Review of Addition and Subtraction from 1st Grade

Review fundamental addition and subtraction concepts from 1st grade: basic operations, number facts, and visual representations with detailed solutions.

Review Problems with Solutions
1 Basic Addition Facts
Problem 1
Solve: 8 + 5
Concept Review

This builds on 1st grade addition facts and counting strategies.

Definition:

Addition: Combining two or more numbers to find their total

Addition method:
  1. Start with the larger number (8)
  2. Count up by the smaller number (5 more)
  3. 8, 9, 10, 11, 12, 13
  4. Or use known facts: 8 + 2 = 10, then 10 + 3 = 13
8 + 5 = 13
Step 1: Identify the numbers

We need to add 8 and 5

Step 2: Use counting strategy

Start at 8, count 5 more: 9, 10, 11, 12, 13

Step 3: Find the sum

8 + 5 = 13

8 + 5 = 13
Final answer:

8 + 5 = 13

Applied rules:

• Commutative Property: 8 + 5 = 5 + 8

• Counting On: Start with larger number and count up

• Known Facts: Use memorized addition facts to solve

2 Basic Subtraction Facts
Problem 2
Solve: 12 - 7
Concept Review

This builds on 1st grade subtraction facts and counting backwards strategies.

12 - 7 = 5
Step 1: Identify the numbers

We need to subtract 7 from 12

Step 2: Use counting strategy

Start at 12, count back 7: 11, 10, 9, 8, 7, 6, 5

Step 3: Find the difference

12 - 7 = 5

12 - 7 = 5
Final answer:

12 - 7 = 5

Applied rules:

• Subtraction: Finding the difference between numbers

• Counting Back: Start with larger number and count down

• Related Facts: 12 - 7 = 5, so 5 + 7 = 12

3 Number Relationships
Problem 3
If 6 + 4 = 10, what is 10 - 4?
Concept Review

This builds on 1st grade understanding of fact families and inverse operations.

10 - 4 = 6
Step 1: Recognize the relationship

Since 6 + 4 = 10, then 10 - 4 = 6

Step 2: Apply inverse operation

Subtraction undoes addition

Step 3: Find the missing part

10 - 4 = 6

10 - 4 = 6
Final answer:

10 - 4 = 6

Applied rules:

• Fact Families: Related addition and subtraction facts

• Inverse Operations: Addition and subtraction undo each other

• Part-Part-Whole: Understanding number relationships

1st Grade Concepts & 3rd Grade Progression
➕
Addition Facts
Memorizing sums up to 10 (1st grade) → Sums up to 1000 (3rd grade)
➖
Subtraction Facts
Memorizing differences up to 10 (1st grade) → Differences up to 1000 (3rd grade)
📊
Number Sense
Understanding numbers 0-20 (1st grade) → Numbers up to 1000 (3rd grade)
🔗
Fact Families
Simple relationships (1st grade) → Complex relationships (3rd grade)
Part + Part = Whole
Part-Part-Whole Relationship
1st Grade Skills

• Add and subtract within 20

• Use strategies like counting on/back

• Understand fact families

• Solve word problems with small numbers

3rd Grade Extension

• Add and subtract within 1000

• Use regrouping strategies

• Apply fact families to larger numbers

• Solve complex word problems

Tip 1: Master basic facts first - they're building blocks for larger numbers.
Tip 2: Use fact families to understand inverse relationships.
Tip 3: Practice mental math with small numbers to build fluency.
Tip 4: Connect addition and subtraction as opposite operations.
Review Concepts & Estimation
8 + 5 ≈ 10 + 5 = 15
Estimation Strategy
Original
8
→
Round
10
+
Keep
5
=
Estimate
15
Addition Fact Strategy
1
Look
2
Know
3
Solve
4
Check
Fact Families:

Definition: A group of related addition and subtraction facts using the same numbers

Example: 3 + 4 = 7, 4 + 3 = 7, 7 - 3 = 4, 7 - 4 = 3

Common Review Mistakes:

• Confusing addition and subtraction operations

• Forgetting basic facts that should be memorized

• Not recognizing inverse relationships

• Miscounting when using counting strategies

Key 1st Grade Facts to Remember:

• Addition: Sums up to 10 (e.g., 5+5=10, 6+4=10)

• Subtraction: Differences up to 10 (e.g., 10-3=7, 8-5=3)

• Doubles: 1+1=2, 2+2=4, 3+3=6, etc.

• Near Doubles: 5+6=11, 7+8=15, etc.

Comprehensive Summary: Addition and Subtraction Review (1st Grade Concepts)

This comprehensive summary reviews fundamental addition and subtraction concepts learned in 1st grade that serve as building blocks for 3rd grade mathematics.

