Solved Exercises on Picture Graphs in Grade 3

Master picture graphs: creating, reading, and interpreting picture graphs through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Creating a Picture Graph
Exercise 1
The 3rd grade class voted for their favorite fruit. The results were: Apples = 12, Bananas = 8, Oranges = 6, Grapes = 10. Create a picture graph where each 🍎 symbol represents 2 fruits.
Definition:

Picture graph (pictograph): A graph that uses pictures or symbols to show data.

Symbol key: Tells how many each picture represents.

Picture graph creation method:
  1. Decide what symbol to use and what it represents
  2. Calculate how many symbols are needed for each category
  3. Draw the symbols for each category
  4. Include a key that explains the symbol meaning
Key:
🍎 = 2 fruits
Apples
🍎🍎🍎🍎🍎🍎
Bananas
🍌🍌🍌🍌
Oranges
🍊🍊🍊
Grapes
🍇🍇🍇🍇🍇
Step 1: Determine symbol value

Each 🍎 represents 2 fruits

Step 2: Calculate symbols needed

Apples: 12 ÷ 2 = 6 symbols

Bananas: 8 ÷ 2 = 4 symbols

Oranges: 6 ÷ 2 = 3 symbols

Grapes: 10 ÷ 2 = 5 symbols

Step 3: Draw the symbols

Place calculated number of symbols for each category

Final answer:

Apples are the most popular (12 fruits)

Oranges are the least popular (6 fruits)

Applied rules:

• Division for symbols: Total ÷ Symbol value = Number of symbols

• Consistent key: Same symbol value for all categories

• Clear key: Always include explanation of symbol meaning

2 Reading a Picture Graph
Exercise 2
Look at this picture graph: Each 🐶 represents 3 dogs. Dogs: 🐶🐶🐶, Cats: 🐱🐱🐱, Birds: 🐦🐦, Fish: 🐠. How many of each animal are there? Which animal is most common?
Definition:

Reading picture graphs: Counting symbols and using the key to find actual values.

Symbol multiplication: Number of symbols × Symbol value = Actual value.

Key:
🐶 = 3 dogs, 🐱 = 3 cats, 🐦 = 3 birds, 🐠 = 3 fish
Dogs
🐶🐶🐶
Cats
🐱🐱🐱
Birds
🐦🐦
Fish
🐠
Dogs:
3 symbols × 3 = 9 dogs
Cats:
3 symbols × 3 = 9 cats
Birds:
2 symbols × 3 = 6 birds
Fish:
1 symbol × 3 = 3 fish
Step 1: Count symbols in each row

Dogs: 3 symbols, Cats: 3 symbols, Birds: 2 symbols, Fish: 1 symbol

Step 2: Apply the key

Each symbol represents 3 animals

Step 3: Calculate actual values

Dogs: 3 × 3 = 9, Cats: 3 × 3 = 9, Birds: 2 × 3 = 6, Fish: 1 × 3 = 3

Final answer:

Dogs: 9, Cats: 9, Birds: 6, Fish: 3

Dogs and Cats are tied as most common (9 each)

Applied rules:

• Symbol counting: Carefully count each symbol in every row

• Multiplication by key: Multiply symbols by their value

• Comparison: Compare final calculated values

3 Interpreting Picture Graph Data
Exercise 3
A picture graph shows books read by students. Each 📚 represents 4 books. Students: Sam = 📚📚📚, Lee = 📚📚, Kim = 📚📚📚📚, Pat = 📚. How many more books did Kim read than Pat? What is the total number of books read by all students?
Definition:

Interpreting picture graphs: Using graph information to answer questions about the data.

Comparative analysis: Finding differences between values.

