📚 Complete Practice Exercises with Solutions
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Exercise 1:
Compare 7 and 4. Which symbol goes between them? 7 ___ 4
Answer: 7 > 4
Explanation: 7 is greater than 4 because 7 comes after 4 when counting. The number 7 is bigger than the number 4. The wide opening of the symbol faces the bigger number (7).
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Exercise 2:
Compare 3 and 8. Which symbol belongs here? 3 ___ 8
Answer: 3 < 8
Explanation: 3 is less than 8 because 3 comes before 8 when counting. The number 3 is smaller than the number 8. The narrow point of the symbol points to the smaller number (3).
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Exercise 3:
What happens when we compare 5 and 5? 5 ___ 5
Answer: 5 = 5
Explanation: Both numbers are exactly the same, so we use the equal sign. The number 5 is equal to the number 5. Neither number is bigger or smaller than the other.
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Exercise 4:
Compare 9 and 6. Which symbol should go here? 9 ___ 6
Answer: 9 > 6
Explanation: 9 is greater than 6 because 9 comes after 6 when counting. The number 9 is bigger than the number 6. The wide opening of the symbol faces the bigger number (9).
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Exercise 5:
Look at 1 and 4. What's the correct sign? 1 ___ 4
Answer: 1 < 4
Explanation: 1 is less than 4 because 1 comes before 4 when counting. The number 1 is smaller than the number 4. The narrow point of the symbol points to the smaller number (1).
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Exercise 6:
Compare 10 and 7. Which symbol goes between them? 10 ___ 7
Answer: 10 > 7
Explanation: 10 is greater than 7 because 10 comes after 7 when counting. The number 10 is bigger than the number 7. The wide opening of the symbol faces the bigger number (10).
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Exercise 7:
Compare 2 and 9. Which symbol belongs here? 2 ___ 9
Answer: 2 < 9
Explanation: 2 is less than 9 because 2 comes before 9 when counting. The number 2 is smaller than the number 9. The narrow point of the symbol points to the smaller number (2).
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Exercise 8:
What happens when we compare 6 and 6? 6 ___ 6
Answer: 6 = 6
Explanation: Both numbers are exactly the same, so we use the equal sign. The number 6 is equal to the number 6. Neither number is bigger or smaller than the other.
📋 Detailed Summary with Complete Understanding
Definitions and Concepts
Comparing Numbers: The process of determining the relationship between two or more numbers to see which is larger, smaller, or if they are the same size. This involves using comparison symbols (>, <, =).
Greater Than (>): A symbol indicating that the number on the left is larger than the number on the right. The wide opening always faces the bigger number.
Less Than (<): A symbol showing that the number on the left is smaller than the number on the right. The narrow point always points to the smaller number.
Equal To (=): A symbol meaning that both numbers have exactly the same value. There is no difference between them.
Number Sense: Understanding the relative size and value of numbers, including their position in the counting sequence.
Core Rules and Principles
- 🔍 Rule 1: The wide part of > and < always faces the larger number
- 🎯 Rule 2: The narrow point of > and < always points to the smaller number
- "=" Rule 3: Use = only when both numbers are exactly identical
- 🔄 Rule 4: If A > B, then B < A - the relationship reverses when you switch the order
- 🔢 Rule 5: Numbers that come later in the counting sequence are greater than earlier numbers
- ⚖️ Rule 6: The equal sign confirms that two quantities are equivalent in value
Step-by-Step Method
- Identify both numbers you want to compare
- Count or visualize the numbers to determine their relative size
- Determine which number is larger or if they are the same
- Select the appropriate symbol based on the relationship
- Apply the visual rule - wide opening toward bigger number, point toward smaller
- Write the complete statement (e.g., 5 > 3)
- Verify your answer by reading it aloud and checking the logic
- Double-check by counting or using manipulatives if needed
Examples: Simple to Advanced
Basic:
Compare 1 and 2
1 < 2
Point to 1
Answer: 1 < 2
Simple:
Compare 4 and 3
4 > 3
Wide to 4
Answer: 4 > 3
Equal:
Compare 5 and 5
5 = 5
Same numbers
Answer: 5 = 5
Advanced:
Compare 12 and 8
12 > 8
Wide to 12
Answer: 12 > 8
💡 Tips and Tricks
Alligator Method: Picture the symbols as an alligator's mouth - it always wants to eat the bigger number! The wide opening faces the larger value.
Dot Method: Place two dots next to the larger number and one dot next to the smaller number, then connect the dots to form the symbol. Two dots create a wide opening (>), one dot creates a point (<).
Letter L Trick: The less than sign (<) resembles the letter L! Less than = Letter L! This helps distinguish it from the greater than sign.
Counting Sequence: Remember that numbers that come later in counting are greater than those that come earlier.
Read Aloud: Always read your comparison out loud to check if it makes sense: "5 is greater than 3" sounds correct!
Common Pitfalls to Avoid
- ❌ Pitfall: Confusing > and < - Always remember the wide part opens toward the bigger number!
- ❌ Pitfall: Writing 3 > 5 instead of 3 < 5 - Check which number is actually larger!
- ❌ Pitfall: Using = when numbers differ - Only use equals for identical values!
- ❌ Pitfall: Forgetting that order matters - 4 > 2 is correct, but 2 > 4 is wrong!
- ❌ Pitfall: Not practicing enough - Repetition helps build automatic recognition!
- ❌ Pitfall: Ignoring place value in larger numbers - Always compare from left to right!
Key Notes and Takeaways
- 📝 Key Point: The visual nature of comparison symbols makes abstract relationships concrete and understandable
- 📝 Key Point: Wide opening = bigger number, narrow point = smaller number
- 📝 Key Point: Practice with physical objects reinforces understanding of number relationships
- 📝 Key Point: These symbols are foundational for all future mathematical learning and problem-solving
- 📝 Key Point: Reading statements aloud strengthens comprehension and verifies accuracy
- 📝 Key Point: Consistent practice leads to mathematical fluency and confidence
- 📝 Key Point: Understanding comparison builds essential number sense and mathematical reasoning skills
- 📝 Key Point: These concepts apply to measurement, money, time, and countless real-world applications