Solved Exercises on Picture Graphs in Grade 2

Master picture graphs: counting symbols, interpreting data, comparing quantities, solving word problems, and creating graphs through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Reading a Picture Graph
Exercise 1
The picture graph shows how many books were read by students in different months:
January:
πŸ“šπŸ“šπŸ“šπŸ“š 4 books
February:
πŸ“šπŸ“šπŸ“šπŸ“šπŸ“š 5 books
March:
πŸ“šπŸ“šπŸ“š 3 books
Question: How many more books were read in February than in March?
Definition:

Picture Graph: A graph that uses pictures or symbols to represent data. Each symbol represents a specific number of items.

Reading Method:
  1. Count the number of symbols in each category
  2. Understand what each symbol represents (the key)
  3. Calculate the total value for each category
  4. Compare or perform operations as needed
Step 1
Count symbols
Step 2
Calculate
Step 3
Find difference
Step 1: Count symbols in each month

January: 4 symbols β†’ 4 books

February: 5 symbols β†’ 5 books

March: 3 symbols β†’ 3 books

Step 2: Identify what each symbol represents

Each πŸ“š symbol represents 1 book

Step 3: Find the difference between February and March

February - March = 5 - 3 = 2

February had 2 more books than March
Final answer:

February had 2 more books than March

Applied rules:

β€’ Symbol Counting: Count each symbol in the category

β€’ Value Calculation: Multiply symbol count by value per symbol

β€’ Comparison: Subtract to find the difference

2 Interpreting Symbol Values
Exercise 2
The picture graph shows favorite fruits. Each 🍎 symbol represents 2 fruits.
Apples:
🍎🍎🍎 6 apples
Bananas:
🍎🍎🍎🍎 8 bananas
Oranges:
🍎🍎 4 oranges
Question: How many fruits were chosen in total?
Definition:

Symbol Value: In some picture graphs, one symbol represents multiple items (e.g., 1 symbol = 2 items).

Expression
Total = 6+8+4
Sum
18 fruits
Step 1: Understand the symbol value

Each 🍎 symbol = 2 fruits

Step 2: Count symbols and calculate actual numbers

Apples: 3 symbols Γ— 2 = 6 apples

Bananas: 4 symbols Γ— 2 = 8 bananas

Oranges: 2 symbols Γ— 2 = 4 oranges

Step 3: Add all quantities together

Total = 6 + 8 + 4 = 18 fruits

Total: 18 fruits were chosen
Final answer:

18 fruits were chosen in total

Applied rules:

β€’ Symbol Value: Always check the key to see what each symbol represents

β€’ Multiplication: Number of symbols Γ— value per symbol = actual quantity

β€’ Addition: Sum all categories for total count

3 Comparing Categories
Exercise 3
Pets owned by students:
Dogs:
🐢🐢🐢🐢🐢🐢 6 dogs
Cats:
🐢🐢🐢 3 cats
Birds:
🐢🐢🐢🐢🐢 5 birds
Question: Which pet is most popular and by how many more than the least popular?
Definition:

Comparison: Finding differences between categories in a picture graph.

Most Popular
6 dogs
Least Popular
3 cats
Difference
6-3=3
Step 1: Count symbols in each category

Dogs: 6 symbols β†’ 6 dogs

Cats: 3 symbols β†’ 3 cats

Birds: 5 symbols β†’ 5 birds

Step 2: Identify most and least popular

Most popular: Dogs (6)

Least popular: Cats (3)

Step 3: Calculate the difference

Difference = 6 - 3 = 3

Dogs are most popular, 3 more than cats
Final answer:

Dogs are most popular, with 3 more than cats

Applied rules:

β€’ Ordering: Arrange categories from highest to lowest count

β€’ Subtraction: Find difference between categories

β€’ Comparison: Use greater than/less than relationships

Picture Graph Rules and Methods
Total = Ξ£(Symbols Γ— Value per Symbol)
Picture Graph Formula
Key
1 symbol = ? items
Symbol Value
Count
Actual Quantity
Number of Items
Compare
More/Less
Category Comparison
Key definitions:

Picture Graph: Uses pictures or symbols to represent data visually

Symbol: Each picture represents a specific number of items

Key: Explains what each symbol represents

Reading Picture Graphs:
  1. Read the title: Understand what data is shown
  2. Check the key: See what each symbol represents
  3. Count symbols: Count how many symbols are in each category
  4. Calculate values: Multiply symbol count by value per symbol
  5. Compare data: Answer questions about the data
Tip 1: Always check the key to see what each symbol represents.
Tip 2: Count symbols carefully and double-check your counts.
Tip 3: When symbols are cut in half, they usually represent half the value.
Tip 4: Look for the most and least symbols to find highest and lowest values.
Common errors: Misreading the key, miscounting symbols, forgetting to multiply by symbol value.
Key notes: Symbols make data easier to understand at a glance compared to numbers.
Essential Rules:

β€’ Each symbol represents a specific number of items (check the key)

β€’ Count symbols carefully in each category

β€’ Multiply symbol count by value per symbol to get actual quantity

β€’ Compare categories by subtracting to find differences

β€’ Add all categories to find totals

Solution: Exercises 4 to 5
4 Solving Word Problems
Exercise 4
At the zoo, children saw different animals. Each 🦁 symbol represents 3 animals:
Lions:
🦁🦁🦁 9 lions
Elephants:
🦁🦁 6 elephants
Monkeys:
🦁🦁🦁🦁 12 monkeys
Question: If the zoo has twice as many giraffes as elephants, how many giraffe symbols would be needed?
Definition:

Word Problem: A problem that combines picture graph reading with arithmetic operations.