Definitions & Key Terms

Addition: The operation of combining two or more numbers to find their total.

Subtraction: The operation of finding the difference between two numbers.

Sum: The result of an addition problem.

Difference: The result of a subtraction problem.

Fact Family: A set of related addition and subtraction facts using the same numbers.

Inverse Operations: Operations that undo each other (addition and subtraction).

Part-Part-Whole: A model showing how parts combine to make a whole number.

Core Rules & Principles

Rule 1: Addition is commutative (order doesn't matter): 3 + 4 = 4 + 3.

Rule 2: Subtraction is not commutative: 7 - 3 ≠ 3 - 7.

Rule 3: Addition and subtraction are inverse operations.

Rule 4: The sum is always greater than or equal to the addends.

Rule 5: The difference is always less than or equal to the minuend.

Rule 6: Fact families connect addition and subtraction facts.

Step-by-Step Methods

Addition Strategies:

1. Count all: Count each item individually

2. Count on: Start with the larger number and count up

3. Use doubles: Know facts like 5+5=10

4. Make 10: Use 10 as a benchmark (8+5=8+2+3=13)

Subtraction Strategies:

1. Count back: Start with the larger number and count down

2. Count up: Count from the smaller number to the larger

3. Use addition facts: If 7+3=10, then 10-3=7

Examples: Simple to Advanced

Simple Examples:

3 + 2 = 5, 6 - 4 = 2

Intermediate:

8 + 7 = 15 (using 8 + 2 + 5 = 15), 14 - 9 = 5 (counting up from 9)

Advanced Application:

Using fact families: If 6 + 8 = 14, then 14 - 8 = 6 and 14 - 6 = 8

These foundational concepts apply to larger numbers in 3rd grade.

Tips & Tricks

Tip 1: Memorize doubles facts first (2+2, 3+3, etc.) as they're easier to remember.

Tip 2: Use your fingers or draw pictures to visualize problems.

Tip 3: Practice with flashcards to build automaticity.

Tip 4: Use the "counting on" strategy for addition and "counting back" for subtraction.

Tip 5: Look for patterns in fact families to understand relationships.

Common Pitfalls & Memorization

Pitfall 1: Mixing up addition and subtraction symbols.

Pitfall 2: Forgetting that subtraction is not commutative.

Pitfall 3: Not recognizing when to use inverse operations.

Memorization Aid: "Plus makes more, minus makes less" for understanding operations.

Memory Device: Use the phrase "Part + Part = Whole" to remember addition, and "Whole - Part = Other Part" for subtraction.

Questions & Answers

Question: Why is it important to review 1st grade addition and subtraction concepts in 3rd grade?

Answer: Reviewing 1st grade concepts is crucial because:

  • Foundation Building: Advanced concepts build directly on basic facts
  • Automaticity: Students need to recall basic facts instantly to handle complex problems
  • Confidence: Mastery of basics builds confidence for new challenges
  • Error Prevention: Strong fundamentals prevent computational errors in complex problems
  • Pattern Recognition: Understanding simple patterns helps with complex patterns

For example, knowing that 8 + 5 = 13 helps students understand that 80 + 50 = 130 and 800 + 500 = 1300. The same foundational understanding applies to regrouping in larger numbers.

Without solid 1st grade foundations, students struggle with 3rd grade concepts like multi-digit addition and subtraction with regrouping.

Question: I sometimes forget my addition and subtraction facts. How can I get better at remembering them?

Answer: Here are effective strategies to remember basic facts:

  • Practice regularly: Just 5-10 minutes daily makes a big difference
  • Use patterns: Notice that 5+6 is one more than 5+5
  • Play games: Math games make practice enjoyable
  • Use flashcards: Physical or digital cards for quick recall
  • Connect to real life: Count objects around you

Focus on the facts you find hardest first. For example, if 7+8 is difficult, practice it more than 2+2. Also, remember that addition facts help with subtraction: if you know 7+8=15, then 15-8=7.

The more you practice, the faster your brain will recall these facts automatically!

Question: How can I help my child practice 1st grade addition and subtraction facts at home?

Answer: Here are effective home practice strategies:

  • Everyday math: Count items during daily activities (stairs, toys, snacks)
  • Math games: Card games, dice games, or online math games
  • Flashcards: Quick daily practice sessions
  • Worksheets: Short, focused practice sheets
  • Real-world problems: "If we have 8 cookies and eat 3, how many are left?"

Keep practice sessions short (10-15 minutes) and positive. Celebrate progress and focus on improvement rather than perfection. Use manipulatives like blocks or counters to make abstract concepts concrete.

Practice fact families together (3+4=7, 4+3=7, 7-3=4, 7-4=3) to reinforce the relationship between addition and subtraction.