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Math · Data Management

Pictographs and Tally Charts: Read the Key, Count Whole and Half Symbols

Read a pictograph key, count whole and half symbols, use tally bundles of five, and compare data. Includes 30 practice questions with explanations.

Grades 3–5 · 29 practice questions · Original material
Learning objectiveRead the key of a pictograph, find values from whole and half symbols, read tally charts in bundles of five, and compare and total data using the key.

The idea

A pictograph uses symbols to show data. The key tells how much each symbol is worth, so counting symbols is only the first step. In this lesson all data are invented examples.

If ● = 5 books and Monday shows 4 symbols, Monday means 4 × 5 = 20 books. If the key changed to ● = 10 books, the same four symbols would mean 40 books. Always read the key before you read the graph.

A half symbol (◐) is worth half of a whole symbol. If ● = 10, then ◐ = 5, so ●●●◐ means 30 + 5 = 35.

A tally chart records each vote as a mark and groups the marks in bundles of five. Count the bundles by fives, then add the single marks: 2 bundles and 3 marks is 10 + 3 = 13.

To compare rows, find the difference in symbols and then multiply by the key. To find the total, add all the symbols (with halves) and multiply once by the key.

Worked examples

Reading a pictograph and a tally chartLeft: a pictograph of invented library books borrowed. The key says one whole circle is 10 books and a half circle is 5 books. Monday has 3 whole circles, 30 books. Tuesday has 2 whole circles and a half circle, 25 books. Wednesday has 4 whole circles, 40 books. Right: a tally chart where each bundle of 5 marks is counted by fives. Two bundles and 3 single marks make 13.Read the key, then countOriginal schematic with invented data.1 · Pictograph: books borrowedMonday= 30Tuesday= 25Wednesday= 40Key:= 10 books= 5 books2 · Tally chart: count by fives510+35 + 5 + 3= 13 votes
Original schematic with invented data. Read the key first: a whole circle is 10 books and a half circle is 5, so 2 whole circles and a half is 25. In the tally chart, each bundle of five marks is counted by fives, then the single marks are added (5 + 5 + 3 = 13).

Example 1 · Whole and half symbols

Key: ● = 10 stickers, ◐ = 5 stickers. Wednesday shows ●●●◐. How many stickers is that?

  1. Read the key: ● = 10 and ◐ = 5.
  2. 3 whole symbols: 3 × 10 = 30.
  3. Add the half symbol: 30 + 5 = 35.

35 stickers

Example 2 · Compare with the key

Key: ● = 6 students. Soccer shows 7 symbols and Swimming shows 4 symbols. How many more chose soccer?

  1. Find the difference in symbols: 7 − 4 = 3.
  2. Multiply by the key: 3 × 6 = 18.
  3. Check: 7 × 6 = 42 and 4 × 6 = 24, and 42 − 24 = 18.

18 more students

Example 3 · Tally chart total

A tally chart shows 3 bundles of five and 2 single marks. How many?

  1. Count the bundles by fives: 3 × 5 = 15.
  2. Add the single marks: 15 + 2 = 17.

17

Example 4 · Choose a key

Totals are 15, 30, 45 and 25. Which key gives only whole symbols?

  1. Test 5: 15 ÷ 5 = 3, 30 ÷ 5 = 6, 45 ÷ 5 = 9, 25 ÷ 5 = 5.
  2. All are whole numbers, so ● = 5 works. A key of 10 would need half symbols.

● = 5

Common mistakes

These are tempting because they use familiar operations. Check what the question is actually measuring.

Counting symbols and ignoring the key (4 symbols with ● = 5 is called 4).

Why this fails: Each symbol is worth the key amount, so 4 symbols are 4 × 5 = 20.

Treating a half symbol as a whole one, or leaving it out.

Why this fails: A half symbol is worth half the key. With ● = 10, ◐ is 5, not 10 and not 0.

Comparing two graphs by symbol count when their keys differ.

Why this fails: Six symbols with ● = 2 is 12, but four symbols with ● = 5 is 20. Multiply by each key first.

Reading each tally bundle as 1, or as 10.

Why this fails: A bundle of five marks is 5. Count by fives, then add the single marks.

Changing the key but keeping the old answers.

Why this fails: Changing the key changes every row. The same symbols mean different amounts.