Key:
📚 = 4 books
Sam
📚📚📚
Lee
📚📚
Kim
📚📚📚📚
Pat
📚
Sam:
3 symbols × 4 = 12 books
Lee:
2 symbols × 4 = 8 books
Kim:
4 symbols × 4 = 16 books
Pat:
1 symbol × 4 = 4 books
Step 1: Calculate each student's books

Sam: 3 × 4 = 12, Lee: 2 × 4 = 8, Kim: 4 × 4 = 16, Pat: 1 × 4 = 4

Step 2: Find difference between Kim and Pat

16 - 4 = 12 more books

Step 3: Calculate total books

12 + 8 + 16 + 4 = 40 books total

Final answer:

Kim read 12 more books than Pat

Total books read by all students: 40

Applied rules:

• Individual calculation: Find value for each category first

• Subtraction for comparison: Larger value - smaller value

• Addition for totals: Sum all individual values

Picture Graph Concepts and Methods
📊 Symbols × Key Value = Actual Value
Picture Graph Formula
🔑
Symbol Key: Tells how many each picture represents
📊
Pictures/Symbols: Visual representations of data
🏷️
Categories: Different groups being compared
Key definitions:

Picture graph (pictograph): A graph that uses pictures or symbols to show data.

Symbol key: A guide that tells how many each picture represents.

Categories: The different groups or items being compared.

Symbol value: The number that each picture stands for (e.g., 1, 2, 5).

Half symbols: Used when data doesn't divide evenly by symbol value.

Picture Graph Creation Process:
  1. Choose symbols: Select appropriate pictures for your data
  2. Set symbol value: Decide what each picture represents
  3. Calculate symbols needed: Divide actual values by symbol value
  4. Draw symbols: Place correct number of symbols for each category
  5. Add key: Include explanation of symbol meaning
Tip 1: Choose symbols that relate to your data (apples for fruit, cars for transportation).
Tip 2: Use simple, clear symbols that are easy to draw and count.
Tip 3: Always include the key so others can understand your graph.
Common errors: Forgetting to use the key, miscalculating symbol numbers, missing half symbols for remainders.
Key points: Consistent symbol values, accurate counting, clear key, relevant symbols.
Important Rules:

• Always include a clear key

• Use the same symbol value for all categories

• Count symbols carefully

• Apply the key when reading values

• Use half symbols for remainders

Solution: Exercises 4 to 5
4 Comparing Categories with Remainders
Exercise 4
A picture graph shows how many pages students read. Each 📖 represents 5 pages. Students: Amy = 📖📖📖, Bob = 📖📖, Cam = 📖📖📖📖, Dan = 📖📖📖. If Dan reads 3 more pages, how many total pages will he have read? How does this compare to Cam?
Definition:

Remainder calculations: When actual values don't divide evenly by symbol value.

Key:
📖 = 5 pages
Amy
📖📖📖
Bob
📖📖
Cam
📖📖📖📖
Dan
📖📖📖
Amy:
3 × 5 = 15 pages
Bob:
2 × 5 = 10 pages
Cam:
4 × 5 = 20 pages
Dan:
3 × 5 = 15 pages
Step 1: Calculate current pages for Dan

3 symbols × 5 pages = 15 pages

Step 2: Add additional pages

15 + 3 = 18 pages total

Step 3: Compare to Cam

Cam: 20 pages, Dan: 18 pages

20 - 18 = 2 more pages

Final answer:

Dan will have read 18 pages in total

Cam read 2 more pages than Dan

Applied rules:

• Sequential addition: Add new values to existing totals

• Direct comparison: Find difference between values

• Symbol accuracy: Maintain consistent symbol values

5 Multi-Step Picture Graph Analysis
Exercise 5
A picture graph shows the number of stickers earned by students. Each 🌟 represents 3 stickers. Students: Mia = 🌟🌟🌟, Nick = 🌟🌟, Olivia = 🌟🌟🌟🌟, Paul = 🌟. If the class goal is 50 stickers, how many more stickers do they need to reach the goal?
Definition:

Multi-step problems: Questions requiring multiple operations to solve.

