Learning to Compare Number Sentences in Grade 1

Master comparing number sentences: addition and subtraction equations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Addition Sentences
Exercise 1
Compare the number sentences:
a) 5 + 3 _____ 4 + 4
b) 7 + 2 _____ 6 + 3
c) 8 + 1 _____ 9 + 0
Definition:

Comparing number sentences: Finding the result of each equation and comparing the results using >, <, or =.

Comparison method:
  1. Solve the first number sentence
  2. Solve the second number sentence
  3. Compare the results using >, <, or =
a) 5 + 3 vs 4 + 4
8 = 8
b) 7 + 2 vs 6 + 3
9 = 9
c) 8 + 1 vs 9 + 0
9 = 9
Step 1: Solve 5 + 3

5 + 3 = 8

Step 2: Solve 4 + 4

4 + 4 = 8

Step 3: Compare results

8 = 8, so 5 + 3 = 4 + 4

a) 5 + 3 = 4 + 4
b) 7 + 2 = 6 + 3
c) 8 + 1 = 9 + 0
Final answer:

a) 5 + 3 = 4 + 4
b) 7 + 2 = 6 + 3
c) 8 + 1 = 9 + 0

Applied rules:

• Solve first: Calculate each side of the equation

• Compare results: Use comparison symbols on the results

• Equality principle: Both sides equal the same value

5 + 3
=
8
4 + 4
=
8
2 Subtraction Sentences
Exercise 2
Compare the number sentences:
a) 9 - 4 _____ 7 - 2
b) 10 - 3 _____ 8 - 1
c) 6 - 2 _____ 5 - 1
Definition:

Subtraction number sentences: Equations with minus signs that require solving before comparing.

a) 9 - 4 vs 7 - 2
5 = 5
b) 10 - 3 vs 8 - 1
7 = 7
c) 6 - 2 vs 5 - 1
4 = 4
Step 1: Solve 9 - 4

9 - 4 = 5

Step 2: Solve 7 - 2

7 - 2 = 5

Step 3: Compare results

5 = 5, so 9 - 4 = 7 - 2

a) 9 - 4 = 7 - 2
b) 10 - 3 = 8 - 1
c) 6 - 2 = 5 - 1
Final answer:

a) 9 - 4 = 7 - 2
b) 10 - 3 = 8 - 1
c) 6 - 2 = 5 - 1

Applied rules:

• Subtract first: Calculate each side of the equation

• Compare results: Use comparison symbols on the results

• Equality principle: Both sides equal the same value

LEFT SIDE
9 - 4
= 5
RIGHT SIDE
7 - 2
= 5
3 Mixed Operations
Exercise 3
Compare the number sentences:
a) 3 + 6 _____ 10 - 2
b) 8 - 3 _____ 4 + 1
c) 5 + 4 _____ 9 - 0
Definition:

Mixed operations: Number sentences with both addition and subtraction that require solving before comparing.

a) 3 + 6 vs 10 - 2
9 = 8
b) 8 - 3 vs 4 + 1
5 = 5
c) 5 + 4 vs 9 - 0
9 = 9
Step 1: Solve 3 + 6

3 + 6 = 9

Step 2: Solve 10 - 2

10 - 2 = 8

Step 3: Compare results

9 > 8, so 3 + 6 > 10 - 2

a) 3 + 6 > 10 - 2
b) 8 - 3 = 4 + 1
c) 5 + 4 = 9 - 0
Final answer:

a) 3 + 6 > 10 - 2
b) 8 - 3 = 4 + 1
c) 5 + 4 = 9 - 0

Applied rules:

• Solve each side: Calculate each side of the equation separately

• Compare results: Use comparison symbols on the results

• Order of operations: Just solve left to right

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Complete Summary: Comparing Number Sentences

Key Concepts and Definitions

Number Sentence: A mathematical statement that shows two expressions are equal or compares them (like 3 + 4 = 7)

Equation: A number sentence with an equal sign (=)

Inequality: A number sentence with > or < symbols

Addition Sentence: A number sentence with addition (+)

Subtraction Sentence: A number sentence with subtraction (-)

Comparing: Determining if one side is greater than, less than, or equal to the other side