Foundation

Foundation practice

Read the key, count half symbols and tally marks.

Read the key

1. A pictograph of books read uses ● = 5 books. Monday shows ●●●●. How many books were read on Monday?

  1. 4
  2. 9
  3. 20
  4. 25
Read the key

2. A pictograph of pencils sharpened uses ● = 2 pencils. Tuesday shows ●●●●●. How many pencils were sharpened on Tuesday?

  1. 10
  2. 5
  3. 7
  4. 12
Half symbols

3. In a pictograph, ● = 10 stickers and ◐ = 5 stickers. Wednesday shows ●●●◐. How many stickers is that?

  1. 4
  2. 30
  3. 40
  4. 35
Read the key

4. A pictograph of pizzas sold uses ● = 4 pizzas. Friday shows ●●●●●●. How many pizzas were sold on Friday?

  1. 6
  2. 24
  3. 10
  4. 20
Tally marks

5. A tally chart shows 2 full bundles of five and 3 single marks for the number of birds seen. How many birds were seen?

  1. 5
  2. 10
  3. 23
  4. 13
Tally marks

6. A tally chart shows 4 full bundles of five and 1 single mark for the number of cars that passed. How many cars passed?

  1. 5
  2. 25
  3. 21
  4. 41
Draw it

7. In a pictograph, ● = 10 books and ◐ = 5 books. Which drawing shows 45 books?

  1. 4 whole symbols
  2. 4 whole symbols and 1 half symbol
  3. 5 whole symbols
  4. 4 whole symbols and 5 half symbols

Practice

Practice practice

Compare rows, find totals and use half symbols.

Compare

8. Students chose a sport. Key: ● = 6 students. Soccer ●●●●●●●, Hockey ●●●●●, Swimming ●●●●. How many more students chose soccer than swimming?

  1. 18
  2. 3
  3. 12
  4. 42
Total

9. Use the same sport graph (● = 6 students): Soccer ●●●●●●●, Hockey ●●●●●, Swimming ●●●●. How many students are shown in all?

  1. 16
  2. 90
  3. 78
  4. 96
Half symbols

10. Key: ● = 20 visitors and ◐ = 10 visitors. Monday shows ●●●◐ and Tuesday shows ●●●●●. How many more visitors came on Tuesday?

  1. 2
  2. 15
  3. 30
  4. 100
Find the key

11. Monday shows 6 symbols and means 30 books. What number must each symbol stand for?

  1. 6
  2. 5
  3. 10
  4. 30
Draw it

12. A school sold 90 raffle tickets one day. If ● = 10 tickets, how many symbols are needed?

  1. 10
  2. 80
  3. 900
  4. 9
Tally total

13. A tally chart shows favourite colours (invented data): Red 12, Blue 9, Green 15, Yellow 7. How many students voted in all?

  1. 43
  2. 34
  3. 41
  4. 45
Tally compare

14. Use the same colour tally chart: Red 12, Blue 9, Green 15, Yellow 7. How many more students chose green than yellow?

  1. 7
  2. 9
  3. 8
  4. 22
Two days

15. Key: ● = 20 cars and ◐ = 10 cars. Thursday shows ●●●●●◐ and Friday shows ●●●. How many cars are shown for the two days?

  1. 9
  2. 170
  3. 160
  4. 180

Think it through

Think it through practice

Change the key, compare graphs and find missing symbols.

Change the key

16. Mia drew 4 symbols for Monday with ● = 5 books. Then she changed the key to ● = 10 books but left the 4 symbols. How many books does Monday show now?

  1. 20
  2. 14
  3. 4
  4. 40
Two keys

17. Graph A uses ● = 2 and shows 6 symbols for Class A. Graph B uses ● = 5 and shows 4 symbols for Class B. Which class has more, and how many?

  1. Class A, with 6
  2. Class A, with 12
  3. Class B, with 20
  4. Class B, with 4
Missing symbols

18. Key: ● = 5 points. Three days total 60 points. Monday shows 5 symbols and Tuesday shows 3 symbols. How many symbols does Wednesday need?