Elephants
6 animals
Giraffes
2Γ—6=12
Symbols
12Γ·3=4
Step 1: Find the number of elephants

Elephants: 2 symbols Γ— 3 = 6 elephants

Step 2: Calculate the number of giraffes

Giraffes = 2 Γ— elephants = 2 Γ— 6 = 12 giraffes

Step 3: Determine how many symbols are needed

Each symbol = 3 animals, so symbols needed = 12 Γ· 3 = 4 symbols

4 giraffe symbols would be needed
Final answer:

4 giraffe symbols would be needed

Applied rules:

β€’ Reading: Interpret the picture graph correctly

β€’ Multiplication: Apply "twice as many" relationship

β€’ Division: Convert total back to symbols using value per symbol

5 Creating a Picture Graph
Exercise 5
Create a picture graph showing ice cream flavors chosen by 15 students:
6 chose chocolate, 4 chose vanilla, 3 chose strawberry, 2 chose mint
Use 🍨 for symbols where 1 symbol = 1 person
Definition:

Creating a Graph: Drawing symbols to represent given data values.

Chocolate
6 symbols
Vanilla
4 symbols
Strawberry
3 symbols
Mint
2 symbols
Step 1: Plan the graph structure

Title: "Favorite Ice Cream Flavors"
Key: 1 🍨 = 1 student

Step 2: Draw symbols for each flavor

Chocolate: 🍨🍨🍨🍨🍨🍨 (6 symbols)

Vanilla: 🍨🍨🍨🍨 (4 symbols)

Strawberry: 🍨🍨🍨 (3 symbols)

Mint: 🍨🍨 (2 symbols)

Step 3: Organize and label

Place each flavor with its corresponding symbols

🍨🍨🍨🍨🍨🍨 Chocolate (6)
πŸ¨ε†°ζ·‡ζ·‹πŸ¨ Vanilla (4)
πŸ¨ε†°ζ·‡ζ·‹ Strawberry (3)
🍨🍨 Mint (2)
Final answer:

Complete picture graph with 6 chocolate, 4 vanilla, 3 strawberry, 2 mint symbols

Applied rules:

β€’ Planning: Decide on symbol and value per symbol

β€’ Accuracy: Draw exact number of symbols for each category

β€’ Organization: Clearly label each category

Picture Graph Laws, Methods, Rules, and Definitions
Actual Value = Symbol Count Γ— Value per Symbol
Picture Graph Formula
Key definitions:

Picture Graph: A visual representation of data using pictures or symbols

Symbol: A picture that represents a specific number of items

Key: Explanation of what each symbol represents

Category: Different groups being compared in the graph

Complete methodology:
  1. Analyze the graph: Read the title and understand what data is shown
  2. Check the key: See what each symbol represents
  3. Count symbols: Carefully count symbols in each category
  4. Calculate values: Multiply symbol count by value per symbol
  5. Answer questions: Use calculated values to solve problems
Tip 1: Always start by reading the key to understand symbol value.
Tip 2: Draw lines or marks to keep track when counting symbols.
Tip 3: Check that your answer makes sense in the context of the problem.
Tip 4: When creating graphs, organize symbols in neat rows.
Common errors: Misreading the key, miscounting symbols, forgetting to multiply by symbol value.
Exam preparation: Practice reading various picture graphs and creating your own.
Formulas to know by heart:

β€’ Actual Value = Symbol Count Γ— Value per Symbol

β€’ Total = Sum of all category values

β€’ Difference = Larger value - Smaller value

β€’ Most Popular = Category with highest symbol count

β€’ Least Popular = Category with lowest symbol count

Questions & Answers

Question: I don't understand why sometimes one picture equals more than one thing. Why doesn't each picture just equal one thing?

Answer: Great question! When we have large numbers to show, drawing hundreds of individual pictures would make the graph too big and hard to read. For example, if a store sold 100 apples, drawing 100 apple pictures would take up too much space. Instead, we might use 1 picture to represent 10 apples, so we'd only need 10 pictures. This makes the graph smaller and easier to understand while still showing the correct amount of data.

Think of it like this: if 1 car symbol = 5 cars, then 3 car symbols = 15 cars. The symbol is like a shortcut that helps us show more information in less space!

Question: How do I know if I counted the symbols correctly? Sometimes I lose track when there are lots of them.

Answer: Here are some helpful strategies for accurate symbol counting:

  • Mark as you count: Put a small dot or checkmark next to each symbol as you count it
  • Count in groups: If symbols are arranged in rows, count each row separately and add them together
  • Count aloud: Say the numbers out loud as you point to each symbol
  • Count twice: Go through the symbols two times to make sure you get the same number both times

For example, if you see 🍎🍎🍎🍎🍎, you can mark each one: πŸŽβœ“πŸŽβœ“πŸŽβœ“πŸŽβœ“πŸŽβœ“ and count: 1, 2, 3, 4, 5. This helps you keep track and not miss any or count any twice!

Question: What do I do when I see a symbol that's cut in half or looks partial? Does it count as a whole symbol?

Answer: Partial symbols represent partial amounts! Usually:

  • A half symbol (like 🍎½) represents half the value of a full symbol
  • If 1 full symbol = 4 items, then 1 half symbol = 2 items
  • A quarter symbol would represent one quarter of the full value

Always check the key of the picture graph because it will tell you what a partial symbol means. For example, if the key says "1 symbol = 2 items" and you see 3 full symbols and 1 half symbol, you would calculate: (3 Γ— 2) + (1 Γ— 1) = 6 + 1 = 7 items total.

The key is your guide - it explains exactly what each symbol and partial symbol represents!