Key:
🌟 = 3 stickers
Mia
🌟🌟🌟
Nick
🌟🌟
Olivia
🌟🌟🌟🌟
Paul
🌟
Mia:
3 × 3 = 9 stickers
Nick:
2 × 3 = 6 stickers
Olivia:
4 × 3 = 12 stickers
Paul:
1 × 3 = 3 stickers
Step 1: Calculate each student's stickers

Mia: 3 × 3 = 9, Nick: 2 × 3 = 6, Olivia: 4 × 3 = 12, Paul: 1 × 3 = 3

Step 2: Calculate total stickers earned

9 + 6 + 12 + 3 = 30 stickers

Step 3: Find remaining stickers needed

Goal: 50, Earned: 30, Remaining: 50 - 30 = 20 stickers

Final answer:

The class has earned 30 stickers so far

They need 20 more stickers to reach the goal of 50

Applied rules:

• Individual calculation: Find value for each category first

• Summation: Add all individual values to get total

• Goal comparison: Subtract earned from goal to find remainder

Comprehensive Picture Graph Guide: Definitions, Rules, and Methods
📊 Actual Value = Symbols × Key Value
Fundamental Picture Graph Formula
Key definitions:

Picture graph (pictograph): A visual way to show data using pictures or symbols to represent numbers.

Symbol key: A guide that explains what each picture or symbol represents.

Symbol value: The number that each symbol stands for (e.g., each apple might represent 2 fruits).

Categories: The different groups or items being compared in the graph.

Half symbols: Used when data doesn't divide evenly by the symbol value (represents half of the symbol value).

Remainder calculation: When actual values don't divide evenly by symbol value.

Complete Picture Graph Creation Methodology:
  1. Choose appropriate symbols: Select pictures that relate to your data
  2. Determine symbol value: Decide how many each symbol will represent
  3. Calculate symbols needed: Divide actual data values by symbol value
  4. Draw symbols: Place correct number of symbols for each category
  5. Handle remainders: Use half symbols when needed
  6. Create key: Include clear explanation of symbol meaning
  7. Label categories: Name each group being compared
Tip 1: Choose symbol values that divide evenly into most of your data numbers.
Tip 2: Use simple, recognizable symbols that are easy to draw and count.
Tip 3: Always double-check your calculations to ensure accuracy.
Tip 4: Include the key prominently so others can read your graph correctly.
Common errors: Forgetting to apply the key, miscalculating symbol numbers, missing half symbols, inconsistent symbol values.
Exam preparation: Practice converting between symbols and actual values, work on multi-step problems, focus on remainder calculations.
Essential Rules and Laws:

• Key consistency: Use the same symbol value for all categories

• Symbol multiplication: Actual value = Symbols × Symbol value

• Remainder handling: Use half symbols when division doesn't result in whole numbers

• Clear labeling: Include key and category names

• Accurate counting: Count symbols carefully and verify calculations

1
Select symbols: Choose appropriate pictures for your data
2
Set value: Decide what each symbol represents
3
Calculate: Determine number of symbols needed for each category
4
Draw: Place correct number of symbols for each category
5
Include key: Add explanation of symbol meaning

Questions & Answers

Question: I made a picture graph where each 🍎 represents 3 apples. If someone has 7 apples, how many symbols should I draw?

Answer: Great question! Let's break it down:

  • Divide the actual number by the symbol value: 7 ÷ 3 = 2 with remainder 1
  • Draw 2 full symbols (representing 6 apples)
  • Draw 1/2 symbol to represent the remaining 1 apple

So you would draw: 🍎🍎 + ½ 🍎

The half symbol represents half of the symbol value (3 ÷ 2 = 1.5, rounded to 1 in this context).

Question: My child is confused about reading picture graphs. How can I help them understand that symbols represent multiple items?

Answer: Use hands-on activities to demonstrate the concept:

  • Physical objects: Use actual items to show groups (3 real apples = 1 drawn apple)
  • Counting practice: Have them count symbols, then multiply by the key value
  • Visual aids: Circle each symbol and write the value next to it
  • Repetition: Practice with different symbol values to build fluency

Start with simple examples (1 symbol = 2 items) and gradually increase complexity.

Question: Why do we sometimes use half symbols in picture graphs? Can't we just use regular symbols?

Answer: Half symbols help us show exact values when our symbol value doesn't divide evenly into the actual number:

  • If each symbol represents 4 items and someone has 10 items
  • 10 ÷ 4 = 2 with remainder 2
  • 2 full symbols represent 8 items
  • Half a symbol represents the remaining 2 items (half of 4)

This makes the graph accurate and shows the exact amount. Without half symbols, we couldn't represent numbers like 10 when each symbol equals 4!