  1. 4
  2. 8
  3. 12
  4. 13
Find the key

19. Friday shows ●●●◐ (3 whole symbols and 1 half symbol) and means 35 students. What does one whole symbol stand for?

  1. 3
  2. 10
  3. 5
  4. 35
Tally marks

20. Which tally shows 17?

  1. 3 bundles of five and 7 single marks
  2. 1 bundle of five and 7 single marks
  3. 17 bundles of five
  4. 3 bundles of five and 2 single marks
Choose the statement

21. Key: ● = 6 students. Hockey shows ●●●●● and Swimming shows ●●●●. Which statement is supported?

  1. Hockey had 1 more student than swimming.
  2. Hockey had 5 students.
  3. Hockey had 6 more students than swimming.
  4. Swimming had 4 more students than hockey.
Best key

22. Class totals are 15, 30, 45 and 25. Which key lets you draw every total with whole symbols only?

  1. 2
  2. 5
  3. 10
  4. 20

Challenge

Challenge practice

Multi-step problems that combine keys, totals and means.

Multi-step

23. Key: ● = 8 stickers, ◐ = 4 stickers. Ana ●●●●●●, Ben ●●●●, Cy ●●●◐, Dee ●●●●●. How many stickers in all?

  1. 148
  2. 18
  3. 37
  4. 144
Share equally

24. Key: ● = 8 stickers. Ana has 6 symbols and Ben has 4 symbols. How many stickers should Ana give Ben so they have the same number?

  1. 2
  2. 5
  3. 16
  4. 8
Draw it

25. A tally chart shows Tuesday had 9 visitors. Key: ● = 2 visitors, ◐ = 1 visitor. Which drawing shows Tuesday?

  1. 9 whole symbols
  2. 5 whole symbols
  3. 4 whole symbols and 1 half symbol
  4. 4 whole symbols
Missing symbols

26. Key: ● = 10 people. The total for three days is 130. Monday shows 3 symbols and Tuesday shows 6 symbols. How many symbols should Wednesday show?

  1. 4.5
  2. 4
  3. 9
  4. 13
Mean

27. Key: ● = 4 books. Five days show 3, 5, 2, 4, 6 symbols. What is the mean number of books per day?

  1. 4
  2. 20
  3. 80
  4. 16
Half symbols

28. Key: ● = 100 people and ◐ = 50 people. Saturday shows ●●●●◐ and Sunday shows ●●●. How many more people came on Saturday?

  1. 150
  2. 1
  3. 15
  4. 750
Best key

29. A pictograph will show 400, 600, 800 and 1 000 visitors. Which key is most sensible?

  1. ● = 1 visitor
  2. ● = 10 visitors
  3. ● = 200 visitors
  4. ● = 1 000 visitors