Solving: Finding the result of a mathematical operation

Mixed Operations: Number sentences with both addition and subtraction

Core Rules and Principles

• Solve First Rule: Always calculate each side of the number sentence before comparing

• Comparison Rule: Compare the final results, not the original expressions

• Equality Rule: Two expressions are equal if they have the same value

• Operation Priority: For mixed operations, solve each side separately

• Symbol Direction Rule: The open end of > and < always faces the larger number

• Verification Rule: Always check your calculations before comparing

Step-by-Step Methods

For Addition Sentences:

  1. Solve the left side of the first equation
  2. Solve the right side of the second equation
  3. Compare the results using >, <, or =
  4. Write the complete comparison statement

For Subtraction Sentences:

  1. Solve the left side of the first equation
  2. Solve the right side of the second equation
  3. Compare the results using >, <, or =
  4. Write the complete comparison statement

For Mixed Operations:

  1. Solve each side of the comparison separately
  2. Compare the final results
  3. Choose the correct symbol (>, <, or =)
  4. Verify your answer makes sense
Examples (Simple to Advanced)

Simple Examples:

• 3 + 2 = 5, 4 + 1 = 5, so 3 + 2 = 4 + 1

• 7 - 3 = 4, 6 - 2 = 4, so 7 - 3 = 6 - 2

Intermediate Examples:

• 5 + 4 = 9, 10 - 1 = 9, so 5 + 4 = 10 - 1

• 8 - 3 = 5, 2 + 4 = 6, so 8 - 3 < 2 + 4

Advanced Examples:

• 6 + 3 vs 12 - 3: 9 vs 9, so 6 + 3 = 12 - 3

• 10 - 4 vs 5 + 3: 6 vs 8, so 10 - 4 < 5 + 3

Tips, Tricks, and Common Pitfalls

Tips:

• Always solve each side completely before comparing

• Use manipulatives or drawings to visualize the equations

• Remember that 5 + 3 and 4 + 4 both equal 8

• Check your work by solving again if needed

Common Mistakes:

• Comparing the original expressions instead of the results

• Making calculation errors when solving the equations

• Confusing the direction of > and < symbols

• Forgetting to solve both sides before comparing

Key Notes for Memorization

• Memorize the process: Solve first, then compare

• Remember the rule: Compare the final answers, not the expressions

• Practice regularly: Daily equation solving builds fluency

• Visual associations: Picture the equations as balance scales

• Use number lines: Position results to see their relative size

Number Sentence Practice
5 + 3 = 8
Addition Example
Comparing Number Sentences Practice
Question 1: Fill in: 4 + 5 ___ 6 + 3
4 + 5 = 6 + 3
Question 2: Compare: 9 - 2 ___ 8 - 1
9 - 2 = 8 - 1
Question 3: Fill in: 7 + 2 ___ 10 - 2
7 + 2 > 10 - 2
Question 4: Compare: 6 - 4 ___ 3 + 1
6 - 4 < 3 + 1
Addition
+
Combine numbers
Subtraction
-
Take away
Equals
=
Same value
Key definitions:

Number sentence: A mathematical statement with numbers and operations

Solving: Calculating the result of an equation

Comparison: Determining the relationship between two values

Complete methodology:
  1. Solve each side: Calculate the value of each expression
  2. Compare results: Determine the relationship between the results
  3. Select symbol: Choose >, <, or = based on comparison
  4. Verify: Double-check your calculations
Tip 1: Always solve each side completely before comparing.
Tip 2: The open end of > and < always faces the larger number.
Tip 3: Use visual aids like counters to help solve equations.
Tip 4: Practice with real-world examples to make it meaningful.
Common errors: Comparing expressions instead of results, calculation mistakes.
Practice strategies: Use manipulatives, draw pictures, solve step-by-step.
Rules to know:

• Solve first: Always calculate each side before comparing

• Compare results: Only compare the final answers

• Equality condition: Both sides must have the same value to be equal

• Symbol direction: Open end faces the larger number

Number Sentence Patterns
7 + 2 = 9
Addition Example
Understanding Number Sentence Patterns:

Equation relationships: How addition and subtraction relate to each other

Balance concept: Both sides of an equation have the same value

Pattern recognition: Identifying equivalent expressions

Operational equivalence: Different operations yielding the same result

Number Sentence Strategies:
  1. Solve systematically: Calculate each side step by step
  2. Check your work: Verify each calculation
  3. Determine relationship: Identify which number is larger
  4. Express with symbols: Use appropriate comparison symbol
Pattern Recognition: 5 + 3 = 8 and 4 + 4 = 8, so they are equal.
Memory Aid: The "mouth" of the symbol always "eats" the larger number.
Visual Help: Draw circles to represent the numbers in equations.
Number Relationships: Each expression has a specific value that can be compared.
Consistent Logic: The same rules apply to all number sentences.
Important Patterns:

• Equivalent expressions: 5 + 3 = 4 + 4 (both equal 8)

• Greater than: Left side result > Right side result

• Less than: Left side result < Right side result

• Equal to: Both sides have the same result

Practice Problems and Solutions
6 + 3 = 9
Example Problem
Practice Problems:

Problem 1: Compare: 5 + 4 ___ 7 + 2

Problem 2: Compare: 9 - 3 ___ 8 - 2

Problem 3: Compare: 4 + 6 ___ 12 - 3

Problem 4: Compare: 10 - 4 ___ 5 + 2

Solution Approach:
  1. Solve left side: Calculate the value of the left expression
  2. Solve right side: Calculate the value of the right expression
  3. Compare results: Determine the relationship between the results
  4. Fill in symbol: Use appropriate comparison symbol
Tip 1: Practice solving equations in everyday situations.
Tip 2: Use manipulatives to visualize the equations.
Tip 3: Remember that the open end of the symbol always faces the larger number.
Tip 4: Always solve each side completely before comparing.
Assessment Focus: Teachers often test equation solving and comparison skills.
Real-world Application: These skills help with problem-solving and reasoning.
Practice Solutions:

• 5 + 4 = 9, 7 + 2 = 9, so 5 + 4 = 7 + 2

• 9 - 3 = 6, 8 - 2 = 6, so 9 - 3 = 8 - 2

• 4 + 6 = 10, 12 - 3 = 9, so 4 + 6 > 12 - 3

• 10 - 4 = 6, 5 + 2 = 7, so 10 - 4 < 5 + 2

Questions & Answers

Question: Why do I have to solve both sides of the number sentence before comparing them? Can't I just look at the numbers?

Answer: Great question! You have to solve both sides because the expressions might look different but have the same value. Look at this example:

  • 5 + 3 looks different than 4 + 4
  • But 5 + 3 = 8 and 4 + 4 = 8
  • So 5 + 3 = 4 + 4, even though the expressions look different!

If you just looked at the numbers without solving, you might think 5 + 3 is bigger because 5 is bigger than 4. But solving shows they're equal. That's why we always solve each side first!

It's like having two different bags of candy that look different but have the same number of pieces inside.

Question: My child sometimes gets confused with mixed operations like 5 + 3 and 10 - 2. How can I help them understand?

Answer: Here are some effective strategies:

  • Step-by-step approach: Have them solve one side completely, then the other side
  • Visual aids: Use counters or objects to represent each equation
  • Color coding: Use different colors for each side of the comparison
  • Practice with manipulatives: Use blocks or chips to physically add and subtract

For 5 + 3 vs 10 - 2, have them calculate: "5 + 3 = 8" and "10 - 2 = 8", so they're equal.

You can also explain that we're comparing the "answers" not the "problems" - like comparing the final scores of two games.

Question: What if I make a mistake when solving one side? Will I get the whole problem wrong?

Answer: Yes, if you make a mistake solving one side, your final comparison will probably be wrong. That's why it's important to:

  • Check your work: Solve the problem again if you have time
  • Use strategies: Count on your fingers or use objects to double-check
  • Look for reasonableness: Does your answer make sense?

For example, if you think 6 + 3 = 8 instead of 9, then when comparing 6 + 3 vs 5 + 4, you'd say 8 vs 9, making 6 + 3 smaller. But the correct answer is that they're equal (both equal 9).

That's why we always solve carefully and check our work!