter-symbol under that key, so a key of 2 with half-symbols may be easier. Never round a real count silently just to make the picture tidy.
Find a missing category
Suppose a fictional four-day total is 50 books, and the first three days total 38. Thursday must represent 50 − 38 = 12 books. Divide by the key: 12 ÷ 4 = 3 whole symbols. Check by adding back: 38 + 12 = 50.
Distinguish a missing row value from a missing key. If three symbols represent 18 books, each symbol means 18 ÷ 3 = 6 books. The division now finds the size of one group. Write the key explicitly before answering later questions; otherwise you may reuse the earlier key of 4 by mistake.
Build your own graph accurately
Use invented counts or a small non-sensitive classroom category such as blocks of three colours. Write the title, labels and key before drawing symbols in aligned rows. Use equal-sized symbols and equal spacing. Start each row at the same position so the representation does not exaggerate a difference.
Have a partner translate your drawing back into numbers. If their numbers differ from yours, check the key and partial symbols together. The goal is a graph someone else can decode, not an attractive set of icons. For a large number of categories or awkward counts, a bar graph may communicate more clearly.
Explain what the graph cannot establish
A chart of borrowed books does not prove which day students enjoy reading most. Perhaps one class visited only on Wednesday. A picture graph describes the recorded quantities; explaining why the quantities differ needs extra information. Separate what is shown from what might be a possible reason.
For home practice, change the key from 4 to 2 while keeping the actual counts 12, 10 and 16. The rows now need 6, 5 and 8 symbols. Quantities stay the same while the representation changes. That is a stronger understanding check than recalling the total 38.
Decode and check the library chart
Copy the record into a notebook or use it to organise your own answer. Blank spaces are for your work.
| Day | Symbols (key: 4 books) | Books | Your calculation |
|---|---|---|---|
| Monday | 3 whole | 12 | ___ |
| Tuesday | 2 whole + 1 half | 10 | ___ |
| Wednesday | 4 whole | 16 | ___ |
| Total | All three days | 38 | ___ |
12 questions with explained answers
Try the questions before opening the answers. Explain the reason, then try a changed example to check your understanding.
Three symbols, key 4 books: how many books?
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12 books
3 × 4 = 12.Two and a half symbols, key 4: how many?
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10
2 × 4 + 2 = 10.Half a symbol, key 6 trees: how many trees?
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3
Half of 6 is 3.Monday 12 and Wednesday 16: how many more on Wednesday?
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4 books
16 − 12 = 4.Find the three-day total 12, 10 and 16.
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38 books
Add all three categories.Total 50, known categories total 38: missing count?
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12
50 − 38 = 12.How many whole symbols show 12 with key 4?
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3
12 ÷ 4 = 3.Three symbols show 18 objects. What is the key?
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6 objects per symbol
18 ÷ 3 = 6.With key 2, how many symbols show 10 objects?
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5
10 ÷ 2 = 5.With key 10, what does half a symbol show?
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5
Half of the key is 5.Can 38 borrowing events prove there were 38 distinct borrowers?
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No
The chart counts borrowed books, not unique people.A row has 11 objects. Can key 4 use only whole or half symbols exactly?
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No
Whole and half symbols represent multiples of 2; 11 would need another representation.
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The examples, diagrams and practice are original BananaLearn work. Grade labels suggest a learning level; teaching sequences and school requirements can differ. Official sources below support the stated facts and resource links. These activities are independent resources, not official exam questions or endorsed campaign materials.
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