3A · Chapter 7 · Lesson 1
Picture Graphs and Bar Graphs
Read pictograph keys and compare category amounts carefully.
Today's challenge
Read the pictograph below (each symbol represents 2 vehicles). How many vehicles are shown altogether? Try your own method, then compare it with a model.
What you'll learn
- Read pictograph keys and compare category amounts carefully.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Counting and multiplication.
Prerequisite competency: PREREQ-PRIOR-EQUAL-GROUPS
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Draw 2 groups of 3 counters and find the total.
Show answer and reasoning
Answer: 6
2 equal groups with 3 in each group make 2 × 3 = 6. This is prerequisite equal-group reasoning.
- E2
Draw 3 groups of 6 counters and find the total.
Show answer and reasoning
Answer: 18
3 equal groups with 6 in each group make 3 × 6 = 18. This is prerequisite equal-group reasoning.
Learn the concept
Words to know
- pictograph
- a graph that uses repeated symbols
- key
- the number of items represented by a symbol
Read pictograph keys and compare category amounts carefully.
Count symbols for each category, multiply by the key value, and then compare or add amounts. A half-symbol only has meaning if the key allows it.
Why this works
A pictograph uses pictures or symbols to stand for amounts. The key tells you the value of one symbol. If one star represents five books, seven stars represent 7 × 5 = 35 books. Count symbols first, then apply the key; do not confuse the symbol count with the amount represented.
Check the meaning
Read the title, labels, and key before answering any graph question.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
Read the pictograph below (each symbol represents 2 vehicles). How many vehicles are shown altogether?
- Count symbols for each category, multiply by the key value, and then compare or add amounts. A half-symbol only has meaning if the key allows it.
- There are 14 symbols across all categories. The key makes each symbol worth 2, so 14×2=28 vehicles.
- Read the title, labels, and key before answering any graph question.
Result: 28
Understanding check 1 — your turn
Use the pictograph key. How many vehicles does Trains represent?
Reveal reasoning
Answer: 14 — The Trains row has 7 symbols and each means 2 vehicles, giving 7×2=14.
Worked example 2
Reason and verify
Read the pictograph below (each symbol represents 5 vehicles). How many vehicles are shown altogether?
- Count symbols for each category, multiply by the key value, and then compare or add amounts. A half-symbol only has meaning if the key allows it.
- There are 20 symbols across all categories. The key makes each symbol worth 5, so 20×5=100 vehicles.
- Read the title, labels, and key before answering any graph question.
Result: 100
Understanding check 2 — your turn
Use the pictograph key. How many books does Science represent?
Reveal reasoning
Answer: 15 — The Science row has 3 symbols and each means 5 books, giving 3×5=15.
Worked example 3
Reason and verify
Use the pictograph key. What is the difference in vehicles between Buses and Trains?
- Count symbols for each category, multiply by the key value, and then compare or add amounts. A half-symbol only has meaning if the key allows it.
- Buses has 6 symbols, or 6 vehicles; Trains has 2 symbols, or 2 vehicles. Difference 4.
- Read the title, labels, and key before answering any graph question.
Result: 4
Understanding check 3 — your turn
Use the pictograph key. How many books does Science represent?
Reveal reasoning
Answer: 5 — The Science row has 5 symbols and each means 1 books, giving 5×1=5.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Use the pictograph. How many items are represented by Paper and Glass COMBINED?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 7
The two rows contain 3+4 symbols. Multiply by the key 1: 7 items.
- G2
Use the pictograph. How many items are represented by Paper and Glass COMBINED?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 22
The two rows contain 4+7 symbols. Multiply by the key 2: 22 items.
- G3
Use the pictograph. How many items are represented by Paper and Glass COMBINED?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 75
The two rows contain 5+10 symbols. Multiply by the key 5: 75 items.
- G4
Use the pictograph. How many votes are represented by Art and Drama COMBINED?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 12
The two rows contain 6+6 symbols. Multiply by the key 1: 12 votes.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Use the pictograph key. What is the difference in votes between Drama and Art?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 25
Drama has 10 symbols, or 50 votes; Art has 5 symbols, or 25 votes. Difference 25.
- I2
Use the pictograph key. What is the difference in votes between Art and Music?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 4
Art has 6 symbols, or 6 votes; Music has 2 symbols, or 2 votes. Difference 4.
- I3
Use the pictograph key. What is the difference in votes between Drama and Music?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 10
Drama has 9 symbols, or 18 votes; Music has 4 symbols, or 8 votes. Difference 10.
- I4
Use the pictograph key. What is the difference in votes between Art and Drama?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 15
Art has 8 symbols, or 40 votes; Drama has 5 symbols, or 25 votes. Difference 15.
- I5
Use the pictograph key. What is the difference in votes between Music and Art?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 5
Music has 8 symbols, or 8 votes; Art has 3 symbols, or 3 votes. Difference 5.
- I6
Use the pictograph key. What is the difference in fruits between Apples and Pears?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 0
Apples has 4 symbols, or 8 fruits; Pears has 4 symbols, or 8 fruits. Difference 0.
- I7
Use the pictograph key. What is the difference in fruits between Peaches and Apples?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 15
Peaches has 8 symbols, or 40 fruits; Apples has 5 symbols, or 25 fruits. Difference 15.
- I8
Use the pictograph key. What is the difference in fruits between Pears and Peaches?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 4
Pears has 8 symbols, or 8 fruits; Peaches has 4 symbols, or 4 fruits. Difference 4.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A pictograph has a key of 1 star = 5 books. One category has 7 stars. Why does 7 not give the number of books?
Show answer and reasoning
Answer: 35 books
Each star represents 5 books; multiply 7×5=35. Read the key before counting.
- C2
A pictograph shows 6 symbols with key 1 symbol=5 votes. A student reads “6 votes.” What is the corrected count and why?
Show answer and reasoning
Answer: 30 votes
Six symbols represent six equal groups of five; 6×5=30, not six.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Read the pictograph below (each symbol represents 1 fruits). How many fruits are shown altogether?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 14
There are 14 symbols across all categories. The key makes each symbol worth 1, so 14×1=14 fruits.
- E2
Use the pictograph key. What is the difference in fruits between Pears and Apples?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 2
Pears has 5 symbols, or 10 fruits; Apples has 4 symbols, or 8 fruits. Difference 2.
- E3
Use the pictograph key. What is the difference in vehicles between Trains and Buses?
Pictograph: read the key and scale carefully before solving. Show answer and reasoning
Answer: 15
Trains has 8 symbols, or 40 vehicles; Buses has 5 symbols, or 25 vehicles. Difference 15.