Answer key

  1. 1. 20
    Each symbol stands for 5 books, so multiply: 4 × 5 = 20. Counting the symbols gives only 4, which ignores the key; adding 5 to 4 gives 9, which does not use the key either; and 25 uses one symbol too many.
  2. 2. 10
    5 symbols × 2 pencils each = 10 pencils. The number 5 only counts symbols, 7 adds instead of multiplying, and 12 uses one extra symbol.
  3. 3. 35
    3 whole symbols are 3 × 10 = 30, and the half symbol adds 5, so 35. The number 4 counts symbols, 30 forgets the half symbol, and 40 treats the half symbol as a whole one.
  4. 4. 24
    6 symbols × 4 pizzas = 24 pizzas. Six counts symbols, 10 adds 6 + 4, and 20 is 5 symbols instead of 6.
  5. 5. 13
    Each bundle is 5, so 2 × 5 = 10, and 3 more marks make 13. The number 5 adds 2 + 3, 10 forgets the single marks, and 23 reads the bundles as tens.
  6. 6. 21
    4 bundles × 5 = 20, plus 1 single mark makes 21. Five adds 4 + 1, 25 treats the single mark as another bundle, and 41 reads the bundles as tens.
  7. 7. 4 whole symbols and 1 half symbol
    45 = 4 × 10 + 5, so draw 4 whole symbols and 1 half symbol. Four whole symbols is 40, five whole symbols is 50, and 4 whole plus 5 half symbols is 40 + 25 = 65.
  8. 8. 18
    The difference is 7 − 4 = 3 symbols, and 3 × 6 = 18 students. The number 3 is only the symbol difference; 12 uses 2 symbols; 42 is the total number of soccer students, not the difference.
  9. 9. 96
    Total symbols: 7 + 5 + 4 = 16, and 16 × 6 = 96 students. The number 16 forgets the key, 90 uses 15 symbols, and 78 uses 13 symbols.
  10. 10. 30
    Monday is 3 × 20 + 10 = 70 and Tuesday is 5 × 20 = 100, so the difference is 30. Two is a symbol count of 5 − 3, which ignores the half symbol and the key; 15 treats half a symbol as 15; 100 is just Tuesday.
  11. 11. 5
    Each symbol stands for 30 ÷ 6 = 5 books. Six is the number of symbols, 10 would give 60 books, and 30 would give 180.
  12. 12. 9
    90 ÷ 10 = 9 symbols. Ten is the key itself, 80 subtracts instead of dividing, and 900 multiplies instead of dividing.
  13. 13. 43
    Add all four tallies: 12 + 9 + 15 + 7 = 43. The number 34 leaves out a colour group, and 41 and 45 are addition slips.
  14. 14. 8
    15 − 7 = 8. Seven is the yellow tally, nine is the blue tally, and 22 adds green and yellow instead of finding the difference.
  15. 15. 170
    Thursday is 5 × 20 + 10 = 110 and Friday is 3 × 20 = 60, so together 170. The number 9 counts only symbols, 160 forgets the half symbol, and 180 counts the half symbol as a whole symbol.
  16. 16. 40
    With the new key, 4 symbols × 10 books = 40 books. The old answer, 20, is for the old key. Fourteen adds the symbols and the key, and 4 counts only symbols. Changing a key changes every row.
  17. 17. Class B, with 20
    Class A has 6 × 2 = 12 and Class B has 4 × 5 = 20, so Class B has more even with fewer symbols. Choosing by symbol count ignores the keys.
  18. 18. 4
    60 ÷ 5 = 12 symbols in all. Monday and Tuesday use 5 + 3 = 8, so Wednesday needs 12 − 8 = 4. Eight is what Monday and Tuesday already use, 12 is the total, and 13 adds instead of subtracting.
  19. 19. 10
    The picture is 3.5 symbols, so one symbol is 35 ÷ 3.5 = 10 students, and half a symbol is 5. A key of 5 would give 17.5, and 35 would give 122.5.
  20. 20. 3 bundles of five and 2 single marks
    3 × 5 + 2 = 17. Three bundles and 7 marks make 22, one bundle and 7 marks make 12, and 17 bundles make 85.
  21. 21. Hockey had 6 more students than swimming.
    One extra symbol is worth 6 students. Saying 1 more, or 5 students, uses symbol counts without the key, and swimming has fewer symbols, not more.
  22. 22. 5
    All four numbers are multiples of 5, so a key of 5 gives 3, 6, 9 and 5 whole symbols. A key of 2 does not divide 15 evenly, 10 would need half symbols (1.5, 4.5 and 2.5), and 20 is larger than 15.
  23. 23. 148
    Symbols: 6 + 4 + 3.5 + 5 = 18.5, and 18.5 × 8 = 148 (the half symbol is 4). Eighteen forgets the key, 37 doubles the symbols, and 144 counts the half symbol as nothing.
  24. 24. 8
    Ana has 48 and Ben has 32, so each should have 40. Ana gives 8. Two is the symbol difference, 5 is half of that symbol difference misread, and 16 is the whole difference rather than half of it.
  25. 25. 4 whole symbols and 1 half symbol
    9 = 4 × 2 + 1, so draw 4 whole symbols and 1 half symbol. Nine whole symbols would be 18, five would be 10, and four would be 8.
  26. 26. 4
    130 ÷ 10 = 13 symbols in all, and 13 − 3 − 6 = 4. Thirteen is the total, and 9 is what Monday and Tuesday already use. The value 4.5 does not come from any correct step.
  27. 27. 16
    Total symbols = 20, so total books = 20 × 4 = 80, and the mean is 80 ÷ 5 = 16. Four is the mean number of symbols, 80 is the total, and 20 is the total symbol count.
  28. 28. 150
    Saturday is 450 and Sunday is 300, so Saturday had 150 more. One ignores the half symbol and the key, 15 is a misplaced digit, and 750 is the total.
  29. 29. ● = 200 visitors
    A key of 200 gives 2, 3, 4 and 5 symbols, which are easy to read. A key of 1 or 10 needs hundreds or dozens of symbols, and a key of 1 000 gives less than one symbol for most rows.

Related practice

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